Kröger: selected publications

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277 selected entries have been cited at least 10048 times (SCI, 02-05-2025)

Article	Y. Feng, D. Gerber, S. Heyden, M. Kröger, E.R. Dufresne, L. Isa, R.W. Style Characterizing hydrogel behavior under compression with gel-freezing osmometry J. Mech. Phys. Solids 201 (2025) 106166
Hydrogels are particularly versatile materials that are widely found in both Nature and industry. One key reason for this versatility is their high water content, which lets them dramatically change their volume and many of their mechanical properties . often by orders of magnitude . as they swell and dry out. Currently, we lack techniques that can precisely characterize how these properties change with water content. To overcome this challenge, here we develop Gel-Freezing Osmometry (GelFrO): an extension of freezing-point osmometry. We show how GelFrO can measure a hydrogel.s mechanical response to compression and shrinkage in response to an applied osmotic pressure, while only using small, ..(100 .L) samples. Because the technique allows measurement of properties over an unusually wide range of water contents, it allows us to accurately test theoretical predictions. We find simple, power-law behavior for both mechanical and osmotic responses, while these are not well-captured by classical Flory.Huggins theory. We interpret this power-law behavior as a hallmark of a microscopic fractal structure of the gel.s polymer network, and propose a simple way to connect the gel.s fractal dimension to its mechanical and osmotic properties. This connection is supported by observations of hydrogel microstructures using small-angle X-ray scattering. Finally, our results motivate simplifications to common models for hydrogel mechanics, and we propose an updated hydrogel constitutive model.
Article	M. Kröger, C. Luap, P. Ilg Ultra-slow self-similar coarsening of physical fibrillar gels formed by semiflexible polymers Soft Matter 21 (2025) 2803-2825
Biopolymers tend to form fibrils that self-assemble into open network structures. While permanently crosslinked flexible polymers are relatively well understood, structure.property relationships of open networks and pseudo-gels formed by bundles of biopolymers are still controversial. Here we employ a generic coarse-grained bead-spring chain model incorporating semiflexibility and cohesive nonbonded interactions, that forms physical instead of chemical crosslinks. For flexible chains, the cohesive forces lead to the formation of a droplet phase while, at the same concentration, stiffer chains form bundles that self-assemble into percolated networks. From comprehensive molecular dynamics simulations we find that the reversible crosslinks allow for permanent relaxation processes. However, the associated reorganization of the filamentous network is severely hindered, leading to aging of its topology. Based on morphometric analyses, the ultra-slow coarsening in these systems is proven to be self-similar, which implies a number of scaling relations between structural quantities as the networks age. The percolated structures are characterized by different dynamic regimes of slow, anomalous diffusion with highly non-Gaussian displacements. Relaxation dynamics is found to become extremely slow already on moderate length scales and further slowing down as coarsening proceeds. Using a minimal model supported by observations on filament rupture and rearrangement, our study helps to shed light on various interrelated structural and dynamical aspects of coarsening nonergodic systems relevant for fibrous networks, pseudo-gels, and physical fibrillar gels.
Article	L.M. Almassalha, M. Carignano, E.P. Liwag, W.S. Li, R. Gong, N. Acosta, C.L. Dunton, P.C. Gonzalez, L.M. Carter, R. Kakkaramadam, M. Kröger, P. Su, T. Kuo, K.I. Medina, J.A. Pritchard, A. Skol, R. Nap, M. Kanemaki, V. Dravid, I. Szleifer, V. Backman Chromatin conformation, gene transcription, and nucleosome remodeling as an emergent system Sci. Adv. 11 (2025) eadq6652
In single cells, variably sized nanoscale chromatin structures are observed, but it is unknown whether these form a cohesive framework that regulates RNA transcription. Here, we demonstrate that the human genome is an emer- gent, self-assembling, reinforcement learning system. Conformationally defined heterogeneous, nanoscopic packing domains form by the interplay of transcription, nucleosome remodeling, and loop extrusion. We show that packing domains are not topologically associated domains. Instead, packing domains exist across a structure- function life cycle that couples heterochromatin and transcription in situ, explaining how heterochromatin en- zyme inhibition can produce a paradoxical decrease in transcription by destabilizing domain cores. Applied to development and aging, we show the pairing of heterochromatin and transcription at myogenic genes that could be disrupted by nuclear swelling. In sum, packing domains represent a foundation to explore the interactions of chromatin and transcription at the single-cell level in human health.
Article	E.N.M. Cirillo, M. Colangeli, M. Kröger, L. Rondoni Particle transport and finite-size effects in Lorentz channels with finite horizons Physica D 472 (2025) 134512
Particle transport is investigated in a finite-size realization of the classical Lorentz gas model. We consider point particles moving at constant speed in a 2D rectangular strip of finite length, filled with circular scatterers sitting at the vertices of a triangular lattice. Particles are injected at the left boundary with a prescribed rate, undergo specular reflections when colliding with the scatterers and the horizontal boundaries of the channel, and are finally absorbed at the left or the right boundary. Thanks to the equivalence with give Correlated Random Walks, in the finite horizon case, we show that the inverse probability that a particle exits through the right boundary depends linearly on the number of cells in the channel. A non-monotonic behavior of such probability as a function of the density of scatterers is also discussed and traced back analytically to the geometric features of a single trap. This way, we do not refer to asymptotic quantities and we accurately quantify the finite size effects. Our deterministic model provides a microscopic support for a variety of phenomenological laws, e.g. the Darcy’s law for porous media and the Ohm’s law in electronic transport.
Article	T. Özer, M. Kröger Anisotropic functionally graded nano-beams and closed-form solutions in plane gradient elasticity Appl. Math. Model. 133 (2024) 108-147
This study delves into the investigation of exact analytical solutions for the plane stress and displacement fields within linear homogeneous anisotropic nano-beam models of gradient elasticity. It focuses on solving the Helmholtz equation, which encompasses a second-order non- homogeneous linear partial differential equation in plane gradient elasticity theory, utilizing polynomial series-type solutions. The analysis centers on the utilization of gradient Airy stress functions to derive stress fields in the gradient theory. The research yields closed-form analytical solutions for Airy stress functions, stress, and strain fields in both classical and gradient theories. The study considers five distinct types of two-dimensional functionally graded cantilever beams with various boundary conditions: a cantilever anisotropic nano-beam subjected to a concentrated force at the free end, a cantilever anisotropic nano-beam under a uniform load, a simple anisotropic nano-beam under a uniform load, a propped cantilever anisotropic nano-beam under a uniform load, and a fixed end cantilever anisotropic nano-beam under a uniform load. General analytical solutions for the gradient stress and displacement fields of two-dimensional and one- dimensional anisotropic nano-beams under different boundary conditions are provided. The study showcases significant strain gradient size effects at the nano-scale through the derived analytical solutions for anisotropic beams. Additionally, it demonstrates that the strain gradient theory results for the limit case of the gradient coefficient � precisely align with results for isotropic and anisotropic materials in elasticity theory and classical theory. Furthermore, real- world applications are discussed, considering stress and displacement fields in real anisotropic materials such as TiSi2 single crystals and orthotropic materials, which are special cases of anisotropic materials like wood and epoxy as documented in the literature.
Article	S. Agrawal, S. Galmarini, M. Kröger Energy formulation for infinite structures: order parameter for percolation, critical bonds and power-law scaling of contact-based transport Phys. Rev. Lett. 132 (2024) 196101
Investigating heterogeneous materials. microstructure, often simulated using periodic images, is crucial for understanding their physical traits. We propose a generic spring-based representation for periodic two-component structures. The equilibrium energy in this framework serves as an order parameter, offering an analytical expression for wrapping and introducing the concept of critical bonds. We show that these minimum bonds for depercolation can be efficiently detected. The number of critical bonds scales with system size, accurately capturing contact-based transport.s scaling. This approach holds potential to analyze functional robustness of networks.
Article	R. Schlickeiser, M. Kröger Mathematics of Epidemics: On the General Solution of SIRVD, SIRV, SIRD and SIR Compartment Models Mathematics 12 (2024) 941
The susceptible.infected.recovered.vaccinated.deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest, not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using an a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave.
Article	R. Schlickeiser, M. Kröger Compartmental description of baryonic matter cycle in galaxies. I. Competition of triggered star formation, stellar feedback and stellar evolution Astron. Astrophys. 692 (2024) A64
Context. The compartmental description, well-known as the description of infection diseases and epidemics, was applied here to describe the temporal evolution of the baryonic matter in interstellar gas and stars. The introduction of gaseous and stellar fractions of the total baryonic matter as the basic dynamical variables is advantageous because it allows us to apply the description to a variety of astrophysical systems. Aims. We aimed to theoretically investigate the competition of spontaneous star formation, stellar feedback, and stellar evolution to understand the baryonic matter cycle including luminous baryonic matter in main-sequence stars and weakly luminous matter in white dwarfs, neutron stars, and black holes (referred to as locked-in matter). Of particular interest was the understanding of cosmic star formation history and the present-day gas fraction with compartmental models. Methods. We derived exact analytical solutions for the time evolution of the fractions of gaseous, luminous stellar, and locked-in stellar matter for stationary rates of spontaneous star formation, continuous stellar feedback, and stellar evolution. The accuracy of the analytical solutions was proven by comparison with the exact numerical solutions of the dynamical equations. Results. The observed cosmological star formation rate and the integrated stellar density as a function of redshift are reasonably well explained by the compartmental model without triggered star formation by the competition of spontaneous star formation and stellar evolution, whereas the influence of stellar feedback is less important. The action of stellar evolution provides a significant redshift-dependent reduction factor when calculating the integrated stellar density from the star formation rate. Without stellar evolution, the observations could not be reproduced very well. Then, the fits to the observation provided conclusions on the relative importance of spontaneous star formation, stellar evolution, and feedback in the early Universe after the recombination era until today. The gas, luminous star, and locked-in stellar matter fractions indicated that the vast majority of the baryons in the present-day Universe reside in the form of locked-in stellar matter in white dwarfs, neutron stars, and black holes.
Article	N.A. Babei, M. Kröger, T. Özer Theoretical analysis of a SIRD model with constant amount of alive population and Covid–19 applications Appl. Math. Model. 127 (2024) 237-258
This study deals with a theoretical analysis of the integrability properties and analytical solutions of an initial-value problem for a SIRD model with a constant amount of alive population (SIRD-CAAP), which is in the form of a fourth-dimensional and first-order coupled system of nonlinear ordinary differential equations, by using the partial Hamiltonian method. This research represents a COVID-19 study as a real-world problem by using the analytical results obtained in the study. The first integrals and the associated exact analytical solutions are investigated of the model with respect to algebraic relations among the model parameters. Then, for both cases, the dynamical behaviors of the model based on the analytical solutions are analyzed, and the graphical representations of the closed-form solutions are demonstrated and compared. In addition, it is shown that the SIRD-CAAP model can be decoupled based on its first integrals for all cases from the mathematical perspective point of view. Furthermore, the periodicity properties and the classification of the regimes of the solutions with respect to the model parameter constraints are discussed. Finally, the COVID-19 applications are given using the data related to the different countries.
Article	N.A. Babei, M. Kröger, T. Özer Dynamical Behavior of the SEIARM-COVID-19 related models Physica D 468 (2024) 134291
In this study, the analytical, integrability, and dynamical properties of an epidemic COVID-19 model called SEIARM, a six-dimensional coupled nonlinear system of ordinary differential equations from the mathematical point of view, are investigated by the artificial Hamiltonian method based on Lie symmetry groups. By constraining some constraint relations for the model parameters using this method, Lie symmetries, first integrals, and analytical solutions of the model are studied. By examining key factors like how many people are susceptible, infected, or recovered, we unveil hidden patterns and ..constraints.. within the model. These 'constraints' show us how the virus might spread under different conditions, especially when a crucial number called Ψ is between 0 and 1, providing valuable insights into the potential spread of COVID-19 and the effectiveness of control measures. The analytical solutions and their graphical representations for some real values of model parameters obtained from China during the pandemic period are also provided.
Article	N. Herard, R. Annapooranan, T. Henry, M. Kröger, S. Cai, N. Boechler, Y. Sliozberg Modeling nematic phase main-chain liquid crystal elastomer synthesis, mechanics, and thermal actuation via coarse-grained molecular dynamics Soft Matter 20 (2024) 9219-9231
This paper presents a coarse-grained molecular dynamics simulation study of the synthesis, mechanics, and thermal actuation of nematic phase main-chain liquid crystal elastomers (LCEs), a type of soft, temperature-responsive, polymeric actuating material. The simulations herein model the crosslinking, mechanical stretching, and additional crosslinking synthesis process, following which, the simulated LCE exhibits a direction-dependent thermal actuation and mechanical response. The thermal actuation response shows good qualitative agreement with experimental results, including the variation of a global order parameter that describes the orientation of the mesogen domains comprising the LCE. The mechanical response due to applied deformation shows less agreement, but manifests the key features observed in experiments on LCEs, namely soft strain and hyperelasticity that is present when loaded perpendicularly and in-line, respectively, to the mesogen alignment direction. We also present a topological analysis of the simulated LCEs, which, in conjunction with the simulated thermomechanical responses, allows us to infer the relative contribution of entanglements and chemical crosslinks on those responses. We suggest that the model proposed herein will help enable improved LCE formulations via mechanistic insights that can be gained via the use of such a relatively computationally inexpensive coarse-grained molecular dynamics model, which may be of further value to application areas including soft robotics, bio-mimicking devices, artificial muscles, and adaptive materials.
Article	M.Kröger, R. Schlickeiser On the analytical solution of the SIRV-model for the temporal evolution of epidemics for general time-dependent recovery, infection and vaccination rates Mathematics 12 (2024) 326
The susceptible–infected–recovered/removed–vaccinated (SIRV) epidemic model is an important generalization of the SIR epidemic model, as it accounts quantitatively for the effects of vaccination campaigns on the temporal evolution of epidemic outbreaks. Additional to the time-dependent infection (a(t)) and recovery (μ(t)) rates, regulating the transitions between the compartments S→I and I→R, respectively, the time-dependent vaccination rate v(t) accounts for the transition between the compartments S→V of susceptible to vaccinated fractions. An accurate analytical approximation is derived for arbitrary and different temporal dependencies of the rates, which is valid for all times after the start of the epidemics for which the cumulative fraction of new infections J(t)≪1. As vaccination campaigns automatically reduce the rate of new infections by transferring persons from susceptible to vaccinated, the limit J(t)≪1 is even better fulfilled than in the SIR-epidemic model. The comparison of the analytical approximation for the temporal dependence of the rate of new infections J˚(t)=a(t)S(t)I(t), the corresponding cumulative fraction J(t), and V(t), respectively, with the exact numerical solution of the SIRV-equations for different illustrative examples proves the accuracy of our approach. The considered illustrative examples include the cases of stationary ratios with a delayed start of vaccinations, and an oscillating ratio of recovery to infection rate with a delayed vaccination at constant rate. The proposed analytical approximation is self-regulating as the final analytical expression for the cumulative fraction J∞ after infinite time allows us to check the validity of the original assumption J(t)≤J∞≪1.
Article	M. Kröger, S. Agrawal, S. Galmarini Generalized geometric pore size distribution code GPSD-3D for periodic systems composed of monodisperse spheres Comput. Phys. Commun. 301 (2024) 109212
The generalized geometric pore size distribution P(r;rp|rc) as function of pore radius r, probe sphere radius r, and coating thickness rc for a periodic two-dimensional system composed of circles (GPSD-2D) had been defined recently. For rp=rc it reduces to the widely accepted pore radius distribution P(r) introduced by Gelb and Gubbins. The three-dimensional counterpart GPSD-3D for periodic systems composed of spheres is implemented here using an efficient Voronoi-based semi-analytic strategy that offers significant advantages compared with both a grid-based implementation and constrained nonlinear optimization with respect to speed, precision and memory requirements. Moreover, GPSD-3D is fully parallelized using OpenMP.
Article	M. Carignano, M. Kröger, L. Almassalha, V. Agrawal, W.S. Li, E.M. Pujadas, R.J. Nap, V. Beckman, I. Szleifer Local volume concentration, packing domains, and scaling properties of chromatin eLife 13 (2024) RP97604
We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally defined domains observed by single-cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as RAD21 degradation.
Article	J. Wen, J. Yang, M. Kröger, M. Ma, T. Hao, Z. Zhou, Y. Nie Molecular details of catalytic effect of long chains on short chains in stretch-induced polymer crystallization Macromolecules 57 (2024) 1612-1624
Using molecular dynamics simulation, strain-induced crystallization of polyethylene blends containing long and short chains was investigated. It was found that both long and short chains can participate in crystal nucleation. Meanwhile, the increase of the content of long chains leads to the decrease of the onset strain for crystallization, demonstrating that the presence of long chains can promote the conucleation of long and short chains. Further investigation revealed that the long-chain segments with a higher orientation along the stretching direction have a promoting effect on the deformation and orientation of short-chain segments located near them. Two effects contribute to this .catalytic effect.: on one hand, there is a low interaction potential energy between the highly oriented long-chain bonds and highly oriented short-chain bonds; on the other hand, long chains can drive the deformation of short chains through the entanglement network between them.
Article	E.N.M. Cirillo, M. Colangeli, M. Kröger, L. Rondoni Steady state fluctuations in a 3D particle model out of equilibrium Springer Proc. Phys. (ICNDA 2024) 405 (2024) 615-631
We analyze, both analytically and numerically, a 3D billiardlike model introduced in Phys. Rev. Res. 5, 043063 (2023) to highlight some aspects of its steady state dynamics. First, we study the equation describing the interface between equilibrium and nonequilibrium phases in the parameter space and show that, in certain regimes, the solution can be expressed in an analytical form. Moreover, we also investigate the statistics of the fluctuations of the stationary particle current and try to establish a connection with the existing framework of the Fluctuation Relations.
Article	E.N.M. Cirillo, M. Colangeli, A. Di Francesco, M. Kröger, L. Rondoni Particle traps and stationary currents captured by an active 1D model Physica A 642 (2024) 129763
We investigate the onset of a non-equilibrium phase transition in a one-dimensional ring, constituted by two urns connected by two strands, called active and passive channels. A set of .. particles move inside the ring with constant individual speeds; collisions against the channel entries produce reflections with certain probabilities, that differ between active and passive channels. The microscopic dynamics differs from a classical 1D billiard owing to the presence of an interaction mechanism acting inside the active channel, which potentially reverses velocities of its particles. We outline a general theory for the feedback-controlled system which describes quantitatively the phase diagram of the model, based on a mixing property, that is analytically predicted and numerically verified. The probability distributions we define and evolve in time are 1D projections of uniform distributions on ..-dimensional spherical surfaces, with d≥1 and d=∞ Consequently results that apply to higher dimensional systems are recovered.
Article	A.V. Karatrantos, L. Bouhala, A. Bick, X. Krokidis, M. Kröger Morphology, structure and dynamics of ionic polydimethylsiloxane-silica nanocomposites MRS Commun. 14 (2024) 653-659
In this paper, we investigate the morphology of ionic poly(dimethylsiloxane) silica nanocomposites of randomly grafted or chain-end-functionalized ionic PDMS melts using atomistic MD simulations. The localization of the charge alters the structure and dynamics of ionic PDMS chains near the nanosilica surface. The chain-end ionic PDMS obtains the largest dimensions, whereas the charge fraction of 10% of the random ionic copolymers leads to a contraction of PDMS chains. The charge fraction dramatically alters the dynamics of the ionic PDMS chains, although they reach the diffusive regime. An anisotropy of PDMS chain dynamics perpendicular and parallel to the nanosilica and an heterogeneity of PDMS dynamics from the nanosilica surface are observed for the longer randomly grafted and chain-end ionic PDMS chains. The longer randomly grafted ionic PDMS chains are strongly adsorbed in the vicinity of the nanosilica surface.
Article	A.A. Galata, M. Kröger Topological biopassive brushes. From linear to cyclic, from atomistic to coarse-grained poly(2-ethyl-2-oxazoline) Macromolecules 57 (2024) 5313-5329
In medicine, the quest for novel materials persists to ensure substancesentering the human body are biopassive, less toxic, and possess improved propertiescompared to their predecessors. Poly(2-ethyl-2-oxazoline) (PEOXA), whether in linear orring form, emerges as a promising alternative, outperforming its precursor, polyethylenglycol(PEG), in common PEG applications. This study aims to uncover the mechanical propertiesof PEOXA through a multiscale approach. To this end, atomistic simulations investigatesingle PEOXA chains (linear and ring) in water, revealing a helix-like structure due tohydrogen bond bridges along the polymer chain. Using these results, a computationallyefficient coarse-grained (CG) model for a single PEOXA chain in water is developed. TheCG model is then employed to create PEOXA polymer brushes with varying graftingdensities (.), allowing the study of nanotribological properties, such as the coefficient offriction. Ring brushes exhibit a lower coefficient of friction, showing relative indifference tografting density increases within certain limits when sheared against a explicit CG wall. Incontrast, linear brush coefficients appear to rise at lower grafting densities, although an opposite trend is observed when shearingagainst a symmetric linear brush.
Article	T. Li, E.R. Dufresne, M.Kröger, S. Heyden Siloxane molecules: Nonlinear elastic behavior and fracture characteristics Macromolecules 56 (2023) 1303-1310
Fracture phenomena in soft materials span multiple length and time scales. This poses a major challenge in computational modeling and predictive materials design. To pass quantitatively from molecular to continuum scales, a precise representation of the material response at the molecular level is vital. Here, we derive the nonlinear elastic response and fracture characteristics of individual siloxane molecules using molecular dynamics (MD) studies. For short chains, we find deviations from classical scalings for both the effective stiffness and mean chain rupture times. A simple model of a nonuniform chain of Kuhn segments captures the observed effect and agrees well with MD data. We find that the dominating fracture mechanism depends on the applied force scale in a nonmonotonic fashion. This analysis suggests that common polydimethylsiloxane (PDMS) networks fail at cross-linking points. Our results can be readily lumped into coarse-grained models. Although focusing on PDMS as a model system, our study presents a general procedure to pass beyond the window of accessible rupture times in MD studies employing mean first passage time theory, which can be exploited for arbitrary molecular systems.
Article	S. Agrawal, S. Galmarini, M. Kröger Voronoi tessellation-based algorithm for determining rigorously defined classical and generalized geometric pore size distributions Phys. Rev. E 107 (2023) 015307
The geometric pore size distribution (PSD) P(r) as function of pore radius r is an important characteristic of porous structures, including particle-based systems, because it allows us to analyze adsorption behavior, the strength of materials, etc. Multiple definitions and corresponding algorithms, particularly in the context of computational approaches, exist that aim at calculating a PSD, often without mentioning the employed definition and therefore leading to qualitatively very different and apparently incompatible results. Here, we analyze the differences between the PSDs introduced by Torquato et al. and the more widely accepted one provided by Gelb and Gubbins, here denoted as T-PSD and G-PSD, respectively, and provide rigorous mathematical definitions that allow us to quantify the qualitative differences. We then extend G-PSD to incorporate the ideas of coating, which is significant for nanoparticle-based systems, and of finite probe particles, which is crucial to micro and mesoporous particles. We derive how the extended and classical versions are interrelated and how to calculate them properly. We next analyze various numerical approaches used to calculate classical G-PSDs and may be used to calculate the generalized G-PSD. To this end, we propose a simple yet sufficiently complicated benchmark for which we calculate the different PSDs analytically. This approach allows us to completely rule out a recently proposed algorithm based on radical Voronoi tessellation. Instead, we find and prove that the output of a grid-free classical Voronoi tessellation, namely, the properties of its triangulated faces, can be used to formulate an algorithm, which is capable of calculating the generalized G-PSD for a system of monodisperse spherical particles (or points) to any precision, using analytical expressions. The Voronoi-based algorithm developed and provided here has optimal scaling behavior and outperforms grid-based approaches.
Article	R. Schlickeiser, M. Kröger Key epidemic parameters of the SIRV model determined from past Covid-19 mutant waves Covid 3 (2023) 592-600
Monitored infection and vaccination rates during past past waves of the coronavirus are used to infer a posteriori two-key parameter of the SIRV epidemic model, namely, the real-time variation in (i) the ratio of recovery to infection rate and (ii) the ratio of vaccination to infection rate. We demonstrate that using the classical SIR model, the ratio between recovery and infection rates tends to overestimate the true ratio, which is of relevance in predicting the dynamics of an epidemic in the presence of vaccinations.
Article	R. Schlickeiser, M. Kröger Determination of a key pandemic parameter of the SIR-epidemic model from past Covid-19 mutant waves and its variation for the validity of the Gaussian evolution Physics 5 (2023) 205-214
Monitored differential infection rates of past corona waves are used to infer, a posteriori, the real time variation of the ratio of recovery to infection rate as a key parameter of the SIR (susceptible-infected-recovered/removed) epidemic model. From monitored corona waves in five different countries, it is found that this ratio exhibits a linear increase at early times below the first maximum of the differential infection rate, before the ratios approach a nearly constant value close to unity at the time of the first maximum with small amplitude oscillations at later times. The observed time dependencies at early times and at times near the first maximum agree favorably well with the behavior of the calculated ratio for the Gaussian temporal evolution of the rate of new infections, although the predicted linear increase of the Gaussian ratio at late times is not observed.
Article	R. Schlickeiser, M. Kröger Analytical solution of the Susceptible-Infected-Recovered/Removed model for the not too late temporal evolution of epidemics for general time-dependent recovery and infection rates Covid 3 (2023) 1781-1796
The dynamical equations of the susceptible-infected-recovered/removed (SIR) epidemics model play an important role in predicting and/or analyzing the temporal evolution of epidemic outbreaks. Crucial input quantities are the time-dependent infection (a(t)) and recovery (μ(t)) rates regulating the transitions between the compartments S→I and I→R, respectively. Accurate analytical approximations for the temporal dependence of the rate of new infections J˚(t)=a(t)S(t)I(t) and the corresponding cumulative fraction of new infections J(t)=J(t0)+∫t0tdxJ˚(x) are available in the literature for either stationary infection and recovery rates or for a stationary value of the ratio k(t)=μ(t)/a(t). Here, a new and original accurate analytical approximation is derived for general, arbitrary, and different temporal dependencies of the infection and recovery rates, which is valid for not-too-late times after the start of the infection when the cumulative fraction J(t)≪1 is much less than unity. The comparison of the analytical approximation with the exact numerical solution of the SIR equations for different illustrative examples proves the accuracy of the analytical approach.
Article	P. Ilg, M. Kröger Field- and concentration-dependent relaxation of magnetic nanoparticles and optimality conditions for magnetic fluid hyperthermia Sci. Rep. 13 (2023) 16523
The field-dependent relaxation dynamics of suspended magnetic nanoparticles continues to present a fascinating topic of basic science that at the same time is highly relevant for several technological and biomedical applications. Renewed interest in the intriguing behavior of magnetic nanoparticles in response to external fields has at least in parts be driven by rapid advances in magnetic fluid hyperthermia research. Although a wealth of experimental, theoretical, and simulation studies have been performed in this field in recent years, several contradictory findings have so far prevented the emergence of a consistent picture. Here, we present a dynamic mean-field theory together with comprehensive computer simulations of a microscopic model system to systematically discuss the influence of several key parameters on the relaxation dynamics, such as steric and dipolar interactions, the external magnetic field strength and frequency, as well as the ratio of Brownian and Né relaxation time. We also discuss the specific and intrinsic loss power as measures of the efficiency of magnetic fluid heating and discuss optimality conditions in terms of fluid and field parameters. Our results are helpful to reconcile contradictory findings in the literature and provide an important step towards a more consistent understanding. In addition, our findings also help to select experimental conditions that optimize magnetic fluid heating applications.
Article	M. Kröger, J.D. Dietz, R.S. Hoy, C. Luap The Z1+package: Shortest multiple disconnected path for the analysis of entanglements in macromolecular systems Comput. Phys. Commun. 283 (2023) 108567
This paper describes and provides Z1+, the successor of the Z- and Z1-codes for topological analyses of mono- and polydisperse entangled linear polymeric systems, in the presence or absence of confining surfaces or nano-inclusions. In contrast to its predecessors, Z1+ makes use of adaptive neighbor lists, and keeps the number of temporary nodes relatively large, yielding improved performance for large system sizes. Z1+ also includes several features its predecessors lacked, including several that are advantageous for analyses of semi-crystalline systems, brushes, nano-composites, and flowing liquids. It offers a graphical user interface that can be used to run Z1+ and visualize the results, and a PPA+ option that allows Z1+ to perform a primitive path analysis more efficiently than the standard procedure (PPA option). In addition to describing Z1+.s and PPA+.s implementation and computational performance in detail, we use it to show that it yields entanglement lengths that agree quantitatively with both a recently proposed unified analytic theory for flexible and semiflexible polymer-melt entanglement and with the available experimental data for these systems. Finally we show that the associated theoretical expressions, which express reduced entanglement-related quantities in terms of the scaled Kuhn segment density Λ, need not describe results for model polymer solutions of different .chemistries., i.e. different angular and dihedral interactions but the same Λ. The Z1+ code can be downloaded from the CPC library following this link Comput. Phys. Commun. 283 (2023) 108567, or alternatively, the library link. In addition, there is a github repository Z1plus-code that provides some utilities that might be useful for Z1+ users.
Article	G. Chen, L. Tao, M. Kröger, Y. Li Inverse Hall-Petch effect in nanocrystalline ice predicted by machine-learned coarse-grained molecular simulations J. Micromech. Molec. Phys. 8 (2023) 1-10
We study the grain-size effect on mechanical behaviors of polycrystalline ice at nanoscale through large-scale molecular dynamics simulations, enabled by an accurate and efficient machine-learned coarse-grained water model [H. Chan, M. J. Cherukara, B. Narayanan, T. D. Loeffler, C. Benmore, S. K. Gray and S. K. Sankaranarayanan. Machine learning coarse grained models for water. Nature Communications 10(1), p. 379, 2019]. Polycrystalline ice systems with different grain sizes in the range of ∼ 30 nm are systematically investigated through uniaxial tensile tests. Simulation results reveal that Young’s modulus and yield strength increase as the grain size increases, leading to an inverse Hall–Petch effect in nanocrystalline ice. Such an observation is significantly different from the conventional Hall–Petch effect in polycrystalline ice observed by experiments at millimeter scale. The deformation behavior suggests that grain boundaries (GBs), rather than grain interiors, play the active role in accommodating external loading in nanocrystalline ice. Further void analysis of nanocrystalline ice during deformation reveals that nanocrack initiates and propagates along GBs and eventually leads to failure of systems with larger grain sizes (≥ 20nm), yielding a sudden drop in the stress–strain curve. While for systems with smaller grain sizes (≤ 15nm), only extensive plastic deformation is presented without significant void growth. Our simulation results demonstrate that the GB sliding is the governing mechanism for the inverse Hall–Petch effect observed in nanocrystalline ice.
Article	F. Nakai, M. Kröger, T. Ishida, T. Uneyama, Y. Doi, Y. Masubuchi Increase of rod diffusivity emerges even in Markovian nature Phys. Rev. E 107 (2023) 044604
Rod-shaped particles embedded in certain matrices have been reported to exhibit an increase in their center of mass diffusivity upon increasing the matrix density. This increase has been considered to be caused by a kinetic constraint in analogy with tube models. We investigate a mobile rodlike particle in a sea of immobile point obstacles using a kinetic Monte Carlo scheme equipped with a Markovian process, that generates gaslike collision statistics, so that such kinetic constraints do essentially not exist. Even in such a system, provided the particle's aspect ratio exceeds a threshold value of about 24, the unusual increase in the rod diffusivity emerges. This result implies that the kinetic constraint is not a necessary condition for the increase in the diffusivity.
Article	E.N.M. Cirillo, M. Colangeli, M. Kröger, L. Rondoni Non-equilibrium phase transitions in feedback-controlled 3D particle dynamics Phys. Rev. Res. 5 (2023) 043063
We consider point particles moving inside spherical urns connected by cylindrical channels whose axes both lie along the horizontal direction. The microscopic dynamics differ from that of standard 3D billiards because of a kind of Maxwell.s demon that mimics clogging in one of the two channels, when the number of particles flowing through it exceeds a fixed threshold. Nonequilibrium phase transitions, measured by an order parameter, arise. The coexistence of different phases and their stability, as well as the linear relationship between driving forces and currents, typical of the linear regime of irreversible thermodynamics, are obtained analytically within the proposed kinetic theory framework, and are confirmed with remarkable accuracy by numerical simulations. This purely deterministic dynamical system describes a kind of experimentally realizable Maxwell.s demon, that may unveil strategies to obtain mass separation and stationary currents in a conservative particle model.
Article	A.V. Karatrantos, C. Mugemana, L. Bouhala, N. Clarke, M. Kröger From ionic nanoparticle organic hybrids to ionic nanocomposites: Structure, dynamics, and properties: A review Nanomater. 13 (2023) 2
Ionic nanoparticle organic hybrids have been the focus of research for almost 20 years, however the substitution of ionic canopy by an ionic-entangled polymer matrix was implemented only recently, and can lead to the formulation of ionic nanocomposites. The functionalization of nanoparticle surface by covalently grafting a charged ligand (corona) interacting electrostatically with the oppositely charged canopy (polymer matrix) can promote the dispersion state and stability which are prerequisites for property .tuning., polymer reinforcement, and fabrication of high-performance nanocomposites. Different types of nanoparticle, shape (spherical or anisotropic), loading, graft corona, polymer matrix type, charge density, molecular weight, can influence the nanoparticle dispersion state, and can alter the rheological, mechanical, electrical, self-healing, and shape-memory behavior of ionic nanocomposites. Such ionic nanocomposites can offer new properties and design possibilities in comparison to traditional polymer nanocomposites. However, to achieve a technological breakthrough by designing and developing such ionic nanomaterials, a synergy between experiments and simulation methods is necessary in order to obtain a fundamental understanding of the underlying physics and chemistry. Although there are a few coarse-grained simulation efforts to disclose the underlying physics, atomistic models and simulations that could shed light on the interphase, effect of polymer and nanoparticle chemistry on behavior, are completely absent.
Article	A.A. Galata, M. Kröger Globular proteins and where to find them within a polymer brush – A case study Polymers 15 (2023) 2407
Protein adsorption by polymerized surfaces is an interdisciplinary topic that has been approached in many ways, leading to a plethora of theoretical, numerical and experimental insight. There is a wide variety of models trying to accurately capture the essence of adsorption and its effect on the conformations of proteins and polymers. However, atomistic simulations are case-specific and computationally demanding. Here, we explore universal aspects of the dynamics of protein adsorption through a coarse-grained (CG) model, that allows us to explore the effects of various design parameters. To this end, we adopt the hydrophobic-polar (HP) model for proteins, place them uniformly at the upper bound of a CG polymer brush whose multibead-spring chains are tethered to a solid implicit wall. We find that the most crucial factor affecting the adsorption efficiency appears to be the polymer grafting density, while the size of the protein and its hydrophobicity ratio come also into play. We discuss the roles of ligands and attractive tethering surfaces to the primary adsorption as well as secondary and ternary adsorption in the presence of attractive (towards the hydrophilic part of the protein) beads along varying spots of the backbone of the polymer chains. The percentage and rate of adsorption, density profiles and the shapes of the proteins, alongside with the respective potential of mean force are recorded to compare the various scenarios during protein adsorption.
Article	R. Schlickeiser, M. Kröger Forecast of omicron wave time evolution Covid 2 (2022) 216-229
The temporal evolution of the omicron wave in different countries is predicted, upon adopting an early doubling time of three days for the rate of new infections with this mutant. The forecast is based on the susceptible–infectious–recovered/removed (SIR) epidemic compartment model with a constant stationary ratio k=μ(t)/a(t) between the infection (a(t)) and recovery (μ(t)) rates. The assumed fixed early doubling time then uniquely relates the initial infection rate a0 to the ratio k; this way the full temporal evolution of the omicron wave is determined here. Three scenarios (optimistic, pessimistic, intermediate) and the resulting pandemic parameters are considered for 12 different countries. Parameters include the total number of infected persons, the maximum rate of new infections, the peak time and the maximum 7-day incidence per 100,000 persons. The monitored data from Great Britain underwent a clear maximum SDI of 1865 on 7 January 2022. This maximum is a factor 5.0 smaller than our predicted value in the optimistic case and may indicate a dark number of omicron infections of 5.0 in Great Britain. For Germany we predict peak times of the omicron wave ranging from 32 to 38 and 45 days after the start of the omicron wave in the optimistic, intermediate and pessimistic scenario, respectively, with corresponding maximum SDI values of 7090, 13,263 and 28,911. Adopting 1 January 2022 as the starting date our predictions imply the maximum of the omicron wave to be reached between 1 February and 15 February 2022. Rather similar values are predicted for Switzerland. Due to an order of magnitude smaller omicron hospitalization rate, in concert with a high percentage of vaccinated and boosted population, the German health system can cope with a maximum omicron SDI value of 2800 which is about a factor 2.5 smaller than the corresponding value 7090 for the optimistic case. By either reducing the duration of intensive care during peak time, and/or by making use of the nonuniform spread of the omicron wave across Germany, it seems that the German health system can barely cope with the omicron wave and thus avoid triage decisions. The reduced omicron hospitalization rate also causes significantly smaller mortality rates compared to the earlier mutants in Germany. Within the optimistic scenario, we predict 7445 fatalities and a maximum number of 418 deaths/day due to omicron. These numbers range in order of magnitude below the ones known from the beta mutant.
Article	P. Ilg, M. Kröger Longest relaxation time versus maximum loss peak in the field-dependent longitudinal dynamics of suspended magnetic nanoparticles Phys. Rev. B 106 (2022) 134433
Magnetic nanoparticles in suspensions provide fascinating model systems to study field-induced effects. Their response to external fields also opens up promising new applications, e.g., in hyperthermia. Despite significant research efforts, several basic questions regarding the influence of external fields on the magnetization dynamics are still open. Here we revisit the classical model of a suspended magnetic nanoparticle with combined internal and Brownian dynamics in the presence of an external field and discuss the field-dependent longitudinal relaxation. While internal and Brownian dynamics are independent in the field-free case, the coupling of both processes when an external field is present leads to richer and more complicated behavior. Using a highly efficient and accurate solver to the underlying Fokker-Planck equation allows us to study a broad parameter range. We identify different dynamical regimes and study their respective properties. In particular, we discuss corrections to the popular rigid-dipole approximation which are captured in terms of a simplified diffusion-jump model in the Brownian-dominated regime with rare Néel relaxation events. In addition, we discover a regime with surprising mode-coupling effects for magnetically soft nanoparticles. We explain our findings with the help of a perturbation theory, showing that in this regime the magnetization relaxation at late times is slaved by the slow Brownian motion of the nanoparticle. We discuss consequences of these findings such as the discrepancy of the longest relaxation time and the inverse frequency of the loss peak of the magnetic susceptibility.
Article	O. Weismantel, A.A. Galata, M. Sadeghi, A. Kröger, M. Kröger Efficient generation of self-avoiding, semiflexible rotational isomeric chain ensembles in bulk, in confined geometries, and on surfaces Comput. Phys. Commun. 270 (2022) 108176
We provide an efficient ready-to-run code gensaw that generates single or large ensembles of self-avoiding, flexible, semiflexible, rotationally isometric or helical chains in the bulk or subject to arbitrary confinement and tethering conditions, where we allow for arbitrary intramolecular bending and dihedral energy functions. The resulting configuration files are provided in various common formats and can be immediately used to do molecular simulations or statistical analysis. We work out analytic expressions for the mean squared end-to-end distance and gyration radius of the semiflexible, helical and rotational isomeric state models with a finite number of bonds and arbitrary interaction potentials for direct comparison and testing of the code in the limiting case of unconfined phantom chains. In addition to the graphics-free linux standalone batch version gensaw that creates configuration and other files for high throughput applications from the command line, we provide an interactive online version gensaw-visualization that serves as platform-independent graphical user interface, and animates the resulting conformations using a remote gensaw server.
Article	M. Sadeghi, M.H. Saidi, M. Kröger, M. Tagliazucchi Stimuli-responsive polyelectrolyte brushes for regulating streaming current magnetic field and energy conversion efficiency in soft nanopores Phys. Fluids 34 (2022) 082022
The electrokinetic energy conversion, electroviscous effect, and induced internal and external magnetic fields in a smart polyelectrolyte grafted .soft. nanopore with pH responsiveness are studied here using an efficient molecular theory approach. The analysis is based on writing the total free energy of the system, including the conformational entropy of the flexible, self-avoiding polymer chains and the translational entropy of the mobile species, the electrostatic interactions, and the free energy due to chemical equilibrium reactions. Then, the free energy is minimized, while satisfying the necessary constraints to find the equilibrium state of the system. The predictions of the model are shown to be in excellent agreement with analytical solutions derived for special cases. We discuss the effect of different influential environmental and polymer brush parameters in detail and show that the electrokinetic energy conversion efficiency is optimal at moderate pH values and low background salt concentrations. It is also shown that the electrokinetic energy conversion efficiency is a complex function depending on both the environmental and polymer brush properties. Notably, high slip coefficients or high polymer grafting densities do not necessarily lead to a high energy conversion efficiency. Magnetic field readouts allow to measure streaming currents through nanopores without the need of electrodes and may be utilized as a secondary electronic signature in nanopore sensing techniques. It is shown that in nanopores modified with polyelectrolyte brushes, the induced magnetic fields can be tens of times larger than those in solid-state nanopores having only surface charges. We show that by tuning the pH, background salt concentration, surface charge, and polyelectrolyte grafting density, the magnitude of the internal and external magnetic fields can be significantly changed and controlled in a wide range.
Article	M. Kröger, R. Schlickeiser SIR-solution for slowly time-dependent ratio between recovery and infection rates Physics 4 (2022) 504-524
The temporal evolution of pandemics described by the susceptible-infectious-recovered (SIR)-compartment model is sensitively determined by the time dependence of the infection (a(t)) and recovery (μ(t)) rates regulating the transitions from the susceptible to the infected and from the infected to the recovered compartment, respectively. Here, approximated SIR solutions for different time dependencies of the infection and recovery rates are derived which are based on the adiabatic approximation assuming time-dependent ratios, k(t)=μ(t)/a(t), varying slowly in comparison with the typical time characteristics of the pandemic wave. For such slow variations, the available analytical approximations from the KSSIR-model, developed by us and valid for a stationary value of the ratio k, are used to insert a posteriori the adopted time-dependent ratio of the two rates. Instead of investigating endless different combinations of the time dependencies of the two rates a(t) and μ(t), a suitably parameterized reduced time, τ, dependence of the ratio k(τ) is adopted. Together with the definition of the reduced time, this parameterized ratio k(τ) allows us to cover a great variety of different time dependencies of the infection and recovery rates. The agreement between the solutions from the adiabatic approximation in its four different studied variants and the exact numerical solutions of the SIR-equations is tolerable providing confidence in the accuracy of the proposed adiabatic approximation.
Article	M. Kröger, P. Ilg Combined dynamics of magnetization and particle rotation of a suspended superparamagnetic particle in the presence of an orienting field: Semi-analytical and numerical solution Math. Mod. Meth. Appl. Sci. 32 (2022) 1349-1383
The magnetization dynamics of suspended superparamagnetic particles is governed byinternal N .eel relaxation as well as Brownian diffusion of the whole particle. We herepresent semi-analytical and numerical solutions of the kinetic equation, describing thecombined rotation of particle orientation and magnetization. The solutions are based onan expansion of the joint probability density into a complete set of bipolar harmonics,leading to a coupled set of ordinary differential equations for the expansion coefficients.Extending previous works, we discuss the spectrum of relaxation times as well as con-vergence and limits of applicability of the method. Furthermore, we also provide thenumerical scheme in electronic form, so that readers can readily implement and use themodel. Supplementary Code for the egg-model available here at Github
Article	J.D. Dietz, M. Kröger, R.S. Hoy Validation and refinement of unified analytic model for flexible and semiflexible polymer melt entanglement Macromolecules 55 (2022) 3613-3626
We combine molecular dynamics simulations and topological analyses (TA) to validate and refine a recently proposed unified analytic model [Hoy, R. S.; Kröger, M. Phys. Rev. Lett. 2020, 124, 147801] for the reduced entanglement length, tube diameter, and plateau modulus of polymer melts. While the functional forms of the previously published expressions are insensitive to the choice of the TA method and Ne-estimator, obtaining better statistics and eliminating all known sources of systematic error in the Ne-estimation alters their numerical coefficients. Our revised expressions quantitatively match bead−spring simulation data over the entire range of chain stiffnesses for which systems remain isotropic, semiquantitatively match all available experimental data for flexible, semiflexible, and stiff polymer melts (including new data for conjugated polymers that lie in a previously unpopulated stiffness regime), and outperform previously developed unified scaling theories.
Article	F. Haas, M. Kröger, R. Schlickeiser Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers J. Phys. A 55 (2022) 225206
We derive a generalized Hamiltonian formalism for a modified suscepti- ble.infectious.recovered/removed (SIR) epidemic model taking into account the population V of vaccinated persons. The resulting SIRV model is shown to admit three possible functionally independent Hamiltonians and hence three associated Poisson structures. The reduced case of vanishing vaccinated sector shows a complete correspondence with the known Poisson structures of the SIR model. The SIRV model is shown to be expressible as an almost Nambu sys- tem, except for a scale factor function breaking the divergenceless property. In the autonomous case with time-independent stationary ratios k and b, the SIRV model is shown to be a maximally super-integrable system. For this case we test the accuracy of numerical schemes that are suited to solve the stiff set of SIRV differential equations.
Article	E.N.M. Cirillo, M. Colangeli, A. Di Francesco, M. Kröger, L. Rondoni Transport and nonequilibrium phase transitions in polygonal urn models Chaos 32 (2022) 093127
We study the deterministic dynamics of N point particles moving at a constant speed in a 2D table made of two polygonal urns connected by an active rectangular channel, which applies a feedback control on the particles, inverting the horizontal component of their velocities when their number in the channel exceeds a fixed threshold. Such a bounce-back mechanism is non-dissipative: it preserves volumes in phase space. An additional passive channel closes the billiard table forming a circuit in which a stationary current may flow. Under specific constraints on the geometry and on the initial conditions, the large N limit allows nonequilibrium phase transitions between homogeneous and inhomogeneous phases. The role of ergodicity in making a probabilistic theory applicable is discussed for both rational and irrational urns. The theoretical predictions are compared with the numerical simulation results. Connections with the dynamics of feedback-controlled biological systems are highlighted.
Article	C. Mugemana, A. Moghimikheirabadi, D. Arl, F. Addiego, D. F. Schmidt, M. Kröger, A. V. Karatrantos Ionic polydimethylsiloxane-silica nanocomposites: Dispersion and self-healing MRS Bull. 47 (2022) 1
Poly(dimethylsiloxane) (PDMS)-based nanocomposites have attracted increasing attention due to their inherent outstanding properties. Nevertheless, the realization of high levels of dispersion of nanosilicas in PDMS represents a challenge arising from the poor compatibility between the two components. Herein, we explore the use of ionic interactions located at the interface between silica and a PDMS matrix by combining anionic sulfonate-functionalized silica and cationic ammonium-functionalized PDMS. A library of ionic PDMS nanocomposites was synthesized and characterized to highlight the impact of charge location, density, and molecular weight of ionic PDMS polymers on the dispersion of nanosilicas and the resulting mechanical reinforcement. The use of reversible ionic interactions at the interface of nanoparticles.polymer matrix enables the healing of scratches applied to the surface of the nanocomposites. Molecular dynamics simulations were used to estimate the survival probability of ionic cross-links between nanoparticles and the polymer matrix, revealing a dependence on polymer charge density
Article	A.V. Karatrantos, J. Khantaveramongkol, M. Kröger Structure and diffusion of ionic PDMS melts Polymers 14 (2022) 3070
Ionic polymers exhibit mechanical properties that can be widely tuned upon selectively charging them. However, the correlated structural and dynamical properties underlying the microscopic mechanism remain largely unexplored. Here, we investigate, for the first time, the structure and diffusion of randomly and end-functionalized ionic poly(dimethylsiloxane) (PDMS) melts with negatively charged bromide counterions, by means of atomistic molecular dynamics using a united atom model. In particular, we find that the density of the ionic PDMS melts exceeds the one of their neutral counterpart and increases as the charge density increases. The counterions are condensed to the cationic part of end-functionalized cationic PDMS chains, especially for the higher molecular weights, leading to a slow diffusion inside the melt; the counterions are also correlated more strongly to each other for the end-functionalized PDMS. Temperature has a weak effect on the counterion structure and leads to an Arrhenius type of behavior for the counterion diffusion coefficient. In addition, the charge density of PDMS chains enhances the diffusion of counterions especially at higher temperatures, but hinders PDMS chain dynamics. Neutral PDMS chains are shown to exhibit faster dynamics (diffusion) than ionic PDMS chains. These findings contribute to the theoretical description of the correlations between structure and dynamical properties of ion-containing polymers.
Article	Z. Shen, H. Ye, Q. Wang, M. Kröger, Y. Li Sticky Rouse time features the self-healing of supramolecular polymer networks Macromolecules 54 (2021) 5053-5064
Supramolecular polymers are fascinating materials due to their strikingly self-healing capabilities empowered by reversible bonds. However, due to the lack of knowledge about the molecular structure evolution at the fractured interfaces, there is no existing theory to explain and predict the diverse healing times of different supramolecular materials observed in experiments. Here, we systematically study the self-adhesion of both unentangled and entangled supramolecular polymer networks through molecular simulations. We find that the recovery of macroscopic interfacial strength almost linearly depends on the microscopic molecular formations at fractured interfaces of supramolecular polymers, including reversible bonds and entanglements (entangled systems only). More importantly, we place the healing time into the context of intrinsic relaxation timescales of supramolecular polymer networks. It is found that the intrinsic sticky Rouse time features the self-adhesion process of all fractured supramolecular polymers, representing the full recovery of interfacial strength. At this critical timescale, two things happened to guarantee the full recovery of fractured systems: (i) polymer chains have diffused across the fractured interface with a displacement comparable to their sizes; (ii) the crossed stickers and polymer chains have updated their reversible bonds and entanglements (entangled systems only), respectively. The clear molecular description and suggested characteristic self-adhesion time will help the molecular design of supramolecular polymers.
Article	Y.R. Sliozberg, M. Kröger, T.C. Henry, S. Datta, D.B. Lawrence, A.J. Hall, A. Chattopadhyay Computational design of shape memory polymer nanocomposites Polymer 217 (2021) 123476
The goal of this work is to understand the underlying mechanisms that govern shape memory of polymer nanocomposites at the molecular level and to utilize them for novel synthetic shape memory polymer (SMP) materials for reconfigurable structures. In this study, we have performed coarse-grained molecular dynamics simulations of buckypaper (BP)/epoxy nanocomposites with a focus on their mechanical and shape memory performances, specifically on prediction of the Young.s modulus of the material as a function of carbon nanotube (CNT) loading. Our results demonstrate that the Young.s modulus linearly increases with CNT volume fraction below 0.16 (40 wt%) followed by a sharp upsurge of the modulus at higher loading where the onset of entanglements of nanotubes was determined. Additionally, we found a significantly greater increase of the modulus at T > Tg compared with the values below the glass transition temperature Tg for all considered systems. The simulation suggests that incorporation of BP restricts relaxation of network strands of the polymer matrix and leads to resistance in the recovery process of composites.
Article	R. Schlickeiser, M. Kröger Reasonable limiting of 7-day incidence per hundred thousand value and herd immunization in Germany and other countries Covid 1 (2021) 130-136
Based on hospital capacities, facts from past experience with the coronavirus disease 2019 (COVID-19) virus and the number of dark infections during the second wave (DII = 2D2), a reasonable limiting value of 140/D2 for the 7-day incidence per 100,000 persons (MSDIHT) and a second wave herd immunization threshold fraction value of 0.26 in Germany were calculated. If the MSDIHT is held below this limiting value, the German hospital system can cope with the number of new seriously infected persons without any triage decisions. On the basis of the SIRV epidemics model, the classical threshold values for herd immunization were calculated for 18 countries. For these countries, the dates regarding when herd immunization against the second COVID-19 wave will be reached were estimated.
Article	R. Schlickeiser, M. Kröger Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions Frontiers Phys. 8 (2021) 593421
Due to the current COVID-19 epidemic plague hitting the worldwide population it is of utmost medical, economical and societal interest to gain reliable predictions on the temporal evolution of the spreading of the infectious diseases in human populations. Of particular interest are the daily rates and cumulative number of new infections, as they are monitored in infected societies, and the influence of non-pharmaceutical interventions due to different lockdown measures as well as their subsequent lifting on these infections. Estimating quantitatively the influence of a later lifting of the interventions on the resulting increase in the case numbers is important to discriminate this increase from the onset of a second wave. The recently discovered new analytical solutions of Susceptible-Infectious- Recovered (SIR) model allow for such forecast. In particular, it is possible to test lockdown and lifting interventions because the new solutions hold for arbitrary time dependence of the infection rate. Here we present simple analytical approximations for the rate and cumulative number of new infections.
Article	R. Schlickeiser, M. Kröger Analytical solution of the SIR-model for the temporal evolution of epidemics. Part B. Semi-time case J. Phys. A: Math. Theor. 54 (2021) 175601
The earlier analytical analysis (part A) of the susceptible.infectious.recovered (SIR) epidemics model for a constant ratio k of infection to recovery rates is extended here to the semi-time case which is particularly appropriate for modeling the temporal evolution of later (than the first) pandemic waves when a greater population fraction from the first wave has been infected. In the semi-time case the SIR model does not describe the quantities in the past; instead they only hold for times later than the initial time t = 0 of the newly occurring wave. Simple exact and approximative expressions are derived for the final and maximum values of the infected, susceptible and recovered/removed population fractions as well the daily rate and cumulative number of new infections. It is demonstrated that two types of temporal evolution of the daily rate of new infections j(.) occur depending on the values of k and the initial value of the infected fraction I(0) = .: in the decay case for k . 1 . 2. the daily rate monotonically decreases at all positive times from its initial maximum value j(0) = .(1 . .). Alternatively, in the peak case for k < 1 . 2. the daily rate attains a maximum at a finite positive time. By comparing the approximated analytical solutions for j(.) and J(.) with the exact ones obtained by numerical integration, it is shown that the analytical approximations are accurate within at most only 2.5 percent. It is found that the initial fraction of infected persons sensitively influences the late time dependence of the epidemics, the maximum daily rate and its peak time. Such dependencies do not exist in the earlier investigated all-time case.
Article	R. Schlickeiser, M. Kröger Analytical modeling of the temporal evolution of epidemics outbreaks accounting for vaccinations Physics 3 (2021) 386-426
With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to a fourth compartment, V, of vaccinated persons. This extension involves the time t-dependent effective vaccination rate, v(t), that regulates the relationship between susceptible and vaccinated persons. The rate v(t) competes with the usual infection, a(t), and recovery, μ(t), rates in determining the time evolution of epidemics. The occurrence of a pandemic outburst with rising rates of new infections requires k+b&lt;1−2η, where k=μ(0)/a(0) and b=v(0)/a(0) denote the initial values for the ratios of the three rates, respectively, and η≪1 is the initial fraction of infected persons. Exact analytical inverse solutions t(Q) for all relevant quantities Q=[S,I,R,V] of the resulting SIRV model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy, yielding the explicit time-dependences Q(t) by inverting the Lambert functions. The values of the three parameters k, b and η completely determine the reduced time evolution of the SIRV-quantities Q(Ï„). The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from in Israel, this can happen in all countries considered.
Article	M.Pourali, N.O. Jaensson, M. Kröger Drag on a spheroidal particle at clean and surfactant-laden interfaces: effects of particle aspect ratio, contact angle and surface viscosities J. Fluid Mech. 924 (2021) A30
Translation of a non-spherical particle trapped at a membrane or at a complex interface between fluids is a relevant situation occurring in biological, technological and everyday life systems. Here, we consider prolate spheroidal particles, translating at a clean or (insoluble) surfactant-laden planar interface located between a viscous fluid and air, protruding into the surrounding subphase. Both the subphase and monolayer contribute to the total resistance experienced by the particle, which in turn is a function of interface and bulk viscosities, particle size and aspect ratio as well as the immersion depth of the particle. We explore how the drag on a spheroidal particle at a viscous interface can both rise or decrease with particle size depending on the dimensionless Boussinesq and Marangoni numbers. For a surfactant-laden interface, the surfactant distribution in the vicinity of the moving spheroid is significantly affected by the particle.s immersion depth. When a particle sinks more in the viscous fluid, as determined by the involved surface tensions, the difference in surfactant concentration between front and rear of the particle decreases. For the drag coefficient of a spherical particle at an incompressible interface at low shear Boussinesq numbers, we propose a correction to previously reported analytic expressions. We probe both parallel and perpendicular friction coefficients as they are significantly different depending on particle shape, qualitatively different depending on surface shear viscosity, and we resolve the full three-dimensional distortion of the flow field around the moving particle.
Article	M. Pourali, M. Kröger, J. Vermant, P.D. Andersson, N.O. Jaensson Drag on a spherical particle at the air-liquid interface: Interplay between compressibility, Marangoni flow, and surface viscosities Phys. Fluids 33 (2021) 062103
We investigate the flow of viscous interfaces carrying insoluble surface active material, using numerical methods to shed light on the complex interplay between Marangoni stresses, compressibility and surface shear and dilatational viscosities. We find quantitative relations between the drag on a particle and interfacial properties as they are required in microrheology, i.e., going beyond the asymptotic limits. To this end we move a spherical particle probe at constant tangential velocity, symmetrically immersed at the either incompressible or compressible interface, in the presence and absence of surfactants, for a wide range of system parameters. A full three-dimensional finite element calculation is used to reveal the intimate coupling between the bulk and interfacial flows and the subtle effects of the different physical effects on the mixed-type velocity field that affects the drag coefficient, both in the bulk and at the interface. For an inviscid interface, the directed motion of the particle leads to a gradient in the concentration of the surface active species which in turn drives a Marangoni flow in the opposite direction, giving rise to a force exerted on the particle. We show that the drag coefficient at incompressible interfaces is independent of the origin of the incompressibility (dilatational viscosity, Marangoni effects or a combination of both) and that its higher value can not only be related to the Marangoni effects, as suggested earlier. In confined flows, we show how the interface shear viscosity suppresses the vortex at the interface, generates a uniform flow, and consequently increases the interface compressibility and the Marangoni force on the particle. We mention available experimental data and provide analytic approximations for the drag coefficient that can be used to extract surface viscosities.
Article	M. Kröger Top cited 2018-2019 papers in the section Polymer Theory and Simulation (Editorial) Polymers 13 (2021) 43
This editorial deals with the most cited papers published in the years 2018.2019 in the section .Polymer Theory and Simulation. of the journal Polymers. They are mainly regular research articles, but two reviews are also present in this analysis. The main topics appear related to (nano)composites, entangled polymers, ring polymers, nanotubes, polyelectrolytes, brushes and polymers at interfaces. The most used simulation methods are molecular dynamics, Brownian dynamics, and Monte Carlo, with the only exception being a paper dealing with metamaterials. The evolution of the fraction of publications falling into one of these fields over the past 50 years is visualized in Figure 1. Figure 2 shows the same data differently, so that the focus is on the qualitative rather than quantitative evolution within areas of research. In the following, and inline with the spirit of this short editorial we are going to review the most cited works in the order of their number of citations, rather than by discipline.
Article	M. Kröger, R. Schlickeiser Verification of the accuracy of the SIR model in forecasting based on the improved SIR model with a constant ratio of recovery to infection rate by comparing with monitored second wave data R. Soc. Open Sci. 8 (2021) 211379
The temporal evolution of second and subsequent waves of epidemics such as Covid-19 is investigated. Analytic expressions for the peak time and asymptotic behaviours, early doubling time, late half decay time, and a half-early peak law, characterizing the dynamical evolution of number of cases and fatalities, are derived, where the pandemic evolution exhibiting multiple waves is described by the semitime SIR model. The asymmetry of the epidemic wave and its exponential tail are affected by the initial conditions, a feature that has no analogue in the all-time SIR model. Our analysis reveals that the immunity is very strongly increasing in several countries during the second Covid-19 wave. Wave-specific SIR parameters describing infection and recovery rates we find to behave in a similar fashion. Still, an apparently moderate change of their ratio can have significant consequences. As we show, the probability of an additional wave is however low in several countries due to the fraction of immune inhabitants at the end of the second wave, irrespective of the ongoing vaccination efforts. We compare with alternate approaches and data available at the time of submission. Most recent data serves to demonstrate the successful forecast and high accuracy of the SIR model in predicting the evolution of pandemic outbreaks as long as the assumption underlying our analysis, an unchanged situation of the distribution of variants of concern and the fatality fraction, do not change dramatically during a wave. With the rise of the α variant at the time of submission the second wave did not terminate in some countries, giving rise to a superposition of waves that is not treated by the present contribution.
Article	M. Kröger, M. Turkyilmazoglu, R. Schlickeiser Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use? Physica D 425 (2021) 132981
An analytic evaluation of the peak time of a disease allows for the installment of effective epidemicprecautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of thefraction of infected persons during an outbreak within the susceptible–infectious–recovered/removed(SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existingapproximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation thatallowonetocomeupwithdifferentexplicitexpressionsforthepeaktimeoftheinfectedcompartment(Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressionsfor any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far(countries, ss, cities). For small populations with less than hundreds of individuals (families, smalltowns),however,theapproximantMToutperformstheotherapproximants.Tobeabletocomparethevariousapproaches,weclarifytheequivalencebetweenthefour-parametricdimensionalSIRequationsand their two-dimensional dimensionless analogue. Using Covid-19 data from various countries andsources we identify the relevant regime within the parameter space of the SIR model.
Article	L. Alvarez, M.A. Fernandez-Rodriguez, A. Alegria, S. Arrese-Igor, K. Zhao, M. Kröger, L. Isa Reconfigurable artificial microswimmers with internal feedback Nat. Commun. 12 (2021) 4762
Self-propelling microparticles are often proposed as synthetic models for biological microswimmers, yet they lack the internally regulated adaptation of their biological counterparts. Conversely, adaptation can be encoded in larger-scale soft-robotic devices but remains elusive to transfer to the colloidal scale. Here, we create responsive microswimmers, powered by electro-hydrodynamic flows, which can adapt their motility via internal reconfiguration. Using sequential capillary assembly, we fabricate deterministic colloidal clusters comprising soft thermo-responsive microgels and light-absorbing particles. Light absorption induces preferential local heating and triggers the volume phase transition of the microgels, leading to an adaptation of the clusters. motility, which is orthogonal to their propulsion scheme. We rationalize this response via the coupling between self-propulsion and variations of particle shape and dielectric properties upon heating. Harnessing such coupling allows for strategies to achieve local dynamical control with simple illumination patterns, revealing exciting opportunities for developing tactic active materials.
Article	A. Moghimikheirabadi, M. Kröger, A.V. Karatrantos Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites Soft Matter 17 (2021) 6362-6373
Conformations, entanglements and dynamics in attractive polymer nanocomposites are investigated in this work by means of coarse-grained molecular dynamics simulation, for both weak and strong confinements, in the presence of nanoparticles (NPs) at NP volume fractions φ up to 60%. We show that the behavior of the apparent tube diameter dapp in such nanocomposites can be greatly different from nanocomposites with nonattractive interactions. We find that this effect originates, based on a mean field argument, from the geometric confinement length dgeo at strong confinement (large φ) and not from the bound polymer layer on NPs (interparticle distance ID < 2Rg) as proposed recently based on experimental measurements. Close to the NP surface, the entangled polymer mobility is reduced in attractive nanocomposites but still faster than the NP mobility for volume fractions beyond 20%. Furthermore, entangled polymer dynamics is hindered dramatically by the strong confinement created by NPs. For the first time using simulations, we show that the entangled polymer conformation, characterized by the polymer radius of gyration Rg and form factor, remains basically unperturbed by the presence of NPs up to the highest volume fractions studied, in agreement with various experiments on attractive nanocomposites. As a side-result we demonstrate that the loose concept of ID can be made a microscopically well defined quantity using the mean pore size of the NP arrangement.
Article	A. Moghimikheirabadi, A.V. Karatrantos, M. Kröger Ionic polymer nanocomposites subjected to uniaxial extension: A nonequilibrium molecular dynamics study Polymers 13 (2021) 4001
We explore the behavior of coarse-grained ionic polymer nanocomposites (IPNCs) under uniaxial extension up to 800% strain by means of nonequilibrium molecular dynamics simulations. We observe a simultaneous increase of stiffness and toughness of the IPNCs upon increasing the engineering strain rate, in agreement with experimental observations. We reveal that the excellent toughness of the IPNCs originates from the electrostatic interaction between polymers and nanoparticles, and that it is not due to the mobility of the nanoparticles or the presence of polymer–polymer entanglements. During the extension, and depending on the nanoparticle volume fraction, polymer–nanoparticle ionic crosslinks are suppressed with the increase of strain rate and electrostatic strength, while the mean pore radius increases with strain rate and is altered by the nanoparticle volume fraction and electrostatic strength. At relatively low strain rates, IPNCs containing an entangled matrix exhibit self-strengthening behavior. We provide microscopic insight into the structural, conformational properties and crosslinks of IPNCs, also referred to as polymer nanocomposite electrolytes, accompanying their unusual mechanical behavior.
Article	X. Shang, M. Kröger Time correlation functions of equilibrium and nonequilibrium Langevin dynamics: Derivations and numerics using random numbers SIAM Rev. 62 (2020) 901-935
We study the time correlation functions of coupled linear Langevin dynamics with and without inertial effects, both analytically and numerically. The model equation represents the physical behavior of a harmonic oscillator in two or three dimensions in the presence of friction, additive noise, and an external field with both rotational and deformational components. This simple model plays pivotal roles in understanding more complicated processes. The analytical solution presented serves as a test of numerical integration schemes, and its derivation is presented in a fashion that allows it to be repeated directly in a classroom. While the results in the absence of fields (equilibrium) or confinement (free particle) are omnipresent in the literature, we write down, apparently for the first time, the full nonequilibrium results that may correspond, e.g., to a Hookean dumbbell embedded in a macroscopically homogeneous shear or mixed flow field. We demonstrate how the inertial results reduce to their noninertial counterparts in the nontrivial limit of vanishing mass. While the results are derived using basic integrations over Dirac delta distributions, we also provide alternative approaches involving (i) Fourier transforms, which seem advantageous only if the measured quantities also reside in Fourier space, and (ii) a Fokker--Planck equation and the moments of the probability distribution. The results, verified by numerical experiments, provide additional means of measuring the performance of numerical methods for such systems. It should be emphasized that this article provides specific details regarding the derivations of the time correlation functions as well as the implementations of various numerical methods, so that it can serve as a standalone piece for lessons in the framework of Ito's stochastic differential equations and calculus.
Article	R.S. Hoy, M. Kröger Unified analytic expressions for the entanglement length, tube diameter, and plateau modulus of polymer melts Phys. Rev. Lett. 124 (2020) 147801
By combining molecular dynamics simulations and topological analyses with scaling arguments, we obtain analytic expressions that quantitatively predict the entanglement length Ne, the plateau modulus G, and the tube diameter a in melts that span the entire range of chain stiffnesses for which systems remain isotropic. Our expressions resolve conflicts between previous scaling predictions for the loosely entangled [Lin-Noolandi: G lK3/kBT ∼ (lK/p)3], semiflexible [Edwards-de Gennes: G lK3/kBT ∼ (lK/p)2], and tightly entangled [Morse: G lK3/kBT ∼ (lK/p)1+ε] regimes, where lK and p are, respectively, the Kuhn and packing lengths. We also find that maximal entanglement (minimal Ne) coincides with the onset of local nematic order.
Article	R. Schlickeiser, M. Kröger First consistent determination of the basic reproduction number for the first Covid-19 wave in 71 countries from the SIR-epidemics model with a constant ratio of recovery to infection rate Global J. Front. Res. F 20 (2020) 37-43
The box-shaped serial interval distribution and the analytical solution of the Susceptible Infectious-Recovered (SIR)-epidemics model with a constant time-independent ratio k of the recovery (μ0) to infection rate (a0) are used to calculate the effective reproduction factor and the basic reproduction number R0. The latter depends on the positively valued net infection number x = 13.5(a0-μ0) as R0(x) = x(1 - e-x)-1 which for all values of x is greater unity. This dependence differs from the simple relation R0 = a0/μ0. With the earlier determination of the values of k and a0 of the Covid-19 pandemic waves in 71 countries the net infection rates and the basic reproduction numbers for these countries are calculated.
Article	R. Schlickeiser, M. Kröger Dark numbers and herd immunity of the first Covid-19 wave and future social interventions Epidem. Int. J. 4 (2020) 000152
The Gauss model for the time evolution of the first corona pandemic wave allows to draw conclusions on the amount of unreported cases per reported case, i.e., .dark number. of infections, the amount of herd immunity, the used maximum capacity of breathing apparati and the effectiveness of various non-pharmaceutical interventions in different countries. In Germany, Switzerland, Sweden, and Austria the dark numbers are 8.4 +/- 4.0, 12.6 +/- 5.8, 21.8 +/- 9.1, and 8.5 +/- 5.2, respectively. Our method of estimating dark numbers from modeling both, infection and death rates simultaneously serves as important benchmark to judge on the completeness of testing large portions of the population. For countries that cannot afford the laborious, timeconsuming and costly testing our method still provides them with a reliable estimate of the fraction of infected persons. In Germany the total number of infected individuals, including the dark number of infections by the first wave is estimated to be 1.6 +/- 0.5 million, corresponding to 1.9±0.6 percent of the German population. We work out direct implications from these predictions for managing the 2nd and further corona waves.
Article	R. Ranganathan, V. Kumar, A.L. Brayton, M. Kröger, G.C. Rutledge Atomistic modeling of plastic deformation in semicrystalline polyethylene: role of interphase topology, entanglements and chain dynamics Macromolecules 53 (2020) 4605-4617
The effects of interphase topology, entanglements, and chain dynamics on the mechanical response of semicrystalline polyethylene have been examined using atomistic simulations. In particular, the prevalence of the cavitation and melting/recrystallization mechanisms for yield and plastic flow were found to depend on both topological and dynamical properties of the molecular segments in the semicrystalline interphase. First, two different protocols were used during preparation of the interphase ensemble to modulate the distribution of (i) loops, bridges, and tails and (ii) entanglements within the noncrystalline domain. A protocol denoted 'step-wise cooling' produced structures having a large fraction of long, entangled segments that yielded by the melting/recrystallization mechanism about 50% of the time. By contrast, the protocol denoted .instantaneous quench. produced structures that yielded by melting/recrystallization about 73% of the time. Second, two different united atom force fields, PYS and TraPPE-UA, that exhibit nearly identical topological characteristics of the noncrystalline domain but different mobilities were used to study the effect of chain dynamics on yield mechanisms. At the slower strain rate used in this work, yield and plastic flow proceeded exclusively via cavitation for the model using the TraPPE-UA force field, whereas both cavitation and melting/recrystallization were observed for the model using the PYS force field. The greater prevalence of melting/recrystallization in the latter case is attributed to faster chain-sliding dynamics in the crystalline domain. The dependences of the yield mechanism on topology and dynamics are found to be related.
Article	P. Ilg, M. Kröger Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation Phys. Chem. Chem. Phys. 22 (2020) 22244-22259
The intriguing properties of magnetic nanoparticles have sparked a growing number of theoretical studies as well as practical applications. Here, we provide the first comprehensive study of the influence of interactions on the two main relaxation mechanisms: internal (Neel) and Brownian relaxation. While non-interacting magnetic nanoparticles show Debye behavior with an effective relaxation time, many authors use this model also for the interacting case. Since Neel relaxation is typically a thermally activated process on times scales that are many orders of magnitude larger than the underlying micromagnetic times, we use extensive computer simulations employing a Brownian dynamics/Monte-Carlo algorithm to show that dipolar interactions lead to significant deviations from the Debye behavior. We find that Neel and Brownian relaxation can be considered as independent processes for short enough times until dipolar interactions lead to a coupling of these mechanisms, making the interpretation more difficult. We provide mean-field arguments that describe these short and long-time, effective relaxation times well for weak up to moderate interaction strengths. Our findings about the coupling of Brownian and Neel process and the effective relaxation time provide an important theoretical insight that will have also important consequences for the interpretation of magnetic susceptibility measurements and magnetorelaxometry analysis.
Article	N. Gheczy, K. Sasaki, M. Yoshimoto, S. Pour-Esmaeil, M. Kröger, P. Stano, P. Walde A two-enzyme cascade reaction consisting of two reaction pathways. Studies in bulk solution for understanding the performance of a flow-through device with immobilised enzymes RSC Adv. 10 (2020) 18655-18676
Enzyme-catalysed cascade reactions in flow-through systems with immobilised enzymes currently are of great interest for exploring their potential for biosynthetic and bioanalytical applications. Basic studies in this field often aim at understanding the stability of the immobilised enzymes and their catalytic performance, for example, in terms of yield of a desired reaction product, analyte detection limit, enzyme stability or reaction reproducibility. In the work presented, a cascade reaction involving the two enzymes bovine carbonic anhydrase (BCA) and horseradish peroxidase (HRP) . with hydrogen peroxide (H2O2) as HRP activator. was first investigated in great detail in bulk solution at pH = 7.2. The reaction studied is the hydrolysis and oxidation of 2',7'-dichlorodihydrofluorescein diacetate (DCFH2-DA) to 2',7'- dichlorofluorescein (DCF), which was found to proceed along two reaction pathways. This two-enzyme cascade reaction was then applied for analysing the performance of BCA and HRP immobilised in glass fiber filters which were placed inside a filter holder device through which a DCFH2-DA/H2O2 substrate solution was pumped. Comparison was made between (i) co-immobilised and (ii) sequentially immobilised enzymes (BCA first, HRP second). Significant differences for the two arrangements in terms of measured product yield (DCF) could be explained based on quantitative UV/vis absorption measurements carried out in bulk solution. We found that the lower DCF yield observed for sequentially immobilised enzymes originates from a change in one of the two possible reaction pathways due to enzyme separation, which was not the case for enzymes that were co-immobilised (or simultaneously present in the bulk solution experiments). The higher DCF yield observed for co-immobilised enzymes did not originate from a molecular proximity effect (no increased oxidation compared to sequential immobilisation).
Article	M. Sadeghi, M.H. Saidi, A. Moosavi, M. Kröger Tuning electrokinetic flow, ionic conductance, and selectivity in a solid-state nanopore modified with a pH-responsive polyelectrolyte brush: A molecular theory approach Phys. Chem. C 124 (2020) 18513-18531
We use an efficient molecular theory approach to study electrokinetic flow within a pH-responsive nanopore grafted with a polyelectrolyte (PE) brush. The flow rate, migration and convective conductance, electric potential and velocity fields, species distributions and the degree of ionization of the weak PE functional groups and nanopore selectivity are obtained and interpreted while considering pH-induced surface charges. The theory is generally based on writing the overall free energy of the system including the entropies arising from the conformations of flexible, excluded volume chains, the mixing of mobile species, electrostatic contribution, and the free energy due to the chemical acid.base equilibrium reactions. We demonstrate how, by controlling the bulk salt concentration, pH, surface grafting density, and PE drag coefficient, the flow inside the pore can be controlled. Generally, the flow rate gets enhanced upon decreasing pH, but the effect of salt concentration is more complex. As long as the pH is small (large), the flow rate decreases (increases) by increasing the salt concentration, while a nonmonotonic trend is evident at moderate pH values. We find that, when the PE drag coefficient is high (low), the flow rate decreases (increases) by increasing surface grafting density. For intermediate drag coefficients, the flow rate varies nonmonotonically with surface grafting density. It is observed that the convective ionic conductance obeys almost the same trend as the flow rate. It is also illustrated that the mean degree of ionization of the polymer chains and the migration ionic conductance enhance on increasing the background salt concentration, whereas the opposite is true for nanopore selectivity. However, when very low salt concentration is accompanied by a high pH value, there is a minimum in the nanopore selectivity. The present approach allows investigation of the application of PE-coated nanopores as smart nanovalves.
Article	M. Kröger, R. Schlickeiser Gaussian doubling times and reproduction factors of the COVID-19 pandemic disease Frontiers Phys. 8 (2020) 276
The Gauss model for the time evolution of the first corona pandemic wave is rendered useful in the estimation of peak times, amount of required equipment, and the forecasting of fade out times. At the same time, it is probably the simplest analytically tractable model that allows us to quantitatively forecast the time evolution of infections and fatalities during a pandemic wave. In light of the various descriptors, such as doubling times and reproduction factors, currently in use to judge the lockdowns and other measures that aim to prevent spreading of the virus, we hereby provide both exact and simple approximate relationships between the two relevant parameters of the Gauss model (peak time and width), the transient behavior of two versions of doubling times, and three variants of reproduction factors, including basic reproduction numbers.
Article	M. Kröger, R. Schlickeiser Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: Time-independent reproduction factor J. Phys. A: Math. Theor. 53 (2020) 505601
We revisit the susceptible-infectious-recovered/removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic solution to the SIR model is known in parametric form for the case of a time-independent infection rate, we derive an analytic solution for the more general case of a time-dependent infection rate, that is not limited to a certain range of parameter values. Our approach allows us to derive several exact analytic results characterizing all quantities, and moreover explicit, non-parametric, and accurate analytic approximants for the solution of the SIR model for time-independent infection rates.We relate all parameters of the SIR model to ameasurable, usually reported quantity, namely the cumulated number of infected population and its first and second derivatives at an initial time t = 0, where data is assumed to be available.We address the question of how well the differential rate of infections is captured by the Gauss model (GM). To this end we calculate the peak height, width, and position of the bell-shaped rate analytically. We find that the SIR is captured by the GM within a range of times, which we discuss in detail. We prove that the SIR model exhibits an asymptotic behavior at large times that is different from the logistic model, while the difference between the two models still decreases with increasing reproduction factor. This part A of our work treats the original SIR model to hold at all times, while this assumption will be relaxed in part B. Relaxing this assumption allows us to formulate initial conditions incompatible with the original SIR model.
Article	J. Schüttler, R. Schlickeiser, F. Schlickeiser, M. Kröger Covid-19 predictions using a Gauss model, based on data from April 2 Physics 2 (2020) 197-212
We study a Gauss model (GM), a map from time to the bell-shaped Gaussian function to model the deaths per day and country, as a simple, analytically tractable model to make predictions on the coronavirus epidemic. Justified by the sigmoidal nature of a pandemic, i.e., initial exponential spread to eventual saturation, and an agent-based model, we apply the GM to existing data, as of 2 April 2020, from 25 countries during first corona pandemic wave and study the model.s predictions. We find that logarithmic daily fatalities caused by the coronavirus disease 2019 (Covid-19) are well described by a quadratic function in time. By fitting the data to second order polynomials from a statistical χ-2-fit with 95% confidence, we are able to obtain the characteristic parameters of the GM, i.e., a width, peak height, and time of peak, for each country separately, with which we extrapolate to future times to make predictions. We provide evidence that this supposedly oversimplifying model might still have predictive power and use it to forecast the further course of the fatalities caused by Covid-19 per country, including peak number of deaths per day, date of peak, and duration within most deaths occur. While our main goal is to present the general idea of the simple modeling process using GMs, we also describe possible estimates for the number of required respiratory machines and the duration left until the number of infected will be significantly reduced.
Article	A. Moghimikheirabadi, P. Ilg, L.M.C. Sagis, M. Kröger Surface rheology and structure of model triblock copolymers at a liquid-vapor interface: a molecular dynamics study Macromolecules 53 (2020) 1245-1257
The structure and surface rheology of two model symmetric triblock copolymers with different degrees of hydrophobicity but identical polymerization degree, spread at an explicit liquid/vapor interface, are investigated employing extensive equilibrium molecular dynamics and innovative nonequilibrium molecular dynamics simulations with semipermeable barriers in both the linear and nonlinear viscoelastic regimes. Results are obtained for interface microstructural and surface rheological quantities under dilatation and surface shear. Our results reveal that the more hydrophilic triblock copolymer (H21T8H21) imparts a higher surface pressure to the interface at a given surface concentration and takes on a conformation with a larger radius of gyration at the interface compared with H9T32H9, where H (hydrophilic) and T (hydrophobic) represent chemically different monomers. Increasing the surface concentration and/or decreasing the degree of hydrophobicity leads to an increase in both dilatational storage and loss moduli. Large amplitude oscillatory dilatation tests show that both interfaces exhibit strain softening at high strain amplitudes, while an intracycle nonlinearity analysis reveals an apparent strain hardening in extension. This paradox was already addressed for air.water interfaces stabilized by Pluronics in a preceding experimental work. Gyration tensor components parallel and normal to the interface as function of dilatational strain are used to characterize the microstructure; we demonstrate their close relationship to nonlinearity indices in both extension and compression. A structure.rheology relationship is obtained by means of the first harmonic analysis of the surface stress and the corresponding amplitude of the microstructure signal. In-plane oscillatory shear flow simulations are performed as well. The presented approach thus renders possible a test of theoretical frameworks, which link interfacial rheological data to the surface microstructure. It is furthermore shown to provide physical insights, which can be used for the interpretation of existing experimental surface rheological data.
Article	A. Moghimikheirabadi, C. Mugemana, M. Kröger, A.V. Karatrantos Polymer conformations, entanglements and dynamics in ionic nanocomposites: A molecular dynamics study Polymers 12 (2020) 2591
We investigate nanoparticle (NP) dispersion, polymer conformations, entanglements and dynamics in ionic nanocomposites. To this end, we study nanocomposite systems with various spherical NP loadings, three different molecular weights, two different Bjerrum lengths, and two types of charge-sequenced polymers by means of molecular dynamics simulations. NP dispersion can be achieved in either oligomeric or entangled polymeric matrices due to the presence of electrostatic interactions. We show that the overall conformations of ionic oligomer chains, as characterized by their radii of gyration, are affected by the presence and the amount of charged NPs, while the dimensions of charged entangled polymers remain unperturbed. Both the dynamical behavior of polymers and NPs, and the lifetime and amount of temporary crosslinks, are found to depend on the ratio between the Bjerrum length and characteristic distance between charged monomers. Polymer.polymer entanglements start to decrease beyond a certain NP loading. The dynamics of ionic NPs and polymers is very different compared with their non-ionic counterparts. Specifically, ionic NP dynamics is getting enhanced in entangled matrices and also accelerates with the increase of NP loading.
Article	Z. Shen, H. Ye, M. Kröger, Y. Li Interplay between ligand mobility and nanoparticle geometry during cellular uptake of PEGylated liposomes and bicelles Nanoscale 11 (2019) 15971-15983
We explore the cellular uptake process of PEGylated liposomes and bicelles by investigating their membrane wrapping process using large-scale molecular dynamics simulations. We find that due to the mobility of ligands on the liposome/bicelle, the membrane wrapping process of a PEGylated liposome/bicelle can be divided into two stages, whose transition is determined by a critical wrapping fraction fc; it is reached when all the ligands are exhausted and bound to receptors within the cell membrane. Before this critical scenario is approached, the grafted polyethylene glycol (PEG) polymers aggregate together within the membrane.wrapped region of the liposome/bicelle, driven by ligand.receptor binding. For wrapping fractions f > fc, membrane wrapping cannot proceed unless a compressive membrane tension is provided. By systematically varying the membrane tension and PEG molar ratio, we establish phase diagrams about wrapping states for both PEGylated liposomes and bicelles. According to these diagrams, we find that the absolute value of the compressive membrane tension required by a fully wrapped PEGylated bicelle is smaller than that of the PEGylated liposome, indicating that the PEGylated bicelle is easily internalized by cells. Further theoretical analysis reveals that compared to a liposome, the flatter surface at the top of a bicelle makes it energetically more favored beyond the critical wrapping fraction fc. Our simulations confirm that the interplay between ligand mobility and NP geometry can significantly change the understanding about the influence of NP geometry on the membrane wrapping process. It can help us to better understand the cellular uptake process of the PEGylated liposome/bicelle and to improve the design of lipid-like NPs for drug delivery.
Article	Z. Shen, D.T. Loe, A. Fisher, M. Kröger, J.L. Rouge, Y. Li Polymer stiffness governs template mediated self-assembly of liposome-like nanoparticles: simulation, theory and experiment Nanoscale 11 (2019) 20179-20193
This study suggests that the self-assembly of a template-mediated liposome (TML) can be utilized as a general method to produce liposomes with controlled sizes. A polymer tethered core is used here as a starting configuration of a TML. Lipids anchored to the free ends of the tethered polymers direct the selfassembly of surrounding free lipid molecules to form liposome-like nanoparticles. Characterizing the flexibility of polymers by their persistence lengths, we performed large scale molecular simulations to investigate the self-assembly process of TMLs with tethered polymers of different stiffness values. The stiffness of tethered polymer is found to play a crucial role in the self-assembly process of TMLs. The flexible and rigid-like polymers can accelerate and delay the self-assembly of TMLs, respectively. In addition, the critical grafting of tethered polymers and required lipid concentrations to from perfectly encapsulated TMLs are found to increase with the flexibility of tethered polymers. To scrutinize these simulation-based findings, we synthesized DNA-polyethylene glycol (PEG) TMLs and performed corresponding experiments. To this end we incorporate increasing concentrations of DNA as a proxy for increasing the rigidity of the tethered polymers. We find that the resulting structures are indeed consistent with the simulated ones. Finally, a theory is developed that allows one to estimate the required free lipid number (or lipid concentration) and grafting density analytically for polymers of a given persistence length. Through these combined computational, experimental, and theoretical studies, we present a predictive model for determining the effect of polymer stiffness on the self-assembly of TMLs, which can be used as a general approach for obtaining perfectly encapsulated TMLs as potential drug delivery vehicles.
Article	W. Wang, F. Shao, M. Kröger, R. Zenobi, A.D. Schlüter Structure elucidation of 2D polymer monolayers based on crystallization estimates derived from tip-enhanced Raman spectroscopy (TERS) polymerization conversion data J. Amer. Chem. Soc. 141 (2019) 9867-9871
Structural elucidation of 2D polymer monolayers proving long-range order is a challenge that limits the pace in which this recent field of polymer chemistry and of synthetic 2D materials develops. To overcome this bottleneck, we here present a method in which tip-enhanced Raman spectroscopy is combined with a random growth crystallization model to obtain global features from local spectroscopic information. Concretely, we prove the nature and determine the conversion number X of the cross-links for two new 2D homopolymers and one (of three) new 2D copolymers. Assuming random and in-plane growth, our model results in crystallinity degrees of 93.1% to 99.7% and mean radii of defect-free crystalline areas of 3.15 nm for conversion numbers of 84% < X < 98%. Thus, we provide strong evidence for the synthetic monolayer 2D materials presented that they qualify as 2D polymers and are therefore perfectly suited for indepth studies both in a more fundamental direction as well as toward application. This example shows how our method can affect current research on covalent sheets.
Article	S. Costanzo, L. Scherz, G. Floudas, R. Pasquino, M. Kröger, A.D. Schlüter, D. Vlassopoulos Hybrid dendronized polymers as molecular objects: viscoelastic properties in the melt Macromolecules 52 (2019) 7331-7342
Two homologous series of dendronized polymers (DPs) of the second and third generations, with different degrees of polymerization of the backbone, were synthesized combining two previously reported approaches. First, methacrylate-based DPs of the first generation were prepared via radical polymerization of the corresponding methacrylate macromonomers. As the side branches of such first-generation DPs can form hydrogen bonds and π-π stacks, they are referred to as 'classic' (intermolecularly interacting) DPs. Second, the first-generation DPs so prepared were grafted with branched oligoethylene glycol groups to increase the size of the dendrons up to the second and third generations. Because of the different chemical structures of the outermost generations with respect to the inner one, these DPs are termed 'hybrid' DPs. The glycol-based generations do not form intermolecular supramolecular associations, which so strongly control the aging dynamics and viscoelastic properties of the interacting DPs. Therefore, the series of hybrid DPs allow for investigating the dynamics of DPs for which synergistic effects because of supramolecular interactions and topology are reduced or absent. We find, at first glance surprisingly, that the loss of intermolecular peripheral interactions increases the equilibration time dramatically. Concerning the viscoelastic behavior of the hybrids of the second generation, the onset of global relaxation is observed at low frequencies. This is in contrast with supramolecular DPs having the same generation and the same backbone degree of polymerization, for which a clear plateau region was previously demonstrated. In addition, the low-frequency plateau of the elastic modulus increases upon increase of the degree of polymerization of the backbone, suggesting that one oligoethylene generation does not suffice to completely shield supramolecular interactions between the branches. Such a scenario is also supported by atomistic simulations. The hybrid DPs of the third generation display two distinct plateau regions of the storage modulus. The first one (at higher frequencies) is of the order of 106 Pa, and attributed to the interpenetration of the side branches, the second is of the order of 103 Pa. In contrast with the behavior of second-generation hybrid DPs, the degree of polymerization of the backbone has no effect on the low-frequency plateau of third-generation hybrid DPs. This suggests that supramolecular interactions do not contribute to the elastic plateau. Hence, we ascribe it to the entanglements of the entire hybrid DPs. The reported results are summarized in a table, which compares the properties of different DPs and provides the needed ingredients for tailoring the rheology of such hyperbranched polymers.
Article	P.S. Stephanou, M. Kröger Assessment of the tumbling-snake model against linear and nonlinear rheological data of bidisperse polymer blends Polymers 11 (2019) 376
We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the academic case of a monodisperse sample. Here, we extend these studies and provide the stationary solutions of the tumbling-snake model both analytically, for small shear rates, and via Brownian dynamics simulations, for a bidisperse sample over a wide range of shear rates and model parameters. We further show that the tumbling-snake model bears the necessary capacity to compare well with available linear and non-linear rheological data for bidisperse systems. This capacity is added to the already documented ability of the model to accurately predict the shear rheology of monodisperse systems.
Article	M. Kröger Efficient hybrid algorithm for the dynamic creation of semiflexible polymer solutions, brushes, melts and glasses Comput. Phys. Commun. 241 (2019) 178-179
We present an updated version of a program that had been published earlier in this journal. The program executes an algorithm for the creation and relaxation of large, dense or diluted homogeneous many particle systems made of wormlike, finite extendable, semiflexible multibead chains and . optionally . solvent particles, which repulse each other. The key feature is its efficiency, its output has been proven to serve as an excellent basis for any subsequent off-lattice computer simulation. The application allows to choose (i) the bead number density or packing fraction, temperature, chain length, system size, concentration, (ii) the interaction potentials, hence the local features such as bond length and bending rigidity of the chains, and (iii) the degree of pre-relaxation, parametrized and expressed through a minimum intermolecular distance. The monodisperse polymers are represented by chains of monomer coordinates in 3D space. During the dynamical two-step process of sample creation the initially (Monte Carlo step 1) predicted global characteristics of the molecular conformations remain as unaffected as possible (during molecular dynamics step 2) and the potential energy and the entropy production are relaxing towards their minima. The potentials, the distribution of bond lengths, the integration time step and temperature are smoothly controlled during the creation/relaxation process until they finally approach their prescribed or physical values. The quality of the algorithm is by its nature independent of concentration, system size or degree of polymerization; the CPU speed is quite independent of the latter quantity and linear in the system size. Chains tethered to a surface (dry polymer brushes) can be generated as well.
Article	M. Colangeli, C. Giberti, C. Vernia, M. Kröger Emergence of stationary uphill currents in 2D Ising models: the role of reservoirs and boundary conditions Eur. Phys. J. ST 228 (2019) 69-91
We investigate the dynamics of a 2D Ising model on a square lattice with conservative Kawasaki dynamics in the bulk, coupled with two external reservoirs that pull the dynamics out of equilibrium. Two different mechanisms for the action of the reservoirs are considered. In the first, called ISF, the condition of local equilibrium between reservoir and the lattice is not satisfied. The second mechanism, called detailed balance (DB), implements a DB condition, thus satisfying the local equilibrium property. We provide numerical evidence that, for a suitable choice of the temperature (i.e. below the critical temperature of the equilibrium 2D Ising model) and the reservoir magnetizations, in the long time limit the ISF model undergoes a ferromagnetic phase transition and gives rise to stationary uphill currents, namely positive spins diffuse from the reservoir with lower magnetization to the reservoir with higher magnetization. The same phenomenon does not occur for DB dynamics with properly chosen boundary conditions. Our analysis extends the results reported in Colangeli et al. [Phys. Rev. E 97, 030103(R) (2018)], shedding also light on the effect of temperature and the role of diffrent boundary conditions for this model. These issues may be relevant in a variety of situations (e.g. mesoscopic systems) in which the violation of the local equilibrium condition produces unexpected phenomena that seem to contradict the standard laws of transport.
Article	D. Messmer, C. Böttcher, H. Yu, A. Halperin, K. Binder, M. Kröger, A.D. Schlüter 3D conformations of thick synthetic polymer chains observed by cryogenic electron microscopy ACS Nano 13 (2019) 3466-3473
The backbone conformations of individual, unperturbed synthetic macromolecules have so far not been observed directly in spite of their fundamental importance to polymer physics. Here we report the dilute solution conformations of two types of linear dendronized polymers, obtained by cryogenic transmission electron stereography and tomography. The three-dimensional trajectories show that the wormlike chain model fails to adequately describe the scaling of these thick macromolecules already beyond a few nanometers in chain length, in spite of large apparent persistence lengths and long before a signature of selfavoidance appears. This insight is essential for understanding the limitations of polymer physical models, and it motivated us to discuss the advantages and disadvantages of this approach in comparison to the commonly applied scattering techniques.
Article	D. Messmer, A. Sanchez-Ferrer, S. Tacke, H. Yu, H. Nüsse, J. Klingauf, R. Wepf, M. Kröger, A. Halperin, R. Mezzenga, A.D. Schlüter Can one determine the density of an individual synthetic macromolecule? Soft Matter 15 (2019) 6547-6556
Dendronized polymers (DPs) are large and compact main-chain linear polymers with a cylindrical shape and cross-sectional diameters of up to ~15 nm. They are therefore considered molecular objects, and it was of interest whether given their experimentally accessible, well-defined dimensions, the density of individual DPs could be determined. We present measurements on individual, deposited DP chains, providing molecular dimensions from scanning and transmission electron microscopy and mass-per-length values from quantitative scanning transmission electron microscopy. These results are compared with density values obtained from small-angle X-ray scattering on annealed bulk specimen and with classical envelope density measurements, obtained using hydrostatic weighing or a density gradient column. The samples investigated comprise a series of DPs with side groups of dendritic generations g = 1-8. The key findings are a very large spread of the density values over all samples and methods, and a consistent increase of densities with g over all methods. While this work highlights the advantages and limitations of the applied methods, it does not provide a conclusive answer to the question of which method(s) to use for the determination of densities of individual molecular objects. We are nevertheless confident that these first attempts to answer this challenging question will stimulate more research into this important aspect of polymer and soft matter science.
Article	A. Moghimikheirabadi, P. Fischer, M. Kröger, L.M.C. Sagis Relaxation behavior and nonlinear surface rheology of PEO-PPO-PEO triblock copolymers at the air-water interface Langmuir 35 (2019) 14388-14396
Surface dilatational viscoelasticity of adsorbed layers of pluronics triblock copolymers at the air.water interface was measured using the oscillating barrier technique. The effect of molecular architecture and concentration on surface viscoelasticity was explored for two different types of pluronics with different degrees of hydrophobicity, Pluronic F-108 (Mw ≈ 14.600 g/mol) and Pluronic P-123 (Mw ≈ 5800 g/mol), the former exhibiting a larger hydrophilic to hydrophobic block length ratio. Frequency sweeps in the linear regime suggested that interfacial films of F-108 have higher surface limiting elasticity and larger in-plane and out-of-plane relaxation times at the same bulk concentration (the former possibly related to in-plane microstructure rearrangements, the latter to surface/bulk diffusion). Increasing the bulk concentration of pluronics from 1 to 100 μM led to a decrease in both in- and out-of-plane relaxation times. Large amplitude oscillatory dilatation (LAOD) tests were performed to capture nonlinear behavior of these interfacial films by means of elastic and viscous Lissajous plots. Nonlinearities in elastic responses were quantified through calculation of the strain-stiffening indices in extension SE and compression SC. Both pluronics exhibited strain softening in extension. In compression, P-123 showed strain-hardening and F-108 displayed a relatively linear response. Apparent strain hardening in extension was observed for the P-123 adsorbed film, at high strain, at a bulk concentration of 100 μM. However, at these strains, the response was dominated by the viscous contribution and calculation of strain rate-thickening factors in extension and compression showed that the overall response was strain rate-thinning in extension and strain rate-thickening in compression.
Article	A. Moghimikheirabadi, L.M.C. Sagis, M. Kröger, P. Ilg Gas-liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach Phys. Chem. Chem. Phys. 21 (2019) 2295-2306
The gas.liquid expanded phase transition of a Langmuir monolayer happens at very low surface concentrations which makes this phenomenon extremely expensive to explore in finite three-dimensional (3D) atomistic simulations. Starting with a 3D model reference system of amphiphilic surfactants at a 2D vapor.liquid interface, we apply our recently developed approach (Phys. Chem. Chem. Phys., 2018, 20, 16238) and map the entire system to an effective 2D system of surfactant center-of-masses projected onto the interface plane. The coarse-grained interaction potential obtained via a force-matching scheme from the 3D simulations is then used to predict the 2D gas.liquid phase equilibrium of the corresponding Langmuir monolayer. Monte Carlo simulations in the Gibbs ensemble are performed to calculate areal densities, chemical potentials and surface pressures of the gaseous and liquid coexisting phases within the monolayer. We compare these simulations to the results of a 2D density functional approach based on Weeks.Chandler.Anderson perturbation theory. We furthermore use this approach to determine the density profiles across the equilibrium gas.liquid dividing line and the corresponding line tensions.
Article	A. Karatrantos, R.J. Composto, K.I. Winey, M. Kröger, N. Clarke Modeling of entangled polymer diffusion in melts and nanocomposites: A Review Polymers 11 (2019) 876
This review concerns modeling studies of the fundamental problem of entangled (reptational) homopolymer diffusion in melts and nanocomposite materials in comparison to experiments. In polymer melts, the developed united atom and multibead spring models predict an exponent of the molecular weight dependence to the polymer diffusion very similar to experiments and the tube reptation model. There are rather unexplored parameters that can influence polymer diffusion such as polymer semiflexibility or polydispersity, leading to a different exponent. Models with soft potentials or slip-springs can estimate accurately the tube model predictions in polymer melts enabling us to reach larger length scales and simulate well entangled polymers. However, in polymer nanocomposites, reptational polymer diffusion is more complicated due to nanoparticle fillers size, loading, geometry and polymer-nanoparticle interactions.
Article	Z. Shen, H. Ye, M. Kröger, Y. Li Aggregation of polyethylene glycol polymers suppresses receptor-mediated endocytosis of PEGylated liposomes Nanoscale 10 (2018) 4545-4560
The PEGylated liposome, composed of an aqueous core and a fluid state lipid bilayer shell, is one of the few Food and Drug Administration (FDA) approved drug delivery platforms. To prevent the absorption of serum proteins, the surface of a liposome is decorated by hydrophilic and bio-compatible polyethylene glycol (PEG) polymers, which can significantly extend the blood circulation time of liposomes. In this work, with the help of dissipative particle dynamics (DPD) simulations, we explore how the tethered PEG polymers will affect the membrane wrapping process of PEGylated liposomes during endocytosis. Specifically, we compare the membrane wrapping process of a PEGylated rigid nanoparticle (NP) with a PEGylated liposome under identical conditions. Due to the mobility of grafted PEG polymers on the liposome.s surface, the complete wrapping of a PEGylated liposome can be dramatically delayed and blocked, in comparison with a PEGylated rigid NP. For the first time, we observe the aggregation of PEG polymers in the contact region between a PEGylated liposome and the membrane, which in turn leads to a ligand-free region on the surface of the liposome during endocytosis. Subsequently, the partially wrapped PEGylated liposome can be bounced back to a less wrapped state. Through free energy analysis, we find that the aggregation of PEG polymers during the membrane wrapping process of a PEGylated liposome introduces a dramatic free energy penalty of about ~800 kBT, which is almost twice that of a PEGylated rigid NP. Here kB and T are the Boltzmann constant and temperature, respectively. Such a large energy barrier and the existence of a ligand-free region on the surface of PEGlylated liposomes prevent their membrane wrapping, thereby reducing the chance of internalization by tumor cells. Therefore, our DPD simulation results provide a possible explanation for the inefficient cellular uptake of PEGylated liposomes. In addition, we suggest that by increasing the repulsive interactions between grafted PEG polymers it might be possible to limit their aggregation, and in turn, facilitate the internalization of PEGylated liposomes. The current study provides fundamental insights into the endocytosis of PEGylated liposomes, which could help to design this platform with high efficacy for drug delivery.
Article	Z. Shen, H. Ye, C. Zhou, M. Kröger, Y. Li Size of graphene sheets determines the structural and mechanical properties of 3D graphene foams Nanotechnol. 29 (2018) 104001 (13 pages)
Graphene is recognized as an emerging 2D nanomaterial for many applications. Assembly of graphene sheets into 3D structures is an attractive way to enable their macroscopic applications and to preserve the exceptional mechanical and physical properties of their constituents. In this study, we develop a coarse-grained (CG) model for 3D graphene foams (GFs) based on the CG model for a 2D graphene sheet by Ruiz et al (2015 Carbon 82 103.15). We find that the size of graphene sheets plays an important role in both the structural and mechanical properties of 3D GFs. When their size is smaller than 10 nm, the graphene sheets can easily stack together under the influence of van der Waals interactions (vdW). These stacks behave like building blocks and are tightly packed together within 3D GFs, leading to high density, small pore radii, and a large Young's modulus. However, if the sheet sizes exceed 10 nm, they are staggered together with a significant amount of deformation (bending). Therefore, the density of 3D GFs has been dramatically reduced due to the loosely packed graphene sheets, accompanied by large pore radii and a small Young's modulus. Under uniaxial compression, rubber-like stress.strain curves are observed for all 3D GFs. This material characteristic is dominated by the vdW interactions between different graphene layers and slightly affected by the out-of-plane deformation of the graphene sheets. We find a simple scaling law ρ4.2 between the density . and Young's modulus E for a model of 3D GFs. The simulation results reveal structure.property relations of 3D GFs, which can be applied to guide the design of 3D graphene assemblies with exceptional properties.
Article	Y.R. Sliozberg, I.-C. Yeh, M. Kröger, K.A. Masser, J.L. Lenhart, J.W. Andzelm Ordering and crystallization of entangled polyethylene melts under uniaxial tension: A molecular dynamics study Macromolecules 51 (2018) 9635-9648
Morphological and mechanical properties of semicrystalline polymers are strongly influenced by flow-induced crystallization during processing. We perform extensive molecular dynamics simulations with more than 1 million atoms to describe orientation, drawability, and crystallization of entangled polyethylene melts under uniaxial tensions at three different strain rates and after a subsequent cooling. During tensile deformation at the lowest strain rate of 107 s.1, the polyethylene melt experiences entanglement loss and crystal nucleation. At higher strain rates of 108 and 109 s.1, we observe a higher degree of chain alignment and void formation in addition to disentanglement and crystal nucleation. Chain segments make sharp turns relative to the neighboring chain orientations at the entanglement points, which manifests as a bimodal distribution of the local order parameter. Upon cooling below the melting temperature, semicrystalline polyethylene with a crystallinity close to 50% is formed. The entanglements are located in the amorphous regions of the semicrystalline polyethylene, with some located in the crystal/amorphous interface region. The chain ends of the semicrystalline polyethylene are preferentially localized at the crystal/amorphous interface, which is in agreement with recent experimental results.
Article	V. Müller, A. Hinaut, M. Moradi, M. Baljozovic, T. Jung, P. Shahgaldian, H. Möhwald, D. Murray, W.B. Thompson, B.T. King, G. Hofer, M. Kröger, T. Glatzel, A.D. Schlüter A two-dimensional polymer synthesized at the air/water interface Angew. Chem. Int. Ed. 57 (2018) 10584-10588
A trifunctional, partially fluorinated anthracene-substituted triptycene monomer was spread at an air/water interface into a monolayer, which was transformed into a long-range.ordered 2D polymer by irradiation with a standard UV lamp. The polymer was analyzed by Brewster angle microscopy, scanning tunneling microscopy measurements, and non.contact atomic force microscopy, which confirmed the generation of a network structure with lattice parameters that are virtually identical to a structural model network based on X.ray diffractometry of a closely related 2D polymer. The nc.AFM images highlight the long-range order over areas of at least 300 × 300 nm2. As required for a 2D polymer, the pore sizes are monodisperse, except for the regions where the network is somewhat stretched because it spans over protrusions. Together with a previous report on the nature of the cross-links in this network, the structural information provided herein leaves no doubt that a 2D polymer has been synthesized under ambient conditions at an air/water interface.
Article	S.A. Vasudevan, A. Rauh, M. Kröger, M. Karg, L. Isa Dynamics and wetting behavior of soft particles at a fluid-fluid interface Langmuir 34 (2018) 15370-15382
We investigate the conformation, position, and dynamics of core.shell nanoparticles (CSNPs) composed of a silica core encapsulated in a cross-linked poly(N-isopropylacrylamide) shell at a water.oil interface for a systematic range of core sizes and shell thicknesses. We first present a freeenergy model that we use to predict the CSNP wetting behavior at the interface as a function of its geometrical and compositional properties in the bulk phases, which is in good agreement with our experimental data. Remarkably, based on the knowledge of the polymer shell deformability, the equilibrium particle position relative to the interface plane, an often elusive experimental quantity, can be extracted by measuring its radial dimensions after adsorption. For all the systems studied here, the interfacial dimensions are always larger than in bulk and the particle core resides in a configuration, wherein it just touches the interface or is fully immersed in water. Moreover, the stretched shell induces a larger viscous drag at the interface, which appears to depend solely on the interfacial dimensions, irrespective of the portion of the CSNP surface exposed to the two fluids. Our findings indicate that tailoring the architecture of CSNPs can be used to control their properties at the interface, as of interest for applications including emulsion stabilization and nanopatterning.
Article	P.S. Stephanou, M. Kröger Tumbling-snake model for polymeric liquids subjected to biaxial elongational flows with a focus on planar elongation Polymers 10 (2018) 329
We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.
Article	P.S. Stephanou, M. Kröger From intermediate anisotropic to isotropic friction at large strain rates to account for viscosity thickening in polymer solutions J. Chem. Phys. (2018) 184903
The steady-state extensional viscosity of dense polymeric liquids in elongational flows is known to be peculiar in the sense that for entangled polymer melts it monotonically decreases.whereas for concentrated polymer solutions it increases.with increasing strain rate beyond the inverse Rouse time. To shed light on this issue, we solve the kinetic theory model for concentrated polymer solutions and entangled melts proposed by Curtiss and Bird, also known as the tumbling-snake model, supplemented by a variable link tension coefficient that we relate to the uniaxial nematic order parameter of the polymer. As a result, the friction tensor is increasingly becoming isotropic at large strain rates as the polymer concentration decreases, and the model is seen to capture the experimentally observed behavior. Additional refinements may supplement the present model to capture very strong flows. We furthermore derive analytic expressions for small rates and the linear viscoelastic behavior. This work builds upon our earlier work on the use of the tumbling-snake model under shear and demonstrates its capacity to improve our microscopic understanding of the rheology of entangled polymer melts and concentrated polymer solutions.
Article	M.K. Singh, C. Kang, P. Ilg, R. Crockett, M. Kröger, N.D. Spencer Combined experimental and simulation studies of crosslinked polymer brushes under shear Macromolecules 51 (2018) 10174-10183
We have studied the effect of cross-linking on the tribological behavior of polymer brushes using a combined experimental and theoretical approach. Tribological and indentation measurements on poly(glycidyl methacrylate) brushes and gels in the presence of dimethylformamide solvent were obtained by means of atomic force microscopy. To complement experiments, we have performed corresponding molecular dynamics (MD) simulations of a generic bead−spring model in the presence of explicit solvent and cross-linkers. Our study shows that cross-linking leads to an increase in friction between polymer brushes and a counter-surface. The coefficient of friction increases with increasing degree of cross-linking and decreases with increasing length of the cross-linker chains. We find that the brush-forming polymer chains in the outer layer play a significant role in reducing friction at the interface.
Article	K.-C. Shih, Z. Shen, Y. Li, M. Kröger, S.-Y. Chang, Y. Liu, H.-M. Lai, M.-P. Nieh What causes the anomaleous aggregation in pluronic aqueous solutions? Soft Matter 14 (2018) 7653-7663
Pluronic (PL) block copolymers have been widely used as delivery carriers, molecular templates for porous media, and process additives for affecting rheological behavior. Unlike most surfactant systems, where unimer transforms into micelle with increased surfactant concentration, anomalous large PL aggregates below the critical micelle concentration (CMC) were found throughout four types of PL (F108, F127, F88 and P84). We characterized their structures using dynamic light scattering and small-angle X-ray/neutron scattering. Molecular dynamics simulations suggest that the PPO segments, though weakly hydrophobic interaction (insufficient to form micelles), promote the formation of large aggregates. Addition of acid or base (e.g. citric acid, acetic acid, HCl and NaOH) in F108 solution significantly suppresses the aggregate formation for up to 20 days due to the repulsion force from the attached H3O+ molecules on the EO segment in both PEO and PL and the reduction of CMC through the salting out effect, respectively. Supplementary Information »»
Article	J. Kirk, M. Kröger, P. Ilg Surface disentanglement and slip in a polymer melt: A molecular dynamics study Macromolecules 51 (2018) 8996-9010
We perform nonequilibrium molecular dynamics shear flow simulations of an entangled polymer melt consisting of flexible linear chains. A steady-state rectilinear shear flow is imposed by sliding explicit walls with permanently grafted chains in a planar Couette flow geometry. As the channel average shear rate is increased, a rapid coil-stretch transition of the surface end-grafted chains is observed. The corresponding primitive path network properties are investigated, revealing a disentanglement between surface grafted and nongrafted chains during the coil-stretch transition. Changes in slip length and surface friction are also measured. Grafted chains develop a trumpet-like conformation at high shear rates, which correlates with an increased relative density of entanglements near the free ends, a phenomenon that has already been considered by scaling models. The same mechanisms leading to slip in the current system may remain relevant for polymer melts of much higher (and more experimentally relevant) molecular weights. Therefore, we use the simulation results to examine the predictions and assumptions of some existing theoretical models. The conclusions drawn from the simulation may be used in the future to further develop theoretical models for the surface rheology of polymer melts.
Article	G. Hofer, F. Grieder, M. Kröger, A.D. Schlüter, T. Weber Unraveling two-dimensional polymerization in the single crystal Appl. Cryst. 51 (2018) 481-497
Two-dimensional single-crystal-to-single-crystal polymerization and depolymerization are described in detail. The results are based on in-house and synchrotron X-ray diffraction experiments conducted on several samples at 100.K and room temperature. The reactions are associated with considerable molecular motions of all components (monomer, template and incorporated solvent molecules), which can be as large as 1.Ã… Continuous polymerization leads to a gradual gap opening between the emerging two-dimensional polymer layers, which allows for increased mobility of the solvent molecules. The positional flexibility of both the solvents and the weakly bound templates buffers the local strain induced by polymerization through a complex chain of movements. As a consequence, the accumulated global strain remains small enough to essentially preserve the single-crystalline state in the course of a complete polymerization/depolymerization cycle. The unit-cell parameters evolve in an unusual way. The a and c axes of the trigonal lattice slightly increase during polymerization, even though van der Waals interactions are replaced by shorter covalent bonds and the involved molecules shrink. However, the c axis experiences a significant drop of more than 1.Ã…during the first depolymerization step. Progressive depolymerization expands the c axis again, but it does not quite reach the value of the fresh crystal. These effects can be explained by local strain formation and compensation mechanisms and by annealing effects during heat-induced depolymerization. An interesting side effect of the polymerization is the reorientation of incorporated solvent molecules, which give the crystal a tunable dipole moment. Of particular importance for the understanding of two-dimensional polymers is the evolution of the connectivity between molecules during polymerization and depolymerization. Combining reaction kinetics with structural information, such as the polymerization-induced displacement of reactive sites, allowed for the development of a propagation model, in which both polymerization and depolymerization proceed in a self-impeding fashion. This model is supported by Monte Carlo simulations.
Article	D. Messmer, M. Kröger, A.D. Schlüter Pushing synthesis toward the maximum generation range of dendritic macromolecules Macromolecules 51 (2018) 5420-5429
The maximum generation gmax of a dendritic molecule denotes the value of the generation number g, above which such a compound cannot be synthesized without defects anymore due to steric constraints. For dendronized polymers (DPs), such a densely packed regime is entered far earlier (gmax ≈ 6) than it is for comparable dendrimers (gmax ≥ 10) because dendritic side chains are confined to a cylindrical rather than a spherical volume. We here report a long sought-after improvement to a key step in the divergent synthesis of high-g DPs which enabled obtaining the polymers of g = 6, 7, and 8. These DPs are of unprecedented dendritic perfection, and the representatives with g > 6 are to our knowledge the first molecules for which gmax has been surpassed. We suggest a straightforward parameter α which allows to assess whether any dendritic molecule is above gmax, given sufficiently efficient chemistry and the possibility of accurately determining the number of defects. Finally, we correlate gel permeation chromatography results and atomic force microscopic images with defect rates.
Article	A. Ramirez-Hernandez, B.L. Peters, L. Schneider, M. Andreev, J.D. Schieber, M. Müller, M. Kröger, J.J. de Pablo A detailed examination of the topological constraints of lamellae-forming block copolymers Macromolecules 51 (2018) 2110-2124
A microscopic molecular model of polymeric molecules that captures the effects of topological constraints is used to consider how microphase segregation can alter the distribution of entanglements both in space and along chain contours. Such topological constraints are obtained by using the Z1 algorithm, and it is found that for diblock copolymers in the lamellar morphology they are not homogeneously distributed, but instead exhibit a spatial dependence as a consequence of the self-organization of the polymer blocks. The specific shape of the inhomogeneous distribution is affected by the molecular weight of the copolymer. The microscopic information obtained by these calculations is then compared with the corresponding results generated from a coarser description of entangled block copolymers that includes soft intermolecular interactions and slip-springs, whose role is to incorporate the effects of entanglements that are lost during coarse-graining. This comparison is helpful for improving coarse-grained simulation approaches for use in multiscale studies of large-scale, self-assembled multicomponent polymer systems.
Article	A. Karatrantos, Y. Koutsawa, P. Dubois, N. Clarke, M. Kröger Miscibility and nanoparticle diffusion in ionic nanocomposites Polymers 10 (2018) 1010
We investigate the effect of various spherical nanoparticles in a polymer matrix on dispersion, chain dimensions and entanglements for ionic nanocomposites at dilute and high nanoparticle loading by means of molecular dynamics simulations. The nanoparticle dispersion can be achieved in oligomer matrices due to the presence of electrostatic interactions. We show that the overall configuration of ionic oligomer chains, as characterized by their radii of gyration, can be perturbed at dilute nanoparticle loading by the presence of charged nanoparticles. In addition, the nanoparticle.s diffusivity is reduced due to the electrostatic interactions, in comparison to conventional nanocomposites where the electrostatic interaction is absent. The charged nanoparticles are found to move by a hopping mechanism.
Article	Z. Shen, M. Röding, M. Kröger, Y. Li Carbon nanotube length governs viscoelasticity and permeability of buckypaper Polymers 9 (2017) 115
The effects of carbon nanotube (CNT) length on the viscoelasticity and permeability of buckypaper, composed of (5,5) single-walled CNTs (SWCNTs), are systematically explored through large-scale coarse-grained molecular dynamics simulations. The SWCNT length is found to have a pronounced impact on the structure of buckypapers. When the SWCNTs are short, they are found to form short bundles and to be tightly packed, exhibit high density and small pores, while long SWCNTs are entangled together at a low density accompanied by large pores. These structure variations contribute to distinct performances in the viscoelasticity of buckypapers. The energy dissipation for buckypapers with long SWCNTs under cyclic shear loading is dominated by the attachment and detachment between SWCNTs through a zipping-unzipping mechanism. Thus, the viscoelastic characteristics of buckypapers, such as storage and loss moduli, demonstrate frequency- and temperature-independent behaviors. In contrast, the sliding-friction mechanism controls the energy dissipation between short SWCNTs when the buckypaper is under loading and unloading processes. Friction between short SWCNTs monotonically increases with rising length of SWCNTs and temperature. Therefore, the tan δ, defined as the ratio of the loss modulus over the storage modulus, of buckypaper with short SWCNTs also increases with the increment of temperature or SWCNT length, before the SWCNTs are entangled together. The permeability of buckypapers is further investigated by studying the diffusion of structureless particles within buckypapers, denoted by the obstruction factor (β). It is found to be linearly dependent on the volume fraction of SWCNTs, signifying a mass-dominated permeability, regardless of the structure variations induced by different SWCNT lengths. The present study provides a comprehensive picture of the structure-property relationship for buckypapers composed of SWCNTs. The methodology could be used for designing multifunctional buckypaper-based devices.
Article	Z. Shen, H. Ye, M. Kröger, Y. Li Self-assembled core-polyethylene glycol-lipid shell nanoparticles demonstrate high stability in shear flow Phys. Chem. Chem. Phys. 19 (2017) 13294-13306
A core-polyethylene glycol-lipid shell (CPLS) nanoparticle consists of an inorganic core coated with polyethylene glycol (PEG) polymers, surrounded by a lipid bilayer shell. It can be self-assembled from a PEGylated core with surface-tethered PEG chains, where all the distal ends are covalently bonded with lipid molecules. Upon adding free lipids, a complete lipid bilayer shell can be formed on the surface driven by the hydrophobic nature of lipid tails, leading to the formation of a CPLS nanoparticle. The stability of CPLS nanoparticles in shear flow has been systematically studied through large scale dissipative particle dynamics simulations. CPLS nanoparticles demonstrate higher stability and less deformation in shear flow, compared with lipid vesicles. Burst leakage of drug molecules inside lipid vesicles and CPLS NPs can be induced by the large pore at their tips. This pore is initiated by the maximum stress at the waist region. It further grows along with the tank-treading motion of vesicles or CPLS NPs in shear flow. However, due to the constraints applied from PEG polymers, CPLS NPs are less deformed than vesicles with comparable size under the same flow conditions. Thus, the less deformed CPLS NPs express a smaller maximum stress at waists, demonstrating higher stability. Pore formation at waists, evolving into large pores on vesicles, leads to the burst leakage of drug molecules and complete rupture of vesicles. In contrast, although similar drug leakage in CPLS nanoparticles can occur under high shear rates, pores initiated under moderate shear rates tend to be short-lived and close due to the constraints mediated by PEG polymers. This kind of `self-healing' capability can be observed under a wide range of shear rates for CPLS nanoparticles. Our results suggest self-assembled CPLS nanoparticles to exhibit high stability during blood circulation without rapid drug leakage. These features render CPLS nanoparticles as candidates for a promising drug delivery platform.
Article	X. Shang, M. Kröger, B. Leimkuhler Assessing numerical methods for molecular and particle simulation Soft Matter 13 (2017) 8565-8578
We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more recently proposed ..pairwise adaptive Langevin.. (PAdL) method, which, like DPD but unlike Langevin dynamics, conserves momentum and better matches the relaxation rate of orientational degrees of freedom. PAdL is easy to code and suitable for a variety of problems in nonequilibrium soft matter modeling; our simulations of polymer melts indicate that this method can also provide dramatic improvements in computational efficiency. Moreover we show that PAdL gives excellent control of the relaxation rate to equilibrium. In the nonequilibrium setting, we further demonstrate that while PAdL allows the recovery of accurate shear viscosities at higher shear rates than are possible using the DPD method at identical timestep, it also outperforms Langevin dynamics in terms of stability and accuracy at higher shear rates.
Article	P.S. Stephanou, T. Schweizer, M. Kröger Communication: Appearance of undershoots in start-up shear: Experimental findings captured by tumbling-snake dynamics J. Chem. Phys. 146 (2017) 161101
Our experimental data unambiguously show (i) a damping behavior (the appearance of an undershoot following the overshoot) in the transient shear viscosity of a concentrated polymeric solution, and (ii) the absence of a corresponding behavior in the transient normal stress coefficients. Both trends are shown to be quantitatively captured by the bead-link chain kinetic theory for concentrated polymer solutions and entangled polymer melts proposed by Curtiss and Bird, supplemented by a non-constant link tension coefficient that we relate to the nematic order parameter. The observed phenomena are attributed to the tumbling behavior of the links, triggered by rotational fluctuations, on top of reptation. Using model parameters deduced from stationary data, we calculate the transient behavior of the stress tensor for this .tumbling-snake. model after startup of shear flow efficiently via simple Brownian dynamics. The unaltered method is capable of handling arbitrary homogeneous flows and has the promising capacity to improve our understanding of the transient behavior of concentrated polymer solutions.
Article	P.S. Stephanou, M. Kröger Non-constant link tension coefficient in the tumbling-snake model subjected to simple shear J. Chem. Phys. 147 (2017) 174903
The authors of the present study have recently presented evidence that the tumbling-snake model for polymeric systems has the necessary capacity to predict the appearance of pronounced undershoots in the time-dependent shear viscosity as well as an absence of equally pronounced undershoots in the transient two normal stress coefficients. The undershoots were found to appear due to the tumbling behavior of the director u when a rotational Brownian diffusion term is considered within the equation of motion of polymer segments, and a theoretical basis concerning the use of a link tension coefficient given through the nematic order parameter had been provided. The current work elaborates on the quantitative predictions of the tumbling-snake model to demonstrate its capacity to predict undershoots in the time-dependent shear viscosity. These predictions are shownto compare favorably with experimental rheological data for both polymer melts and solutions, help us to clarify the microscopic origin of the observed phenomena, and demonstrate in detail why a constant link tension coefficient has to be abandoned.
Article	C. Luo, M. Kröger, J.-U. Sommer Molecular dynamics simulations of polymer crystallization under confinement: Entanglement effect Polymer 109 (2017) 71-84
We carried out molecular dynamics simulations to study the crystallization of polymer melts subjected to confinement between two parallel walls. Two types of walls, bare and grafted walls, are studied. The bare walls are slippery for chain motions, and the interactions between polymer chains and the walls are moreover chosen either attractive or repulsive. The crystallization in the case of bare walls generally consists of surface-induced processes close to the walls followed by homogeneous nucleation in both the boundary and middle regions. In the case of grafted walls, parts of polymer chains residing close to the walls are adhesive to the surfaces and become permanent graft points. We find that the surface-induced crystallization is increasingly suppressed with increasing grafting density. At high grafting densities, only crystallization in the middle regions is observed. We calculated the spatial distribution of entanglement lengths and related it to the crystallization behavior. The entanglement length close to the walls is found to decrease with increasing grafting density, as the adhesion points act as effective entanglement knots. In light of our recent results that less entangled polymer melts lead to faster crystallization and higher crystallization order, we now show that this conclusion stands also for the case of confined polymer melts. Our results suggest entanglements to be an universal factor towards the understanding of polymer crystallization under different situations, in particular at supercooling.
Article	Z. Shen, D.T. Loe, J.K. Awino, M. Kröger, J.L. Rouge, Y. Li Self-assembly of core-polyethylene glycol-lipid shell (CPLS) nanoparticles and their potential as drug delivery vehicles Nanoscale 8 (2016) 14821-14835
Herein a new multifunctional formulation, referred to as a core-polyethylene glycol-lipid shell (CPLS) nanoparticle has been proposed and studied in silico via large scale coarse-grained molecular dynamics simulations. A PEGylated core with surface tethered polyethylene glycol (PEG) chains is used as the starting configuration, where free ends of the PEG chains are covalently bonded with lipid molecules (lipid heads). A complete lipid bilayer is formed at the surface of the PEGylated particle core upon addition of free lipids, driven by the hydrophobic properties of the lipid tails, leading to the formation of a CPLS nanoparticle. The self-assembly process is found to be sensitive to the grafting density and molecular weight of the tethered PEG chains, as well as the amount of free lipids added. At low grafting densities the assembly of CPLS nanoparticles cannot be accomplished. As demonstrated by simulations, a lipid bud/vesicle can be formed on the surface when excessive amount of free lipids are added at high grafting density. Therefore, the CPLS nanoparticles can only be formed under the proper conditions of both PEG and free lipid. The CPLS nanoparticle is recognized to be able to store a large quantity of water molecules, particularly with high molecular weight of PEG chains, signaling its capacity for carrying hydrophilic molecules such as therapeutic biomolecules or imaging agents. Under identical size and surface chemistry conditions of a liposome, it has been observed that the CPLS particle can be more efficiently wrapped by the lipid membrane, indicating its potential for greater efficiency in delivering its hydrophilic cargo. As a proof-of-concept, the experimental realization of CPLS nanoparticles is explicitly demonstrated in this study. To test the CPLS’s capacity to store small molecule cargo a hydrophilic dye was successfully encapsulated in the particles’ water soluble layer. The results of this study show the power and potential of simulation-driven approaches for guiding the design of more efficient nanomaterial delivery platforms.
Article	Y.R. Sliozberg, M. Kröger, T.L. Chantawansri Fast equilibration protocol for million atom systems of highly entangled linear polyethylene chains J. Chem. Phys. 144 (2016) 154901
Equilibrated systems of entangled polymer melts cannot be produced using direct brute force equilibration due to the slow reptation dynamics exhibited by high molecular weight chains. Instead, these dense systems are produced using computational techniques such as Monte Carlo-Molecular Dynamics hybrid algorithms, though the use of soft potentials has also shown promise mainly for coarse-grained polymeric systems. Through the use of soft-potentials, the melt can be equilibrated via molecular dynamics at intermediate and long length scales prior to switching to a Lennard-Jones potential. We will outline two different equilibration protocols, which use various degrees of information to produce the starting configurations. In one protocol, we use only the equilibrium bond angle, bond length, and target density during the construction of the simulation cell, where the information is obtained from available experimental data and extracted from the force field without performing any prior simulation. In the second protocol, we moreover utilize the equilibrium radial distribution function and dihedral angle distribution. This information can be obtained from experimental data or from a simulation of short unentangled chains. Both methods can be used to prepare equilibrated and highly entangled systems, but the second protocol is much more computationally efficient. These systems can be strictly monodisperse or optionally polydisperse depending on the starting chain distribution. Our protocols, which utilize a soft-core harmonic potential, will be applied for the first time to equilibrate a million particle system of polyethylene chains consisting of 1000 united atoms at various temperatures. Calculations of structural and entanglement properties demonstrate that this method can be used as an alternative towards the generation of entangled equilibrium structures.
Article	Y. Li, S. Tang, M. Kröger, W.K. Liu Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers J. Mech. Phys. Solids 88 (2016) 204-226
Viscoelasticity characterizes the most important mechanical behavior of elastomers. Understanding the viscoelasticity, especially finite strain viscoelasticity, of elastomers is the key for continuation of their dedicated use in industrial applications. In this work, we present a mechanistic and physics-based constitutive model to describe and design the finite strain viscoelastic behavior of elastomers. Mathematically, the viscoelasticity of elastomers has been decomposed into hyperelastic and viscous parts, which are attributed to the nonlinear deformation of the cross-linked polymer network and the diffusion of free chains, respectively. The hyperelastic deformation of a cross-linked polymer network is governed by the cross-linking density, the molecular weight of the polymer strands between cross-linkages, and the amount of entanglements between different chains, which we observe through large scale molecular dynamics (MD) simulations. Moreover, a recently developed non-affine network model (Davidson and Goulbourne, 2013) is confirmed in the current work to be able to capture these key physical mechanisms using MD simulation. The energy dissipation during a loading and unloading process of elastomers is governed by the diffusion of free chains, which can be understood through their reptation dynamics. The viscous stress can be formulated using the classical tube model (Doi and Edwards, 1986); however, it cannot be used to capture the energy dissipation during finite deformation. By considering the tube deformation during this process, as observed from the MD simulations, we propose a modified tube model to account for the finite deformation behavior of free chains. Combing the non-affine network model for hyperelasticity and modified tube model for viscosity, both understood by molecular simulations, we develop a mechanism-based constitutive model for finite strain viscoelasticity of elastomers. All the parameters in the proposed constitutive model have physical meanings, which are signatures of polymer chemistry, physics or dynamics. Therefore, parametric materials design concepts can be easily gleaned from the model, which is also demonstrated in this study. The finite strain viscoelasticity obtained from our simulations agrees qualitatively with experimental data on both un-vulcanized and vulcanized rubbers, which captures the effects of cross-linking density, the molecular weight of the polymer chain and the strain rate.
Article	S.H. Jeong, J.M. Kim, J. Yoon, C. Tzoumanekas, M. Kröger, C. Baig Influence of molecular architecture on the entanglement network: topological analysis of entangled linear, long- and short-chain branched polyethylene melts via Monte Carlo simulation Soft Matter 12 (2016) 3770-3786
We present detailed results on the effect of chain branching on the topological properties of entangled polymer melts via an advanced connectivity-altering Monte Carlo (MC) algorithm. Eleven representative model linear, short-chain branched (SCB), and long-chain branched (LCB) polyethylene (PE) melts were employed, based on the total chain length and/or the longest linear chain dimension. Directly analyzing the entanglement [or the primitive path (PP)] network of the system via the Z-code, we quantified several important topological measures: (a) the PP contour length Lpp, (b) the number of entanglements Zes per chain, (c) the end-to-end length of an entanglement strand des, (d) the number of carbon atoms per entanglement strand Nes, and (e) the probability distribution for each of these quantities. The results show that the SCB polymer melts have significantly more compact overall chain conformations compared to the linear polymers, exhibiting, relative to the corresponding linear analogues, (a) ∼20% smaller values of 〈Lpp〉 (the statistical average of Lpp), (b) ∼30% smaller values of 〈Zes〉, (c) ∼20% larger values of 〈des〉, and (d) ∼50% larger values of 〈Nes〉. In contrast, despite the intrinsically smaller overall chain dimensions than those of the linear analogues, the LCB (H-shaped and A3AA3 multiarm) PE melts exhibit relatively (a) 7–8% larger values of 〈Lpp〉, (b) 6–11% larger values of 〈Zes〉 for the H-shaped melt and ∼2% smaller values of 〈Zes〉 for the A3AA3 multiarm, (c) 2–5% smaller values of 〈des〉, and (d) 7–11% smaller values of 〈Nes〉. Several interesting features were also found in the results of the probability distribution functions P for each topological measure.
Article	S. Costanzo, L.F. Scherz, T. Schweizer, M. Kröger, G. Floudas, A.D. Schlüter, D. Vlassopoulos Rheology and packing of dendronized polymers Macromolecules 49 (2016) 7054-7068
A series of homologous dendronized polymers (DPs) with generations (g) 1.3 and backbone nominal degrees of polymerization (Pn) in the range 50-3000 have been synthesized and characterized in order to investigate the g- and Pn-dependent viscoelastic properties and packing of this class of densely grafted, associating and effectively thick macromolecules in their molten state. Rheological measurements reveal an unusually long thermal equilibration time, attributed to (i) the tendency of DPs to minimize local density gradients, as realized via their mutual weak interpenetration, and (ii) the intermolecular DP.DP correlations and inter- and intramolecular hydrogen bonding and π-π stacking interactions. With the help of simulations and X-ray scattering measurements, a scenario emerges, according to which DPs interact via local cooperative rearrangements of the dendrons, akin to a Velcro fastening process. In this picture, neighboring bonds accelerate the local interpenetration process. Results from X-ray scattering show increased lateral backbone-backbone correlations with a columnar arrangement of backbones and a liquid crystalline underlying order. Linear viscoelasticity is characterized by plateau moduli which originate from intermolecular bonding and whose extent in frequency and absolute value depends on Pn and g and can be lower than or comparable to that of the backbone. Very long relaxation times can be probed (sometimes via creep measurements) and attributed to the lifetime of the bonds. The nonlinear shear rheology data suggest a resemblance in behavior to unentangled linear chains with finite extensibility and point to reduced deformability of the DPs in flow. These findings indicate that DPs constitute a promising class of functional macromolecules with tunable properties.
Article	P.S. Stephanou, M. Kröger Solution of the complete Curtiss-Bird model for polymeric liquids subjected to simple shear flow J. Chem. Phys. 144 (2016) 124905
The complete kinetic theory model for concentrated polymer solutions and melts proposed by Curtiss and Bird is solved for shear flow: (a) analytically by providing a solution for the single-link (or configurational) distribution function as a real basis spherical harmonics expansion and then calculating the materials functions in shear flow up to second order in the dimensionless shear rate and, (b) numerically via the execution of Brownian dynamics simulations. These two methods are actually complementary to each other as the former is accurate only for small dimensionless shear rates where the latter produces results with increasingly large uncertainties. The analytical expansions of the material functions with respect to the dimensionless shear rate reduce to those of the extensively studied, simplified Curtiss-Bird model when ε' = 0, and to the rigid rod when ε' = 1. It is known that the power-law behavior at high shear rates is very different for these two extremal cases. We employ Brownian dynamics simulation to not only recover the limiting cases but to find a gradual variation of the power-law behaviors at large dimensionless shear rates upon varying ε'. The fact that experimental data are usually located between these two extremes strongly advocates the significance of studying the solution of the Curtiss-Bird model. This is exemplified in this work by comparing the solution of this model with available rheological data for semiflexible biological systems that are clearly not captured by the original Doi-Edwards or simplified Curtiss-Bird models.
Article	M.K. Singh, P. Ilg, R.M. Espinosa-Marzal, N.D. Spencer, M. Kröger Influence of chain stiffness, grafting density and normal load on the tribological and structural behavior of polymer brushes: a nonequilibrium-molecular-dynamics study Polymers 8 (2016) 254
We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equilibrium behavior of the model brushes, we first study the shearing behavior of flexible chains at different grafting densities covering brush and mushroom regimes. Next, we focus on the effect of chain stiffness on the tribological behavior of polymer brushes. The tribological properties are interpreted by means of the simultaneously recorded density profiles. We find that the friction coefficient decreases with increasing persistence length, both in velocity and separation-dependency studies, over the stiffness range explored in this work.
Article	M.K. Singh, P. Ilg, R.M. Espinosa-Marzal, M. Kröger, N.D. Spencer Effect of crosslinking on the microtribological behavior of model polymer brushes Tribol. Lett. 63 (2016) 17
Polymer brushes in good solvents are known to exhibit excellent tribological properties. We have modeled polymer brushes and gels using a multibead-spring model and studied their tribological behavior via nonequilibrium molecular dynamics. Simulations of brush-against-wall systems were performed using an implicit solvent-based approach. Polymer chains were modeled as linear chains, randomly grafted on a planar surface. Quantities extracted from the simulations are the normal stress, shear stress and concentration profiles. We find that while an increase in the degree of crosslinking leads to an increase in the coefficient of friction, an increase in the length of crosslinker chains does the opposite. The effect of crosslinking can be understood in two ways: (1) There is a lower polymer concentration in the outer layer to take part in brush-as- sisted lubrication as the degree of crosslinking increases and (2) crosslinked polymer chains are more resistant to shear than noncrosslinked ones.
Article	M. Schuppler, F.C. Keber, M. Kröger, A.R. Bausch Boundaries steer the contraction of active gels Nat. Commun. 7 (2016) 13120
Cells set up contractile actin arrays to drive various shape changes and to exert forces to their environment. To understand their assembly process, we present here a reconstituted contractile system, comprising F-actin and myosin II filaments, where we can control the local Q2 activation of myosin by light. By stimulating different symmetries, we show that the force balancing at the boundaries determine the shape changes as well as the dynamics of the global contraction. Spatially anisotropic attachment of initially isotropic networks leads to a self-organization of highly aligned contractile fibres, being reminiscent of the order formation in muscles or stress fibres. The observed shape changes and dynamics are fully recovered by a minimal physical model.
Article	C. Luo, M. Kröger, J.-U. Sommer Entanglements and crystallization of concentrated polymer solutions: molecular dynamics simulations Macromolecules 49 (2016) 9017-9025
We carried out molecular dynamics simulations to study the crystallization of long polymers in a concentrated solution made by an explicit solvent of short chains. The weight-averaged entanglement length in the concentrated solution is found to exhibit power-law behavior with respect to the polymer volume fraction. The crystalline stem length obtained by quenching the solutions below melting temperature displays a linear relation with the entanglement length in the homogeneous solution above the crystallization temperature. Chain folding numbers are found to be very close to those in pure melts at different initial temperatures, and they tend to moderately decrease with increasing concentration of the long polymers. While our results are directly obtained from a coarse-grained model, they seem to suggest that the topological restriction of entanglements is a universal property to control the thickness selection during polymer crystallization.
Article	A. Karatrantos, N. Clarke, M. Kröger Modeling of polymer structure and conformations in polymer nanocomposites from atomistic to mesoscale: A Review Polym. Rev. 56 (2016) 385-428
Over the past two decades polymer nanocomposites have received tremendous interest from industry and academia due to their advanced properties comparative to polymer blends. Many computational studies have revealed that the macroscopic properties of polymer nanocomposites depend strongly on the microscopic polymer structure and conformations. In this article we review computer simulation studies of the fundamental problem of homopolymers structure and dimensions in nanocomposites containing bare or grafted spherical or rod nanoparticles. Experimentally, there is controversy over whether the addition of nanoparticles in a polymer matrix can perturb the polymer chains.
Article	Y. Li, M. Kröger, W.K. Liu Shape effect in cellular uptake of PEGylated nanoparticles: Comparison between sphere, rod, cube and disk Nanoscale 7 (2015) 16631-16646
The size, shape, surface property and material composition of polymer-coated nanoparticles (NPs) are four important parameters in designing efficient NP-based carriers for targeted drug delivery. However, due to the complex interplay between size, shape and surface property, most studies lead to ambiguous descriptions of the relevance of shape. To clarify its influence on the cellular uptake of PEGylated NPs, large scale molecular simulations have been performed to study differently shaped convex NPs, such as sphere, rod, cube and disk. Comparing systems with identical NP surface area, ligand.receptor interaction strength, and grafting density of the polyethylene glycol, we find that the spherical NPs exhibit the fastest internalization rate, followed by the cubic NPs, then rod- and disk-like NPs. The spherical NPs thus demonstrate the highest uptake among these differently shaped NPs. Based on a detailed free energy analysis, the NP shape effect is found to be mainly induced by the different membrane bending energies during endocytosis. The spherical NPs need to overcome a minimal membrane bending energy barrier, compared with the non-spherical counterparts, while the internalization of disk-like NPs involves a strong membrane deformation, responsible for a large free energy barrier. Besides, the free energy change per tethered chain is about a single kBT regardless of NP shape, as revealed by our self-consistent field theory calculations, where kB and T denote Boltzmann constant and temperature, respectively. Thus, the NP shape only plays the secondary role in the free energy change of grafted PEG polymers during internalization. We also find that star-shaped NPs can be quickly wrapped by the cell membrane, similar to their spherical counterparts, indicating star-shaped NPs can be used for drug delivery with high efficacy. Our findings seem to provide useful guidance in the molecular design of PEGylated NPs for controllable cellular uptake and help establish quantitatively rules in designing NP-based vectors for targeted drug delivery.
Article	O. Bertran, B. Zhang, A.D. Schlüter, M. Kröger, C. Aleman Modeling nanosized single molecule objects: Dendronized polymers adsorbed onto mica J. Phys. Chem. C 119 (2015) 3746-3752
We attempt to provide direct evidence for the suggested behavior of dendronized polymers as molecular objects (i.e., single shape persistent macromolecules). For this purpose, the microscopic structure of dendronized polymers adsorbed onto mica has been investigated using atomistic molecular dynamics simulations. We find that the shape of the second to fourth generation dendronized polymers is basically kept upon adsorption due to substantial backfolding within their interior. The fluctuation strength of the polymer backbones, which is seen to decrease with increasing generation, also indicates that these individual macromolecules exhibit molecular object behavior in the nanosize range.
Article	M.K. Singh, P. Ilg, R. M. Espinosa-Marzal, M. Kröger, N.D. Spencer Polymer brushes under shear: Molecular dynamics simulations compared to experiments Langmuir 31 (2015) 4798-4805
Surfaces coated with polymer brushes in a good solvent are known to exhibit excellent tribological properties. We have performed coarse-grained equilibrium and nonequilibrium molecular dynamics (MD) simulations to investigate dextran polymer brushes in an aqueous environment in molecular detail. In a first step, we determined simulation parameters and units by matching experimental results for a single dextran chain. Analyzing this model when applied to a multichain system, density profiles of end-tethered polymer brushes obtained from equilibrium MD simulations compare very well with expectations based on self-consistent field theory. Simulation results were further validated against and correlated with available experimental results. The simulated compression curves (normal force as a function of surface separation) compare successfully with results obtained with a surface forces apparatus. Shear stress (friction) obtained via nonequilibrium MD is contrasted with nanoscale friction studies employing colloidal-probe lateral force microscopy. We find good agreement in the hydrodynamic regime and explain the observed leveling-off of the friction forces in the boundary regime by means of an effective polymer.wall attraction.
Article	M. Kröger Simple, admissible, and accurate approximants of the inverse Langevin and Brillouin functions, relevant for strong polymer deformations and flows J. Non-Newtonian Fluid Mech. 223 (2015) 77-87
Approximants to the inverse Langevin and Brillouin functions appear in diverse contexts such as polymer science, molecular dynamics simulations, turbulence modeling, magnetism, theory of rubber. The exact inverses have no analytic representations, and are typically not implemented in software distributions. Various approximants for the inverse Langevin function L-1 had been proposed in the literature. After proving asymptotic features of the inverse functions, that had apparently been overlooked in the past, we use these properties to revisit this field of ongoing research. It turns out that only a subset of existing approximations obeys the relationships. Here we are able to derive improved (or 'corrected') approximations analytically. We disqualify the classical Padéolution approach that is typically used to obtain coefficients for approximate forms, and recommend a simple rational function L-1FENE(y)/(1+y2) that has a maximum relative error of 1-2 orders of magnitude smaller compared with the usually employed approximations L-1FENE(y) = 3y/(1-y2) (50% maximal relative error) or also L-1Cohen(y)=L-1FENE(y)(1-y2/3) (4.94%), while it is exactly as efficiently implemented and convenient for analytic (both force and energy) calculations. A number of applications is worked out. Moreover is the strategy proposed in this manuscript general and can be equally applied to fitting problems when asymptotic features are known.
Article	E. Cordova-Mateo, O. Bertran, A.D. Schlüter, M. Kröger, C. Aleman Internal organization of macromonomers and dendronized polymers based on thiophene dendrons Soft Matter 11 (2015) 1116-1126
The internal organization of macromonomers (MGs) consisting of all-thiophene dendrons of generation g= 2 and 3 attached to a phenyl core, as well as of the dendronized polymers resulting from polymerization of these macromonomers (PG2 and PG3, respectively), has been investigated using theoretical methods. The conformational preferences of the MGs, determined using density functional theory calculations, are characterized by the relative orientation between dendrons and core. We find that the strain of the MGs increases with the generation number and is alleviated by small conformational re-arrangements of the peripheral thiophene rings. The conformations obtained for the MGs have subsequently been used to construct models for the dendronized polymers. Classical molecular dynamics simulations have evidenced that the interpenetration of dendrons belonging to different repeat units is practically null for PG2. In contrast, the degree of interpenetration is found to be very high for PG3, which also shows a significant degree of backfolding (i.e. occurrence of peripheral methyl groups approaching the backbone). Consequently, PG2 behaves as a conventional linear flexible polymer bearing bulk pendant groups, whereas PG3 is better characterized as a semirigid homogenous cylinder. The two polymers are stabilized by π-π stacking interactions, even though these are significantly more abundant for PG3 than for PG2; the average number of interactions per repeat unit is 3.0 and 8.8 for PG2 and PG3, respectively. While in these interactions the thiophene rings can adopt either parallel (sandwich) or perpendicular (T-shaped) dispositions, the former scenario turns out to be the most abundant.
Article	A. Halperin, M. Kröger, F.M. Winnik Poly(N-isopropylacrylamide) phase diagrams: Fifty years of research Angew. Chem. Int. Ed. 54 (2015) 15342-15367
In 1968, Heskins and Guillet published the first systematic study of the phase diagram of poly(N-isopropylacrylamide) (PNIPAM), at the time a “young polymerâ€� first synthesized in 1956. Since then, PNIPAM became the leading member of the growing families of thermoresponsive polymers and of stimuli-responsive, “smartâ€� polymers in general. Its thermal response is unanimously attributed to its phase behavior. Yet, in spite of 50 years of research, a coherent quantitative picture remains elusive. In this Review we survey the reported phase diagrams, discuss the differences and comment on theoretical ideas regarding their possible origins. We aim to alert the PNIPAM community to open questions in this reputably mature domain. Supplemental Material »»
Article	A. Halperin, M. Kröger, F.M. Winnik Poly(N-isopropylacrylamid)-Phasendiagramme: 50 Jahre Forschung Angew. Chem. 127 (2015) 15558-15586
Im Jahr 1968 publizierten Heskins und Guillet die erste systematische Studie über das Phasendiagramm von Poly(N-isopropylacrylamid) (PNIPAM), einem zu jener Zeit “jungen Polymerâ€�, das erstmalig 1956 synthetisiert worden war. Seitdem ist PNIPAM zu einem führenden Vertreter der wachsenden Familie temperatur- und reizempfindlicher Polymere geworden. Seine thermische Antwort ist fraglos durch sein Phasenverhalten begründet. Nach nunmehr 50 Jahren Forschung zeichnet sich noch immer kein einheitliches, quantitatives Bild seines Verhaltens ab. In diesem Aufsatz treten wir eine Reise zu den beobachteten Phasendiagrammen an. Wir kommentieren theoretische Überlegungen zu den möglichen Ursachen der dabei offensichtlich werdenden Unterschiede. Dabei ist es unser Ziel, nach wie vor offene Fragen auf diesem altehrwürdigen Gebiet vor Augen zu führen. Supplemental Material »»
Article	Y. Li, M. Kröger, W.K. Liu Endocytosis of PEGylated nanoparticles accompanied by structural changes of the grafted polyethylene glycol Biomaterials 35 (2014) 8467-8478
Nanoparticles (NPs) demonstrate promising properties as therapeutic carriers to efficiently deliver drug molecules into diseased cells. The surfaces of NPs are usually grafted with polyethylene glycol (PEG) polymers, during so-called PEGylation, to improve water solubility, avoid aggregation, and prevent opsonization during blood circulation. The interplay between grafting density σp and grafted PEG polymerization degree N makes cellular uptake of PEGylated NPs distinct from that of bare NPs. To understand the role played by grafted PEG polymers, we study the endocytosis of 8 nm sized PEGylated NPs with different σp and N through large scale dissipative particle dynamics (DPD) simulations. The free energy change Fpolymer of grafted PEG polymers, before and after endocytosis, is identified to have an effect which is comparable to, or even larger than, the bending energy of the membrane during endocytosis. Based on self-consistent field theory Fpolymer is found to be dependent on both σp and N. By incorporating Fpolymer, the critical ligand-receptor binding strength for PEGylated NPs to be internalized can be correctly predicted by a simple analytical equation. Without considering Fpolymer, it turns out impossible to predict whether the PEGylated NPs will be delivered into the diseased cells. These simulation results and theoretical analysis not only provide new insights into the endocytosis process of PEGylated NPs, but also shed light on the underlying physical mechanisms, which can be utilized for designing efficient PEGylated NP-based therapeutic carriers with improved cellular targeting and uptake.
Article	Y. Li, M. Kröger, W.K. Liu Dynamic structure of unentangled polymer chains in the vicinity of non-attractive nanoparticles Soft Matter 10 (2014) 1723-1737
Using coarse-grained molecular dynamics simulation, we study the motion of unentangled polymer chains dynamically confined by non-attractive nanoparticles (NPs). Both normal mode and dynamic structure factor S(q, t) analysis are adopted to analyze chain's dynamics. Relaxation behaviors of chains are found to be significantly slowed down by NPs. The relaxation times of chain's normal modes are monotonically increasing with the NP volume fraction φ. At the same time, chains' dynamics are becoming non- Gaussian. Inspection of S(q, t) reveals that chain's dynamics can be attributed to two .phases., a bulk polymer phase and a confined polymer phase between NPs. The dynamics of a confined polymer is slower than that of a bulk polymer, while still exhibiting high mobility. The amount of the bulk polymer phase is found to exponentially decay with increasing φ. With this figure at hand, we establish a simple relationship between NP and confined/interphase polymer volume fractions. This work seems to provide the first quantitative prediction on the relationship between NP and confined/interphase polymer volume fractions.
Article	T.L. Chantawansri, T.W. Sirk, R. Mrozek, J.L. Lenhart, M. Kröger, Y.R. Sliozberg The effect of polymer chain length on the mechanical properties of triblock copolymer gels Chem. Phys. Lett. 612 (2014) 157-161
An ABA triblock copolymer in a midblock selective solvent is studied as a function of the chain length,using a novel dissipative particle dynamics (DPD) model which includes a modified segmental repulsivepotential (mSRP) that restricts chain crossing. Deformation under uniaxial tension using the DPD method,with and without the mSRP, was used to extract the cross-link and entanglement portions of the modulus.The results exhibit the expected theoretical scaling with chain length for lower strain rates. Structuralproperties, such as bridge fraction and the extent of entanglements in the polymer matrix, were alsoquantified.
Article	R.J.A. Steenbakkers, C. Tzoumanekas, Y. Li, W.K. Liu, M. Kröger, J.D. Schieber Primitive-path statistics of entangled polymers: Mapping multi-chain simulations onto single-chain mean-field models New J. Phys. 16 (2014) 015027
We present a method to map the full equilibrium distribution of the primitive path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field .target. model. Most previous works used the Doi.Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which includes fluctuations in all these variables as well as in the spatial positions of the entanglements. This turns out to be essential to obtain qualitative and quantitative agreement with the equilibrium PP-length distribution obtained from multi-chain simulations. By fitting this distribution, we are able to determine two of the three parameters of the model, which govern its equilibrium properties. This mapping is executed for four different linear polymers and for different molecular weights. The two parameters are found to depend on chemistry, but not on molecular weight. The model predicts a constant plateau modulus minus a correction inversely proportional to molecular weight. The value for well entangled chains, with the parameters determined ab initio, lies in the range of experimental data for the materials investigated.
Article	E. Panagiotou, M. Kröger Pulling-force-induced elongation and alignment effects on entanglement and knotting characteristics of linear polymers in a melt Phys. Rev. E 90 (2014) 042602
We employ a primitive path (PP) algorithm and the Gauss linking integral to study the degree of entanglement and knotting characteristics of linear polymer model chains in a melt under the action of a constant pulling force applied to selected chain ends. Our results for the amount of entanglement, the linking number, the average crossing number, the writhe of the chains and their PPs and the writhe of the entanglement strands all suggest a different response at the length scale of entanglement strands than that of the chains themselves and of the corresponding PPs. Our findings indicate that the chains first stretch at the level of entanglement strands and next the PP (tube) gets oriented with the ``flow'' These two phases of the extension and alignment of the chains coincide with two phases related to the disentanglement of the chains. Soon after the onset of external force the PPs attain a more entangled conformation, and the number of nontrivially linked end-to-end closed chains increases. Next, the chains disentangle continuously to attain an almost unentangled conformation. Using the linking matrix of the chains in the melt, we furthermore show that these phases are accompanied by a different scaling of the homogeneity of the global entanglement in the system. The homogeneity of the end-to-end closed chains first increases to a maximum and then decreases slowly to a value characterizing a completely unlinked system.
Article	E. Córdova-Mateo, O. Bertran, B. Zhang, D. Vlassopoulos, R. Pasquino, A.D. Schlüter, M. Kröger, C. Alemán Interactions in dendronized polymers: Intramolecular dominates intermolecular Soft Matter 10 (2014) 1032-1044
In an attempt to relate atomistic information to the rheological response of a large dendritic object, inter- and intramolecular hydrogen bonds and π,π-interactions have been characterized in a dendronized polymer (DP) that consists of a polymethylmethacrylate backbone with tree-like branches of generation four (PG4) and contains both amide and aromatic groups. Extensive atomistic molecular dynamics simulations have been carried out on (i) an isolated PG4 chain and (ii) ten dimers formed by two PG4 chains associated with different degrees of interpenetration. Results indicate that the amount of nitrogen atoms involved in hydrogen bonding is ~11% while 15% of aromatic groups participate in π,π-interactions. Furthermore, in both cases intramolecular interactions clearly dominate over intermolecular ones, while exhibiting markedly different behaviors. Specifically, the amount of intramolecular hydrogen bonds increases when the interpenetration of the two chains decreases, whereas intramolecular π,π-interactions remain practically insensitive to the amount of interpenetration. In contrast, the strength of the corresponding two types of intermolecular interactions decreases with interpenetration. Although the influence of complexation on the density and cross-sectional radius is relatively small, interpenetration affects significantly the molecular length of the DP. These results support the idea of treating DPs as long colloidal molecules.
Article	B. Huber, M. Harasim, B. Wunderlich, M. Kröger, A.R. Bausch Microscopic origin of the non-Newtonian viscosity of semiflexible polymer solutions in the semidilute regime ACS Macro Lett. 3 (2014) 136-140
One of the great goals in polymer physics is to relate the various macroscopic features of polymeric fluids with the microscopic behavior of single chains. Here, we directly visualize the conformational dynamics of individual semiflexible polymers in a semidilute solution above the overlap concentration under shear. We observe that the tumbling dynamics are significantly slowed down, in marked contrast to the case of a dilute solution, due to steric interactions with neighboring filaments. The observed macroscopic shear thinning effect can be rationalized by a simple model based on the single filament dynamics.
Article	A.D. Schlüter, A. Halperin, M. Kröger, D. Vlassopoulos, G. Wegner, B. Zhang Dendronized polymers: Molecular objects between conventional linear polymers and colloidal particles ACS Macro Lett. 3 (2014) 991-998
The term molecular object (MO) is introduced to describe single, shape persistent macromolecules that retain their form and mesoscopic dimensions irrespective of solvent quality and adsorption onto a surface. The concept is illustrated with results concerning homologous series of dendronized polymers (DP). In particular, we discuss imaging experiments quantifying deformation upon adsorption, defect characterization, and atomistic molecular dynamics simulations of DP structure. We argue that MOs such as high generation DP, with their large dimensions and high internal density, provide an opportunity to address fundamental questions regarding the onset of bulk-like behavior in single molecules. Illustrative examples of such questions concern the smallest MO exhibiting a glass transition, glassy behavior or a constant bulk density. The characteristics of DP MO are highlighted by comparison to polymer beads, polymeric micelles, globular proteins, and carbon nanotubes. We discuss future research directions and speculate on possibilities involving multiarmed and toroid DP and the effect of DP on friction and rheology, as well as their utilization for nanoconstruction.
Article	Y.R. Sliozberg, R.A. Mrozek, J.D. Schieber, M. Kröger, J.L. Lenhart, J.W. Anzelm Effect of polymer solvent on the mechanical properties of entangled polymer gels: Coarse-grained molecular simulation Polymer 54 (2013) 2555-2564
Polymer gels are composed of a chemically or physically cross-linked polymer that is highly swollen with solvent. Two important limitations for the practical application of polymer gels are low toughness and a limited ability to tailor the strain-rate dependent mechanical response. Both these limitations are due to the high loadings of small molecule solvents that are typically incorporated into the gel formulation. Here, we provide insight into the role of physical entanglements on the performance of polymer gels, when the solvent molecular weight is large enough to entangle with the polymer network. Our simulations demonstrate that the solvent entanglements dominate the time-dependent elastic modulus of polymer gels with high-molecular-weight solvent. We have found that entanglement contribution to the modulus is essentially equal for the entangled polymer melt and loosely cross-linked entangled polymer gel at high strain rate. At lower strain rate, the modulus of the polymer gels develops a long-lived plateau that originates from .semi-trapped. entanglements formed between network strands and polymer solvent. The simulations were validated with selected experiments of chemically cross-linked polydimethylsiloxane (PDMS) elastomers loaded with a non-reactive silicone oil solvent, where the solvent molecular weight was varied. The simulations and experimental results demonstrate that highly entangled solvent can be used to tune the rate dependent modulus of polymer gels.
Article	Y. Li, B.C. Abberton, M. Kröger, W.K. Liu Challenges in multiscale modeling of polymer dynamics Polymers 5 (2013) 751-832
The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale modeling of polymeric materials and how these methods can help us to optimize and design new polymeric materials.
Article	O. Bertran, B. Zhang, A.D. Schlüter, A. Halperin, M. Kröger, C. Aleman Computer simulations of dendronized polymers: organization and characterization at the atomistic level RSC Adv. 3 (2013) 126-140
Atomistic molecular dynamics simulations in chloroform and solvent-free environments are used to build and study a homologous series of neutral dendronized linear polymers (DPs), whose repeat units are regularly branched dendrons of generations g=1-7, excluding g=5. We find that a DP with g≤4 displays an elongated conformation, while a DP with g=6 furthermore exhibits a helical backbone. The conformations essentially differ in their alternating (elongated) or regular (helical) twist with respect to the macromolecular axis, at similar average distance between repeat units (2.1-2.3 A). With increasing g the dendrons tend to induce an increasing strain, stiffness and overall cylindrical shape onto the DP; the existence of DPs with g≥7 is excluded. The fractal dimensionality of the backbone appears similar for DPs with g≤4, while a discontinuous fractal behavior found for g=6 is consistent with its helical backbone. Profiles describing the variation of the density as a function of the distance to the molecular backbone are extracted to analyze conformational effects of both backbone and sidegroups. For the solvent-free case the average density grows from 0.97 to 1.11 g/cm3 upon increasing g, while the radial density profile is basically constant at 1.1-1.2 g/cm3 and insensitive to g at intermediate distances, where dendrons are able to interpenetrate. The variation of obtained DP thicknesses is successfully compared with experimental estimates deduced from transmission electron microscopy measurements of polymers deposited onto attractive mica surfaces. Finally, we examine and discuss the distribution of solvent molecules inside elongated structures.
Article	O. Bertran, B. Zhang, A. D. Schlüter, M. Kröger, C. Aleman Computer simulation of fifth generation dendronized polymers: Impact of charge on internal organization J. Phys. Chem. B 117 (2013) 6007-6017
The internal organization of a fifth-generation dendronized polymer (PG5) has been investigated by atomistic molecular dynamics simulations in a vacuum. This study reveals an exceptional behavior of PG5 within the homologous series of g-generation PGg polymers. Three molecular configurations, which present a heterogeneous distribution of dendrons and an amount of backfolding lower than PG4 and PG6, have been obtained for PG5. The highest stability and closest agreement with available experimental data corresponds to a helical conformation characterized by a pitch of about 30 thickness of 105 A and average density of 0.861 g/cm3. While small angle neutron scattering studies of PG5 in solution show a constant radial density distribution around the backbone, we here in our vacuum studies find a cylindrical volume element of sharply reduced density reminiscent of a pore. This neutral PG5 was compared with its charged deprotected analogue, de-PG5 in water, to see in as much the positive charges in the periphery of this macromolecule would a affect its conformational behavior. During deprotection of PG5, the tert-butyloxycarbonyl protected amine groups are converted into ammonium, mimicking the experimental situation during a divergent synthesis procedure. The repulsive interactions among the positively charged ammonium groups are responsible for a huge (~30%) reduction of the average density and a small (~1%) increase of elongation of the helical backbone, which results in a structure with a spongy appearance. Also here, we find a reduced dendron density near the backbone which is compensated for by the pore being filled with water.
Article	M.B. Harasim, B. Wunderlich, O. Peleg, M. Kröger, A.R. Bausch Direct observation of the dynamics of semiflexible polymers in shear flow Phys. Rev. Lett. 110 (2013) 108302
The flow behavior of polymeric liquids can be traced back to the complex conformational dynamics of polymer molecules in shear flow, which poses a major challenge to theory and experiment alike due to the inherently large number of degrees of freedom. Here we directly determine the configurational dynamics of individual actin filaments with varying lengths in a well defined shear geometry by combining microscopy, microfluidics, and a semiautomated moving stage. This allows the identification of the microscopic mechanisms and the derivation of an analytical model for the dynamics of individual filaments based on the balance of drag, bending, and stochastic forces. Supplemental Material, Movies »»
Article	M. Tagliazucchi, O. Peleg, M. Kröger, Y. Rabin, I. Szleifer Effect of charge, hydrophobicity, and sequence of nucleoporins on the translocation of model particles through the nuclear pore complex (vol 110, pg 3363, 2013) Proc. Natl. Acad. Sci. 110 (2013) 10336-10337
The original article for this erratum is available here »»
Article	M. Tagliazucchi, O. Peleg, M. Kröger, Y. Rabin, I. Szleifer Effect of charge, hydrophobicity and sequence of nucleoporins on the translocation of model particles through the nuclear pore complex Proc. Natl. Acad. Sci. 110 (2013) 3363-3368
The molecular structure of the yeast nuclear pore complex (NPC) and the translocation of model particles have been studied with a molecular theory that accounts for the geometry of the pore and the sequence and anchoring position of the unfolded domains of the nucleoporin proteins (the FG-Nups), which control selective transport through the pore. The theory explicitly models the electrostatic, hydrophobic, steric, conformational, and acid-base properties of the FG-Nups. The electrostatic potential within the pore, which arises from the specific charge distribution of the FG-Nups, is predicted to be negative close to pore walls and positive along the pore axis. The positive electrostatic potential facilitates the translocation of negatively charged particles, and the free energy barrier for translocation decreases for increasing particle hydrophobicity. These results agree with the experimental observation that transport receptors that form complexes with hydrophilic/ neutral or positively charged proteins to transport them through the NPC are both hydrophobic and strongly negatively charged. The molecular theory shows that the effects of electrostatic and hydrophobic interactions on the translocating potential are cooperative and nonequivalent due to the interaction-dependent reorganization of the FG-Nups in the presence of the translocating particle. The combination of electrostatic and hydrophobic interactions can give rise to complex translocation potentials displaying a combination of wells and barriers, in contrast to the simple barrier potential observed for a hydrophilic/neutral translocating particle. This work demonstrates the importance of explicitly considering the amino acid sequence and hydrophobic, electrostatic, and steric interactions in understanding the translocation through the NPC. ERRATUM available here »»
Article	M. Sadati, C. Luap, B. Lüthi, M. Kröger, H.C. Öttinger Application of full flow field reconstruction to a viscoelastic liquid in a 2D cross-slot channel J. Non-Newtonian Fluid Mech. 192 (2013) 10-19
High quality flow kinematics reconstruction from noisy and spatially scattered data requires the use of a regularization technique. Enforcing incompressibility, we employ the recently proposed Tikhonov regularization method combined with a high--order finite element approximation in its stream function formulation. The method is applied to experimental particle tracking velocimetry data, obtained for an incompressible polymer melt in a cross--slot channel. To overcome a potential regularization bias, where the velocity changes rapidly over small distances, regularization is performed on the departure of the velocity field from its Newtonian counterpart. It is compared with a more trivial approach, in which the data are smoothed locally and the velocity gradient fields computed using finite differences. The reconstructions are evaluated in terms of the quality of the streamlines and the velocity gradient histories. Regularization leads to significant noise reduction and to an improved utility of existing data for subsequent applications as we demonstrate by analyzing the principal stress--difference obtained by applying a constitutive equation to the reconstructed flow fields.
Article	M. Kröger, A.D. Schlüter, A. Halperin Branching defects in dendritic molecules: Coupling efficiency and congestion effects Macromolecules 46 (2013) 7550-7564
An analytical model supplemented by Monte Carlo simulations specifies the statistics of branching defects in dendritic molecules as a function of the generation g as well as the maximal g for which defect free synthesis is possible, gmax. The defects arise because of (i) imperfect coupling efficiency characterized by an constant fraction P ≤ 1 of successful add-on reactions in the absence of excluded volume effects, and (ii) packing constraints associated with steric congestion at high g when the maximal density is approached. The model specifies ng, the number of junctions, and the number of defects for both g ≤ gmax and g > gmax, as well as gmax and its dependence on P. The branching polydispersity is characterized by the average number of junction-junction bonds, Xgeff. For g < gmax and efficient synthesis Xgeff is weakly reduced with respect to X, its value in defect-free molecules, and ng ~ (Xeff-1)g increases exponentially. In the congested regime, at g > gmax, branching is strongly reduced and Xgeff slowly approaches 2 as Xgeff-2 ~ 1/g while ng eventually exhibits power law growth: ng ~ g3 for dendrimers and ng ~ g2 for dendronized polymers. The branching defects can be interrogated by different forms of end group analysis utilizing the theory framework proposed.
Article	E. Panagiotou, M. Kröger, K.C. Millet Writhe and mutual entanglement combine to give the entanglement length Phys. Rev. E 88 (2013) 062604
We propose a method to estimate Ne, the entanglement length, that incorporates both local and global topological characteristics of chains in a melt under equilibrium conditions. This estimate uses the writhe of the chains, the writhe of the primitive paths, and the number of kinks in the chains in a melt. An advantage of this method is that it works for both linear and ring chains, works under all periodic boundary conditions, does not require knowing the contour length of the primitive paths, and does not rely on a smooth set of data.We apply this method to linear finitely extendable nonlinear elastic chains and we observe that our estimates are consistent with those from other studies.
Article	B. Zhang, H. Hu, A.D. Schlüter, A. Halperin, M. Kröger Synthetic regimes due to packing constraints in dendritic molecules confirmed by labelling experiments Nat. Commun. 4 (2013) 1993
Classical theory predicts that branching defects are unavoidable in large dendritic molecules when steric congestion is important. Here we report first experimental evidence of this effect via labelling measurements of an extended homologous series of generations g=1 .. 6 of dendronized polymers. This system exhibits a single type of defect interrogated specifically by the Sanger reagent thus permitting to identify the predicted upturn in the number of branching defects when g approaches gmax and the polymer density approaches close packing. The average number of junctions and defects for each member of the series is recursively obtained from the measured molar concentrations of bound labels and the mass concentrations of the dendritic molecules. The number of defects increases at g=5 and becomes significant at g=6 for dendronized polymers where the gmax was estimated to occur at 6.1 ≤ gmax ≤ 7.1. The combination of labelling measurements with the novel theoretical analysis affords a method for characterizing high g dendritic systems.
Article	Y. Li, S. Tang, B.C. Abberton, M. Kröger, C. Burkhart, B. Jiang, G.J. Papakonstantopoulos, M. Poldneff, W.K. Liu A predictive multiscale computational framework on viscoelastic properties of linear polymers Polymer 53 (2012) 5935-5952
A predictive multiscale computational framework has been proposed to study the viscoelastic properties of polymeric materials. Using the Inverse Boltzmann Method, both the static structures and dynamic behavior of all-atomistic models of polymers can be reproduced by a simple coarse-grained model, which bridges the scale from nano to meso. On this coarse-grained level, the entangled network of polymer chains is described via a primitive path analysis (Z1 code). This description allows extraction of the tube diameter and primitive chain length, quantities required to bridge the scale from meso to micro. Furthermore, by making the affine-deformation assumption, a continuum constitutive law for polymeric materials has been developed from the tube model of primitive paths, which bridges the scale from micro to macro. In this way, the different scales are crossed by using different bridging laws, which enables us to directly predict the viscoelastic properties of polymeric materials using a bottom-up approach. Our predicted dynamic moduli, zero-rate shear viscosities, and relaxation moduli of polyisoprene and polytheylene polymers are found to be in excellent agreement with experimental results. The proposed multiscale computational framework can also be naturally extended to the finite-deformation regime. Both the tube diameter a and primitive chain length L are found to increase with deformation, which enhances the viscous energy dissipation of polymers under extremely large deformations. To the authors. knowledge, this is the first work in which a multiscale computational framework has been proposed to predict the viscoelastic properties of entangled polymeric materials from the molecular level. Not only can the method put forth in this research be used to predict the viscoelastic properties of polymeric materials in a bottom-up fashion, it can also be applied to design the polymeric materials with targeted functions, within a top-down approach.
Article	Y. Li, M. Kröger Viscoelasticity of carbon nanotube buckypaper: Zipping-unzipping mechanism and entanglement effects Soft Matter 8 (2012) 7822-7830
It has been reported that carbon nanotube (CNT) buckypaper demonstrates frequency- and temperature-invariant viscoelastic properties [Xu et al., Science, 2010, 330, 1364]. In an attempt to provide microscopic insight, we performed coarse-grained molecular dynamics simulations on the viscoelastic properties of model CNT buckypaper. First of all, the model is shown to exhibit the observed frequency- and temperature-invariant viscoelastic features. Analyzing snapshots of the buckypaper under cyclic shear deformation, we furthermore confirm that a zipping.unzipping mechanism plays an important role in the molecular origin of the particular viscoelastic properties of buckypaper. Quantitative inspection of the amount of inter-tube entanglements per CNT, < Z >, reveals that CNT buckypaper is faced with reversible entanglement loss during the shear loading process; the equilibrium < Z > is fully recovered if shear loading is removed. The variation of < Z > during a loading. unloading.reloading cycle is found to be insensitive to both frequency and temperature. Our study highlights an energy dissipation mechanism for carbon nanomaterials, which can help us design new energy-adsorption coatings/damping devices under extreme conditions, and seems to rule out a recently proposed scenario of unstable detachments.attachments.
Article	Y. Li, M. Kröger Computational study on the entanglement length and pore size of carbon nanotube buckypaper Appl. Phys. Lett. 100 (2012) 021907 [article also included in the Virtual J. Nanoscale Sci. Tech. 25:4 (2012)]
In this letter, both entanglement length and pore size of carbon nanotube (CNT) buckypaper are studied numerically and found to scale with a characteristic length (EI/γ)1/2, where EI and γ denote the bending stiffness and binding energy of a CNT, respectively. For (EI/γ)1/2<40 nm, the CNTs in buckypaper are interwound with a short entanglement length and a small pore size. However, when (EI/γ)1/2>40 nm, CNT ring/racket structures dominate the buckypaper, exhibiting longer entanglement length and larger pore size. The acquired understanding of microscopic structures allows us to propose that CNT buckypaper with different mechanical properties and pore size can be designed through the choice of (EI/γ)1/2 values.
Article	Y. Li, M. Kröger A theoretical evaluation of the effects of carbon nanotube entanglement and bundling on structural and mechanical properties of buckypaper Carbon 50 (2012) 1793-1806
Structural formation mechanisms of carbon nanotube (CNT) buckypaper and their effects on its mechanical properties are studied with numerical simulations. A bond swap algorithm, resulting from coupling the molecular dynamics and Monte Carlo methods, has been developed to equilibrate initial structures of buckypaper, generated by a random walk approach. Entanglement and bundling mechanisms are found to affect major structural features of buckypaper. Both mechanisms are evaluated quantitatively by calculating the entanglement network and pore size of buckypaper. Compared with (8,8)-(12,12) doublewalled CNT, the structure of (5,5) single-walled CNT buckypaper is mainly dominated by entanglement, due to its smaller adhesion energy. We show that the pore size of modeled buckypaper, containing both types of CNTs, can be tuned from 7 nm to 50 nm by increasing the double-walled CNT content from 0 wt% to 100 wt%, due to the transformation from entanglement-dominated to bundling-dominated structures. Such an observation agrees exceptionally well with experimental results. Both entanglement and bundling mechanisms are also found to play important roles in the mechanical properties of buckypaper. The findings open a way to tailor both structural and mechanical properties of buckypaper, such as Young.s modulus or Poisson.s ratio, by using different CNTs and their mixtures.
Article	Y. Li, M. Kröger, W.K. Liu Nanoparticle geometrical effect on structure, dynamics and anisotropic viscosities of polyethylene nanocomposites Macromolecules 45 (2012) 2099-2112
Addition of nanoparticles into a polymer matrix can significantly alter its structure, dynamics as well as viscosity. In this paper, we study the structural, dynamical and viscous behaviors of polyethylene (PE) matrices under the influence of five differently shaped nanoparticles: buckyball, graphene, nanodiamond (ND), X-shaped and Y-shaped junctions, at fixed volume fraction (4 vol %). These nanoparticles have different surface-area- to-volume ratios, arranged as graphene, X-shaped junction, Y-shaped junction, buckyball, and ND, from the largest to the smallest. In turn, different interaction energies between nanoparticles and PE matrices are enabled according to their surface-area-to-volume ratios. The graphene sheet is expected to have the strongest interaction with the PE matrix in accord with its largest surface-area-to-volume ratio. The interaction between NDs and their PE matrix is the smallest, due to their truncated octahedron shapes and the smallest surfacearea- to-volume ratio. However, the graphene sheets tend to aggregate at the PE melting temperature (450 K), lowering their interactions with the PE matrix. Because of this interplay, the interactions between nanoparticles and polymer matrices can be tailored through the shapes (also surface-area-to-volume ratios) of nanoparticles as well as their dispersions. The polymer chains are found to be densely packed around these nanoparticles in the range of 2 nm, except NDs, due to their strong interactions with PE matrices. Thus, these nanoparticles are found to be able to nucleate polymer entanglements around their surfaces and to increase the underlying entanglement densities of PE matrices. Both the polymer chain relaxation and anisotropic viscosity of PE nanocomposites are shown to be greatly affected by oriented nanoparticles. Our simulation results indicate that the surface-areato- volume ratio of nanoparticles plays the dominated role in the structural, dynamical and viscous properties of PE nanocomposites.
Article	Y. Li, M. Kröger, W.K. Liu Nanoparticle effect on the dynamics of polymer chains and their entanglement network Phys. Rev. Lett. 109 (2012) 118001
We explore the dynamics of entangled polymer chains embedded into nanocomposites. From primitive path analysis, highly entangled polymer chains are found to be significantly disentangled during increment of the volume fraction of spherical non-attractive nanoparticles (NPs) from 0 to 42%. A critical volume fraction, φc = 31%, is found to control the crossover from polymer chain entanglements to `NP entanglements'. While below φc, the polymer chain relaxation accelerates upon filling, above φc, the situation reverses: Polymer dynamics becomes geometrically constrained upon adding NPs. Our findings provide a microscopic understanding of the dynamics of entangled polymer chains inside their composites, and they offer an explanation for the unusual rheological properties of polymer composites.
Article	O. Peleg, T. Savin, G.V. Kolmakov, I.G. Salib, A.C. Balazs, M. Kröger, V. Vogel Fibers with integrated mechanochemical switches: Minimalistic design principles derived from fibronectin Biophys. J. 103 (2012) 1909-1918
Inspired by molecular mechanisms that cells exploit to sense mechanical forces and convert them into biochemical signals, chemists dream of designing mechano-chemical switches integrated into materials. Using the adhesion protein fibronectin, where essentially each of its multiple repeats displays another molecular recognition motif, a computational model was derived asking how minimalistic designs of repeats translate into mechanical characteristics of their fibrillar assemblies: the hierarchy of repeat-unfolding within fibrils is not just controlled by their relative mechanical stabilities, as found for single molecules, but also by the strength of cryptic interactions between adjacent molecules that become activated by stretching. The forceinduced exposure of cryptic sites furthermore regulates the nonlinearity of stress-strain curves, the strain at which such fibers break, as well as the refolding kinetics and fraction of misfolded repeats. Gaining such computational insights at the mesoscale is significant since translating protein-based concepts into novel polymer designs has proven difficult. See also New and Notable
Article	N.C. Karayiannis, R. Malshe, M. Kröger, J.J. de Pablo, M. Laso Evolution of fivefold local symmetry during crystal nucleation and growth in dense hard-sphere packings Soft Matter 8 (2012) 844-858
Crystal nucleation and growth of monodisperse hard spheres as a function of packing density is studied by collision-driven Molecular Dynamics simulations. We demonstrate, that short-range order in the form of sites with fivefold symmetry acts as an inhibitor to crystal growth. As a consequence, crystallization at high volume fractions is significantly delayed in random hardsphere packings where sites with fivefold symmetry are abundant. A cluster-based approach shows that configurations having initially a similar average fraction of fivefold sites can crystallize in completely different patterns both in terms of dynamics and morphology based on the half life of fivefold sites. The growth of a critical crystal nucleus is significantly affected by existing fivefold sites: it is observed that its shape and size evolves so as to avoid close proximity to regions rich in fivefolds. This trend could provide an explanation for the highly anisotropic shape of the critical nucleus observed in recent experiments and simulations and which is in contradiction with predictions of the classical nucleation theory. Eventually, once a given structure transits to the ordered phase, fivefold symmetry either diminishes or arranges in specific geometric patterns. Such defects are spatially strongly correlated with twinning planes at crystalline boundaries.
Article	A. Karatrantos, R.J. Composto, K.I. Winey, M. Kröger, N. Clarke Entanglements and dynamics of polymer melts near a SWCNT Macromolecules 45 (2012) 7274-7281
We investigate the topological constraints (entanglements) and dynamics of monodisperse polymer melts in the presence of a single wall carbon nanotube (SWCNT) in comparison to inclusion-free polymer melts by molecular dynamics simulations. The SWCNT has an infinite aspect ratio and radius smaller than the polymer radius of gyration. In the presence of SWCNT with or without attractive interactions, the contour length of the primitive path increases indicating more entanglements. We also find that there is a large heterogeneity in the polymer dynamics due to the polymers in contact with the SWCNT. The overall polymer diffusion decreases compared to its melt value and is affected by the enthalpic interaction between monomeric units and SWCNT, and the SWCNT radius. Moreover, the polymer chain diffusivity perpendicular to SWCNT is less than that parallel to the SWCNT in the entangled polymer systems where there is attraction between polymers and SWCNT surface. In the absence of SWCNT-polymer attractions, the polymer diffusion retains its melt value.
Article	A. Halperin, M. Kröger Thermoresponsive cell culture substrates based on PNIPAM brushes functionalized with adhesion peptides: Theoretical considerations of mechanism and design Langmuir 28 (2012) 16623-16637
Thermoresponsive tissue culture substrates based on PNIPAM brushes are used to harvest confluent cell sheets for tissue engineering. The prospect of clinical use imposes the utilization of culture medium free of bovine serum, thus suggesting conjugation with adhesion peptides containing the RGD minimal recognition sequence. The optimum position of the RGD along the chain should ensure both cell adhesion at 37 C and cell detachment at TL below the lower critical solution temperature of PNIPAM. Design guidelines are formulated from considerations of brush confinement by the cells: (i) Cell adhesion at 37 C is controlled by the RGDs accessible without brush compression. (ii) Cell detachment at TL is driven by a disjoining force due to confinement of the swollen brush by cells retaining integrin.RGD bonds formed at 37 C. These suggest placing the RGDs at the grafting surface or its vicinity. Randomly placed RGDs do not enable efficient detachment because a large fraction of the integrin.RGD bonds are not sufficiently tensioned at TL, in line with experimental observations (Ebara, M.; Yamato, M.; Aoyagi, T.; Kikuchi, A.; Sakai, K.; Okano, T. Immobilization of celladhesive peptides to temperature-responsive surfaces facilitates both serum-free cell adhesion and noninvasive cell harvest. Tissue Eng.2004, 10, 1125.1135). The theory framework enables analysis of culture media based on polymer brushes conjugated with adhesion peptides in general.
Article	A. Halperin, M. Kröger Theoretical considerations on mechanisms of harvesting cells cultured on thermoresponsive polymer brushes Biomaterials 33 (2012) 4975-4987 [Leading opinion paper]
Poly (N-isopropylacrylamide) (PNIPAM) brushes and hydrogels serve as temperature-responsive cell culture substrates. The cells adhere at 37 Â°C and are detached by cooling to below the lower critical solution temperature TLCST ≈ 32 Â°C, an effect hitherto attributed to change in PNIPAM hydration. The article proposes a mechanism coupling the change of hydration to integrin mediated environmental sensing for cell culture on brushes and hydrogels in serum containing medium. Hydration is associated with swelling and higher osmotic pressure leading to two effects: (i) The lower osmotic pressure in the collapsed brush/hydrogel favors the adsorption of serum borne extracellular matrix (ECM) proteins enabling cell adhesion; (ii) Brush/hydrogel swelling at T < TLCST gives rise to a disjoining force fcell due to confinement by the ventral membrane of a cell adhering via integrin-ECM bonds. fcell places the integrin.ECM bonds under tension thus accelerating their dissociation and promoting desorption of ECM proteins. Self consistent field theory of PNIPAM brushes quantifies the effect of the polymerization degree N, the area per chain Σ, and the temperature, T on ECM adsorption, fcell and the dissociation rate of integrin-ECM bonds. It suggests guidelines for tuning Σ and N to optimize adhesion at 37 Â°C and detachment at T < TLCST. The mechanism rationalizes existing experimental results on the influence of the dry thickness and the RGD fraction on adhesion and detachment.
Article	Y. Li, M. Kröger, W.K. Liu Primitive chain network study on uncrosslinked and crosslinked cis-polyisoprene polymers Polymer 52 (2011) 5867-5878
In this paper, the polymer chain packing and primitive path (PP) network of uncrosslinked and crosslinked cis-polyisoprene (PI) polymer are analyzed upon employing coarse-grained molecular dynamics simulation. The crosslinking effect is found to enhance intra-chain packing of PI polymers, while weakening their inter-chain packing. Surprisingly, these effects cancel each other in the global packing behavior of this polymeric system. We systematically study the effects of molecular weight (MW) and crosslink density on the PP. Both the PP contour length and number of entanglements per chain, ⟨Z⟩, are found to increase linearly with MW for uncrosslinked cis-PI. The corresponding entanglement molecular length Ne of cis-PI is estimated to be 76 +/- 1, in good agreement with experimental results. The polymer end-to-end distance, the PP contour length as well as hZi of crosslinked PI are reduced by higher intrachain packing density, compared with uncrosslinked PI, if the crosslinkers are ignored in the PP analysis. At the same time, the tube diameter of crosslinked PI is enlarged by the sparse inter-chain packing. By dividing the crosslinked cis-PI chain network into subchains through crosslinked or crosslinker beads, the PP networks of these partial systems are treated as well. We obtain scaling laws between MW/crosslinking density and ⟨Z⟩ for crosslinked PI polymers. The simulation results indicate that the random walk assumption, often encountered during the analysis of PPs, can only be applied to the entanglement-dominated (low crosslink density) polymers. For crosslink-dominated (high crosslink density) polymers, whose subchains have a molecular length below 100, this assumption would imply a greatly overestimated entanglement density; we thus avoid the assumption in our analysis. To our best knowledge, this is the first work to uncover the PP of crosslinked polymers.
Article	P. Ilg, M. Kröger Molecularly derived constitutive equation for low-molecular polymer melts from thermodynamically guided simulation J. Rheol. 55 (2011) 69-93
We develop a systematic method for the derivation of closed-form and thermodynamically consistent constitutive equations of complex fluids from microscopic models. The method builds upon our recent work [Phys.~Rev.~E 79, 011802 (2009)] on thermodynamically-guided simulations within a consistent coarse-graining scheme. The method is illustrated for low-molecular polymer melts subjected to imposed, homogeneous flow fields. The differential constitutive equation we obtain for this model system is a simple, nonlinear equation of change for the conformation tensor, from which the stress tensor is readily obtained. The proposed constitutive model shows shear thinning (shear viscosity exhibiting fractional power laws in the range -0.40 to -0.86, the corresponding range for the first viscometric function is -1.20 to -1.43), stress overshoots, normal stress coefficients and elongational viscosities in agreement with reference results. The constitutive equation can be interpreted as a molecularly derived, modified Giesekus model with conformation- and rate-dependent coefficients.
Article	P. Ilg, M. Hütter, M. Kröger Ideal contribution to the macroscopic, quasiequilibrium entropy of anisotropic fluids Phys. Rev. E 83 (2011) 061713
The Landau-de Gennes free energy plays a central role in the macroscopic theory of anisotropic fluids. Here, the ideal, entropic contribution to this free energy.that is always present in these systems, irrespectively of the detailed form of interactions or applied fields.is derived within the quasiequilibrium ensemble and successfully tested. An explicit and compact form of the macroscopic, ideal entropy is derived. This entropy is nonpolynomial in the order parameter, diverging logarithmically near the fully oriented state and therefore restricting the order parameter to physical admissible values. As an application, it is shown that the isotropic-nematic transition within the Maier-Saupe model is described in a simple and very accurate manner.
Article	O. Peleg, M. Tagliazucchi, M. Kröger, Y. Rabin, I. Szleifer Morphology control of hairy nanopores ACS Nano 5 (2011) 4737-4747
The properties of polymer layers end-grafted to the inner surface of nanopores connected to solvent reservoirs are studied theoretically as a function of solvent quality and pore geometry. Our systematic study reveals that nanoconfinement is affected by both pore radius and length and that the conformations of the polymer chains strongly depend on their grafting position along the nanopore and on the quality of the solvent. In poor solvent, polymer chains can collapse to the walls, form a compact plug in the pore, or self-assemble into domains of different shape due to microphase separation. The morphology of these domains (aggregates on pore walls or stacked micelles along the pore axis) is mainly determined by the relationship between chain length and pore radius. In other cases the number of aggregates depends on pore length. The presence of reservoirs decreases confinement at pore edges due to the changes in available volume and introduces new organization strategies not available for infinite nanochannels. In good solvent conditions, chains grafted at the pore entrances stretch out of the pore, relieving the internal osmotic pressure and increasing the entropy of the polymers. Our study also addresses the experimentally relevant case of end-grafted chains on the outer walls of the membrane surrounding the nanopore. The effect of these polymer chains on the organization within the nanopore depends on solvent quality. For good solvents the outer chains increase the confinement of the chains at the entrance of the pore; however, the effect does not result in new structures. For poor solvents the presence of the outer polymer layer may lead to changes in the morphology of the microphaseseparated domains. Our results show the complex interplay between the different interactions in a confined environment and the need to develop theoretical and experimental tools for their study.
Article	M. Sadati, C. Luap, M. Kröger, H.C. Öttinger Hard vs. soft constraints in the full field reconstruction of incompressible flow kinematics from noisy scattered velocimetry data J. Rheol. 55 (2011) 1187-1203
High quality flow kinematics reconstruction from noisy and spatially scattered data requires the use of regularization techniques but remains a challenge. We set out to test the effect and practical relevance of additional incompressibility constraints. To this end, we present two methods for reconstructing smooth velocity and velocity gradient fields from such data in an incompressible two-dimensional complex flow. One is based on a generalized Tikhonov regularization combined with a finite element approximation and uses a stream function formulation, which enforces incompressibility (hard constraint). This approach is compared to that in which incompressibility is asymptotically achieved by adding a divergence penalty term in the regularization expression (soft constraint). The methods are compared on synthetic velocity data, obtained for an incompressible Oldroyd-B fluid in a cross-slot channel with added noise. For such data sets, both methods are seen to lead to essentially identical results. However, for a given grid size, the stream function formulation uses a single regularization parameter and less degrees of freedom to provide the required continuity of the gradient fields. The fidelity of the reconstruction is investigated in terms of the quality of the streamlines and velocity gradient history. Incompressibility constraints turn into significant and valuable improvement for applications as we demonstrate by analyzing the stress and optical signal fields obtained by applying a constitutive equation to the reconstructed flow fields.
Article	M. Sadati, C. Luap, M. Kröger, A.A. Gusev, H.C. Öttinger Smooth full field reconstruction of velocity and its gradients from noisy scattered velocimetry data in a cross-slot flow J. Rheol. 55 (2011) 353-377
We present a method combining generalized Tikhonov regularization with a finite element approximation for reconstructing smooth velocity and velocity gradient fields from spatially scattered and noisy velocity data in a two-dimensional complex flow domain. Synthetic velocity data for a cross-slot geometry are generated using the Oldroyd-B solution, subsequently perturbed by random noise. Performances of diverse finite element continuity-regularization criterion combinations are tested against noise-free data, while the optimum regularization parameter is determined using generalized cross-validation. The best performance is achieved for the velocity field and its gradients simultaneously by C2 continuous Hermite finite elements and minimization of a norm of the velocity's third derivative. The standard regularization criterion based on the second derivative is shown to lead to systematic distortions in boundary regions, allowing therefore a lower reduction in the statistical error. Furthermore, optical fields are calculated by applying a differential constitutive equation directly to the reconstructed flow kinematics; high quality velocity gradient fields are shown to be an essential prerequisite for their reliable prediction. Overall, the method is expedient to implement and does not require boundary conditions.
Article	L. Isa, E. Amstad, K. Schwenke, E. del Gado, P. Ilg, M. Kröger, E. Reimhult Adsorption of core-shell nanoparticles at liquid-liquid interfaces Soft Matter 7 (2011) 7663-7675
The use of nanoparticles as building blocks for the self-assembly of functional materials has been rapidly increasing in recent years. In particular, two-dimensional materials can be effectively self-assembled at liquid interfaces thanks to particle localization and mobility at the interface in combination with tailoring of specific interactions. Many recent advances have been made in the understanding of the adsorption and assembly at liquid interfaces of small hydrophobic nanoparticles, stabilized by short-chain rigid dispersants, but the corresponding studies on core-shell nanoparticles sterically stabilized by extended hydrophilic polymer brushes are presently missing. Such particles offer significant advantages in terms of fabrication of functional, responsive and bio-compatible materials. We present here a combination of experimental and numerical data together with an intuitive and simple model aimed at elucidating the mechanisms governing the adsorption of iron oxide nanparticles (5-10nm) stabilized by low molecular weight poly(ethylene glycol) (1.5-10 kDa). We show that the adsorption dynamics and the structure of the final assembly depend on the free energy of the particles at the interface and discuss the thermodynamics of the adsorption in terms of the polymer solubility in each phase.
Article	I.G. Salib, G.V. Kolmakov, B.J. Bucior, O. Peleg, T. Savin, M. Kröger, V. Vogel, K. Matyjaszewski, A.C. Balazs Using mesoscopic models to design strong and tough biomimetic polymer networks Langmuir 27 (2011) 13796-13805
Using computational modeling, we investigate the mechanical properties of polymeric materials composed of coiled chains, or globules, which encompass a folded secondary structure and are cross-linked by labile bonds to form a macroscopic network. In the presence of an applied force, the globules can unfold into linear chains and thereby dissipate energy as the network is deformed; the latter attribute can contribute to the toughness of the material. Our goal is to determine how to tailor the labile intra- and intermolecular bonds within the network to produce material exhibiting both toughness and strength. Herein, we use the lattice spring model (LSM) to simulate the globules and the cross-linked network. We also utilize our modified Hierarchical Bell model (MHBM) to simulate the rupture and reforming of N parallel bonds. By applying a tensile deformation, we demonstrate that the mechanical properties of the system are sensitive to the values of N(in) and N(out), the respective values of N for the intra- and intermolecular bonds. We find that the strength of the material is mainly controlled by the value of N(out), with the higher value of N(out) providing a stronger material. We also find that, if N(in) is smaller than N(out), the globules can unfold under the tensile load before the sample fractures and, in this manner, can increase the ductility of the sample. Our results provide effective strategies for exploiting relatively weak, labile interactions (e.g., hydrogen bonding or the thiol/disulfide exchange reaction) in both the intra- and intermolecular bonds to tailor the macroscopic performance of the materials.
Article	G.N. Toepperwein, N.C. Karayiannis, R.A. Riggleman, M. Kröger, J.J. de Pablo Influence of nanorod inclusions on structure and primitive path network of polymer nanocomposites at equilibrium and under deformation Macromolecules 44 (2011) 1034-1045
Addition of nanoparticles to polymer melts can significantly alter the mechanical properties of the resulting composite systems. Here we address the influence of nanorods on nanocomposite behavior and, in particular, on the entanglement network of the composites through extensive Monte Carlo and molecular dynamics simulations at equilibrium and under uniaxial deformation. Recently proposed topological algorithms are used to determine the primitive path network and the entanglement molecular weight of polymer-rod composites. A systematic study is presented of the effects of particle size, aspect ratio and volume fraction on their structure and entanglement state. For the primitive path analysis we consider two physical cases: the .frozen particle limit. where nanoparticles with fixed coordinates are explicitly present in the minimization process for the extraction of the primitive path network, and the .phantom particle limit. where nanoparticles are removed prior to the entanglement analysis. Simulation results indicate that the inclusion of nanoparticles into the polymer matrix does not significantly alter the polymer-polymer primitive path network. Instead, it enriches the nanocomposite system by nucleating additional topological constraints of polymer-particle origin.
Article	B. Zhang, R. Wepf, M. Kröger, A. Halperin, A.D. Schlüter Height and width of adsorbed dendronized polymers: Electron and atomic force microscopy of homologous series Macromolecules 44 (2011) 6785-6792
The width, w, and height, h, of dendronized polymers (DPs) adsorbed onto mica and highly oriented pyrolitic graphite (HOPG) were characterized by atomic force microscopy (AFM) and electron microscopy (EM). The study utilized a homologous series of generations g = 1-5, hence enabling coadsorption and characterization under identical conditions and thus facilitating comparison. The w and h values, as acquired by AFM and EM on HOPG and mica are comparable and can be collapsed onto a single master curve by a constant horizontal shift of each set of points. This master curve exhibits the scaling behavior of a cylinder and supports the visual impression that DPs adsorb as weakly deformed cylinders. The h and w curves suggest a dendron density of ρ=1.35 to 1.45 g/cm3. Density measurements of solutions of the 'attached-to monomer' suggest ρ = 1.10 g/cm3. The corresponding estimates of the maximal generation of structurally perfect DP for this family is gmax = 6 to 7 and close to the currently explored range of g = 1-5.
Article	B. Zhang, R. Wepf, K. Fischer, M. Schmidt, S. Besse, P. Lindner, B.T. King, R. Sigel, P. Schurtenberger, Y. Talmon, Y. Ding, M. Kröger, A. Halperin, A.D. Schlüter The largest synthetic structure with molecular precision: Towards a molecular object Angew. Chem. Int. Ed. 50 (2011) 737-740
Since the advent of their discipline, organic chemists have sought to imitate biology through synthesis. This challenge combines four themes: chemical structure, function, size, and molecular shape. While structure and function are better understood, size and shape remain challenging. So far, chemists have not succeeded at making well-defined molecules as large as those found in biology.the highest molecular-weight structurally precise synthetic polymer, a polystyrene, has a mass of only 40 MDa, a tiny fraction of the size of the largest DNA molecules. The control of shape in large synthetic molecules is even less advanced. This feat is routine for biology.even the simplest organisms have welldefined shapes, as exemplified by the rodlike tobacco mosaic virus (TMV). Indeed, to the chemist, the TMVis a paragon: a massive supramolecule with perfect control of chemical structure, function, size, and molecular shape. We report herein a dendronized polymer that approximates the size and cylindrical shape of the TMV, thus advancing these chemical frontiers.
Article	A. Halperin, M. Kröger Collapse of thermoresponsive brushes and the tuning of protein adsorption Macromolecules 44 (2011) 6986-7005
Protein adsorption onto brush displaying surfaces is strongly affected by collapse, an effect utilized in protein chromatography and in harvesting cell sheets for tissue engineering applications. For relatively small particles the free energy penalty incurred upon insertion into the brush Fins is related to the work expended against the osmotic pressure of the unperturbed brush. Within the self consistent field (SCF) theory of brushes, the scale of Fins decreases with the brush thickness < z >. because the value of the osmotic pressure at the grafting surface Π(0) ~ < z > irrespective of the interaction free energy. Brush collapse thus favors adsorption because it reduces Fins via two effects: (i) lowering of the osmotic pressure and (ii) a possible decrease of the inserted volume of the particle. These general results are supplemented by numerical solutions of SCF equations for the collapse of thermoresponsive Poly(N-isopropylacrylamide) (PNIPAM) brushes as described by the empirical free energy of Afroze et al. (Afroze, F.; Nies, E.; Berghmans, H. J. Mol. Struct. 2000, 554, 55). These yield the monomer concentration profiles c(z) and the corresponding osmotic pressure profiles Π(z) as functions of the altitude z and temperature T. c(z) and Π(z) are then used to characterize Fins for collapsed and swollen brushes as well as the adsorption isotherms for three adsorption mechanisms of relevance to ex vivo biotechnology applications involving PNIPAM brushes: (a) primary adsorption at the wall (b) adsorption onto a ligand embedded within the brush and (c) ternary adsorption due to weak attraction between the polymer and the adsorbing particle. Our results rationalize existing experimental results concerning the interactions between proteins and PNIPAM brushes and predict the effects of tuning parameters such as grafting density, polymerization degree and protein dimensions.
Article	A. Halperin, M. Kröger, E.B. Zhulina Colloid-brush interactions: The effect of solvent quality Macromolecules 44 (2011) 3622-3638
Solvent quality affects the interactions between neutral polymer brushes and colloids as manifested in the concentration profiles of the colloidal particles, cprt(z), and the corresponding adsorption isotherms. Lowering the solvent quality, and eventual brush collapse, reduce the osmotic pressure at height z within the brush, Π(z), and with it the associated free energy penalty of inserting a particle into the brush, Fins(z). Brush collapse thusfavors penetration into the brush and adsorption within it, an effect utilized in tissue engineering, chromatography etc. In the self consistent field theory of brushes the effect reflects both the amplitude and form of Π(z). For good, &Thetao; and poor solvents, denoted by i = g, Θ, p, the Π(z) profile is Πi(z)=Πi(0)uimi(z/Hi) where Hi is the brush height and ui =1 − z2/Hi2. The analysis utilizes the known mg =2, mΘ =3/2 as well as the derived mp =1 together with Πp(0)/Πg(0) ∼ Hp/Hg and ΠΘ(0)/Πg(0) ∼ HΘ/Hg. Fins(z) ≈ Πi(z)R3 incurred by spherical particles of radius R ≪ Hi is significant for R>Rins(i) ∼ Πi(0)-1/3 where Rins(i) scales with the grafting density σ as σ−4/9, σ−1/2 and σ−2/3, respectively. For non-adsorbing particles with R≫Rins(i) the particles penetrate the brush to a depth of δi≈ Hi(Rins(i)/R)ri with ri =3/2, 2, 3, and δg >δΘ >δp. Primary adsorption at the wall due to wall-particle contact attraction energy E is repressed when R> (E/kBT)1/3Rins(i). Ternary adsorption due to weak monomer-particle attraction is driven by a free energy scaling as ϕ(z)R2 and thus stronger in poor solvents when the monomer volume fraction ϕ(z) is higher. Accordingly the associated cprt(z) is high for particles large enough to accumulate kBT or more of attractive monomer-particle contacts but small enough to avoid large Fins(z).
Article	Y. Ding, M. Kröger Rubik cylinder model for dendronized polymers J. Comput. Theor. Nanosci. 7 (2010) 661-674
The authors introduce the semiflexible Rubik cylinder (RC) model, a toy model for investigating and illustrating the self-assembly of fibular-like macromolecules with complex internal structure. The RC model allows to reproduce basic experimental findings for dendronized polymers and serves to motivate another coarse-grained model, the less detailed Janus chain model, which has been recently introduced to capture the dynamics and superstructure formation of dendronized polymers. The RC model is solved by applying off-lattice Monte Carlo using mostly conventional moves, but also some model--adapted ones, which can be of use for other polymeric systems. This includes a so-called phonebook/-move, where parts of chains are regrown by using a memory-saving lookup-table which represents a whole chain conformation for chains of arbitrary length by a single integer, the seed value of the random number generator. Quantities characterizing the RC model will be defined and monitored and set in relation with RC conformations.
Article	S. Fransson, O. Peleg, N. Loren, A.-M. Hermansson, M. Kröger Modelling and confocal microscopy of biopolymer mixtures in confined geometries Soft Matter 6 (2010) 2713-2722
The morphology of a phase separating and gelling biopolymer mixture (gelatin.maltodextrin) is strongly affected not only by thermodynamic conditions, but also by the presence of a restricted geometry. Phase separation within droplets is analysed using confocal laser scanning microscopy and image analysis by varying concentration (4% gelatin and 4%-7.3% maltodextrin), quench temperature (10 C to 25 C) and droplet diameters (10μm-120μm). The effects of confinement as well as quench temperature increase with increasing maltodextrin concentration in 120μm sized droplets. In small droplets below 20μm, the confinement and surface dominate the microstructure. The trends observed show good agreement with predictions of the elastic Lennard.Jones (ELJ) model, adapted to handle confinement, that is solved via conventional molecular dynamics. A one.dimensional spin.chain with variable bond length is furthermore introduced and shown to capture a number of qualitative behaviors. The findings reveal that the confined biopolymer mixture can be characterized by the very few parameters of the ELJ model, which incorporates the basic mechanism of short range attraction (collapse, crystallization) versus long range elastic repulsion (osmotic penalty). Accordingly, the study suggests that the model provides a handle towards the morphological design of binary polymer mixtures in microcapsules, droplets or other geometries of well defined size and shape.
Article	P.S. Stephanou, C. Baig, G. Tsolou, V.G. Mavrantzas, M. Kröger Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model J. Chem. Phys. 132 (2010) 124904
The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static statistical properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics (MD) trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability Ψ(s,t) that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time. The computed Ψ(s,t) curves account directly for both of these phenomena, as well as for contour length fluctuations, since all of them are automatically captured in the atomistic simulations. Linear viscoelastic properties such as the zero shear rate viscosity and the spectra of storage and loss moduli obtained on the basis of the obtained Ψ(s,t) curves for three different polymer melts (polyethylene, cis-1,4-polybutadiene, and trans-1,4-polybutadiene) are consistent with experimental rheological data and in qualitative agreement with the double reptation and dual constraint models. The new methodology is general and can be routinely applied to analyze primitive path dynamics and chain reptation in atomistic trajectories (accumulated through long MD simulations) of other model polymers or polymeric systems (e.g., bidisperse, branched, grafted, etc.); it is thus believed to be particularly useful in the future in evaluating proposed tube models and developing more accurate theories for entangled systems.
Article	M. Kröger, O. Peleg, A. Halperin From dendrimers to dendronized polymers and forests: Scaling theory and its limitations Macromolecules 43 (2010) 6213-6224
A unified Flory-type theory of dendron brushes, dendrimers, dendronized polymers and forests, yields scaling rules, state diagrams and information on the collapse transition. The theory also describes the corresponding brushes of linear chains: stars, bottle brushes and planar brushes. It thus permits a detailed discussion of various tuning parameters and their effects for the different brush types. The discussion addresses the effects of solvent quality, grafting density, the persistence length and branching functionality. The theory is formulated for the case of ''identical monomers'' assuming that spacer monomers, junctions and ends are identical in shape and interactions.
Article	M. Kröger, M. Hütter Automated symbolic calculations in nonequilibrium thermodynamics Comput. Phys. Commun. 181 (2010) 2149-2157
We cast the Jacobi identity for continuous fields into a local form which eliminates the need to perform any partial integration to the expense of performing variational derivatives. This allows us to test the Jacobi identity definitely and efficiently and to provide equations between different components defining a potential Poisson bracket. We provide a simple MathematicaTM notebook which allows to perform this task conveniently, and which offers some additional functionalities of use within the framework of nonequilibrium thermodynamics: reversible equations of change for fields, and the conservation of entropy during the reversible dynamics. Accompanying software: MathematicaTM notebook PoissonBracket.nb is available from the authors or for download at the CPC library
Article	C. Baig, V.G. Mavrantzas, M. Kröger Flow effects on the melt structure and entanglement network of linear polymer melts: Results from a nonequilibrium molecular dynamics simulation study of a polyethylene melt in steady shear Macromolecules 43 (2010) 6886-6902
We present detailed results about the structural, conformational, rheo-optical, and topological properties of an entangled of C400H802 linear polyethylene (PE) melt over a wide range of shear rates (covering both the linear and the highly nonlinear viscoelastic regimes) from direct nonequilibrium molecular dynamics (NEMD) simulations of a large system containing 192 chains (corresponding to 79200 interacting atomistic units). We discuss results for (i) the probability distribution of the mean-square chain end-to-end distance and its radius of gyration, (ii) the conformation tensor, (iii) the material functions in steady shear (viscosity, normal stress differences, nonequilibrium shear compliance, hydrostatic pressure), (iv) the flow birefringence, (v) the orientation angle and order parameter, (vi) the interaction energies and their relative importance, (vii) the intermolecular pair distribution function, and (viii) the intrinsic molecular shape of the chains (represented by the isosurface plots in terms of their monomer number density), all as a function of flow strength. A detailed primitive path (PP) analysis has allowed us to examine how the flow field alters the statistical properties of the underlying topological network of the melt (probability distribution functions and mean values of PP contour length, of the number and size of entanglement strands, etc.). Our results reveal significant distortions of all these distributions due to applied flow. One of the most important results of our work is that as the shear rate is increased, the average value of the contour length goes through a maximum and the number of entanglements per chain exhibits a shear-thinning behavior which bears many similarities with the corresponding behavior of the shear viscosity. Overall, most of the computed rheological properties of the C400H802 melt change in a nonlinear way with the applied shear rate due to the simultaneous effect of (a) chain orientation and stretching, (b) chain rotation and tumbling under shear, and (c) chain disentanglement.
Article	C. Baig, P.S. Stephanou, G. Tsolou, V.G. Mavrantzas, M. Kröger Understanding dynamics in binary mixtures of entangled cis-1,4-polybutadiene melts at the level of primitive path segments by mapping atomistic simulation data onto the tube model Macromolecules 43 (2010) 8239-8250
We study dynamics in bidisperse melts of linear cis-1,4-polybutadiene composed of probe and matrix chains at the level of the segment survival probability function .(s,t) which is computed directly in the course of long atomistic molecular dynamics simulations [Stephanou et al. J. Chem. Phys. 2010, 132, 124904]. By controlling precisely the matrix chain length and composition, the effect of contour length fluctuations (CLFs) and constraint release (CR) on melt dynamics is quantified. Our study shows that (a) the values of the static topological properties of the probe chains (e.g., the average value of their primitive path (PP) contour length and its fluctuation) remain unaltered in the different matrices, but (b) their dynamical properties (including Ψ(s,t) and its average over all segments s, Ψ(t), the time autocorrelation function of the PP contour length, and the time autocorrelation function of the chain end-to-end vector) vary significantly from matrix to matrix. As the length of the matrix chains decreases, the functions Ψ(s,t) and .(t) describing the reptation relaxation of the probe chains are found to decrease more rapidly. Furthermore, the relaxation of longer probe chains is seen to be delayed as the concentration of shorter matrix chains decreases. Overall, our direct computational study proves that CR is the dominant relaxation mechanism in melts of long and short cis-1,4-polybutadiene chains accounting for the majority of differences observed in their relaxation dynamics in different environments (since CLFs appear to be unaffected by compositional differences); as a result, it has a profound effect on the linear viscoelastic properties of the melt, such as the spectra of storage and loss moduli. By further analyzing the mean-square displacement of atomistic segments in the different matrices, we find that while the tube diameter is constant in the mixtures with MS . Me where MS is the molecular weight of short chains and Me the entanglement molecular weight, it gradually increases in the mixtures with MS < Me. How the simulation results compare with laboratory measurements on melts of bidisperse polymers reported in the literature is also discussed.
Article	Y. Guo, J.D. van Beek, B. Zhang, M. Colussi, P. Walde, A. Zhang, M. Kröger, A. Halperin, A.D. Schlüter Tuning polymer thickness: Synthesis and scaling theory of homologous series of dendronized polymers J. Am. Chem. Soc. 131 (2009) 11841-11854
The thickness of dendronized polymers can be tuned by varying their generation g and the dendron functionality X. Systematic studies of this effect require (i) synthetic ability to produce large samples of high quality polymers with systematic variation of g, X and of the backbone polymerization degree N, (ii) a theoretical model relating the solvent swollen polymer diameter, r, and persistence length, λ, to g and X. This article presents an optimized synthetic method and a simple theoretical model. Our theory approach, based on the Boris-Rubinstein model of dendrimers predicts r . n1/4g1/2 and λ~n2 where n = [(X - 1)g - 1]/(X - 2) is the number of monomers in a dendron. The average monomer concentration in the branched side chains of a dendronized polymer increases with g in qualitative contrast to bottle brushes whose side chains are linear. The stepwise, attach-to, synthesis of X=3 dendronized polymers yielded gram amounts of g=1-4 polymers with N ≈ 1000 and N ≈ 7000 as compared to earlier maxima of 0.1 g amounts and of N ≈ 1000. The method can be modified to dendrons of different X. The conversion fraction at each attach-to step, as quantified by converting unreacted groups with UV labels, was 99.3% to 99.8%. Atomic force microscopy on mixed polymer samples allows to distinguish between chains of different g and suggests an apparent height difference of 0.85 nm per generation as well as an increase of persistence length with g. We suggest synthetic directions to allow confrontation with theory.
Article	Y. Ding, M. Kröger Phase behavior and formation dynamics of helically wound networks: generalized Janus chain model Macromolecules 42 (2009) 576-579
The recently proposed Janus chain (JC) model for dendronized polymers with minor modifications is able to describe the self-assembly of achiral molecules into multi.helical complexes, quaternary structures and bundles. The Janus vectors, which add vectorial degrees of freedom to a semiflexible polymer characterizing polymer chains on a classical coarse-grained level, serve to effectively capture three-body effects and induced spontaneous curvature. We report, for the first time, about phase behavior of the JC model and discuss the underlying physical mechanism. In particular, we discuss the effect of solvent quality on the dynamics and microscopic mechanisms of helical network formation. Addon material »»
Article	R.S. Hoy, K. Foteinopoulou, M. Kröger Topological analysis of polymeric melts: Chain-length effects and fast-converging estimators for entanglement length Phys. Rev. E 80 (2009) 031803
Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length Ne which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive and test new estimators which eliminate these systematic errors using information obtainable from the variation of entanglement characteristics with chain length. The new estimators produce accurate results for Ne from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.
Article	P. Ilg, H.C. Öttinger, M. Kröger Systematic time-scale-bridging molecular dynamics applied to flowing polymer melts Phys. Rev. E 79 (2009) 011802 [article also included in the Virtual J. Biol. Phys. 17:2 (2009)]
We present a novel thermodynamically guided, low-noise, time-scale bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for low-molecular polymeric systems subjected to homogeneous flow fields. We use established concepts of nonequilibrium thermodynamics and an alternating Monte-Carlo-molecular dynamics iteration scheme in order to obtain the model equations for the slow variables. For chosen flow situations of interest, the established model predicts structural as well as material functions beyond the regime of linear response. As a by-product, we present the first steady state equibiaxial simulation results for polymer melts. The method is simple to implement and allows for the calculation of time-dependent behavior through quantities readily available from the nonequilibrium steady states
Article	O. Peleg, M. Kröger, Y. Rabin Effect of network topology on phase separation in two-dimensional Lennard-Jones networks Phys. Rev. E 79 (2009) 040401(R) [article also included in the Virtual J. Biol. Phys. 17:8 (2009)]
We generate 2D Lennard-Jones networks with random topology, by preparing a perfect 4-functional network of identical harmonic springs and randomly cutting some of the springs. Using molecular dynamics simulations we find that the fraction p of active springs affects both the temperature of phase separation and the type of structures observed below this temperature, from network-like high density patterns at p>0.5 ('gel') to droplet-like structures at p<0.5 ('sol'). In the gel domain, these patterns are determined by the interplay between free energy and network topology, with the former dominant as p->1 and the latter as p->0.5. Addon material »»
Article	N.C. Karayiannis, M. Laso, M. Kröger Detailed atomistic molecular-dynamics simulations of α-conotoxin AuIB in water J. Phys. Chem. B 113 (2009) 5016-5024
We present results about the shape, size, structure, conformational stability and hydrodynamics of α-conotoxin (AuIB, a disulfide-rich peptide from the venom of Conus Aulicus, recognized as a nicotinic acetylcholine antagonist with great pharmaceutical potential) from very long (0.5 μs) massively-parallel Molecular Dynamics (MD) simulations in full atomistic detail. We extract coarse-grained descriptors of protein shape (ellipsoid), and of translational and rotational mobilities, i.e., the basic components at the lowest hierarchical level in a multiscale modeling strategy. Structural analysis reveals the folded conformation and an asymmetric shape to be strongly favored for AuIB. In accordance with experimental findings, conformational stability is observed and found to be linked to the presence of the α-helix along the 15 residues and to the existence of the two disulfide bonds. We find rotational (Dr) and translational (Dt) diffusivities to be suitable descriptors of coarse-grained dynamics, i.e. of the hydrodynamic behavior, and obtain Dr=3.62 (±0.17) × 10 s-1 and Dt = 1.08 (±0.4) × 10-10 m2s-1 from 10 ns and 100 ns MD trajectories, respectively. We further compare the MD-computed coarse-grained descriptors with first principles theoretical predictions which relate particle shape and dimensions to diffusion coefficients. The comparison strongly suggests that diffusivities of rigid biomolecules much larger than the α-conotoxin AuIB studied here can be obtained from the coarse-grained shape descriptor (ellipsoid) derived from relatively short MD simulations.
Article	N.C. Karayiannis, M. Kröger Combined molecular algorithms for the generation, equilibration and topological analysis of entangled polymers: Methodology and performance Int. J. Mol. Sci. 10 (2009) 5054-5089
We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In particular, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, and the effect of definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network which have in part been previously reported in the literature.
Article	M. Laso, N.C. Karayiannis, K. Foteinopoulou, M.L. Mansfield, M. Kröger Random packing of model polymers: local structure, topological hindrance and universal scaling Soft Matter 5 (2009) 1762-1770
While the problem of packing single hard spheres in a dense, random fashion has been extensively investigated over the past 50 years, it was only recently that the analogous problem for chains of hard spheres could be solved numerically. We highlight the relevance of these recent advances, and describe the most salient characteristics of such maximally random jammed state of hard-sphere chains, with particular emphasis on the universal character for scaling behavior. We also discuss the potentially far-reaching implications of the unexpected connection found between knots, arising from intramolecular topological hindrance, and entanglements, of intermolecular origin, regarding their dependence on volume fraction.
Article	M. Colangeli, M. Kröger, H.C. Öttinger Boltzmann equation and hydrodynamic fluctuations Phys. Rev. E 80 (2009) 051202
We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case ofMaxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.
Article	K. Foteinopoulou, N.C. Karayiannis, M. Laso, M. Kröger Structure, dimensions, and entanglement statistics of long linear polyethylene chains J. Phys. Chem. B 113 (2009) 442-455
This work elucidates the effect of both temperature and molecular length on the conformational and structural properties as well as on the entanglement statistics of long amorphous and melted linear polyethylene (PE). A large number of PE samples are modelled in atomistic detail, with average molecular lengths ranging from C24 up to C1000 over a wide range of temperatures in the interval 300K ≤ T ≤ 600K under constant pressure (P = 1 atm). Monte Carlo (MC) simulations are performed for the generation and equilibration of polydisperse PE systems characterized by a uniform distribution of molecular lengths. By employing advanced chain-connectivity altering moves, full-scale equilibration is achieved within modest computational time even for the longest molecules (C500 and C1000) at standard conditions. All equilibrated Monte Carlo trajectories are subjected to direct geometrical analysis which provides the primitive paths and intermolecular entanglements from the corresponding atomistic chains. Simulation findings regarding characteristic ratio, density and packing, as quantified through the intra- and intermolecular pair distribution functions and the static structure factor, are in excellent agreement with available experimental data. The primitive path analysis reveals the dependence of the entanglement spacing, the population of entanglements along a chain and the tube diameter on chain length and temperature. The average contour length, < Lpp >, number of entanglements, < Z >, and entanglement spacing, < Ne >, are found to exhibit a simple exponential-type of dependence on temperature. The predicted value for the plateau modulus (1.7 - 1.9 MPa) based on our simulations is in excellent agreement with experimental values.
Article	A. Halperin, M. Kröger Ternary protein adsorption onto brushes: Strong versus weak Langmuir 25 (2009) 11621-11634
Attractive interactions between proteins and polyethylene glycol (PEG) give rise to ternary adsorption within PEG brushes. Experimental evidence suggests two ternary adsorption modes: (i) Weak, due to non-specific weak attraction between PEG monomers and the surface of the protein, exemplified by serum albumin; (ii) Strong, due to strong binding of PEG segments to specific protein sites, occurring for PEG antibodies, can involve terminal adsorption of free chain ends or backbone adsorption due to binding to ''interior'' chain segments. Ternary adsorption affects the capacity of brushes to repress protein adsorption. The strong adsorption of antibodies can trigger immune response affecting the biocompatibility of the surface. Theoretical adsorption isotherms and protein concentration profiles of the three cases are compared for ''parabolic'' brushes allowing for the grafting density, 1/Σ and polymerization degree of the PEG chains, N, as well as the volume and surface area of the proteins. The amount of adsorbed protein per unit area, $\Gamma,$ exhibits a mode specific maximum in all three cases. For backbone and weak adsorption Γ~N while for terminal adsorption $Γ~N0. In every case, the concentration profile of adsorbed proteins, ctern(z), exhibits a maximum at zmax>0 that shifts outwards as Σ decreases; zmax=0 occurs only for weak and backbone adsorption at a high Σ value.
Article	A. Abedijaberi, J. Soulages, M. Kröger, B. Khomami Flow of branched polymer melts in a lubricated cross-slot channel: A combined computational and experimental study Rheol. Acta 48 (2009) 97-108
Numerical simulations have been performed to evaluate the applicability of the multimode Giesekus model in predicting the flow behavior of a rheologically well characterized low density polyethylene melt (LDPE) in a lubricated cross-slot channel. Specifically, the fidelity of the numerical results are established by detailed comparison with flow induced birefringence measurements in a new optical rheometer whose front and back viewing windows are lubricated to create an ideal two-dimensional flow kinematics that leads to the elimination of end effects commonly encountered in flow birefringence measurements. These comparisons demonstrate the ability of the multimode Giesekus model to accurately capture the flow characteristics at moderate Weissenberg numbers (Wi). However, the model predictions at large Wi are at best qualitative particularly in the vicinity of the stagnation point and the outflow channel. The inability of the simulations in predicting the stress profiles in the stagnation region is partly attributed to the inaccuracy of the experimental data resulting from multiple orders of retardation occurring within the measurement volume in these regions. Specifically, the laser beam diameter, together with lubricant reflections and data analysis issues render the current experimental protocol of limited value in characterizing the polymeric stresses in the vicinity and downstream of the stagnation point.
Article	W. Zhuang, E. Kasemi, Y. Ding, M. Kröger, A.D. Schlüter, J.P. Rabe Self-folding of charged single dendronized polymers Adv. Mater. 20 (2008) 3204-3210
Supporting Information (SI) »» This article has no abstract. Keywords: Supramolecular chemistry, dendrimers, atomic force microscopy, Janus chain model, molecular dynamics simulation, buttom-up approach, polyelectrolytes
Article	O. Peleg, M. Kröger, Y. Rabin Model of microphase separation in two-dimensional gels Macromolecules 41 (2008) 3267-3275
We have recently introduced a simple model which contains the basic features of phase separation in cross-linked polymer gels: a stretched elastic network of Lennard-Jones particles [O. Peleg et al., EPL 77 (2007) 58007]. While the original work clearly demonstrated the phenomenology of the model at a limited set of system parameters, this manuscript explores quantitative details, and gives answers to many of the questions which remained open. We define and analyze an order parameter, explore the phase diagram and identify the range of elastic constants in which microphase separation is observed, and analyze the microphase separation patterns. We discuss the microscopic origin of the formation of linear rather than globular filaments, monitor and quantify the reorganisation of the network, not only in equilibrium, but also its dynamics upon applying a shear deformation. These simulations provide us with the elastic properties, most importantly, the shear modulus, whose magnitude is shown to correlate with the order parameter.
Article	M. Kröger, O. Peleg, Y. Ding, Y. Rabin Formation of double helical and filamentous structures in models of physical and chemical gels Soft Matter 4 (2008) 18-28
This invited review highlights two recent models, one that captures physical network formation starting from the molecular architecture of its constituents and another that contains the basic features of phase separation in cross-linked polymer gels: A) the Janus chain (multibead bead-spring type) model exhibiting semiflexibility and induced curvature and B) a stretched elastic network of Lennard-Jones particles. The length scales and related structures predicted by the two generic models are different. Model B, a generic soft solid model, exhibits hysteresis and the formation of filamentous structures in two dimensions. The Janus chain model A is able to describe the process of the formation of double helical superstructures, will be operated in three dimensions, and its internal parameters are directly deduced from atomistic simulation. Both models rely on classical ingredients which have been separately studied extensively: i) the Lennard-Jones particle system, ii) the elastic solid, iii) the FENE-B model for semiflexible, finitely extendable nonlinear elastic (FENE) polymer chains. While model A combines i) and iii), model B combines i) and ii). This aspect of technical simplicity, however, is contrasted by the rich phenomenology observed for these models. The Janus model even resolves structure formation on the molecular scale. Intriguingly, the coarse dynamical models capture a wide range of known superstructures known for polymeric networks and therefore clearly serve to understand their underlying physical mechanisms.
Article	M. Kröger, A. Ammar, F. Chinesta Consistent closure schemes for statistical models of anisotropic fluids J. Non-Newtonian Fluid Mech. 149 (2008) 40-55
We propose a rational approach to approximating the various alignment tensors. It preserves the correct symmetry and leads to consistent results. For the case of uniaxial nematic fluids, the decoupling approximation for a tensor of rank l involves (l-2)/2 scalar functions Sl(S2) in terms of a scalar arguments S2, with Sl(0)=0 and Sl(1)=1. Nothing else can be concluded about the mathematical relationship between moments of the distribution function, and in particular, all consistent decoupling approximations for fourth order moment in terms of second order moments can be characterized by a single S4(S2)=0 function. We will review several decoupling approximations which appeared in the literature (linear, quadratic, natural, Hinch-Leal, Maier-Saupe, Bingham etc.) and discuss their validity. We propose using a convex shaped S4(S2) parameterized by a single scalar to characterize the decoupling approximation. Its value can be motivated by a maximum entropy argument, or determined empirically. This manuscript aims at illustrating some implications from basic symmetry considerations, proposes new and simple closures valid in the uniaxial phase, and also extends the arguments to the polar and biaxial phases and tensors of arbitrary rank.
Article	K. Foteinopoulou, N.C. Karayiannis, M. Laso, M. Kröger, M.L. Mansfield Universal scaling, entanglements, and knots of model chain molecules Phys. Rev. Lett. 101 (2008) 265702 (4 pages) article also included in the Virtual J. Quant. Info. 9:1 (2009)] [article also included in the Virtual J. Biol. Phys. 17:1 (2009)]
By identifying the maximally random jammed state of freely-jointed chains of tangent hard spheres we are able to determine the distinct scaling regimes characterizing the dependence of chain dimensions and topology on volume fraction. Calculated distributions of i) the contour length of the primitive paths, and ii) the number of entanglements per chain agree remarkably well with recent theoretical predictions in all scaling regimes. Furthermore, our simulations reveal a hitherto unsuspected connection between purely intra- (knots) and inter- (entanglements) molecular topological constraints.
Article	J.M. Kim, D.J. Keffer, M. Kröger, B.J. Edwards Rheological and entanglement characteristics of linear chain polyethylene liquids in planar Couette and planar elongational flows J. Non-Newtonian Fluid Mech. 152 (2008) 168-183
In this article, we compare and contrast the rheological and microstructural entanglement properties of a series of linear-chain polyethylene liquids under both planar Couette and planar elongational flow. We measure and compare the viscosities of the liquids in the two types of flow, and notice that both exhibit thinning behavior with increasing strain rate as the chains elongate and orient within the flow field. From the microstructural perspective, we examine the contributions of the chain energetics, such as bond-bending and bond-torsion, to the stress tensor and the degree of extension of the chains, as well as to the overall chain flexibility. Furthermore, entanglement characteristics, such as the shortest primitive path length, and the network configurations, are investigated--for the first time--as functions of strain rate in both vastly different flow fields.
Article	J. Soulages, T. Schweizer, D.C. Venerus, M. Kröger, H.C. Öttinger Lubricated cross-slot flow of a low density polyethylene melt J. Non-Newtonian Fluid Mech. 154 (2008) 52-64
Flow-induced birefringence and particle tracking velocimetry are used to investigate the lubricated flow of a low density polyethylene melt in a cross-slot geometry. The numerical predictions of the eXtended Pom-Pom model of Verbeeten et al. in its original (XPP) [J. Rheol., 45, 823 (2001); J. Rheol., 45, 1489 (2001)] and modified (mXPP) [J. Non- Newtonian Fluid Mech., 117, 73 (2004)] version as well as those of the Giesekus model [Rheol. Acta, 5, 29 (1966); J. Non-Newtonian Fluid Mech., 11, 69 (1982)] are analyzed along selected streamlines in two-dimensional (2D) complex flows involving a mixture of shear and planar extensional deformations at two Weissenberg numbers of Wi=21 and 29. Oil film light reflections perturbing the particle tracking velocimetry data analysis together with multiple orders of retardation occurring within the laser beam close to the stagnation point prevent a conclusive discrimination between the mentioned models. Although the agreement with the experimental data is mostly qualitative, the Pom-Pom model does not overestimate the data along the cross-slot symmetry lines as reported in a previous study [J. Non-Newtonian Fluid Mech., 108, 301 (2002)]. This is a clear indicator that end effects play a central role in unlubricated cross-slot geometries having a large aspect ratio.
Article	J. Soulages, T. Schweizer, D.C. Venerus, J. Hostettler, F. Mettler, M. Kröger, H.C. Öttinger Lubricated optical rheometer for the study of two-dimensional complex flows of polymer melts J. Non-Newtonian Fluid Mech. 150 (2008) 43-55
We describe a novel optical cross-slot channel rheometer whose front and back viewing windows are lubricated so that a complex two-dimensional, isothermal melt flow is created. Flow-induced birefringence and particle tracking velocimetry are reviewed and used to investigate mixed flows of shear and planar elongation of a low density polyethylene melt. The new device solves the issue of end effects in flow birefringence experiments where no variations of the optical properties along the light path are expected. It greatly facilitates the interpretation of stress field data by providing reliable measurements of the polymer melt extinction angle χ and retardation δ with a spatial resolution of one tenth of a millimeter. The rheo-optical device at the same time offers enhanced temperature control and increased optical accuracy due to an improved laser beam shaping. Capabilities and performances of this unique type of lubricated rheometer are discussed in detail and compared with previous approaches.
Article	I.V. Karlin, M. Colangeli, M. Kröger Exact linear hydrodynamics from the Boltzmann equation Phys. Rev. Lett. 100 (2008) 214503 (4 pages)
Exact (to all orders in Knudsen number) equations of linear hydrodynamics are derived from the Boltzmann kinetic equation with the Bhatnagar-Gross-Krook collision integral. The exact hydrodynamic equations are cast in a form which allows us to immediately prove their hyperbolicity, stability, and existence of an H-theorem.
Article	E. Del Gado, P. Ilg, M. Kröger, H.C. Öttinger Nonaffine deformations of inherent structure as signature of cooperativity in supercooled liquids Phys. Rev. Lett. 101 (2008) 095501 (4 pages)
We unveil the existence of non-affinely rearranging regions in the inherent structures (IS) of supercooled liquids by numerical simulations of two- and three-dimensional model glass formers subject to static shear deformations combined with local energy minimizations. In the liquid state IS, we find a broad distribution of rather large rearrangements which are correlated only over small distances. At low temperatures, the onset of the cooperative dynamics corresponds to much smaller displacements correlated over larger distances. This finding indicates the presence of nonaffinely rearranging domains of relevant size in the IS deformation, which can be seen as the static counterpart of the cooperatively rearranging regions in the dynamics. This idea provides new insight into possible structural signatures of slow cooperative dynamics of supercooled liquids and supports the connections with elastic heterogeneities found in amorphous solids.
Article	Y. Ding, H.C. Öttinger, A.D. Schlüter, M. Kröger From atomistic simulation to the dynamics, structure and helical network formation of dendronized polymers: The Janus chain model J. Chem. Phys. 127 (2007) 094904 (7 pages) [article also included in the Virtual J. Biol. Phys. Res. 14:6 (2007)]
It is the purpose of this communication to establish a buttom-up multiscale approach for dendronized polymers. Based on our understanding of the phenomenology of an atomistic model for this class of polymers we introduce a Janus Chain (JC) model, which adds a vectorial degree of freedom (Janus vector) - related to the sectorial amphiphilicity - to each segment of the linear backboneof a (classical) uncharged, semiflexible, multibead chain representation of a polymer. The JC features induced-spontaneous polymeric curvature ultimately triggering complexation. JC parameters related to the topology and chemical details are obtained from the atomistic level. Available experimental observations including the formation of superstructures and double-helical conformations are well reproduced by the JC model. JC is efficiently solved via Brownian dynamics simulation, and can be seen as a ember of a universality class which is one (two) levels above the magnetic (semiflexible) chain model. It therefore should allow to model not only dendronized polymers, but also structures belonging to the same class - exhibiting spontaneous curvature - such as single stranded DNA.
Article	S. Shanbhag, M. Kröger Primitive path networks generated by annealing and geometrical methods: Insights into differences Macromolecules 40 (2007) 2897-2903
Existing methods to obtain the primitive path network for monodisperse, linear polymers in the molten state are critically compared. A connection is established between the original ``annealing'' and newer geometrical approaches. A discrepancy of about 15% is observed in the mean primitive path length obtained by these methods for well-entangled polymers. This deviation is attributed to disentanglement that occurs during annealing. A number of well-equilibrated polymeric systems and some toy-configurations (rings) were studied to estimate the relative contributions of slip and constraint release by end-looping to the observed disentanglement. We found that about half (~ 7.7%) of the discrepancy persists for ring polymers in which end-looping is not possible, and may be attributed to slip alone. It is argued that the characteristics of the network obtained by annealing become practically equivalent to those obtained by geometrical methods in the asymptotic limit of small chain diameter and rapid quenching.
Article	O. Peleg, M. Kröger, I. Hecht, Y. Rabin Filamentous networks in phase-separating two-dimensional gels Europhys. Lett. 77 (2007) 58007 (5 pages)
We introduce a toy model that contains the basic features of microphase separation in polymer gels: a stretched elastic network of Lennard-Jones particles, studied in two dimensions. When temperature is lowered below some value T*, attraction between particles dominates over both thermal motion and elastic forces, and the network separates into dense domains of filaments connected by three-fold vertices, surrounded by low density domains in which the network is homogeneously stretched. The length of the filaments decreases and the number of domains increases with decreasing temperature. The system exhibits hysteresis characteristic of first order phase transitions: pre-formed filaments thin upon heating and eventually melt at a temperature T** (>T*). Although details may vary, the above general features are independent of network topology (square or hexagonal), system size, distribution of spring constants, and perturbations of initial conditions.
Article	M. Kröger Landmark paper index: Application to rheological (η-) journals Appl. Rheol. 17 (2007) 66494 (6 pages)
We apply the Landmark Paper Index (LPI), calculate and analyze indices for all papers published in rheological journals (`η-journals') between 1991 and 2007. We discuss the effect of formal criteria on the LPI.
Article	M. Kröger, P. Ilg Derivation of Frank-Ericksen elastic coefficients for polydomain nematics from mean-field molecular theory for anisotropic particles J. Chem. Phys. 127 (2007) 034903 (17 pages)
The complete free energy density, including all eight Frank-Ericksen elastic coefficients and all anisotropic Ericksen-Leslie viscosities of nematic and discotic polydomain nematic liquid crystals are derived from the kinetic model of a spatially inhomogeneous system of uniaxial liquid crystal molecules with given shape. We take into account the known anisotropy of the translational diffusion tensor and its dependence on shape, rotational diffusion, and a macroscopic flow field for elongated particles (including disks). In this manuscript we release all of the previously made assumptions about closure relationships or the interrelationship between Frank elastic coefficients (such as a simple quadratic closure, or the one-constant approximation) in order to derive results which not only generalize or improve earlier results, but also apply to more general cases, and for arbitrary forms of the mean-field potential in terms of the scalar order parameter (or temperature). The kinetic model is shown to confirm all proposed inequalities between Frank-Ericksen-Leslie coefficients, i.e., satisfies the main result of the macroscopic approaches. We resolve quantitatively the effect of molecular shape, order parameters, and mean-field strength and form of the mean-field potential on all results, compare with experimental findings, theoretical predictions, and discuss some implications for various special cases of the general result derived in this work.
Article	M. Colangeli, I.V. Karlin, M. Kröger Hyperbolicity of exact hydrodynamics for three-dimensional linearized Grad's equations Phys. Rev. E 76 (2007) 022201 (4 pages)
We extend a recent proof of hyperbolicity of the exact (to all orders in Knudsen number) linear hydrodynamic equations [M. Colangeli et al, Phys. Rev. E (2007)] to the three-dimensional Grad's moment system. A proof of an H-theorem is also presented.
Article	M. Colangeli, I.V. Karlin, M. Kröger From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations Phys. Rev. E 75 (2007) 051204 (10 pages)
Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a toy kinetic model - a thirteen moment Grad system.
Article	M. Kröger Landmark Paper Index: Definition and Application to Rheological (η-)Journals Appl. Rheol. 16 (2006) 329-333
We define a Landmark Paper Index (LPI), calculate and analyze indices for all papers published in rheological journals ('η-journals' between 1990 and 2006. This paper offers some information about the criteria influencing the impact of publications on the (scientific) community. In opposite to the well known Impact Factor (journal sensitive) or the number of citations (article sensitive, publication year insensitive) the LPI helps to identify established and potential breakthrough contributions by considering the number of citations per year after publication, in a way which does not overestimate the few, highly cited, articles when performing averages. We discuss the effect of formal criteria on the LPI.
Article	M. Kröger, M. Hütter Unifying kinetic approach to phoretic forces and torques for moving and rotating convex particles J. Chem. Phys. 125 (2006) 044105 (15 pages)
We derive general expressions and present several examples for the phoretic forces and torques acting on a convex tracer particle, usually a sub-microsized aerosol particle, assumed to be small compared to the mean free path of the surrounding nonequilibrium gas. Point of departure is an expression of the stress tensor in terms of half-sphere integrals to be evaluated with the inhomogeneous velocity distribution function of the surrounding gas, more specifically, its approximation in terms of a finite number of moments. A worked out example covers Grad's 13 moment approximation in and out of the so-called hydrodynamic approximation. We implement an accommodation coefficient characterizing the collision process in order to derive the tracer particle's equation of motion in a form which offers the possibility for immediate numerical implementation, and the analytical exploration of the effect of particle shape and size on phoretic drift velocity. Explicit expressions for spherical, cylindrical, ellpsoidal, cuboidal, rodlike, and oblate particles are presented, discussed and successfully compared with the rarely available, previously treated special cases, thus supporting the unifying approach presented in this manuscript.
Article	M. Kröger, M. Hütter Symbolic computation of the phoretic acceleration of convex particles suspended in a non-uniform gas Comput. Phys. Commun. 175 (2006) 650-664
A package has been developed for calculating analytic expressions for forces and torques onto an arbitrarily shaped convex tracer (aerosol) particle small compared to the mean free path of the surrounding nonequilibrium gas. The package Phoretic allows to compute analytical (and also numerical) expressions for forces and torques stemming from elastic and diffusive scattering processes parameterized by an accommodation coefficient. The method is based on calculating half sphere integral tensors of arbitrary rank and on integrating forces and torques acting on surface elements. The surrounding gas is completely specified by an arbitrarily shaped velocity distribution function. Accordingly, Phoretic requires two inputs: A particle (surface) geometry and a velocity distribution function. For example, the particle may be a cylinder with flat end caps, and the distribution function the one of Maxwell (isotropic) or Grad (13th moment approximation). The package reproduces analytic results for spheres which were available in the literature, and the ones for other geometries (cylinders, cuboids, ellipsoids) which were, however, only partially available (some works considered only elastic collisions, others temperature, or pressure, or only velocity gradients etc.). In addition, Phoretic takes into account angular velocities which have been usually neglected and become relevant for non-spherical particles. The package is geared towards the implementation of dynamical equations for aerosol particles suspended in dilute or semidilute gases and as such helps to obtain concentration profiles and mobilities of aerosol particles depending on their shape (distribution) and environmental conditions.
Article	M. Hütter, M. Kröger Phoretic forces on convex particles from kinetic theory and nonequilibrium thermodynamics J. Chem. Phys. 124 (2006) 044511 (13 pages)
In this article we derive the phoretic forces acting on a tracer particle, which is assumed to be small compared to the mean free path of the surrounding nonequilibrium gas, i.e., usually a nanoparticle << 100 nm. First, we review and extend the calculations of Waldmann [L. Waldmann, Z. Naturforsch. 14a, 589 (1959)] using half sphere integrations and an accommodation coefficient characterizing the collision process. The presented methodology is applied to a gas subject to temperature, pressure and velocity gradients. Corresponding thermophoretic, barophoretic and rheophoretic forces are derived, and explicit expressions for spherical particles are compared to known results. Second, nonequilibrium thermodynamics is used to join the diffusion equation for the tracer particle with the continuum equations of nonisothermal hydrodynamics of the solvent. So doing, the distinct origin of the thermophoretic and barophoretic force is demonstrated. While the latter enters similarly to an interaction potential, the former is given by flux-flux correlations in terms of a Green-Kubo relation, as shown in detail.
Article	M. Ellero, M. Kröger, S. Hess Multiscale modeling of viscoelastic materials containing rigid nonrotating inclusions Multiscale Model. Simul. 5 (2006) 759-785
We introduce and apply a simulation method for the investigation of sheared viscoelastic materials containing rigid non-rotating cylindrical inclusions. The method is based on a classical Smoothed Particle Hydrodynamics (SPH) algorithm, modified for viscoelastic flows. The modified SPH incorporates a constitutive equation for the stress tensor (actually based on the corotational Jaumann-Maxwell model). This algorithm had been tested by Ellero et al. [J. Non-Newtonian Fluid Mech. 105, 35 (2002)] for transient flows in a channel geometry. In the present article, a bulk composite material subjected to steady shear is simulated in the case of a Newtonian solvent. For this example, we observe the expected linear increase of the macroscopic effective viscosity vs. the volume fraction ρ_v of the inclusions. Up to small values of ρ_v, excellent agreement with theoretical results for non-rotating inclusions is obtained. The effective shear viscosity increases linearly with ρ_v with a proportionality factor of about 3. This result differs from the two dimensional Einstein-like relation for a dilute suspension of freely-rotating cylinders, [Ann. d. Physik. 19, 289 (1906)], where a factor 2 is prescribed, and it is associated to the effect of an external applied torque. For larger values of the volume ratio, also the expected non-linear increase is observed indicating that interactions between inclusions become relevant. As a second example, a suspension of inclusions in a viscoelastic matrix is simulated showing an effective increase of the viscometric functions over all the range of Deborah number considered. The results indicate that the macroscopic rheology of the composite is determined by the constitutive equation governing the matrix only, but characterised by ρ_v-dependent effective material functions. Finally, a detailed analysis of the hydrodynamics field within the viscoelastic matrix is presented.
Article	K. Foteinopoulou, N.C. Karayiannis, V.G. Mavrantzas, M. Kröger Primitive path identification and entanglement statistics in polymer melts: Results from direct topological analysis on atomistic polyethylene models Macromolecules 39 (2006) 4207-4216
A large number of well equilibrated atomistic configurations of linear, strictly monodisperse polyethylene (PE) melts of molecular length ranging from C24 up to C1000, obtained through extensive Monte Carlo simulations built around chain-connectivity altering algorithms, have been subjected to a detailed topological analysis. Primitive paths are geometrically constructed connecting the two ends of a polymer chain (which in all cases are considered as fixed in space) under the constraint of no chain crossability, such that the multiple disconnected (coarse-grained) path has minimum contour length. When applied on a given, dense polymer configuration in 3-D space, the algorithm returns the primitive path (PP) and the related number and positions of entanglements (kinks) for all chains in the simulation box thus providing extremely useful information for the topological structure (the primitive path network) hidden in bulk PE. In particular, our analysis demonstrates that once a characteristic chain length value (around C174) is exceeded, the entanglement molecular length for PE at T = 450 K reaches a plateau value, characteristic of the entangled polymeric behavior. We further validate recent analytical predictions [Schieber, J. Chem. Phys. 118 (2003) 5162] about the shape of the distribution for the number of strands in a chain at equilibrium. At the same time, we show that the number of entanglements obtained by assuming random walk statistics [Everaers et al., Science 303 (2004) 823] deviates significantly from these predictions which we regard as a clear evidence that by directly counting the entanglements and their distribution functions, as proposed here, offers advantages for a quantitative analysis of the statistical na Selected raw data for erratum (full data available upon request): Z1revised_All_Lpp_for_various_N.zip (posted 25 Aug 2007)
Article	P. Ilg, M. Kröger Anisotropic self-diffusion in ferrofluids studied via Brownian dynamics simulation Phys. Rev. E 72 (2005) 031504 (7 pages)
The anisotropic self-diffusion in ferrofluids in the presence of a magnetic field is studied by Brownian dynamics simulations. It is found that the diffusion parallel to the magnetic field is hindered when compared to the case without field. Depending on the strength of dipolar interactions, the diffusion perpendicular to the applied field is either enhanced or hindered due to the field. The average diffusion coefficient is found to decrease with increasing concentration and dipolar interaction strength, but to be independent of the magnetic field strength for moderate dipolar interactions. Comparison to mean-field models show agreement for moderate dipolar interaction strengths but significant deviations in the regime of strong dipolar interactions.
Article	P. Ilg, M. Kröger, S. Hess Magnetoviscosity of semidilute ferrofluids and the role of dipolar interactions: Comparison of molecular simulation and dynamical mean-field theory Phys. Rev. E 71 (2005) 031205 (11 pages)
Extensive molecular simulations on a model ferrofluid are performed in order to study magnetoviscous and viscoelastic phenomena in semi-dilute ferrofluids. Simulation results of the nonequilibrium magnetization, shear viscosity and normal stress differences are presented. Rotational and configurational contributions to the shear viscosity are analyzed and their influence on the magnetoviscous effect is discussed. The simplified model of non-interacting magnetic dipoles describes the nonequilibrium magnetization and the rotational viscosity, but does not account for configurational viscosity contributions and normal stress differences. Improved mean-field models that overcome these limitations show good agreement with the simulation results for weak dipolar interactions where the models should apply. Comparisons to simulation results for various interaction strengths allows to determine the range of validity of the mean-field models.
Article	P. Ilg, M. Kröger, S. Hess Anisotropy of the magnetoviscous effect in ferrofluids Phys. Rev. E 71 (2005) 051201 (6 pages)
The anisotropy of the magnetoviscous effect in ferrofluids subjected to planar Couette flow is investigated by extensive molecular simulations. The field- and concentration dependence of the viscosity coefficients are found to depend on the relative orientation of the magnetic field with respect to the flow geometry. Comparison with dynamical mean-field models shows satisfactory agreement for moderate interaction strengths. In the semi-dilute regime it is found that the anisotropy contains valuable information on particle interaction.
Article	P. Ilg, M. Kröger, S. Hess Structure and rheology of model-ferrofluids under shear flow J. Magnetism Magn. Mater. 289 (2005) 325-327
Nonequilibrium simulations of ferromagnetic colloids in the presence of a magnetic field and plane shear flow are performed. Results for the nonequilibrium magnetization and the nonequilibrium structure factor are presented. We observe that the nonequilibrium magnetization and the magnetoviscosity are enhanced due to dipolar interactions. Structure formation due to magnetic field and shear flow are observed in qualitative agreement with experimental results.
Article	M. Kröger Shortest multiple disconnected path for the analysis of entanglements in two- and three-dimensional polymeric systems Comput. Phys. Commun. 168 (2005) 209-232
We present an algorithm which returns a number of entanglements for a given configuration of a polymeric system in 2 or 3 dimensions. Rubinstein and Helfand, and later Everaers et al. introduced a concept to extract primitive paths for dense polymeric melts made of linear chains (a multiple disconnected path), where each primitive path is defined as a path connecting the (space-fixed) ends of a polymer under the constraint of excluded volume between primitive paths of different chains, such that the multiple disconnected path fulfills a minimization criterion. The present algorithm uses geometrical operations and does not only provide a -- model independent -- efficient approximate solution to this hard problem, but releases several shortcomings of alternate approaches. In particular, primitive paths are treated as 'infinitely' thin (optionally: thick), and tensionless lines rather than multibead chains, excluded volume is taken into account without a force law. The present implementation allows to construct a shortest multiple disconnected path (SP) for 2D systems (polymeric chain within spherical obstacles) and an optimal SP for 3D systems (collection of polymeric chains). The number of entanglements is then simply obtained from the SP as either the number of kinks, or from the average length of a line segment. Further, information about structure (and potentially also the dynamics) of entanglements is immediatly available from the SP.
Article	M. Kröger Publication specific impact of articles published by rheological journals Appl. Rheol. 15 (2005) 406-409
The Impact Factor of a journal is a quantitative way of assessing its worth and relevance to the academic community it serves. Many librarians see the ratio between Impact Factor and price as a suitable yardstick by which to measure the value of their collections. In addition, the research assessment exercises which, in many countries, are now being carried out on a more formal basis mean that authors submitting original research must publish it in a journal with the highest perceived worth possible in order to secure future funding, job promotions and peer recognition. It has been suspected [T. Opthof, Cardiovasc. Res. 33 (1997) 1; J. Stegmann, Nature 390 (1990) 550], however, that a particular author's impact is not much related to the journals in which her/he publishes. As will be demonstrated in this letter, the impact of articles published in rheological journals is largely influenced by criteria such as length of article, number of authors, number of cited references.
Article	M. Kröger, E. De.Angelis An extended FENE dumbbell model theory for concentration dependent shear-induced anisotropy in dilute polymer solutions: addenda J. Non-Newtonian Fluid Mech. 125 (2005) 87-90
Schneggenburger et al. [J. Non-Newtonian Fluid Mech. 62 (1996) 235-251] extended the original FENE dumbbell kinetic theory to describe concentration dependent shear-induced anisotropy in dilute polymer solutions by a mean-field approach. Besides providing an errata to the above mentioned paper and two revised figures we present related analytic results for steady shear and uniaxial elongational flow. Within the same framework we further consider a modified FENE potential and briefly discuss its implications.
Article	S. Hess, M. Kröger Regular and chaotic orientational and rheological behaviour of liquid crystals J. Phys.: Condens. Mat. 16 (2004) S3835-S3859
The dynamic behavior of the molecular alignment strongly affects the rheological properties of nematic liquid crystals. The closed nonlinear inhomogeneous relaxation equation for the five components of the alignment tensor which was derived within the framework of irreversible thermodynamics and also inferred from a generalized Fokker-Planck equation, led to to the prediction (G. Rienäcker, M. Kröger, and S. Hess, Phys. Rev. E 66, 040702(R) (2002); Physica A 315, 537 (2002)) that the rather complex orientational behavior of tumbling nematics can even be chaotic in a certain range of the relevant control variables. Here the rheological consequences, in particular the shear stress and the normal stress differences, as well as the underlying dynamics of the alignment tensor are computed and discussed. For selected state points, long-time averages are evaluated for imposed shear rates. Orientational and rheological properties are presented. The transitions between different dynamic states are detected and discussed. Representative examples of alignment orbits and rheological phase portraits give insight into the dynamic behavior.
Article	M. Kröger, H.C. Öttinger Beyond-equilibrium molecular dynamics of a rarefied gas subjected to shear flow J. Non-Newtonian Fluid Mech. 120 (2004) 175-187
We present a simulation strategy, beyond-equilibrium molecular dynamics (BEMD), which demonstrates the application of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) and the calculation of the friction matrix. The method is based on - and restricted to - the regime, where a generalized canonical ensemble provides a sufficiently rigorous description in terms of microscopic expressions for nonequilibrium variables. Multiplostatted equations of motion (Nosé-Hoover variants of Hamilton's classical equations) are employed to maintain this ensemble. The friction matrix appearing in the dynamical equation is iteratively obtained employing a Green-Kubo type expression. Since the remaining `building blocks' for the GENERIC equation are readily accessible via static Monte Carlo simulation (for the present application they are available analytically), BEMD provides the desired information to perform multiscale simulations. We demonstrate the efficiency of BEMD for the calculation of rheological properties of a rarefied gas in the weak shear flow regime and discuss its limitations. Here, our choice of variables is inspired by Grad's moment method for gases.
Article	M. Kröger Simple models for complex nonequilibrium fluids Phys. Rep. 390 (2004) 453-551
This review is concerned with the nonequilibrium dynamics and structure of complex fluids based on simple micro- and mesoscopic physical models which are not rigorously solvable by analytic methods. Special emphasis is placed on the finitely extendable nonlinear elastic (FENE) chain models which account for molecular stretch, bending, and topology. More coarse-grained descriptions such as primitive path models, and elongated particle models are reviewed as well. We focus on their inherently anisotropic material - in particular rheological - properties via deterministic and stochastic approaches. A number of representative examples are given on how simple (often high-dimensional) models can, and have been implemented in order to enable the analysis of the microscopic origins of the nonlinear viscoelastic behavior of polymeric materials. These examples are shown to provide us with a number of routes for developing and establishing coarse-grained (low-dimensional) models devoted to the prediction of a reduced number of significant material properties. At this stage approximations which allow for an analytical treatment are discussed as well. Concerning the types of complex fluids, we cover the range from flexible to semiflexible polymers in melts and solutions, wormlike micelles, actin filaments, structural suspensions including ferrofluids in field-induced anisotropic or liquid crystalline phases. Simple models for complex nonequilibrium fluids . Review article Physics Reports, Volume 390, Issue 6, 1 February 2004, Pages 453-551 Kroger, M.
Article	M. Ellero, M. Kröger The hybrid BDDFS method: memory saving approach for CONNFFESSIT-type simulations J. Non-Newtonian Fluid Mech. 122 (2004) 147-158
In this manuscript we propose and test a strategy `Brownian Dynamics and Distribution Function Storing' (BDDFS) for performing numerical calculations of viscoelastic complex flows based on the unapproximated CONNFFESSIT-type approach. Hardware limits this established approach for the `Calculation Of Non-Newtonian Flows using Finite Elements and Stochastic Simulation Techniques' for highly complex flows due to fluctuations which come together with the stochastic determination of the macroscopic extra stress tensor. As soon as the number of cells in the flow domain becomes large an even much larger number of freedom degrees must be used to extract accurate results. Usually, variance reduction techniques are used to suppress noise, lower the memory requirements, produce correlated dynamics, and obtain approximate, and `good' results. BDDFS is a numerical method for the still approximate, but `uncorrelated' solution of the same problem with limited memory needs. It relies on a discrete storage of the configurational distribution function (D-CDF) for dumbbells, or polymers. Configurational variables subject to standard BD are sampled consistently with the D-CDF. Compared with the original approach, the memory requirement is reduced by the ratio between the number of D-CDF grid points and the number of molecules. The hybrid method has similarities with both spectral methods and BD, but remains conceptually simple and computationally feasible also for short chains. The strategy has yet been tested against a homogeneous shear flow of dumbbells where the advantages should be reduced to a minimum. Results reveal that the BDDFS concept may offer advantages upon alternative approaches which must become larger with the complexity of the system under study and whenever molecular correlations on length scales larger than the grid size contain information relevant to interpret experiments.
Article	J.G. Hernández Cifre, S. Hess, M. Kröger Linear viscoelastic behavior of unentangled polymer melts via nonequilibrium molecular dynamics Macromol. Theory Simul. 13 (2004) 748-753
In this brief report we present and assess the use of nonequilibrium molecular dynamics simulation method for the direct study of the linear viscoelastic behavior of polymer melts. The melt is modeled by a collection of repulsive, anharmonic multibead chains and subjected to small amplitude oscillatory shear flow. We present results for chain lengths below the critical entanglement length and obtain good agreement with theoretical results for the viscoelastic behavior of melts of low molecular weight. The range of oscillation frequencies attainable in the simulation is of a few decades. Thus we use, as in experiments, the time-temperature superposition principle to extend the frequency domain.
Article	I. Stankovic, S. Hess, M. Kröger Microscopic structure, dynamics and wear at metal-metal interfaces in sliding contact Phys. Rev. E 70 (2004) 066139 (14 pages)
The ``generic embedded atom model (GEAM) has been investigated^M recently [Phys. Rev. E {\bf 69}, 021509 (2004)] to analyze the^M qualitative equilibrium and nonequilibrium properties of bulk^M metals in both undeformed and shear deformed states. In the^M present work, a natural extension of the GEAM is proposed and^M applied to characterize the microscopic structure, dynamics and^M wear at clean commensurate metal$_A$-metal$_A$ and^M metal$_A$-metal$_B$ sliding interfaces. Non-equilibrium molecular^M dynamics simulation, used as a GEAM solver, reveals that the^M dynamics of dislocations, crystalline domains, and related flow^M behaviors (stress tensor, shear moduli) are coupled. The rotation^M of crystal domains is detected to trigger material mixing at the^M interface in early stages of sliding. Further, we study the^M dependence of structural changes in inhomogeneous metal interfaces^M on the relevant model parameters. A relation is established^M between shear moduli, effective shear rate and shear stress across^M the interface.
Article	I. Stankovic, M. Kröger, S. Hess Structural changes and viscoplastic behavior of a generic embedded atom model metal in steady shear flow Phys. Rev. E 69 (2004) 021509 (15 pages)
We study equilibrium and nonequilibrium properties of a simple generic embedded atom model (GEAM) for metals. The model allows to derive simple analytical expressions for several zero-temperature constitutive properties - in overall agreement with real metals. The model metal is then subjected to shear deformation and strong flow via nonequilibrium molecular dynamics simulation in order to discuss the origins of some qualitative properties observed using more specific embedded atom potentials. The common neighbor analysis, based on planar graphs is used to obtain information about the transient structures accompanying viscoplastic behavior on an atomic level. In particular, pressure tensor components and plastic yield are investigated and correlated with underlying structural changes. A simple analytical expression for the isotropic pressure at finite temperatures is proposed. A nonequilibrium phase diagram is obtained by semianalytic calculation.
Article	B. Bandow, M. Kröger, S. Hess Pressure, dynamics, and structure of a simple particle system confined in a soft nanopore Physica A 337 (2004) 443-469
The formation and dynamics of long living metastable structures, the pressure tensor and diffusion properties of a simple particle system confined by a (infinite) nanopore with rectangular cross section is investigated using molecular dynamics simulation. The system is characterized by a short range and radially symmetric interparticle (SHRAT, Lennard-Jones type) potential between mass points. The lateral confinement is considered as soft, repulsive, and unstructured. Periodic images are used in the longitudinal direction. Spontaneous condensation is observed as well as merging of patterns induced by the confinement. Structures, pressure, and diffusion coefficient are found depending on both the pore's lateral aspect ratio and its absolute width, temperature and density. Theoretical expectations are rarely available but tested against the simulation results under appropriate conditions.
Article	V.A. Harmandaris, V.G. Mavrantzas, D.N. Theodorou, M. Kröger, J. Ramírez, H.C. Öttinger, D. Vlassopoulos Crossover from the Rouse to the entangled polymer melt regime: Signals from long, detailed atomistic molecular dynamics simulations, supported by rheological experiments Macromolecules 36 (2003) 1376-1387
Results are presented from 300 ns long atomistic molecular dynamics (MD) simulations of polyethylene (PE) melts, ranging in molecular length from C78 to C250. Above C156, the self-diffusion coefficient D is seen to exhibit a clear change in its power-law dependence on the molecular weight (M), significantly deviating from a Rouse (where D ~ M^(-1) ) toward a reptation-like (where D ~ M^(-2.4) ) behavior. The mean- square displacement (msd) of chain segments and the dynamic structure factor is also calculated and the crossover from the Rouse to entangled behavior is again observed above C156. A novel strategy is also developed for projecting atomistic chain configurations to their primitive paths and thereby mapping simulation trajectories onto the reptation model. Results for the friction factor, the zero-shear rate viscosity and the self-diffusion coefficient are found to be internally consistent and in agreement with experimental rheological data.
Article	T. Erdmann, M. Kröger, S. Hess Phase behavior and structure of Janus fluids Phys. Rev. E 67 (2003) 041209 (17 pages)
The equilibrium phase behavior of Janus fluids is examined based on a model potential for the interaction between their constituents. Janus fluids consist of axisymmetric particles possessing to different `faces', e.g. one hydrophobic and one hydrophilic surface, and the interaction depends on the relative orientation. Starting from a short range, isotropic potential we make an ansatz for an anisotropic model interaction potential. The Helmholtz free energy and the pressure are calculated by the help of an augmented van der Waals approximation. A qualitative phase diagram is obtained. The appearance of a polar phase and the corresponding transition temperature are examined adapting a Landau de Gennes expansion of the orientational part of the free energy. Monte Carlo simulations are performed to test the approximation involved in the analytical description.
Article	S. Hess, M. Kröger, D.J. Evans Crossover between short- and long-time behavior of stress fluctuations and viscoelasticity of liquids Phys. Rev. E 67 (2003) 042201 (4 pages)
An effective viscosity coefficient is introduced based on definite time averages of equilibrium stress fluctuations rather than stress correlations. Analysis of this quantity via molecular dynamics of a simple model liquid reveals a crossover between the expected short-time elastic and the long-time viscous behavior with increasing averaging time. The procedure allows us to extract the zero-rate shear viscosity when the averaging time becomes one order of magnitude larger than the relevant relaxation time. A relationship between this effective viscosity and the dynamic viscosities is established.
Article	P. Ilg, M. Kröger, S. Hess, A.Y. Zubarev Dynamics of colloidal suspensions of ferromagnetic particles in plane Couette flow: Comparison of approximate solutions with Brownian dynamics simulations Phys. Rev. E 67 (2003) 061401 (8 pages)
The stationary and oscillatory properties of dilute ferromagnetic colloidal suspensions in plane Couette flow are studied. Analytical expressions for the off-equilibrium magnetization and the shear viscosity are obtained within the so-called effective field approximation. We also investigate the predictions of a different approximation based on the linearized moment expansion. Direct numerical simulation of the kinetic model are performed in order to test the range of validity of these approximations.
Article	P. Ilg, M. Kröger, S. Hess Magnetization dynamics from kinetic theory of ferromagnetic units in dilute suspension Magnetohydrodyn. 39 (2003) 41-48
The derivation of the magnetization dynamics from a kinetic model of a dilute suspension of ferromagnetic ellipsoidal units is presented. The derivation is based on the effective field approximation, where canonical distribution functions are used in order to obtain closed equations for the macroscopic variables. The range of validity and efficiency of the dynamical equation for the magnetization is estimated by comparison with Brownian dynamics simulations of the underlying kinetic model for several flow conditions. Comparisons with recent experimental results are made.
Article	P. Ilg, M. Kröger Magnetization dynamics, rheology, and an effective description of ferromagnetic units in dilute suspension (vol 66, art no 021501, 2002) Phys. Rev. E 67 (2003) 049901
Erratum for this article.
Article	P. Ilg, I.V. Karlin, M. Kröger, H.C. Öttinger Canonical distribution functions in polymer dynamics: II Liquid-crystalline polymers Physica A 319 (2003) 134-150
The quasi-equilibrium approximation is employed as a systematic tool for solving the problem of deriving constitutive equations from kinetic models of liquid-crystalline polymers. It is demonstrated how kinetic models of liquid-crystalline polymers can be approximated in a systematic way, how canonical distribution functions can be derived from the maximum entropy principle and how constitutive equations are derived therefrom. The numerical implementation of the constitutive equations based on the intrinsic dual structure of the quasi-equilibrium manifold thus derived is developed and illustrated for particular examples. Finally, a measure of the accuracy of the quasi-equilibrium approximation is proposed that can be implemented into the numerical integration of the constitutive equation.
Article	M. Kröger, P. Ilg, S. Hess Magnetoviscous model fluids J. Phys.: Condens. Mat. 15 (2003) S1403-S1423
We review, apply and compare diverse approaches to the theoretical understanding of the dynamical and rheological behavior of ferrofluids and magnetorheological (MR) fluids subject to external magnetic and flow fields. Simple models are introduced which are directly solvable by nonequilibrium Brownian or molecular dynamics computer simulation. Particularly, the numerical results for ferrofluids quantify the domain of validity of uniaxial alignment of magnetic moments (in and) out of equilibrium. A Fokker-Planck equation for the dynamics of the magnetic moments - corresponding to the Brownian dynamics approach - and its implications are analyzed under this approximation. The basic approach considers the effect of external fields on the dynamics of ellipsoidal shaped permanent ferromagnetic domains (aggregates), whose size should depend on the strength of flow and magnetic field, the magnetic interaction parameter, and concentration (or packing fraction). Results from analytic calculations and from simulation are summarized for the anisotropy of the viscosity. In order to study the effect of flow on the anisotropic viscosities and shear-induced structures of MR fluids and ferrofluids subject to a strong external magnetic field, a simple model of perfectly oriented particles is considered.
Article	M. Kröger, M. Müller, J. Nievergelt A geometric embedding algorithm for efficiently generating semiflexible chains in the molten state CMES - Comput. Model. Eng. Sci. 4 (2003) 559-570
We present a novel method for generating starting polymer structures for molecular simulations in the dense phase. The work describes the ingredients of an algorithm for the creation of large, dense or diluted amorphous polymeric systems close to equilibrium and provides measures for its quality. The model systems are made of semiflexible (wormlike) repulsive multibead chains. The key feature of the method is its efficiency, in particular for large systems, while approaching given local and global chain characteristics. Its output has been proven to serve as an excellent basis for subsequent off-lattice molecular dynamics computer simulation. By combining chain growing with an iterative relaxation technique we remove overlaps of monomers. The computing time is linear in the number of beads and independent of chain length. The method succeeds in generating large and dense (bulky and confined) systems of up to 100,000 beads in less than an hour on todays workstations.
Article	M. Kröger, I. Stankovic, S. Hess Towards multiscale modeling of metals via embedded particle computer simulation Multiscale Model. Simul. 1 (2003) 25-39
The embedded atom method is adapted to study solid friction and the mechanical behavior of a model metal which incorporates the effect of electronic glue in its structure. The elastic properties of real metals are reproduced by a set of basic model potentials as revealed by analytic considerations. A slightly modified version of a classical NonEquilibrium Molecular Dynamics (NEMD) computer simulation is employed to study the dynamics and structural changes of the model metal undergoing a process of solid friction and an uniaxial compression, in order to analyze, e.g. plastic yield, transient friction coefficients, and the underlying structure. Under appropriate choice of parameters, the model turns out to be also applicable to study multiscale structures in porous metals.
Article	M. Kröger Modeling of metals and metal sponges via embedded particle computer simulation Adv. Solid State Phys. 43 (2003) 617-631
In this article we review the embedded atom method when adapted to study solid friction and the mechanical behavior of model metals.The method incorporates the e ect of electronic glue through e ective many-body potentials. The elastic properties of real metals are reproduced by a set of basic model poten- tials as revealed by analytic considerations.A slightly modi ed version of appropri- ate choice of parameters,the model is also applicable to study porous metals.
Article	S. Hess, M. Kröger Elastic and plastic behavior of model solids Techn. Mech. 22 (2002) 79-88
A short ranged attractive (SHRAT) potential is employed here which is of the type of the effective two-particle interaction used in a variant of the 'embedded atom' method for metals. Properties of the (pure) SHRAT model system in its gaseous, (metastable) liquid, and solid states have been computed earlier by molecular dynamics and, where possible, successfully compared with analytical calculations, as well as with the behavior of real substances. After some remarks on scaling and reference values, elastic properties of the model metal are characterized by the bulk and shear moduli, and their corresponding Born-Green and fluctuation contributions. It is demonstrated that plastic flow implies significant structural changes, being reflected by the Born--Green contribution to the cubic shear modulus. Not only stick-slip behavior, but the detailed elastic response and plastic flow of the model solid is analyzed. In order to interpret and reproduce the simulated rheological quantities, a simple, but generalized Maxwell model is tested. Its tensorial generalization may be used in simulation schemes such as smoothed particle dynamics, which are applicable on length and time scales significantly larger than those accessible in molecular dynamics simulations.
Article	P. Ilg, M. Kröger, S. Hess Magnetoviscosity and orientational order parameters of dilute ferrofluids J. Chem. Phys. 116 (2002) 9078-9088
The linear and nonlinear rheological behavior of dilute ferrofluids is determined from an underlying kinetic model and the dependence of the viscosity coefficient on the scalar orientational order parameters is obtained. In case of uniaxial symmetry, the antisymmetric contribution to the hydrodynamic stress tensor is of the same form as in the classical Ericksen-Leslie theory of uniaxial nematic liquid crystals and the linear magnetoviscosity is found to coincide with earlier results obtained by the so-called effective field method. While the assumption of uniaxial symmetry is fulfilled exactly in the limit of strong vorticity and weak magnetic field, the exact result for the linear magnetoviscosity shows corrections due to contributions from biaxial symmetry. Measures for the deviations from uniaxial symmetry are introduced and the generalization of the stress tensor in case of biaxial symmetry is obtained. The investigations are accompanied by numerical simulation of the kinetic equation and reveal that the assumption of uniaxial symmetry seems to be a good approximation for most values of the magnetic field and vorticity.
Article	P. Ilg, M. Kröger Magnetization dynamics, rheology, and an effective description of ferromagnetic units in dilute suspension Phys. Rev. E 66 (2002) 021501 (16 pages)
The rheological properties of a dilute suspension of ellipsoidal ferromagnetic particles in the presence of a magnetic field are studied on the basis of a kinetic model, where the flow and magnetic external fields couple in qualitatively different ways to the orientational behavior of the ferrofluid. In the uniaxial phase the stress tensor is found to be of the same form as in the Ericksen-Leslie theory for nematic liquid crystals in the steady state. Expressions for a complete set of viscosity coefficients in terms of orientational order parameters are worked out. In the low Peclet number regime, the viscosity coefficients are given as explicit functions of the magnetic field and a particle shape factor, where the shape factor may equally represent a non-spherical unit (agglomerate, chain) composed of spherical particles. Further, by considering the magnetization as the only relevant variable, a magnetization equation within an effective field approach is derived from the kinetic equation and compared to existing magnetization equations. The alignment angle of the magnetization and the first and second normal stress coefficient are studied for the special case of plane Couette flow. The assumptions employed are tested against a Brownian dynamics simulation of the full kinetic model, and a few comparisons with experimental data are made. Corrigenda: Equation 28: replace 3/35 by 1/35 Equation 29: replace 16/35 by 8/7
Article	M. Kröger, J. Ramirez, H.C. Öttinger Projection from an atomistic chain contour to its primitive path Polymer 43 (2002) 477-487
In this note we propose a mapping from the spatial coordinates of an atomistic polymer chain to its `primitive path' (PP), a concept being frequently used in the framework of reptation models. For the model to be presented, the projection preserves as much structure of the atomistic chain as appropriate to replace an atomistic chain on a prescribed (parameterized) coarse-grained level. We present an efficient numerical method to extract a PP as well as an analytic approach to study the conformational properties of the coarse-grained chain in an approximate fashion. The knowledge of the PP is a prerequisite to facilitate tests of mesoscopic descriptions of polymeric fluids, in particular in the framework of nonequilibrium thermodynamics, and allows for a thorough analysis of atomistic chain configurations on a `relevant' coarse-grained level.
Article	M. Ellero, M. Kröger, S. Hess Viscoelastic flows studied by Smoothed Particle Dynamics J. Non-Newtonian Fluid Mech. 105 (2002) 35-51
A viscoelastic numerical scheme based on Smoothed Particle Dynamics is presented. The concept goes a step beyond Smoothed Particle Hydrodynamics (SPH) which is a grid free Lagrangian method describing the flow by fluid-pseudo particles. The relevant properties are interpolated directly on the resulting movable grid. In this work the effect of viscoelasticity is incorporated into the ordinary conservation laws by a differential constitutive equation supply for the stress tensor. In order to give confidence in the methodology we explicitly consider the non-stationary simple corotational Maxwell model in a channel geometry. Without further developments the scheme is applicable to `realistic' models relevant for three-dimensional viscoelastic (viscoplastic, etc.) flows in complex geometries.
Article	I. Stankovic, M. Kröger, S. Hess Recognition and analysis of local structure in polycrystalline configurations Comput. Phys. Commun. 145 (2002) 371-384
A method is described for obtaining information about the local order existing in monoatomar model solids or real materials based on their atomistic configurations. An algorithmic implementation is provided. The shape of the polyhedra formed by `relevant' neighbors of each atom enter a pattern recognition method to resolve the type of the (usually non-ideal) crystal structure to which atoms surrounded by their relevant neighbors belong: hexagonal close-packed, face-centered cubic or body-centered cubic. Further, this approach allows for the analysis of amorphous solids (icosahedral structure). Results of a molecular dynamics computer simulation illustrate how this method can be applied to contribute to an understanding of the mechanical and structural properties of solids i) undergoing a steady shear stress and ii) upon increasing temperature.
Article	G. Rienäcker, M. Kröger, S. Hess Chaotic orientational behavior of a nematic liquid crystal subjected to a steady shear flow Phys. Rev. E 66 (2002) 040702 (4 pages)
Based on a relaxation equation for the second rank alignment tensor characterizing the molecular orientation in liquid crystals we report about a number of symmetry-breaking transient states and simple periodic and irregular, chaotic out-of-plane orbits under steady flow. Both an intermittency route and a period-doubling route to chaos are found for this 5 dimensional dynamic system in a certain range of parameters (shear rate, tumbling parameter at isotropic-nematic coexistence, and reduced temperature). A link to the corresponding rheo-chaotic states, present in complex fluids, is made. (ITP preprint NSF-ITP-02-30)
Article	G. Rienäcker, M. Kröger, S. Hess Chaotic and regular shear-induced orientational dynamics of nematic liquid crystals Physica A 315 (2002) 537-568
Based on a relaxation equation for the alignment tensor characterizing the molecular orientation in liquid crystals under flow we present results for the full orientational dynamics of homogeneous liquid crystals in a shear flow. We extend the analysis of the symmetry-adapted states by Rienäcker and Hess (Physica A 267 [1999] 294), which invoke only 3 of the 5 components of the tensor to full alignment. The steady and transient states of the adapted model are preserved in this more general description, except for log-rolling, which turns out to be unstable in the range of parameters considered. However, the states reported earlier are only stable within a certain range of the parameters and there is a variety of new, symmetry-breaking transient states with the director out of the shear plane, which partially coexist with the in-plane states. The new, out-of-plane states can be divided in two classes: simple periodic and complex orbits. The first class consists of a kayaking-tumbling and a kayaking-wagging state, where the projection of the director onto the shear plane describes a tumbling or wagging motion, respectively. The second class of states, which can be found only in a small parameter range, consists of a variety of either complicated periodic or irregular, chaotic orbits. Both an intermittency route and a period-doubling route to chaos are found.
Article	C. Aust, S. Hess, M. Kröger Rotation and deformation of a finitely extendable flexible polymer in a steady shear flow Macromolecules 35 (2002) 8621-8630
In this article we establish the validity of an `angular momemtum-optic rule' for a dilute polymer solution in the case of a steady shear flow by means of nonequilibrium molecular dynamics computer simulation. The microscopic model for a polymer molecule immersed in a solution composed of monomers incorporates the effects of hydrodynamic interaction through the presence of explicit solvent monomers, and of finite stretchability of chains.In the strong flow regime we observe regular and irregular dynamical behavior which is inherently connected with the nonlinearities in the equations of motion which come along with finite extendability of polymer chains. The microscopic dynamics underlying the simple rule, and in particular times series, the correlated rotation and deformation behavior, and cross-correlations between several structural quantities are investigated in detail. A comparison is made with a reduced model which is also introduced here. The results allow for a test of more efficient implementations which aim to describe polymer dynamics considering hydrodynamic interactions by using ad hoc Langevin equations for the conformational variables.
Article	S. Hess, T. Weider, M. Kröger Viscous properties and structure of ferro-fluids and magneto-rheological fluids. Non-equilibrium molecular dynamics (NEMD) studies of simple model systems Magnetohydrodyn. 37 (2001) 297-306
A simple model is introduced for the theoretical treatment of ferro-fluids and magneto-rheological (MR) fluids. Results from analytic calculations and from non-equilibrium molecular dynamics (NEMD) computer simulations are presented for the anisotropy of the viscosity and for shear--induced structural changes in fluids containing particles with perfectly oriented magnetic moments. Furthermore, the rheological behavior of fluids containing chains of particles is discussed.
Article	S. Hess, M. Kröger Thermophysical properties of gases, liquids and solids composed of particles interacting with a short range attractive potential Phys. Rev. E 64 (2001) 011201 (11 pages)
A short range polynomial interaction potential is introduced which has both a repulsive core and an attractive part. It is cut-off smoothly such that its first and second derivatives vanish at the cut-off distance. The potential therefore enables efficient simulation studies of a model material which exhibits similarities to a full (but computational expensive) classical Lennard-Jones system. Thermophysical properties of the model are calculated by (non-equilibrium) molecular dynamics computer simulations and compared with analytical results. Upon the quantities studied are the pressure as function of the density for various temperatures. Equations of state for the fluid and the solid are tested. The coexistence of gaseous, (metastable) liquid and fcc solid phases is found for a range of temperatures. Bulk and shear moduli are computed. The response of the system to a shear deformation with a constant shear rate is analyzed. The liquid shows a visco-elastic behavior which can be described with a Maxwell model. The solid behaves as an elastic medium up to a finite deformation and then undergoes a transition to a plastic flow, which is stick-slip like at small shear rates and continuous at higher ones.
Article	M. Kröger, M. Hütter, H.C. Öttinger Symbolic test of the Jacobi identity for given generalized 'Poisson' bracket Comput. Phys. Commun. 137 (2001) 325-340
We developed and provide an algorithm which allows to test the Jacobi identity for a given generalized 'Poisson' bracket. Novel frameworks for nonequilibrium thermodynamics have been established, which require that the reversible part of motion of thermodynamically admissible models is described by Poisson brackets satisfying the Jacobi identity, in order to ensure the full time-structure invariance of equations of motion for arbitrary function(al)s on state space. For a nonassociative algebra obeyed by objects such as the Lie bracket, the elements of Lie groups fulfill this identity. But the manual evaluation of Jacobi identities relevant for applications and even basic examples is often very time consuming. The efficient algorithm presented here can be obtained as a package to be used within the framework of the symbolic programming language Mathematica(TM). The tool handles Poisson brackets acting either on functions or on functionals, depending on whether the system is described in terms of discrete or of continuous variables.
Article	S. Hess, M. Kröger Pressure of fluids and solids composed of particles interacting with a short range repulsive potential Phys. Rev. E 61 (2000) 4629-4631
A simple short range repulsive potential (shrep), with an even smoother cut off than the WCA-Lennard-Jones potential, yields practically the same pressure, both in the fluid state and for the fcc solid, when the potential parameters are chosen such that the forces are the same at the distance where the the two potential curves are equal to kT. The comparison of the pressure for the shrep and the WCA systems is based on MD computer simulations. The fluid branch of the equation of state is rather well described by a modified Carnahan-Starling expression.
Article	M. Kröger, S. Hess Solid friction studied via non-equilibrium molecular dynamics computer simulations Z Angew. Math. Mech. 80, Suppl. 1 (2000) S49-S52
The embedded atom method is adapted to study solid friction and the mechanical behavior of a model metal. The elastic properties of real metals are reproduced by a set of basic model potentials as revealed by analytic considerations. NonEquilibrium Molecular Dynamics NEMD computer simulations are performed to study the dynamics and structural changes of the model metal undergoing a process of solid friction and an uniaxial compression, in order to analyze, e.g. plastic yield and transient friction coefficients.
Article	M. Kröger, S. Hess Rheological evidence for a dynamical crossover in polymer melts via nonequilibrium molecular dynamics Phys. Rev. Lett. 85 (2000) 1128-1131
A certain `critical' molecular weight controls rheological properties of the multibead finitely extensible nonlinear elastic (FENE) chain model polymer melt. The rheological crossover manifests itself in a change of power law behavior for the viscous properties at a critical number of beads per chain Nc=100 +/- 10. This finding confirms a newly proposed relationship between dimensionless critical weight, characteristic length and flexibility which we obtain as a side-result. Results further suggest, that the entanglement molecular weight Ne for the flexible FENE chain model could be comparable in size or even larger than its critical molecular weight Nc.
Article	M. Kröger, A. Alba, M. Laso, H.C. Öttinger Variance reduced Brownian simulation of a bead-spring chain under steady shear flow considering hydrodynamic interaction effects J. Chem. Phys. 113 (2000) 4767-4773
In order to obtain numerical estimates for the properties of a general model for polymers in dilute theta solutions in its long-chain limit we follow a stochastic approach to polymer kinetic theory. The model takes into account configuration-dependent hydrodynamic interaction (HI) and simplifies to the Zimm bead-spring chain model in the limit of preaveraged HI, for which parameter-free `universal ratios' such as the ratio between radius of gyration and hydrodynamic radius are known. The Chebyshev polynomial method and a variance reduction simulation technique is used to implement an efficient Brownian dynamics simulation. We resolve the full dependence of several characteristic ratios vs. both chain length and hydrodynamic interaction parameter, we extrapolate their values to determine universal behaviors, and compare with analytical and experimental results.
Article	J. Fang, M. Kröger, H.C. Öttinger A thermodynamically admissible reptation model for fast flows of entangled polymers. II. Model predictions for shear and extensional flows J. Rheol. 44 (2000) 1293-1317
Numerical predictions of a previously proposed thermodynamically consistent reptation model for linear entangled polymers are presented for shear and extensional flows. Comparisons with experimental data and two alternative molecular-based models are given in detail. The model studied in this paper incorporates the essence of double reptation, convective constraint release and chain stretching, and it avoids the independent alignment approximation. Here, no use is made of the ingredient of anisotropic tube cross sections of the previously proposed model. Simulation results reveal that the model at a highly simplified level with few structural variables, i.e., four degrees of freedom, is able to capture qualitatively all features of the available experimental observations and is highly competitive with recently proposed models in describing nonlinear rheological properties of linear entangled polymers.
Article	W. Muschik, S. Gümbel, M. Kröger, H.C. Öttinger A simple example for comparing GENERIC with non-equilibrium rational thermodynamics Physica A 285 (2000) 448-466
During the last 15 years a bracket formalism of dissipative continuum physics has been developed which resulted in a formulation which is shortly denoted as GENERIC. GENERIC has been applied to different problems of continuum thermodynamics, often in this way, that a well-known problem was reformulated in GENERIC formalism. To learn some more about the GENERIC procedure we consider a gas which is contained in a cylinder closed by a piston moving with friction. We treat this simple discrete system with rational non-equilibrium thermodynamics by using Liu's procedure and, for comparison, also with the GENERIC formalism. Both different procedures yield in the same results, especially in the same entropy production. Differences, similarities and fundamental presuppositions of both formalisms are discussed and compared.
Article	M. Kröger Efficient hybrid algorithm for the dynamic creation of semiflexible polymer solutions, brushes, melts and glasses Comput. Phys. Commun. 118 (1999) 278-298
We present an algorithm for the creation and relaxation of large, dense or diluted homogeneous many particle systems made of wormlike, finite extendable, semiflexible multibead chains and - optionally - solvent particles, which repulse each other. The key feature is its efficiency, its output has been proven to serve as an excellent basis for any subsequent off-lattice computer simulation. The application allows to choose i) the bead number density or packing fraction, temperature, chain length, system size, concentration, ii) the interaction potentials, hence the local features such as bond length and bending rigidity of the chains, and iii) the degree of pre-relaxation, parametrized and expressed through a minimum intermolecular distance. The monodisperse polymers are represented by chains of monomer coordinates in 3D space. During the dynamical two-step process of sample creation the initially (Monte Carlo step 1) predicted global characteristics of the molecular conformations remain as unaffected as possible (during molecular dynamics step 2) and the potential energy and the entropy production are relaxing towards their minima. The potentials, the distribution of bond lengths, the integration time step and temperature are smoothly controlled during the creation/relaxation process until they finally approach their prescribed or physical values. The quality of the algorithm is by its nature independent of concentration, system size or degree of polymerization; the CPU speed is quite independent of the latter quantity and linear in the system size. Chains tethered to a surface (dry polymer brushes) can be generated as well. We provide a benchmark table.
Article	C. Aust, M. Kröger, S. Hess Structure and dynamics of dilute polymer solutions under shear flow via nonequilibrium molecular dynamics Macromolecules 32 (1999) 5660-5672
We present and discuss data obtained by an extensive nonequilibrium molecular dynamics computer simulation study of polymer solutions under shear, where the chain consists of $N$ beads connected by a finitely extendable nonlinear elastic (FENE) spring force and the solvent is explicitly taken into account. Various scaling laws are extracted from the data which allow one to predict the qualitative - to certain extent also quantitative - structural and rheological behavior of polymer solutions under good solvent conditions. For most quantities, the results drawn from simulation are compared with experimental data and theoretical predictions which are based on similar models, (e.g., harmonic bond potentials or Brownian dynamics methods). Specifically, and in contrast to common theoretical approaches, the simulation yield information about a set of different but characteristic relaxation times, which determine the rheological and structural behavior (for example, flow birefringence, structure factor, rotational dynamics) separately - the difference either resulting from the underlying static or dynamic nature or from relaxation processes which act on different length scales.
Article	A. Chrzanowska, M. Kröger, H.S. Sellers Mesosocopic model for the viscosities of nematic liquid crystals Phys. Rev. E 60 (1999) 4226-4234
Basing on the definition of the mesoscopic concept by Blenk and others in 1991 an approach to calculate the Leslie viscosity coefficients for nematic liquid crystals is presented. The approach rests upon the mesoscopic stress tensor, whose structure is assumed similar to the macroscopic Leslie viscous stress. The proposed form is also the main dissipation part of the mesoscopic Navier Stokes equation. On the basis of the correspondence between micro and meso scale a mean field meso potential is introduced. It allows to obtain the necessary in the stress tensor angular velocity of the free rotating molecules with the help of the orientational Fokker-Planck equation. Macroscopic stress tensor is calculated as an average of the mesoscopic counterpart. Appropriate relations among mesoscopic viscosities have been found. The mesoscopic analysis results are shown to be consistent with the diffusional model of Kuzuu Doi and Osipov Terentjev (KDOT) with exception of the shear viscosity alpha_4. In the nematic phase alpha_4 is shown to consist from two contributions: isotropic and nematic. There exists an indication that the influence of the isotropic part is dominant over the nematic part. The so called microscopic stress tensor used in the microscopic theories is shown to be the mean field potential dependent representation of the mesoscopic stress tensor. In the limiting case of total alignment the Leslie coefficients are estimated for the diffusional and mesoscopic models. They are compared to the results of the AT model of the perfectly ordered systems. This comparison shows disagreement concerning the rotational viscosity, whereas the coefficients characteristic for the symmetric part of the viscous stress tensor remain the same. The difference is caused by the hindered diffusion in the affine model case.
Article	M. Kröger, P.L. Luisi, H.C. Öttinger, P. Smith, U.W. Suter From the picometer towards the megameter (Vom Pikometer zum Megameter) ETH Bulletin 274 ETH, Zurich (1999) 16-19
Sind denkende Materialien, die sich einer Situation anpassen können, nur Zukunftsvision? Sind Werkstoffe, die ihre Qualität selbstständig verbessern können, Science Fiction? Nein, aus welchem Stoff sie gemacht sind, und vor allem wie und wie passend sie zusammengesetzt und verarbeitet werden, das bestimmt die Eigenschaften `intelligenter' und `funktioneller' high-tech Werkstoffe. Sie können mit fast jeder denkbaren physikalischen, chemischen, optischen oder elektrischen Eigenschaft versehen werden. Bisher stösst man dabei aber immer wieder auf Grenzen. Zu wenig weiss man bisher darüber, wie die genaue Zusammensetzung des Materials seine Eigenschaften bestimmt.
Article	S. Hess, M. Kröger, H. Voigt Thermo-mechanical properties of the WCA-Lennard-Jones model system in its fluid and solid states. Physica A 250 (1998) 58-82
Thermomechanical properties of the WCA-Lennard-Jones model system in its fluid and fcc crystalline states are computed via molecular dynamics (MD) simulations, both with constant volume (NVT) and with constant pressure (NPT). Data for the pressure, energy, specific heat, bulk and shear elasticity coefficients, and for other quantities are presented in graphical form, as functions of the density, for a few selected temperatures. Those quantities which can be computed from the free energy, in the fluid state, are compared with theoretical expressions based on a modified Carnahan-Starling (CS) theory. This involves the second virial coefficient and a temperature-dependent effective volume of a particle for which various expressions are discussed. Good agreement between theory and simulation is found for a simple specific choice of the effective volume. Additional thermodynamical quantities are displayed graphically for this case. Some MD data are also given in tabular form in the appendix.
Article	M. Kröger Nonequilibrium dynamics simulations of simple and complex fluids Curr. Opin. Colloid & Interf. Sci. 3 (1998) 614-619
Computer simulations on classic model systems are continuing to enable significant progress to be made in research concerning the inter-relation between dynamics, structure and rheology of simple and polymeric fluids that are under the influence of an external field. This work includes studies on flow-induced alignment, self-assembly, phase transitions, anisotropic diffusion and the validation and improvement of the underlying models and techniques. The best insight into chain-structure relationships has come from idealized models.
Article	M. Kröger Micro/mesoscopic approaches to the ring formation in linear wormlike micellar systems Macromol. Symp. 133 (1998) 101-112
We hereby present i) a microscopic model for the self-assembly of linear wormlike micelles for which scission/recombination processes and loop formation are allowed, and ii) a mesoscopic analytic description of such systems. Both approaches predict the extent of loop formation as function of the micellar concentration, the end-cap energy and the flexibility of micelles. As a matter of fact, even if loop formation is unfavorable under many conditions, e.g., for stiff micelles and low end cap energies, they have to be treated correctly in any statistical approach to their behavior, since their presence can significantly affect the relaxation time spectrum, the rheological behavior and correlation function of various types.
Article	M. Kröger Flow-induced alignment of rodlike and flexible polymers in the molten state Physica A 249 (1998) 332-336
The flow-induced alignment of polymer chains in melts is calculated based on a Fokker-Planck equation for the single-link orientational distribution function of polymer segments. Analytic results, under the assumption of a vanishing 6th anisotropic moment of this function, are discussed for the case A) flexible polymers subjected to a stationary plane Couette flow and B) rigid polymers subjected to a time dependent shear flow. The results are expressed in terms of the orientational and reptational diffusion coefficients, the chain length, the shape of segments and the shear rate. In order to account for recent findings from computer simulations, the effect of flow-induced orientation of chain ends on the alignment of the polymer coil are analyzed. We also discuss the related rheological properties.
Article	W. Carl, R. Makhloufi, M. Kröger On the Shape and Rheology of Linear Micelles in Dilute Solutions J. Phys. France II 7 (1997) 931-946
We calculate the length distribution of linear (wormlike) micelles modeled as flexible bead-spring chains from both microscopic and mesoscopic models. The latter model is based on an expression for the free energy of Gaussian chains, modified by a term which takes into account a finite scission energy in order to describe micelles, or breakable polymer chains. In equilibrium, the length distribution then depends on two parameters, namely the micellar concentration and the scission energy. Results of this approach are compared both with previous mesoscopic descriptions and Molecular Dynamics (MD) computer simulation results of the FENE-C model of linear micellar solutions (Phys. Rev. E 53 (1995) 2531). The mesoscopic model is extended to describe flow situations. Implications are discussed and compared with NonEquilibrium MD (NEMD) computer simulation results for the length distribution and flow alignment of linear micelles as well as the corresponding rheological behavior. For the case of steady shear flow both models do predict a decrease of the average micellar size with increasing shear rate.
Article	S. Kröger, M. Kröger A program to compute the angular coefficients of the relativistic one-electron hyperfine structure parameters (Erratum) Comput. Phys. Commun. 103 (1997) 97-99
Nature of physical problem The atomic hyperfine structure splitting is characterized by the hyper- fine interaction constants A and B. Within the effective tensor operator formalism [1] these hyperfine interaction constants can be expressed as a linear combination of products between the relativistic one-electron hyperfine structure parameters a nl kskl and b nl kskl and corresponding angular coefficients alpha nl kskl and beta nl kskl, respectively [2]. The problem is to calculate the angular coefficients for the case of pure SL-coupling and, alternatively, the case of intermediate coupling for electronic configurations with up to four open electron shells. Method of solution The program Chfs calculates the angular coefficients alpha nl kskl and beta nl kskl directly by evaluating explicit expressions for the matrix elements, which have been derived by the method of Racah algebra from effective Hamiltonians of hyperfine structure. The program Chfs allows two types of couplings to compute the matrix elements: |[(Psi1,Psi2)Psi12,(Psi3,Psi4)Psi34]Psi> as derived in [3] and |{[(Psi1,Psi2)Psi12,Psi3]Psi13],Psi4}Psi>, see ref. [4]. In the case of intermediate coupling the angular coefficients are obtained by summing up a set of matrix elements, with fine structure mixing coefficients as weighting factors. Restrictions on the complexity of the problem A configuration may have up to maximal four open electron (sub)shells. Because of the limited availability of fractional parentage routines [5-7], the program Chfs is restriced to handle s-, p-, d- and f-shells and at most two particles in higher shells. Typical running time some minutes on 486PC References [1] P.G.H. Sandars and J. Beck, Proc. R. Soc. London, Ser. A 289(1965)97 [2] W.J. Childs, Case Stud. At. Phys. 3(1973)215 [3] H.-D. Kronfeldt, G. Klemz, S. Kroger and J.-F. Wyart, Phys. Rev. A 48(1993)4500 [4] H.-D. Kronfeldt, G. Klemz and S. Kroger, in preparation [5] D.C.S. Allison, Comp. Phys. Comm. 1(1969)15 [6] A.T. Chivers, Comp. Phys. Comm. 6(1973)88 [7] D.C.S. Allison and J.E. McNulty, Comp. Phys. Comm. 8(1974)246
Article	S. Hess, M. Kröger, W.G. Hoover Shear modulus of fluids and solids Physica A 239 (1997) 449-466
The shear modulus tensor, whose components are Voigt elastic moduli, is expressed as an N-particle average. The Born-Green and the fluctuation contributions are identified and, where possible, also expressed in terms of integrals over the pair-correlation function. Symmetry considerations are invoked for systems of spherical particles in both isotropic and cubic states. Results from molecular dynamics simulations are presented for particles with a purely repulsive Lennard-Jones interaction. Shear and bulk moduli are displayed graphically as functions of the density for fluid and cubic crystalline states. The shear modulus proves to be a good indicator for the fluid-solid phase transition.
Article	S. Hess, C. Aust, L. Bennett, M. Kröger, C. Pereira Borgmeyer, T. Weider Rheology: From simple and to complex fluids Physica A 240 (1997) 126-144
The method of non-equilibrium molecular dynamics, with special emphasis on the simulation of a plane Couette flow, and results for simple fluids are reviewed briefly. Then simulation data are presented for complex fluids, in particular for polymeric liquids and anisotropic fluids such as nematic liquid crystals and ferro-fluids, magneto- or electro-rheological fluids.
Article	M. Kröger, H.S. Sellers Viscosities of Nematic and Discotic Nematic Liquid Crystals according to the Affine Transformation Model Mol. Cryst. Liq. Cryst. 300 (1997) 245-262
An affine transformation model is used to calculate the macroscopic stress tensor for uniaxial liquid crystals. In the special case of constant degrees of alignment, it is shown to be of the form occurring in the Ericksen-Leslie director theory for nematic liquid crystals, resolving an apparent discrepancy on the form of the stress tensor. The corresponding Leslie and Miesowicz viscosities are calculated in terms of the alignment order parameters and those of the affine model. These results improve the approximate calculations of Ehrentraut and Hess [Phys. Rev. E 51, 2203 (1995)] based on a hindered rotation assumption. It is further shown that the calculated orientation-dependence of the viscosities based on the affine model is the same as that resulting from calculations based on an alternative Fokker-Planck equation for the one particle orientational distribution function.
Article	M. Kröger, H.S. Sellers On the signs of the Leslie viscosities alpha_2 and alpha_3 for nematics and discotic nematics Mol. Cryst. Liq. Cryst. 293 (1997) 17-28
The signs of the Leslie viscosities alpha_2 and alpha_3 for rod-like and disc-like molecules in the uniaxial nematic phase are calculated using a dynamic molecular mean field theory based upon a Fokker-Planck equation. The viscosities are shown to depend on the particle geometry and alignment order parameters. In particular, for positive degree of alignment S_2, the calculations tend to confirm Carlsson's conjecture relating the signs of the two viscosities to the particle geometry. Furthermore, a transition in the signs of alpha_2 for discotics and alpha_3 for nematics is predicted with increasing order parameter S_2 in accord with recent experiments. For small degree of alignment S_2, the results reproduce previous calculations obtained by Hess in a truncation approximation. The qualitative flow behavior (e.g., tumbling) depends upon the signs of these viscosities.
Article	M. Kröger, H.S. Sellers Fokker-Planck calculations of the viscosities of biaxial fluids Phys. Rev. E 56 (1997) 1804-1807
A Fokker-Planck equation for the orientation distribution function is used to calculate the viscosity coefficients of the flow-induced biaxial phase. The results correspond to a special case of proposed phenomenological expressions for biaxial liquid crystals, but with a reduced number of coefficients, apparently due to assumptions on the symmetry of particles. In contrast to a previous calculation, our results satisfy the Onsager relations for the viscosities of biaxial fluids. Sample numerical values indicate that the contribution of flow induced biaxiality can be significant in the shear viscosities, produce sign changes in the viscosity differences, and thus be important for the interpretation of shear flow data.
Article	M. Kröger, C. Luap, R. Muller Polymer melts under uniaxial elongational flow: stress-optical behavior from experiments and NEMD computer simulations Macromolecules 30 (1997) 526-539
Tensile stress and birefringence in both real and model amorphous polymer melts have been measured during constant rate uniaxial elongational flow. We focus on investigations where deviations from the linear stress-optical behavior are pronounced. A rate-dependent contribution to the stress which is not directly related to the intramolecular conformations ('stress offset') is detected for both types of macromolecular fluids. Independent of the flow history during relaxation a linear stress-optical behavior is revealed. Nonequilibrium molecular dynamics (NEMD) computer simulations on the multibead anharmonic spring model are shown to provide insight into the molecular mechanisms underlying the viscoelastic behavior: during relaxation the intermolecular interactions become dominant in correlation with linear stress-optical behavior; the stress offset is shown to be very similar to the stress arising in the corresponding simple fluid; the total stress can well be approximated by a sum of three parts which are based on single-particle and single-link distribution functions only; the yield point behavior at high elongation rates reflects the transition from affine to non-affine motion of bonds and is understood without reference to strong inhomogeneities resulting from local plastic strain production, the chemical structure does not influence the qualitative behavior; distinct microscopic stress contributions under elongation and subsequent relaxation such as inter- and intramolecular, attractive and repulsive, kinetic and potential contributions are resolved.
Article	M. Kröger, A. Ben-Shaul On the presence of loops in linear self-assembling systems Cah. Rheol. 16 (1997) 1-6
In this note we present i) a microscopic model for the self-assembly of linear wormlike micelles for which loop formation is allowed, and ii) an analytical mesoscopic description of such systems. Both approaches predict the extent of loop formation under different conditions. As a matter of fact, even if loop formation is unfavorable under certain conditions, e.g., for stiff micelles and low end cap energies, they have to be treated correctly in any statistical approach to their behavior, since their presence can significantly affect the relaxation time spectrum, the rheological behavior and correlation function of various types.
Article	M. Kröger, R. Makhloufi Wormlike micelles under shear flow: a microscopic model studied by nonequilibrium molecular dynamics computer simulations Phys. Rev. E 53 (1996) 2531-2536
We propose a microscopic model for solutions of wormlike micelles and report results from NonEquilibrium Molecular Dynamics ( NEMD ) computer simulations under shear flow. Our model ('FENE-C') introduces the concept of scission-recombination and is an extension of a recent model established by one of us (M.~Kroger) for polymer melts. In this first study our interest is focused on the relevance of the microscopic model by comparing the results of the simulations with the predictions of mesoscopic theories. The simulated behavior shows an exponential distribution for the micellar length and an exponential dependence of the average length against the scission energy at equilibrium. These results are in accordance with those calculated from Cates mesoscopic theory. Simulations results of shear effect on the size distribution and on the size of the micelles are also reported and discussed.
Article	M. Kröger, B. Kröger A novel algorithm to optimize classification trees Comput. Phys. Commun. 95 (1996) 58-72
We present a new version of the program MedTree which is of use to calculate classification trees beyond the quality of trees which are based on direct evaluation of a splitting criterion. MedTree calculates a large number of possible segments of trees and recursively selects the best of these parts to form an 'optimal' tree which requires the discussion of the definition of 'optimal'. The characteristics of the improved version are as follows: analysis of incomplete data, higher performance, reduction of field dimensions, higher portability, rejection of irrelevant parts of trees in an early stage, additional coupling scheme to produce either very short or longer trees with better quality by coupling the selection rule to the vicinity of an incomplete tree to the conditions of closing a tree and a interactive mode to view and adjust the selection and closing rules. Examples in order to demonstrate the improvements are given
Article	M. Kröger Optimization of classification trees: strategy and algorithm improvement Comput. Phys. Commun. 99 (1996) 81-93
Nature of physical problem The problem is to find best trees of classification for a specific subject to one of two groups [1,2]. Initially, a set of features for a (sufficient) large number of representative subjects from both groups must be sampled by the user. A good tree is expected to be found if there exist schemes of behaviour, or even complex correlations within the input information. The algorithm allows to take into account boundary conditions, to fit the practical purpose of the classification tree. Method of solution See reference in CPC to previous version. The method of solution can be affected in direction of specific goals by setting variables (see Tab. 2). Restrictions on the complexity of the problem See reference in CPC to previous version. New rejection mechanisms reduce the number of objects and thus allow to calculate trees with higher quality. Parameters which limit the field dimensions of the variables are collected in Tab. 3 of Ref [1] Reasons for the new version The reasons are to decrease the large field dimensions in order to account for more temporary trees at a given hardware; to be able to analyze incomplete data; to produce especially short trees with strong coupling to the given closing conditions; to simplify the adjustment and introduce the possibility to view the effect of selection mechanisms. Typical running time The typical running time is one order of magnitude lower than the computing time of the original version. The program gives you a preestimation about the needed computing time at start up. If the needed time is too high to be practicable, the problem can be treated by modifying program variables. References [1] M. Kroger and B. Kroger, Comp. Phys. Commun. 95 (1996) 58-72. [2] L. Breimann, J. Friedman, R.A. Olshen and C.J. Stone, Classification and regression trees (Belmont, CA, Wadsworth, 1984).
Article	F. Affouard, M. Kröger, S. Hess Molecular dynamics of model liquid crystals composed of semiflexible molecules Phys. Rev. E 54 (1996) 5178-5186
Results of molecular dynamics computer simulations are presented for a simple microscopic model of thermotropic liquid crystals. The system is composed of short semiflexible chains where the beads are connected by an anharmonic FENE spring. The inter-molecular bead-bead interactions are modelled by Lennard-Jones potentials, the attractive part is taken into account only between the stiff parts. Heating the system, solid, smectic A and liquid phases are found. For the symmetric molecules and anisotropic potentials studied first, the smectic A phase is clearly defined over a wide range of temperatures whereas the nematic phase is not present or too narrow in temperature to be seen clearly. The evolution of the systems has also been studied as function of the length of flexible parts and the strength of the stiff-stiff potential.
Article	C. Schneggenburger, M. Kröger, S. Hess An extended FENE dumbbell theory for concentration dependent shear-induced anisotropy in dilute polymer solutions J. Non-Newtonian Fluid. Mech. 62 (1996) 235-251
The original FENE dumbbell kinetic theory is extended to describe concentration dependent shear-induced anisotropy in dilute polymer solutions. A mean field term is introduced into the model equations to take into account intermolecular forces. For the case of stationary shear flow the corresponding coupled non-linear relaxation equations for the components of the tensor of gyration are solved numerically. We present results for the shear and concentration dependence of different quantities related to the tensor, i.e.~the orientation angle, radius of gyration, the eigenvalues, and different pseudospherical components. They are in good qualitative agreement with data from light scattering experiments. Corresponding results for the rheological quantities are briefly discussed.
Article	S. Kröger, M. Kröger A program to compute the angular coefficients of the relativistic one-electron hyperfine structure parameters Comput. Phys. Commun. 90 (1995) 381-387
The Chfs program calculates the angular coefficients alpha_{nl}^{k_sk_l} and beta_{nl}^{k_sk_l} of the relativistic one-electron hyperfine structure parameters for the case of pure SL-coupling or, alternatively, the case of intermediate coupling. The calculation is based on SL-basis states and, optionally, mixing coefficients of the electronic wave functions of atoms. The derivation of the necessary matrix elements is based on the effective tensor operator formalism; explicit expressions are cited. Chfs is the first program which is able to compute the angular coefficients for electronic configurations with up to four electron shells.
Article	M. Kröger, H.S. Sellers Viscosity coefficients for anisotropic, nematic fluids based on structural theories of suspensions J. Chem. Phys. 103 (1995) 807-817
The relation between the governing equations for low Reynolds number flow of suspensions of rigid, axisymmetric particles and director theories of anisotropic fluids is examined in detail. The role of directors for modelling suspensions is illustrated and it is shown in what sense and how the equations for 3 common models of suspensions may be related to a director theory with variable degree of alignment. The viscosity coefficients and molecular fields of the director theory are then expressed in terms of the parameters characterizing the suspension. Some implications of these results are discussed for tumbling/non-tumbling of the director in shear flow, for Parodi's relations, and for thermodynamic restrictions of the viscosity coefficients. Additionally, several previous calculations of the Leslie viscosities are compared to the results obtained. Corrigendum: Equation 5.1 on page 811: replace S2 by S4
Article	M. Kröger NEMD computer simulation of polymer melt rheology Rheol. 5 (1995) 66-71
Nonequilibrium molecular dynamics (NEMD) computer simulation methods are used for analyzing microscopic models of polymer melts. Examples are presented showing that rheological and structural properties calculated in simulations agree with experimental data. Thus, such simulations provide insight into the molecular origins of viscoelastic behavior of real polymer melts. This work presents results of the first NEMD computer simulation conducted on high molecular weight polymers.
Article	M. Kröger, H. Voigt On a quantity describing the degree of entanglement in linear polymer systems Macromol. Theory Simul. 3 (1994) 639-647
In the present paper we define a quantity which describes how strong a polymer system is entangled. In MD computer simulations we apply this definition to samples of polymer melts which were generated with a specific large scale structure, as characterized by their radius of gyration, end-to-end distance and the ''degree'' of mutual entanglement of the chains. The quantities mentioned above are monitored over the relaxation of the samples towards equilibrium.
Article	M. Kröger Flow-alignment and rheology of polymer melts. Computation of the single-link orientational distribution function. Makromol. Chem. -- Macromol. Symp. 81 (1994) 83-90
The single-link orientational distribution function and the space-averaged stresses in the fluid are computed for the case of steady shear flow of polymer melts. The computation is achieved with Galerkin's method with spherical harmonics and Euler polynomials as trial functions. The stress components become power functions of shear rate when the latter is large. The single-link orientational distribution function f solves the Fokker-Planck equation subject to a boundary condition for f at the chain ends. A solution is obtained for every shear rate and ratio of the orientational and one-dimensional diffusion coefficient. It is demonstrated that the Fokker-Planck equation with appropriate boundary condition is useful in order to predict the flow-alignment and stresses in good agreement with experimental data as well as with recent results of a nonequilibrium molecular dynamics computer simulation on polymer melts.
Article	M. Kröger, W. Loose, S. Hess Rheology and structural changes of polymer melts via nonequilibrium molecular dynamics J. Rheol. 37 (1993) 1057-1079
Results of Nonequilibrium Molecular Dynamics (NEMD) computer simulations of a planar Couette flow are presented for the multibead anharmonic-spring model. The finitely extensible nonlinear elastic (FENE) force law is used to connect the up to 100 beads of a chain molecule. Rheological data (shear viscosity, normal pressure differences) are discussed and compared with quantities describing the chain conformation (e.g., alignment tensor, static structure factor). This renders possible a test of the theoretical approaches which connect these quantities. In agreement with recent experiments, the static strucure factor exhibits characteristic elliptical distortions of the polymer coil whose magnitude depends on the distance from the gyration center. In our simulations the zero shear rate viscosity is found to scale linearly with the number of beads N up to chains with N=60. A weak upturn of the viscosity per bead for N=100 is found which may indicate the onset of the reptation regime.
Article	M. Kröger, S. Hess Viscoelasticity of polymeric melts and concentrated solutions. The effect of flow-induced alignment of chain ends Physica A 195 (1993) 336-353
The viscous properties of polymeric liquids and the underlying microscopic distribution function for the segment orientations are investigated by a Fokker-Planck approach. The solution of the Fokker-Planck equation depends on the alignment of chain ends under shear flow, which is usually disregarded. However, it has been inferred from Nonequilibrium molecular dynamics (NEMD) computer-simulations, that it is nonzero. Since the viscous properties depend critically on the magnitude of this end alignment it has been taken into account in the theoretical description. This turns out to be crucial for the plateau region and the high frequency behavior of the complex viscosity. The results are in good agreement with experimental data. Furthermore a significant chain length dependence of the viscous behavior is found.

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