Day 1: Sunday afternoon, September 3, 2006

18:30  Welcome remarks - Motivation - Organizational details
V.G. Mavrantzas

Session 1 Non-equilibrium thermodynamics and Statistical Mechanics
Chair: H.C. Öttinger

18:40  The Fluctuation and NonEquilibrium Free Energy Theorems - Theory & Experiment
D.J. Evans, E. Sevick, G. Wang, D. Carberry, J. Reid, D.J. Searles
¹ Australian National University, Canberra, Australia
² Griffith University, QLD, Australia
We give a brief summary of the derivations of the Evans-Searles Fluctuation Theorems (FTs) and the NonEquilibrium Free Energy Theorems (Crooks and Jarzynski). The discussion is given for time reversible Newtonian dynamics. We emphasize the role played by thermostatting. We also highlight the common themes inherent in the Fluctuation and Free Energy Theorems. We discuss a number of simple consequences of the Fluctuation Theorems including the Second Law Inequality, the Kawasaki Identity and the fact that the dissipation function which is the subject of the FT, is a nonlinear generalization of the spontaneous entropy production, that is so central to linear irreversible thermodyanamics. Lastly we give a brief update on the latest experimental tests of the FTs (both steady state and transient) and the NonEquilibrium Free Energy Theorem, using optical tweezer apparatus.

19:10  Non-Affine deformation - The basis of material irreversibility
K. Valanis
Endochronics, 544 NW View Ridge Way Cams, WA 98607, USA
The notion of deformation as an affine map is the foundation of constitutive theory in continuum mechanics. However, while (non-thermal) reversible processes are evolutions of affine maps, irreversibility, other than heat conduction, i.e., 'material irreversibility' for lack of a better term, owes its origin to non-affine deformation of material neighborhoods. In effect, material irreversibility occurs at the local level. These ideas do not translate directly to fluids, since laminar flows are in fact dissipative.The basis of the idea begins with the observation that the reference domain of a material need not be Euclidean, in general, but may have a material metric G, either initially or as a result of subsequent deformation In such a case, the distance squared ds2 between two proximal material points, in the domain, with initial co-ordinates xi and xi + dxi is thus Gijdxidxj. The central idea then, is that the origin of material irreversibility is the in-constancy of material metric G, in the course of deformation.The physical process that underlies the in-constancy of G is the breakdown in the prescribed order that is assigned to the material particles in their reference configuration. Specific processes that cause such breakdown are, slip, dislocation formation and motion, damage and/or other types of loss of connectivity of the material domain. All such processes are associated with loss of free energy and are thus a primary source of dissipation. Because of the evolving loss of connectivity, the deformation is no longer one-to-one and on-to and thus non-affine. The material integrity at the neighborhood level is lost. This idea has not yet been fully recognized or exploited in the development of constitutive equations of solid domains. In this work we show that G plays the role of an internal variable q, thus giving a geometric meaning to this fundamental thermodynamic variable. In their simplest form the ensuing (isothermal) equations are: ψ = ψ(C, G, θ_o) (equation of state), η = - δψ/δθ_o (entropy equation), τ = 2 δψ/δC ( stress-deformation relation),- (δψ/δG).dG >= (dissipation inequality),(δψ/δG) + b.δG/δt = 0 (equation of evolution), where θ_o is the (constant) temperature, η the entropy density, τ is the second Piola-Kirchhoff stress tensor, C is the (Right) Cauchy Green deformation tensor and b a fourth order viscosity tensor. In the ensuing analysis with multiple metrics for multiple material sub-spaces, specific constitutive equations for polymers, appropriate to large deformation, are derived.

19:40  Non-equilibrium steady states, what do we know?
J.-P. Eckmann
Departement de Physique Theorique and Section de Mathematiques Universite de Geneve, Switzerland
In this talk, I intend to review recent progress in our understanding of non-equilibrium steady states. If a system is driven from outside with stochastic forces which move it out of equilibrium, one would like to know whether a non-equilibrium steady state exists, and, if it exists, describe its properties. I will show with one or two examples what are the important issues for this question.

20:05  Discussion
H.C. Öttinger

20:30  Welcome Buffet

22:30 End of workshop day 1/5

   Day 2: Monday morning, September 4, 2006

Session 2 Multiscale modeling and molecular simulations
Chair: T. Tzavaras

08:00  Atomistic simulation of polymers with a non-linear molecular architecture: Calculation of branch point friction and chain reptation time of an H-shaped polyethylene melt
N.Ch. Karayiannis^1,2, V.G. Mavrantzas^1,2
1 Department of Chemical Engineering, University of Patras, GR 26504, Greece
² Institute of Chemical Engineering and High-Temperature Chemical Processes (FORTH-ICE/HT), Patras GR 26504, Greece
A hierarchical simulation strategy is presented for simulating structure and dynamics in polymers characterized by a non-linear molecular architecture, such as the H-shaped macromolecules [1]. First, a novel Monte Carlo (MC) algorithm is employed to generate well equilibrated atomistic configurations of these highly non-linear chain structures. The new algorithm is built around state-of-the-art chain connectivity altering moves, like the end-bridging and double-bridging, and is many orders of magnitude more efficient than Molecular Dynamics (MD) in equilibrating these systems, even if multi-step time integration schemes are incorporated in the MD algorithm. In a second step, the equilibrated structures generated by the new MC algorithm are used as initial configurations in detailed NPT MD simulations of H-shaped polyethylene (PE) melts for very long times, on the order of microseconds. In our simulations, the average number of carbon atoms in the backbone has ranged from 48 up to 300 corresponding to both unentangled and entangled crossbars, while the average branch length was kept relatively small (it ranged from 24 up to 50 carbon atoms) corresponding always to unentangled arms. The MD simulation results provide convincing evidence for the different relaxation mechanisms exhibited by an H-polymer melt: the fast relaxation due solely to arm breathing (on the order of a few ns, for an H_300_50 melt), and the slow branch point diffusion which is accompanied by a sluggish backbone diffusion due to reptation (on the order of a few μs, for an H_300_50 melt). They have further demonstrated that the center-of-mass diffusivity in an H-polymer follows faithfully that of branch points, thus validating from first-principles the main assumption of the McLeish-Larson pom-pom theory that all friction in an H-molecule is concentrated at the branch points. For the longest H-polymers studied, logarithmic plots of the msd of the inner crossbar segments against time were seen to exhibit the four different regimes predicted by the reptation theory of Doi-Edwards for entangled linear polymer melts, with corresponding exponents remarkably close to those of the theory. This allowed us to extract the characteristic relaxation times τe, τR, and τd for each one of the simulated systems and their effective tube diameter.

[1] N.Ch. Karayiannis and V.G. Mavrantzas, Macromolecules 38, 8583 (2005).

08:25  Entanglements and Underlying Topology in Polymer Melts: from Atomistic Models to Entanglement Networks
C. Tzoumanekas^1,2, D.N. Theodorou^1
1 School of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, Zografou Campus, Athens, 15780, Greece
² Dutch Polymer Institute (DPI), The Netherlands
Polymer melts of large molecular weight demonstrate complex rheological and dynamical properties which are very interesting both from a theoretical and a technological point of view. A successful conceptual framework for investigating this complex behavior at the molecular level is offered by the tube model. The tube model is based on the notion that the mutual uncrossability of polymer chains generates topological constraints which are generally called entanglements. Entanglements affect chain motion by effectively restricting individual chain conformations in a curvilinear tube-like region enclosing each chain. Accordingly, chain motion is confined laterally to the length scale of the tube diameter. Large-scale motion is promoted via de Gennes reptation, an effective one-dimensional diffusion of a chain along its tube axis which is called the Primitive Path (PP). PPs characterize the system topology by creating a large scale topological substructure, which is conceived as an entanglement network underlying the melt structure. We introduce a novel algorithm, referred to as CReTA (Contour Reduction Topological Analysis), which is capable of reducing a computer generated atomistic sample to a corresponding entanglement network of PPs. A topological analysis, based on scaled PP and entanglement network statistics of thermodynamically equilibrated Polyethylene, cis-1,4 Polybutadiene and Poly(ethylene terephthalate) (PET) melts, leads to a unifying microscopic description of the topology of flexible polymers. The distribution of the number of monomers between successive topological constraints along a chain reveals a non-uniform network mesh, while a dilute gas of entanglements is revealed by the network radial distribution functions. By mapping PP conformations to random walks, we predict an entanglement molecular weight and a tube diameter which are in accordance with experimental estimates from rheological measurements, for all the polymers under study. Moreover, we will provide a stochastic interpretation of our results in terms of a renewal point process model which treats topological constraints as stochastic events placed along the monomer sequence of a polymer chain.

08:50  Primitive Path Identification and Entanglement Statistics in Polymer Melts: Results from a Direct Topological Analysis on Atomistically Detailed Polyethylene Models
K. Foteinopoulou^1,2, N.Ch. Karayiannis^1,2, V.G. Mavrantzas^1,2, M. Kröger^3
1 Department of Chemical Engineering, University of Patras, GR 26504, Greece
² FORTH-ICE/HT, Patras GR 26504, Greece
³ ETH Zurich, Polymer Physics, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland
A large number of well equilibrated atomistic configurations of linear, strictly monodisperse polyethylene (PE) melts of molecular length ranging from C78 to C1000, obtained with the Double Bridging Monte Carlo algorithm, have been subjected to a detailed topological analysis with the Z code [Kröger, Comp. Phys. Comm., 2005]. The code constructs primitive paths that connect the two ends of a polymer chain (which in all cases are considered as fixed in space) geometrically under the constraint of no chain crossability, such that the multiple disconnected (coarse-grained) path has minimum contour length. When applied to a given, dense polymer configuration in 3-d space, it allows us to obtain the primitive path (PP) and the related number and positions of entanglements (kinks) for all chains in the simulation box, and extract information about the topological structure (the primitive path network) hidden in bulk PE. Results will be presented for the distribution and mean values of the number of entanglements per chain, the entanglement length, the tube diameter, the Kuhn step length and the contour length [1]. In particular, our analysis demonstrates that with increasing chain length, the entanglement molecular length reaches a plateau value characteristic of entangled polymeric behavior, which for the PE systems analyzed here comes out to be about 60 carbon atoms. We further validate recent predictions [Schieber, J. Chem. Phys., 2003] about the shape of the distribution of 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, 2004] deviates significantly from these predictions which we regard as a clear sign of evidence that the direct counting of entanglements and related quantities, as proposed here, offers advantages for a quantitative analysis of the statistical nature of entanglements in polymeric systems.

[1] K. Foteinopoulou, N.Ch. Karayiannis, V.G. Mavrantzas, M. Kröger, Macromolecules 39, 4207 (2006) »

09:15  Multiscale Simulations of Chemically Complex Polymer Melts
K. Kamio¹, K. Moorthi¹, D.N. Theodorou^2
1 Mitsui Chemicals, Inc., Japan
² National Technical University of Athens, Greece
A new methodology for multiscale simulations of chemically complex polymers has been proposed and verified by applying it to poly(ethylene terephthalate) melt. A coarse-graining scheme has been applied to reduce the chemical complexity of the polymer. The resulting structurally simpler model facilitates the process of generalizing the connectivity-altering Monte Carlo method, which has been used to equilibrate the coarse-grained system, and accelerates computations due to the reduction of the degrees of freedom. The melt density, characteristic ratio and other conformational properties agree with experiment. The analysis of the subchain Kuhn length indicates that the melt is adequately equilibrated within Kuhn and chain length scale range. Topological analyses of the melt using CReTA and Z algorithms reveal that the melt system is also well equilibrated with respect to entanglement density.

09:40  Hierarchical Modeling of Polystyrene: From Atomistic to Coarse-Grained Simulations
V. Harmandaris, N. van der Vegt, K. Kremer
Max-Planck-Institute for Polymer Research, D-55021 Mainz, Germany
We present a hierarchical approach that combines atomistic and mesoscopic simulations which can generally be applied to vinyl polymers. As a test case the approach is applied to atactic polystyrene (PS). First a specific model for atactic PS is chosen. The bonded parameters in the coarse-grained force field, based on data obtained from atomistic simulations of isolated PS dimers, are chosen in a way which allows to differentiate between meso- and racemic dyads. This approach allows to study isotactic and syndiotactic melts. Nonbonded interactions between coarse-grained beads were chosen as purely repulsive. The proposed mesoscopic model reproduces both the local structure and the chain dimensions properly. An explicit time mapping is performed, based on the atomistic and CG mean square displacements of short chains, demonstrating an effective speed up of about three orders of magnitude compared to brute force atomistic simulations. Finally the equilibrated coarse-grained chains are back mapped onto the atomistic systems. This opens new routes for obtaining well equilibrated high molecular weight polymeric systems and also providing very long dynamic trajectories at the atomistic level for these polymers.

10:05  Coffee break

10:20  AdResS for hybrid atomistic/coarse-grained molecular dynamics simulations
M. Praprotnik, L. Delle Site, K. Kremer
Max Planck Institute for Polymer Research, Mainz, Germany
A new Adaptive resolution scheme (AdResS) for efficient hybrid atomistic/coarse-grained particle-based molecular dynamics (MD) simulations is presented. The key feature of this approach is that it allows for a dynamical change of the number of molecular degrees of freedom during the course of a MD simulation by an on-the-fly switching between the atomistic and mesoscopic levels of detail.

[1] M. Praprotnik, L. Delle Site, and K. Kremer, J. Chem. Phys. 123, 224106, 2005.
[2] M. Praprotnik, L. Delle Site, and K. Kremer, Phys. Rev. E. 73, 2006.

10:45  Bridging time scale is amorphous glassy polymers
D. Tsalikis, G.C. Boulougouris, L. Peristeras, D.N. Theodorou
School of Chemical Engineering, National Technical University of Athens, Greece
Polymer glasses are complex non-equilibrium materials. Although significant advances have been achieved in modelling deformation, yield and fracture of polymer glasses at the macroscopic level [1], connecting these properties to the chemical constitution and to the formation and processing history of a glass is still a challenge. This is because of the extremely broad spectra of characteristic times that govern molecular motion in the glassy state. Conventional atomistic simulation techniques, such as molecular dynamics (MD), employ an integration time step of approximately 10-15 s to track fast vibrational motions and thus can only address time scales up to 100 ns and length scales up to 10 nm with currently available computational means. As a consequence, they face two very serious challenges: (a) It is impossible to obtain a computer glass with a formation history that is both well-defined and realistic: MD vitrification experiments necessarily impose cooling rates of at least 108 K s-1, nine orders of magnitude higher than the rates of typical laboratory experiments. (b) Even if one is able to form molecular configurations that are truly representative of a real glass, an MD deformation experiment has to be performed at a strain rate of at least 106 s-1, which is much higher than those encountered in most applications. In this work we discuss a strategy for addressing challenge (b) described above leading to a better understanding of yield and strain softening phenomena, as well as physical ageing. It is based on the idea that the local configuration of a glass is trapped in the vicinity of a local minimum of the energy, undergoing infrequent transitions to neighbouring minima across free energy barriers that may vary widely in height. This .energy landscape. picture focusses on the determination of representative energy minima and of the transition paths leading from those to neighbouring minima in the multidimensional configuration space of the glass. Thermodynamic properties and elastic constants in the individual energy minima are estimated by invoking a quasiharmonic approximation for the energy, and the corresponding properties of the glass are obtained through arithmetic (.quenched.) averaging over all minima. The rate constants for transitions from a minimum to neighbouring minima are estimated using the principles of multidimensional transition-state theory and the temporal evolution of the system, in the presence or absence of external stress, is tracked by Kinetic Monte Carlo (KMC) simulation as a succession of transitions between the minima. Such .quasi-dynamics. simulations can deal with arbitrarily slow transition rates and thus overcome the long-time problems of .brute-force. MD. The steps used in our approach could be described as follows: We focus on a small region of a polymer glass containing a few hundreds of atoms. We envision that the configuration of this region fluctuates in the vicinity of a local minimum of the potential energy, or .inherent structure. [2]. Transitions between minima are largely inhibited by the presence of energy barriers that are high relative to kBT. Configuration space is thus partitioned into .basins of attraction.. The measured volumetric properties and elastic constants of the glass are shaped by the restricted probability distributions of configurations within individual basins. Physical ageing brings about a gradual redistribution among the basins through infrequent transitions across the energy barriers, and therefore a gradual change in the properties of the glass. We invoke a quasi-harmonic approximation (QHA) by assuming that the potential energy of a glassy region of given spatial extent, while it fluctuates in the vicinity of its inherent structure, is well approximated by a Taylor expansion to second order around the inherent structure. At given stress, the glassy region will adopt that strain which minimizes G. For the simulation of time-dependent plastic deformation and physical ageing phenomena, it is essential to determine all relevant transition pathways out of a given minimum. We begin by finding as many as possible saddle points around the minimum in the multidimensional configuration space of the polymer using the .dimer method. of Henkelman and J�on [5], which does not require second derivatives. In this procedure it is essential to recognize already visited minima on the basis of their energy and configuration. For each transition path between energy minima A and B, the rate constant is estimated according to transition-state theory, computed via the QHA as described above. Tracking the temporal evolution of the system thus reduces to a KMC simulation of a sequence of elementary transitions between basins, their rate constants being computed .on the fly.. Even at this level of description, there is a wide distribution of time scales (as one would expect in a glassy system), resulting from the wide distribution of free energy barriers connecting the .inherent structures.. This makes the use of classical KMC schemes highly inefficient. For this reason we have developed a novel KMC scheme that allows us to sample efficiently over a wide range of time scales.

[1] Meijer, H.E.H. and Govaert, L.E. Prog. Polym. Sci. 2005, 30, 915-938.
[2] Stillinger, F.H. Science 1995, 267, 1935-1939.
[3] Kopsias, N.P. and Theodorou, D.N. J. Chem. Phys. 1998, 109, 8573-8582.
[4] Lyulin, A.V. Europhys. Lett. 2005, 71, 618-624.
[5] Henkelman, G. and Jonsson, H. J. Chem. Phys. 1999, 111, 7010-7022.

11:10  Computer Simulation of Colloidal Electrophoresis
B. Dünweg, V. Lobaskin, K. Seethalakshmy-Hariharan, C. Holm
Max Planck Institute for Polymer Research, Mainz, Germany
We study the motion of a charged colloidal sphere surrounded by solvent, counterions, and salt ions, under the influence of an external electric field. The ions are modeled as particles which interact dissipatively with a lattice Boltzmann background, such that hydrodynamic interactions are taken into account. Similarly, the colloid is modeled as a spherical array of such point particles. Finite concentration values are taken into account by simulating the system in a box with periodic boundary conditions. In terms of dimensionless reduced parameters, the results compare favorably with experimental data. As a complementary approach, we solve the electrokinetic equations by a finite element method.

11:35  Discussion
T. Tzavaras

12:05  Lunch

   Day 2: Monday afternoon, September 4, 2006

Session 3 Non-equilibrium thermodynamics and Molecular Dynamics
Chair: M. Kröger

14:00  A molecular dynamics study of the stress-optical behavior of a linear short-chain polyethylene melt under shear
C. Baig, B.J. Edwards, D.J. Keffer
Department of Chemical Engineering, University of Tennessee, Knoxville, TN 37996-2200, USA
In this study, we investigate details of the stress-optical behavior of a linear polyethylene melt under shear using a realistic potential model. We demonstrate the existence of the critical shear stress, above which the stress-optical rule (SOR) begins to fail. The critical shear stress of the SOR of this melt turns out to be approximately 5.5 MPa, which is fairly higher than 3.2 MPa at which shear thinning starts. This indicates that the SOR is valid up to a point well beyond the incipient point of shear thinning. Furthermore, contrary to conventional wisdom, the breakdown of the SOR turns out not to be exactly correlated with the saturation of chain extension and orientation: it is observed to occur at shear rates well before maximum chain extension is obtained. In addition to the stress and birefringence tensors, we also compare two important coarse-grained second-rank tensors, the conformation and orientation tensors. The birefringence, conformation, and orientation tensors display nonlinear relationships to each other at high values of the shear stress, and the deviation from linearity begins at approximately the critical shear stress for the breakdown of the SOR.

14:25  Microscopic chaos in shear and elongational flows
F. Frascoli¹, D.J. Bernhardt (nee Searles)², B.D. Todd^1
1 Centre for Molecular Simulation, Swinburne University of Technology, PO Box 218, Hawthorn, Victoria 3122, Australia
² School of Science, Griffith University, Brisbane, Queensland 4111, Australia
The simulation of atoms and molecules under planar elongational flow in a nonequilibrium steady state for arbitrarily long times has recently been made possible by an appropriate implementation of nonequilibrium molecular dynamics (NEMD) with suitable periodic boundary conditions. We address some fundamental questions regarding the chaotic behaviour of this type of flow and compare its chaotic properties with the behaviour of fluids under planar shear flow. We analyse the spectra of Lyapunov exponents for a number of state points where the energy dissipation is the same for both flows, simulating a nonequilibrium steady state for isoenergetic and isokinetic constrained dynamics. We test the conjugate pairing rule and confirm its validity for planar elongation flow, as is expected from the Hamiltonian nature of the adiabatic equations of motion. Discussion about the chaoticity of the convective part of the flows, the link between Lyapunov exponents and viscosity and phase space contraction will also be presented.

14:50  Simulations of shear banding in paints
W.J. Briels, A. van den Noort
University of Twente, The Netherlands
A coarse grain model to simulate the rheological properties of paints will be presented. The model shows extreme shear thinning at shear rates as low as several reciprocal seconds. In several cases shear banding was found along the gradient direction. Not only were shear rates different in different bands, but also their densities. Special attention will be paid to the evolution of the stress during the period when the systems settles from its initial homogeneous state to the final banded state.

15:15  Flow and Motion of Polymer Droplets on Polymer Brushes
M. Müller¹, C. Pastorino², K. Binder^2
1 Institut für Theoretische Physik, Georg-August Universität, D37077 Göttingen, Germany
² Institut für Physik, WA331, Johannes Gutenberg Universität, D55099 Mainz, Germany
Polymer brushes are soft, elastically deformable substrates giving rise to a rich wetting behavior and additional molecular dissipation mechanisms for the motion of droplets. We study thin polymer films and droplets on flat brush-covered substrates by non-equilibrium molecular dynamics simulation of a coarse-grained bead-spring model. The brush consists of identical polymers as the droplets. Upon increasing the grafting density the free polymers are expelled from the brush and a brush-melt interface gradually builds up. Molecular conformations and the overlap between brush and melt are studied in equilibrium and under shear. The velocity profile across a thin polymer film is investigated. The slip length adopts large positive values (perfect slip) for low grafting densities, but decreases and becomes negative for densely grafted, autophobic brushes. At high grafting density the polymer melt dewets from the brush and forms droplets. Nanoscopic polymer droplets driven by volume forces are investigated in their steady state.

15:40  A Generalized Hamiltonian-Based Algorithm for Rigorous Equilibrium Molecular Dynamics Simulation in the NVT, NpT, and μVT Ensembles
J. Santiago, D.J. Keffer, B.J. Edwards, C. Baig
University of Tennessee, Knoxville, TN 37996-2200, USA
We provide a methodical procedure for generating equations of motion for rigorous simulation in three different statistical ensembles, the canonical ensemble (NVT), the isothermal-isobaric ensemble (NpT), and the grand canonical ensemble (μVT) under equilibrium conditions. The procedure begins with a Hamiltonian in terms of laboratory coordinates in a mathematical frame of reference where time and/or mass is dilated. The equations of motion are derived relying on the symplectic relationship between the Hamiltonian and the equations of motion. We define a non-canonical transformation from the laboratory coordinates in the mathematical frame of reference to laboratory coordinates in the physical frame of reference, in much the same way as the original NVT development of Nose and Hoover. However, the new equations are completely general, unlike their predecessors, in that they are valid whether or not an external force field is present. Several illustrations of simulations involving these ensembles will be presented which validate the new algorithms.

16:05  Coffee break

16:20  Discussion
M. Kröger

17:00 End of workshop day 2/5

   Day 3: Tuesday morning, September 5, 2006

Session 4 Complex fluid deformation and rheology: Theories and thermodynamic relationships
Chair: M. Grmela

08:00  Dynamic van der Waals theory
A. Onuki
Physics Department, Kyoto University, Japan
We present a dynamic van der Waals theory including gradient entropy and energy. We introduce the temperature as a functional of the number density and the energy density. Our model is useful to study phase separation when the temperature varies in space. As an example, we show that if heat flow is applied to liquid suspending as droplet at zero gravity, a convective flow occurs such that the temperature gradient within the droplet nearly vanishes. As the heat flux is increased, the droplet becomes attached to the heated boundary that is wetted by liquid in equilibrium. In one case corresponding to partial wetting by gas, an apparent contact angle can be defined. In the other case with larger heat flux, the droplet completely wets the heated boundary expelling liquid. As another example, we study wetting dynamics with evaporation and condensation.

[1] A. Onuki, Phys. Rev. Lett. 94 (2005), 054501.

08:50  Thermodynamic relationships for shearing viscoelastic fluids
P.J. Daivis
Applied Physics, School of Applied Sciences, RMIT University, Melbourne, Australia
It is shown that the work done in taking a viscoelastic fluid from equilibrium into a shearing steady state can be separated into viscous and elastic parts. This separation is completely phenomenological and therefore does not require any special assumptions about the substance being studied. It is also expected to be valid for non-linear viscoelastic materials. In the limit of zero shear rate, it is possible to use the standard machinery of thermodynamics to derive a Maxwell relation between the shear rate dependence of the pressure and the reversible part of the work required to establish a shearing steady state. This leads to a useful relationship between the stored energy in a shearing linear viscoelastic fluid and the limiting zero shear rate value of the first normal stress coefficient. This relationship explicitly confirms the expectation that the first normal stress coefficient of a linear viscoelastic fluid is associated with elasticity.

09:15  Relationship between heterogeneous dynamics and internal stress
M.T. Downton, M.P. Kennett
Simon Fraser University, USA
The low temperature breakdown of the linear relationship between viscosity and translational diffusion is commonly attributed to the appearance of heterogeneous dynamics that occurs when a liquid is cooled. While diffusion is predominantly due to mobile particles (fast relaxation), viscosity is related to the stress autocorrelation function (slow relaxation), this difference in averages, coupled with the broadened distribution of relaxation timescales leads to the breakdown. In this work we consider the relaxation and spatial variance of the local stress tensor and its relationship to the particle mobility and force network using simulations of cooled binary mixtures. We make direct comparisons of our off-lattice results with recent work on dynamic facilitation.

09:40  Dynamics of an interface or membrane between two fluids
B.U. Felderhof
RWTH Aachen, Aachen, Germany
The dynamics of a flat interface or membrane between two viscous fluids is studied on the basis of the linearized Navier-Stokes equations. The dispersion equation for interfacial waves involves surface tension and elasticity moduli of the interface, besides gravitational acceleration. It is shown that in a symmetric case, where the two fluids have equal viscosity and equal mass density, there is a decoupling of the capillary-gravity wave and the longitudinal elastic wave. The displacement of the interface due to a force density applied at the interface is characterized by a susceptibility tensor. Wave excitation due to a monochromatic plane wave source or a monochromatic line source located at some distance from the interface are discussed.

10:05  Coffee break

10:20  Polymer rheology and nonlinear transient elasticity
O. Müller¹, M. Liu¹, H. Pleiner², H.R. Brand^3
1 Theoretical Physics, University of Tübingen, Germany
² Max Planck Institute for Polymer Research, Mainz, Germany
³ Theoretical Physics III, University of Bayreuth, Germany
We simplify our previously derived general macroscopic equations incorporating transient elasticity by assuming incompressibility as well as linear response for the dissipation. We take into account terms up to quartic order in the elasticity (3 independent coefficients) and have in addition only two dissipative constants: the shear viscosity and the relaxation time of transient elasticity. This simple model can account for many experimentally observed rheological effects qualitatively and sometimes even quantitatively. Flow phenomena discussed include the Weissenberg effect, overshoot, relaxation spectra and elongational flows.

10:45  Plastic flow of solids
A. Minami, A. Onuki
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
A phase field model is presented to study dislocation formation (coherency loss) in one- and two-phase binary alloys. In our model, the elastic energy density is a periodic function of the strain components, which allows multiple formation of dislocations. The composition is coupled to the elastic field twofold via lattice misfit and via composition-dependence of the elastic moduli. By numerically integrating the dynamic equations in two and three dimensions, we find that dislocations appear in pairs in the interface region in two dimensions and as a loop with the ends trapped at the interface in three dimensions. They glide under uniaxial stretching in the softer region and do not penetrate into the harder domains. This process gives rise to a plastic flow, where stress increases gradually with increasing applied strain. Particularly in three dimensions, we follow the dislocation loop formation and growth around hard domains. We also observe growth of spiral-shaped domains rich in the softer component around screw dislocations.

[1] Akihiko Minami and Akira Onuki ''Dislocation formation and plastic flow in binary alloys in three dimensions'' Phys. Rev. B 72, 100101(R) (2005).
[2] Akihiko Minami and Akira Onuki, ''Dislocation formation in two-phase alloys'' Phys. Rev. B 70, 184114 (2004).

11:10  Thermodynamics of Non-Isothermal Polymer Flows: Experiment, Theory and Simulation
T.C. Ionescu¹, B.J. Edwards¹, D.J. Keffer¹, V.G. Mavrantzas^2
1 Department of Chemical Engineering, University of Tennessee, Knoxville, TN 37996-2200, USA
² Department of Chemical Engineering, University of Patras, Patras GR 26504, Greece
We provide a critical evaluation of the so-called ''Theory of Purely Entropic Elasticity'', which states that the free energy change of a flowing, non-isothermal viscoelastic fluid is entirely due to entropic effects, and contains no contributions due to elastic energy changes. Our investigation consists of both theoretical and experimental parts. In the theoretical part, we perform non-equilibrium Monte Carlo simulations to calculate both the energetic and entropic contributions to the free energy of the material under uniaxial elongational flow. This results in measurable energetic effects at higher strain rates, and these effects increase as temperature decreases. Experimentally, we measured the heat capacity at constant volume of LDPE under steady-state shear and uniaxial elongational flow conditions, and calculated the conformational contribution to this quantity. According to the Theory of Purely Entropic Elasticity, the conformational contribution to the heat capacity should be negligible, however, significant non-vanishing contributions are measurable at high strain rates. Results are qualitatively consistent between theory and simulation.

11:35  Discussion
M. Grmela

12:05  Lunch

   Day 3: Tuesday afternoon, September 5, 2006

14:00  A general methodology to predict the linear rheology of branched polymers
E. van Ruymbeke¹, R. Keunings², C. Bailly², D. Vlassopoulos^1,3
1 IESL - FORTH, Heraklion, Greece
² UCL, Louvain La Neuve, Belgium
³ University of Crete, Department of Materials Science and Technology, Heraklion, Greece
We present a general coarse-grained model for predicting the linear viscoelasic properties of branched polymers from the knowledge of their molecular structure and three viscoelastic parameters, i.e. the Rouse time of an entanglement segment, the plateau modulus and the entanglement molecular weight. The model uses the ingredients of the tube-based theories of McLeish and co-workers, and its implementation is based on a time-marching algorithm, this conceptual approach was already successfully applied to linear and star polymers, and is appropriately modified here to account for more complex branched architectures, within the framework of dynamic tube dilation (using the extended criteria of Graessley). While the fluctuations of the external branches segments are quite well described in literature, the motion of the molecular segments localized between two branching points is still an open question that we study in this work. With proper account of polydispersity and use of macromolecular coordinates for the diffusion of the branching points, successful description of a wide range of rheological data of H, pom-pom, tree-like or comb polymers is obtained. The good quality of predictions gives us confidence about this approach. More notably, we do not need to use ad hoc parameter modifications (in particular the p2 parameter) to get good results. The proposed methodology thus represents a generic approach for predicting the linear rheology of branched polymers.

14:25  2-Fluid Viscoelasticity
H. Pleiner¹, J.L. Harden^2
1 Max Planck Institute for Polymer Research, 55021 Mainz, Germany
² Dept. Physics, University of Ottawa, Ottawa Ontario K1N 6N5, Canada
We combine the nonlinear hydrodynamic description of viscoelastic fluids with a general 2-fluid hydrodynamics of 2-component (mass density) and 2-momentum (velocity) systems to give a generalized hydrodynamics model for disperse polymers and colloids. This description deals with hydrodynamic equations for the two (generally conserved) mass densities, the total (conserved) momentum density and for the non-hydrodynamic, relaxing relative velocity, the thermal degree of freedom, and either the relaxing elasticity, or transient orientation dynamics. There are special problems with this 2-fluid extension of ordinary hydrodynamics, like the choice of the transport and convection velocities or the separation of the stress tensor between the two subsystems. Generally it turns out that transport and convective velocities are material dependent and can be different for the different variables or even from each other. However, there are certain restrictions and interdependencies among them due to thermodynamic requirements. In addition, the stress division problem is not independent from the transport and convective velocity problem.

14:50  Selected nonlinear physical properties of liquid crystalline elastomers
A.M. Menzel, H.R. Brand
Theoretical Physics III, University of Bayreuth, Germany
Side-chain liquid single crystal elastomers (SCLSCEs) are unique materials combining the properties of ordinary rubbers with those of a liquid crystalline phase. Furthermore the director describing the broken symmetry in the liquid crystalline phase is coupled to deformations of the elastomer, which allows for example the reorientation of the director by external mechanical forces. In a linearized continuum theory this coupling is determined by two terms in the free energy density, which were introduced by de Gennes and contain relative rotations between the director and the polymer network. A central goal of our studies, where we analyze the macroscopic behavior of SCLSCEs in external fields, is to generalize these two terms and the complete expression for the free energy into the nonlinear domain. Physical consequences of the nonlinear terms will be discussed.

15:15  Suspensions of rodlike molecules: phase transition and equlilibration time scale for a shear flow
F. Otto, C. Löschke, J. Wachsmuth
University of Bonn, Germany
We consider the Doi-model for suspensions of rodlike molecules. We perform a bifurcation analysis for the isotropic-nematic phase transition in the force-free case. It shows that the type of bifurcation almost does not depend on the choice of the integral kernel modelling the excluded volume effect. We rigorously show the existence of exactly two branches of steady states up to rotations near the point where the isotropic phase becomes unstable. We consider as well a dilute solution exposed to a shear flow with large Deborah-number. The rod distribution will converge to an equilibrium asymptotically concentrated in flow direction. However the mean flux does not vanish (but the rods are constantly rotated). We prove that the equilibration is exponential on a time scale (Deborah number)^(-2/3). The difficulty is that the generator of the stochastic process is not symmetric. We give a hypocoercivity argument based on commutators between diffusion and mean flux in the equilibrium.

15:40  Coffee break

15:45  Poster Session »

16:35  Free time

17:00  Excursion

20:30 End of workshop day 3/5

   Day 4: Wednesday morning, September 6, 2006

Session 5 Non-equilibrium thermodynamics: Approaches and formalisms
Chair: A.N. Beris

08:00  Towards a thermodynamics of complex systems
G. Nicolis
Interdisciplinary Center for Nonlinear Phenomena and Complex Systems, Universite Libre de Bruxelles, C.P. 231, Bvd. du Triomphe, 1050 Brussels, Belgium
The limitations of the traditional thermodynamic approach in dealing with complex phenomena far from thermodynamic equilibrium are reviewed. An enlarged formulation of thermodynamics incorporating concepts and tools from nonlinear science and stochastic processes is outlined and shown to provide universal relationships of a new kind linking the relevant variables, as well as efficient methods for characterizing the structure and dynamics of large classes of complex nonlinear systems. Some implications of this formalism in selected problems of current concern are explored.

08:50  Non-Equilibrium Thermodynamics of Boundary Conditions
H.C. Öttinger
ETH Zürich, Department of Materials, Institute of Polymers, HCI H 543, CH-8093 Zürich, Switzerland
While the field equations for complex fluids are usually formulated such that they respect the principles of nonequilibrium thermodynamics, the choice of appropriate boundary conditions is often considered as a purely mathematical problem. We here emphasize that also the formulation of boundary conditions should be guided by thermodynamics. The GENERIC framework is generalized to systems consisting of coupled 3-d bulk and 2-d boundary variables. The ideas and concepts are illustrated for two examples: (i) bulk and surface diffusion phenomena for a dilute suspension of Brownian particles, and (ii) velocity slip of entangled polymer melts at solid walls.

09:15  Extended thermodynamics of polymers and superfluids
D. Jou¹, J. Casas-Vazquez¹, M. Criado-Sancho², M.S. Mongiovi^3
1 Universitat Autonoma de Barcelona, Bellaterra, Catalonia, Spain
² UNED (Universidad Nacional de Education a Distancia), Madrid, Spain
³ Universita di Palermo, Palermo, Italy
The viscous pressure tensor may be used as a thermodynamic independent variable in a variety of situations. This leads to evolution equations for the viscous pressure tensor, and to generalized non-equilibrium entropy and chemical potential depending on the viscous pressure. We will illustrate the application of this extended thermodynamic formalism to polymer solutions and blends, and to quantum turbulence in superfluids. For polymer solutions, we will deal with shear-induced effects on the stability of the solution and phase separation, for superfluids, we will focus our attention on quantum turbulence induced by a combination of a heat flux and rotation.

09:40  Kinematics of turbulence in simple and polymeric fluids
M. Grmela
Ecole Polytechnique de Montreal, Montreal H3C 3A7, Canada
How to detect and describe the complex features of solutions of hydrodynamic equations representing turbulent flows? A new route, based on the Hamiltonian (GENERIC) formulation of Lagrangian viewpoint of fluid motion is explored. Two-point distribution function of fluid particles is chosen as the state variable. The Hamiltonian formulation of its time equation allows to consider separately the kinematics (Poisson bracket) and the dynamics (generating potential). Only the kinematics is discussed. The Poisson bracket expressing it is rigorously identified. The resulting time evolution equations are shown, in a particular case, to unify and extend the equations arising in Reynolds and Lagrange averaging. Parallel discussion of the turbulent kinematics in simple and polymeric fluids offers a new view of the difference in their turbulent flows.

10:05  Coffee break

10:20  Nonequilibrium thermodynamics of elasto-viscoplastic deformation
M. Hütter, T.A. Tervoort, H.C. Öttinger
Department of Materials, ETH Zurich, Switzerland
Plasticity theories describe the transition from compressible elastic behavior at low stress to isochoric plastic deformation at high stress levels, and are often formulated by relating the elastic strain rate to an objective stress rate. In this contribution, the modeling of such behavior by way of nonequilibrium thermodynamics is examined, namely by using the GENERIC formalism. First, nonisothermal general elasticity is formulated in terms of the left Cauchy-Green strain tensor, the temperature, and the momentum density. In a second step, we study specific relaxation mechanisms of the strain tensor to describe elasto-viscoplastic behavior with emphasis on volume relaxation, and discuss the relation to common inelastic deformation models. For various equations of state, predictions of the model for specific mechanical tests are presented.

10:45  On a possible difference between the barycentric velocity and the velocity that gives translational momentum in fluids
D. Bedeaux¹, S. Kjelstrup¹, H.C. Öttinger^2
1 Dept. of Chem, Norw. Univ. of Sc. and Techn, Trondheim, Norway
² ETH Zürich, Dept. of Materials, Polymer Physics, Switzerland
This contribution explores the rather controversial proposal by Howard Brenner that the velocities that follow from the mass flux and from the translational momentum in a fluid are not equal. We show that standard non-equilibrium thermodynamics can be formulated such that it is in full agreement with this proposal. We argue that the merits of the proposal must be based on the physics of the problem. It cannot be dismissed as being in contradiction with non-equilibrium thermodynamics. We show that Brenner's proposal gives a separation in a binary mixture beyond that of the Soret equilibrium, due to a gradient in the pressure divided by the temperature. Experiments to verify this are proposed.

11:10  Non-Equilibrium Thermodynamic Fluctuations within the Framework of Path Integrals
A. McKane¹, F. Vazquez², M.A. Olivares-Robles^3
1 Theory Group, School of Physics and Astronomy, University of Manchester M13 9PL, United Kingdom
² Facultad de Ciencias, UAEM, Av. Universidad 1001, Cuernavaca, Morelos 62209, Mexico
³ Seccion de Investigacion y Posgrado, ESIME-Culhuacan, IPN, Mexico D.F.
Fluctuational non-equilibrium thermodynamics is formulated in terms of path integrals. The theory is presented in such a way that it will be applicable to a wide class of stochastic processes, including non-Markovian processes. In particular, we show how to construct the path-integral scheme when the noise-correlation matrix is singular, which is the case for fluctuations in non-equilibrium thermodynamics, since the continuity equation has no stochastic term associated with it. The theory is illustrated by calculating the light-scattering spectrum in fluids. Non-linear contributions to this quantity are also computed.

11:35  Discussion
A.N. Beris

12:05  Lunch

   Day 4: Wednesday afternoon, September 6, 2006

Session 6 Coarse-graining and mesoscopic dynamics - some mathematical aspects
Chair: B.J. Edwards

14:00  Dissipation and Stress
P. Constantin
Department of Mathematics, The University of Chicago, Chicago, IL 60637, USA
I will discuss energetics, dynamics and asymptotics of systems consisting of fluids and particles from a mathematical perspective.

14:25  Self-similarity in Smoluchowski's coagulation equation
G. Menon¹, R.L. Pego^2
1 Division of Applied Mathematics, Brown University, USA
² Depat. of Mathematical Sciences, Carnegie Mellon University, USA
Smoluchowski's coagulation equations are a fundamental mean-field model of coalescence describing for example, the formation of clouds, and the kinetics of polymerization. An issue of importance is `dynamic scaling' or the approach to self-similarity. I will describe some interesting mathematical features of this non-equilibrium system related to the dynamic scaling hypothesis.

14:50  Stress relaxation theories in the approximation of polyconvex elastodynamics by viscoelasticity
T. Tzavaras
Department of Mathematics, University of Maryland, USA
We consider a model of stress relaxation approximating the equations of elastodynamics in Lagrangian coordinates. Necessary and sufficient conditions are derived for the model to be equipped with a global free energy and to have positive entropy production. For convex equilibrium potentials, we prove a relative energy estimate that provides convergence to the equations of elastodynamics when the solutions are smooth. In the case of polyconvex elastodynamics the situation is delicate because it is known from general theory of relaxation processes that the approximating system cannot have a convex energy as well. On the other hand, the equations of polyconvex elastodynamics can be embedded to an augmented symmetric hyperbolic system. We devise a model of stress relaxation motivated by the format of the enlargement process which formally approximates the equations of polyconvex elastodynamics. The model is endowed with an entropy function which is not convex but rather of polyconvex type. Using relative entropy ideas we prove a stability estimate and convergence of the stress relaxation model to polyconvex elastodynamics in the smooth regime.

15:15  Numerical analysis of coarse-graining for stochastic systems
P. Plechac
Mathematics Institute, University of Warwick, United Kingdom
We discuss some general mathematical issues arising in problems where the microscopic Markov process is approximated by a hierarchy of coarse-grained processes. In applications the microscopic model is often coupled with continuum description (using PDEs) on larger scales. We describe hierarchy of coarse-grained stochastic processes that approximate, on larger scales, microscopic lattice systems simulated by (kinetic) Monte Carlo algorithm. We present mathematical tools (e.g., estimates on the loss of information between the coarse-grained and the microscopic probability measures) developed for error control in microscopic simulations using the coarse-grained stochastic processes. On specific examples of lattice spin dynamics we demonstrate that computational implementation of constructed coarse-grained approximation leads to significant CPU speed up of simulations.

15:40  Coffee break

15:55  Mathematical and computational methods for coarse-graining
M.A. Katsoulakis
University of Massachusetts, Amherst, USA
In this talk we discuss recent progress in obtaining coarse-grained stochastic approximations of microscopic lattice dynamics. We prove rigorous error estimates both at equilibrium and non-equilibrium in terms of weak convergence and relative entropy calculations and obtain a posteriori estimates that can guide adaptive coarse-grained simulations. We also demonstrate, with direct comparisons between microscopic Monte Carlo and coarse-grained simulations, that the derived mesoscopic models provide a substantial CPU reduction in the computational effort. Finally we discuss the use of such coarse-grained models in the simulation of hybrid systems. Such models arise as couplings of stochastic, spatially distributed systems representing active small scales to deterministic macroscopic equations and are commonplace in applications ranging from catalysis and deposition processes to complex biological cell networks.

16:20  Some mathematical issues arising in the multiscale modelling of complex fluids
C. Le Bris
CERMICS, Ecole Nationale des Ponts et Chaussees, France
We will investigate some mathematical issues related to the modeling of complex fluids. The focus will be both on polymeric fluid flows and suspensions. In particular, we will deal with the well-posedness of the equations and their long-time behaviour.

16:45  Discussion
B.J. Edwards

17:00  Free time

20:30  Gala dinner

22:30 End of workshop day 4/5

   Day 5: Thursday morning, September 7, 2006

Session 7 Applications to complex materials: glasses, micelles, colloids, blends, interfaces
Chair: V.G. Mavrantzas

08:00  Ergodicity-breaking in glassforming liquids (and related systems), and relaxation processes below the glass temperature, Tg
C.A. Angell
Dept. of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287-1604, USA
We first discuss briefly the factors that frustrate the drive to crystallization below the melting point in certain substances called ''glassformers'', thereby permitting long-lived supercooled liquid states. We then consider how to predict the temperature at which such metastable liquids will become glasses during steady cooling (the ergodicity-breaking criterion). In the state of ''broken ergodicity'', there are various dynamic processes that are of interest. Firstly, we consider the primary (structural) relaxation process. Below their Tg systems evolve (''age'', or ''anneal'') at rates determined by their thermal history - which are predictable if the departures from equilibrium are not too great. Secondly we consider processes which are only weakly coupled to the primary relaxation, hence remain active even when the primary relaxation is completely frozen. Examples are the diffusion of small cations responsible for superionic conductivity in inorganic glasses, and the motion of molecules that cause most polymers, glassy or otherwise, to be permeable to gases. These subsystems have their own quasi-equilibrium states which can be lost below their own ''mobile species glass transition''s. Below this subsystem Tg, a new and mostly unexplored sort of ageing behavior can be observed.

08:50  Entropy production of oscillatory flows between parallel plates
M. Lopez de Haro¹, S. Cuevas¹, M.A. Olivares-Robles², F. Vazquez^3
1 Centro de Investigacion en Energia, UNAM, Temixco, Morelos 62580, Mexico
² Seccion de Investigacion y Posgrado, ESIME-Culhuacan, IPN, Mexico D.F.
³ Facultad de Ciencias, UAEM, Cuernavaca, Morelos 62209, Mexico
The heat transfer problem of a zero-mean oscillatory flow of both a Newtonian and a Maxwell fluid between infinite parallel plates with boundary conditions of the third kind is considered. With the analytic solutions for the velocity and temperature fields at hand, the local and global time-averaged entropy production are computed. The consequences of convective cooling of the plates are assessed for this problem.

09:15  A thermodynamically consistent model for the thixotropic rheological behavior of concentrated colloidal star polymer solutions
A.N. Beris¹, D. Vlassopoulos^2
1 Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716, USA
² Foundation for Research and Technology - Hellas (FORTH), Institute of Electronic Structure & Laser, and University of Crete, Department of Materials Science & Technology, P.O.Box 1527, Road to Voutes, Vasilika Vouton 71110 Heraklion, Crete, Greece
In this work we report a new model for the rheological thixotropic behavior of colloidal star polymer solutions. Given the excellent capabilities of controlling the molecular structure star polymers constitute an ideal system for exploring the soft matter rheology. The stars exhibit dual, colloidal and polymeric, behavior manifested in several physical properties and in particular their relaxation and flow. Detailed optical and rheological experiments have revealed the interplay between their molecular microstructure and their macroscopic rheological properties often characterized by viscoplasticity (yield stress) and thixotropy (time dependent rheological behavior) [1]. In the present work we use them as a model system in order to better understand thixotropy. Thixotropy is typically modeled phenomenologically as a structurally-dependent viscoplastic behavior [2]. However, the resulting models are often restricted to simple shear flows and are not presented in a form that can be shown do be consistent with nonequilibrium thermodynamics. In the present work we present a new thixotropy model for a well defined system of colloidal star polymer suspensions that is based on previous ideas from the description of polymeric liquid crystals and viscoelasticity. As a result, the model is presented in a thermodynamically admissible form, which is also generally applicable to arbitrary flows. In addition, the model parameters are connected to the system's molecular microstructure. A comparison of the model's predictions against steady and transient rheological viscometric data as well as some optical (DLS) experiments allows for the first time a direct connection of rheology to the system's microstructure for a system exhibiting yield stress and thixotropy.

[1] E. Stiakakis et al., PRE, 66, 051804 (2002)
[2] A. Mujumdar, A.N. Beris and A.B. Metzner, J. Non-Newtonian Fluid Mech., 102:157-178 (2002)

09:40  Extrudate swell control by balancing short and long polyethylene chains using multi-scale modeling
C.F.J. den Doelder
Dow Benelux B.V., P.O. Box 48, 4530AA, Terneuzen, The Netherlands
The presentation first introduces the current trends in complex fluids modeling at Dow. Second, as an example, a multi-scale modeling based polymer design study is presented. Designed molar mass distributions enabled from polyethylene synthesis capabilities are fed to a double reptation mesoscale model to derive polymer elasticity. The calculated compliance is used as correlator to extrudate swell, improving on existing empirical correlations. The correlation comprises a connection between linear viscoelasticity and non-linear complex processing behavior. Its validity is made plausible from the related dynamics of recovery after deformation, but an intriguing timescale mismatch needs to be bridged. Non-equilibrium thermodynamics might provide theoretical tools to build this bridge.

10:05  Coffee break

10:20  Flow of Polymer blends between Concentric Cylinders
M. Dressler¹, B.J. Edwards², E.J. Windhab^1
1 Institute of Food Science and Nutrition, ETH Zurich, Switzerland
² Department of Chemical Engineering, University of Tennessee, Knoxville, TN 37996-2200, USA
A thermodynamically consistent model for polymer blends with matrix phase viscoelasticity and break-up/coalescence is solved for laminar flows in the gap between concentric cylinders. The model has been developed using a Hamiltonian framework of non-equilibrium Thermodynamics. The model is solved for Poiseuille (axial), Couette (angular), and mixed Couette-Poiseuille (helical) flow to understand qualitatively viscometric material properties and droplet deformation in non-homogeneous shearing flows. Therefore, the model equations are formulated in terms of a two-point boundary value problem and a shooting algorithm is adopted to compute the non-linear flow fields together with the elastic stresses, the droplet shapes, and the break-up/coalescence rates in the gap. We investigate the profiles of the stress tensor components in connection with the droplet characteristics, we valuate viscometric material functions at the wall, and we discuss the narrow gap approximation. Moreover, we examine the influence of centrifugal forces on the flow behavior, and in particular on the break-up/coalescence rates in the gap for the three flows.

10:45  On the rheology of a dilute suspension of vesicles
C. Misbah, G. Danker
LSP, Univ. J. Fourier, Grenoble I andCNRS, BP 87, 38402 Saint Martin d'Heres, France
From the hydrodynamical equations of vesicle dynamics under shear flow, we extract a rheological law for a dilute suspension. This is made analytically in the small excess area limit. In contrast to droplets and capsules, the rheological law obtained here is, apart from an objective derivative, nonlinear even to the first leading order. We exploit it by evaluating the effective viscosity η_eff and the normal stress differences N₁ and N₂. We make a link between rheology and microscopic dynamics. For example, η_eff is found to exhibit a cusp singularity at the tumbling threshold, while N_1,2 undergoes a collapse.

11:10  Atomistic molecular dynamics simulation of the temperature and pressure dependences of local and terminal relaxations in cis-1,4-polybutadiene
G. Tsolou, V.G. Mavrantzas
¹ Department of Chemical Engineering, University of Patras, GR 26504, Greece
² Institute of Chemical Engineering and High-Temperature Chemical Processes (FORTH-ICE/HT), Patras GR 26504, Greece
We have explored features of local and terminal relaxation in cis-1,4-polybutadiene (cis-1,4-PB) over a wide range of temperature and pressure conditions by conducting atomistic molecular dynamics simulations (MD) with a united atom model on a 32-chain C128 cis-1,4-PB system [1]. Segmental relaxation was analyzed in terms of the dipole moment time autocorrelation function (DACF) of the simulated polymer. By Fourier transforming the DACF, the dielectric spectrum was computed and the validity of the time-temperature and time-pressure superposition principles were checked to decide for the appearance or not of additional relaxation mechanisms at low enough temperatures or high enough pressures. The relative contribution of thermal energy and volume to segmental relaxation was also calculated and evaluated in terms of the ratio QV/QP [2]. In contrast to experimental studies in other polymers [3], our results support that, in the temperature and pressure range studied, segmental and chain relaxations are influenced similarly by pressure and temperature variations. Further information about the dynamics of the intermediate chain segments has been extracted through the calculation of the dynamic structure factor. Current efforts focus on the determination of characteristic relaxation times in cis-1,4-PB and their variation with density or temperature and pressure, separately.

[1] G. Tsolou, V.A. Harmandaris, V.G. Mavrantzas, Macromol. Theory Simul. 15, 381 (2006).
[2] G. Tsolou, V.A. Harmandaris, V.G. Mavrantzas, J.Chem.Phys. 124, 084906 (2006).
[3] G. Floudas, T. Reisinger, J. Chem.Phys. 111, 5201 (1999).

11:35  Discussion
V.G. Mavrantzas

12:00  Lunch

14:00  Discussion - Closing remarks
V.G. Mavrantzas