Regularization of the Burnett Hydrodynamics
M. Colangeli¹, I.V. Karlin², H.C. Öttinger^1
1 ETH Zürich, Dept. of Materials, Polymer Physics, Switzerland
² Institute of Energy Technology, ETH Zurich, Zurich 8092, Switzerland
As it was first demonstrated by Bobylev [1], even in the simplest regime (one-dimensional linear deviations around the global equilibrium), the Burnett hydrodynamic equations violate the basic physics behind the Boltzmann equation. Namely, sufficient short acoustic waves are amplified with time instead decaying. This contradicts the H-theorem, since all near-equilibrium perturbations must decay. The lower order truncation of the Chapman-Enskog expansion also contradicts the dissipative properties of Grad moment equations [2]. The mathematical reason for the instability paradox is shown and a method to regularize the equations of hydrodynamics is proposed.

[1] Bobylev, A.V., Instabilities in the Chapman-Enskog Expansion and Hyperbolic Burnett Equations, Journal of Stat. Phys., DOI: 10.1007/s10955-005-8087-6 (2006).
[2] Gorban, A.N, Karlin, I.V., Hydrodynamics from Grad's equations: What can we learn from exact solutions? Ann. Phys. (Leipzig) 11 (2002).

Toward a thermodynamic description of chemical reaction networks
A.G. Cantu, G. Nicolis
Interdisciplinary Center for Nonlinear Phenomena and Complex Systems, Universit�ibre de Bruxelles, C.P. 231, Bvd. du Triomphe, 1050 Brussels, Belgium
The relation between the topology of a chemical reaction network and its thermodynamic properties, particularly the energy dissipation patterns, is analyzed. Both regular and complex structures are considered. For networks consisting of linear reactions this task is analytically accomplished by formulating the network dynamics in terms of the network.s connectivity matrix. The thermodynamic effect of nonlinear feedback dynamics on chemical networks is considered in the limits of close to and far away from equilibrium and discussed in connection with the robustness of the response to external disturbances.

Structure and dynamics of polyethylene melts bearing short chain branches frequently spaced along their backbone as revealed from atomistic simulations
V. Dimitriadis¹, N. Karayiannis¹, V.G. Mavrantzas¹, E. Chiotellis², D. Mouratides², C.D. Kiparissides^2
1 Department of Chemical Engineering, University of Patras & FORTH-ICE/HT, Patras GR 26504, Greece
² Department of Chemical Engineering, Aristotle University of Thessaloniki & CPERI-CERTH, Thessaloniki 54124, Greece
Based on the molecular architecture of the constituent chains polyethylene (PE) is usually classified as HDPE (High Density PE), LLDPE (Linear Low Density PE), and LDPE (Low Density PE). HDPE consists of linear chains resulting from the catalytic reaction of pure ethylene monomers, LLDPE consists of chains bearing short branches sparsely distributed along their main backbone and LDPE consists of chains with densely packed branches of variable length that may carry additional arms thus creating a complex, dendritic-like structure. LDPE and other well-defined polymers with several kinds of molecular architecture are nowadays synthesized by metallocene and other single-site catalysts through anionic living polymerization techniques by employing organolithium initiators. Also, dangling branches are considered in general as ''long'' or ''short'' if their length longer or shorter, respectively, than the characteristic molecular length between entanglements, Ne, which for PE is around C70. In this work, we will present results for the effect of short chain branching (SCB) on the volumetric, structure, conformational and dynamic properties of PE obtained from detailed atomistic MC and MD simulations with two families of PE microstructures: the first corresponded to a total of 142 carbon atoms per chain (MW = 1990 g/mol) and the second to a total of 320 carbon atoms per chain (MW = 4482 g/mol). We will show that short-chain branched (SCB) PE melts are characterized by significantly smaller dimensions than linear PE melts of the same total chain length under the same temperature and pressure conditions, due to the more symmetric arrangement of their material around the chain center-of-mass. In contrast, SCB and linear PE melts of the same chain length exhibit practically identical volumetric properties, suggesting that the differences recorded at temperatures below their melting point in the densities of the ''LLDPE'' and ''HDPE'' end-products of PE are due to their totally different degrees of crystallinity. We will also show that short-chain branching causes a decrease in the chain self diffusion coefficient compared to the value exhibited by the linear melt of the same total chain length by a factor which can range from 10 up to 40% depending on the molecular characteristics of the simulated system (branch length, branching frequency, and total chain length).

Acceleration of Relaxation of an Entangled Polymer Chain in a Melt by Confinement into a Slit
K. Hagita¹, H. Takano^2
1 Department of Applied Physics, National Defense Academy, Japan
² Department of Physics, Keio University, Japan
Relaxation modes and rates of a polymer chain in a melt confined into a slit by repulsive walls are studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Reduction of the glass transition temperatures Tg, which means a decrease of the relaxation time, of unentangled chains in thin polymer films as the films become thinner has been examined by experiments and simulations. Polymer chains of N segments are located on an L x L x W simple cubic lattice under periodic boundary conditions in the x- and y-directions. The N- and W-dependences of the longest relaxation time are examined for N = 32 -- 512 and W = 8, 16, 32 and 64 at the volume fraction 0.5. For W = 8, the relaxation time of a polymer chain of N=512 segments is shorter than that in the bulk. The apparent exponent of the power law dependence of the relaxation time on N is estimated to be 2.8 for N=256 and 512, while the apparent exponent in the bulk is 3.5.

Studying the Curvature Elasticity of Biomembranes Through Numerical Simulations
V. Harmandaris, M. Deserno
Max-Planck-Institute for Polymer Research, D-55021 Mainz, Germany
One of the main aspects in the study of biological membranes is the curvature elasticity of membranes. A well known way to predict the free energy is from the spectrum of equilibrium membrane fluctuations: according to Helfrich theory if one expands the interface in modes in the Fourier space then in the limit of the linear curvature elasticity this can be directly related to the bending modulus. This method, however, cannot be easily generalized to higher than linear curvature models. Here we propose an alternative methodology for studying the curvature elasticity of membranes. The basic idea is to impose a deformation of the membrane and measure the force required to hold it in the deformed state. Specifically we stretch a cylindrical vesicle and measure the force needed for such an extension. Results are presented about the force acting on the stretching cylindrical vesicle as well as about the bending modulus as a function of the curvature. The values for the bending modulus are also compared with the predictions from the analysis of the spectrum of equilibrium membrane fluctuations.

Nonequilibrium thermodynamics aspects of a disspative electromagnetism
A. Jelic, M. Hütter, H.C. Öttinger
ETH Zurich, Department of Materials, Switzerland
The standard macroscopic Maxwell equations are obtained from the microscopic ones by spatial and/or ensemble averaging. However, in both cases, only single time properties are considered, while temporal correlations and two-time ensemble averages are neglected. In this work we examine specifically dissipative effects in electromagnetism on macroscopic scales by coarse-graining the microscopic Maxwell equations with respect to time. Particular emphasis is put on the derivation of the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them, which give rise to dissipative processes such as Ohmic currents, the thermoelectric effect, and also to irreversible contributions to the electric and magnetic fields. In order to capture the interplay between the thermodynamic behavior of the medium and the electromagnetic field, and to discuss dissipative effects in electromagnetism in a consistent manner we have used the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework. The results are compared to the ones of Liu and coworkers, who previously incorporated dissipative effects into the Maxwell equations [1].

[1] Phys. Rev. Lett. 70, 3580 (1993) and later papers.

Models for polymeric and anisotropic liquids
M. Kröger
ETH Zurich, Polymer Physics, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland
We summarize some recent developments in the area of the simulation and theory of complex fluids. Emphasis is placed on tensorial symmetries, FENE models for polymeric liquids, ferrofluids, and beyond-equilibrium molecular dynamics [1,2].

[1] M. Kröger, Phys. Rep. 390 (2005) 453 ».
[2] M. Kröger, Models for polymeric and anisotropic liquids (Springer, Berlin, 2005) »

Coarse Grained Molecular Dynamics Simulation of the Adhesion between End-grafted Polymer Films
H. Morita¹, H. Miura, M. Yamada², T. Yamaguchi¹, M. Doi^1
1 The University of Tokyo & JST-CREST, Japan
² Nagoya University, Japan
Adhesion between two polymer films consisting of end grafted polymer is studied by coarse-grained molecular dynamics. The stress-distance curve for the end-grafted polymers is obtained at various temperatures with changing the grafted polymer density and topology of chain conformations. From our result, we can organize three types of the separation patterns, brittle, fibril, and cavity separations. We can find that the adhesion force (stress) for brittle separation is much stronger than those for other separations. On the other hand, the adhesion energy for fibril separation is largest one among three separations. In the presentation, we will present the relation between the separation pattern (separated structure) and the adhesion force/energy.

A stochastic dynamics of a linear macromolecule and viscoelasicity of entangled systems
G.V. Pyshnograi¹, Y.A. Altukhov¹, V.N. Pokrovskii^2
1 Altai State Technical University, Barnaul, Russia
² University of Malta, Malta
To interpret the relaxation behaviour of entangled linear polymers in terms of dynamics of a single macromolecule, we have been developing the approach, which allows one to study systematically deviations from the Rouse dynamics, when adding non-Markovian and anisotropic noise. It was shown earlier, that the introduction of specific form of non-Markovian dynamics leads to emerging of an intermediate length, which has the meaning of a tube radius and/or the length of a macromolecule between adjacent entanglements. The additional introduction of local anisotropy of mobility of particles allows one to get the results of the conventional reptation-tube model for both mobility and relaxation times of macromolecular coil and, beyond it, to estimate a transition point between weakly (the length of macromolecules M < 10 Me, no reptation) and strongly (the length of macromolecules M > 10 Me, reptation) entangled polymer systems. The adequate mesoscopic equation allows us to develop theory of different relaxation phenomena, in particular, a theory of viscoelasticity and to formulate constitutive equations for linear polymers, which, due to the difference of mechanisms of relaxation, appear to be different for the two types of entangled systems.

Relaxation of Knotted Ring Polymers
S. Saka, H. Takano
Department of Physics, Keio University, Japan
The relaxation of a knotted ring polymer with N segments is studied by Brownian dynamics simulations. The relaxation rate of the Fourie transform with the wave number p of the segment positions is estimated by the least square fit of the equilibrium time-displaced autocorrelation function of the Fourie transform to a single exponential decay at long times. For the trivial knot, the relaxation rate distribution appears to be proportional to (1/N)^2.17 for p=1 and to (p/N)^2.14 for p>1. These exponents are similar to that found for a linear polymer chain. Even in the case of the trivial knot, the topological effect appears as the difference between the amplitudes of the power law dependences of the relaxation rates for p=1 on 1/N and those for p>1 on p/N. Note that no such difference appears for a linear polymer chain. For the trefoil knot, not p=1 but p=2 corresponds to the slowest relaxation rate for each N. For p=1, the relaxation rates for the trefoil knot are larger than those for the trivial knot, while they are smaller for p>1.

A consideration on the Discrete Boltzmann Equation using the analytical result of the relaxation equation
M. Seino¹, T. Tanahashi^2
1 Keio University Graduate School, Japan
² Keio University, Japan
The calculation method on the relaxation equation based on Discrete Boltzmann Equation (DBE) is discussed. The characteristic of this method is using analysis result of the relaxation equation, therefore the equation can be calculated using this method with bigger time step number and higher precision than using conventional time integration methods. As the result, this formulation is expected of the achievement of the hard calculation condition using DBE.