Fathollah Varnik

Computer simulations of supercooled polymer melts in the bulk and in confined geometry

We survey results of computer simulations for the structure and dynamics of supercooled polymer melts and films. Our survey is mainly concerned with features of a coarse grained polymer model?a bead?spring model?in the temperature regime above the critical glass temperature Tc of the ideal mode-coupling theory (MCT). We divide our discussion into two parts: a part devoted to bulk properties and a part dealing with thin films. The discussion of the bulk properties focuses on two aspects: a comparison of the simulation results with MCT and an analysis of dynamic heterogeneities. We explain in detail how the analyses are performed and what results may be obtained, and we critically assess their strengths and weaknesses. In discussing the application of MCT we also present first results of a quantitative comparison which does not rely on fits, but exploits static input from the simulation to predict the relaxation dynamics. The second part of this review is devoted to extensions of the simulations from the bulk to thin films. We explore in detail the influence of the boundary condition, imposed by smooth or rough walls, on the structure and dynamics of the polymer melt. Geometric confinement is found to shift the glass transition temperature Tg (or Tc in our case) relative to the bulk. We compare our and other simulation results for the Tg shift with experimental data, briefly survey some theoretical ideas for explaining these shifts and discuss related simulation work on the glass transition of confined liquids. Finally, we also present some technical details of how to perform fits to MCT and give a brief introduction to another approach to the glass transition based on the potential energy landscape of a liquid.

Reduction of the glass transition temperature in polymer films: a molecular-dynamics study.

We present results of molecular-dynamics simulations for a nonentangled polymer melt confined between two completely smooth and repulsive walls, interacting with inner particles via the potential U(wall)=(sigma/z)(9), where z=/z(particle)-z(wall) and sigma is (roughly) the monomer diameter. The influence of this confinement on the dynamic behavior of the melt is studied for various film thicknesses (wall-to-wall separations) D, ranging from about 3 to about 14 times the bulk radius of gyration. A comparison of the mean-square displacements in the film and in the bulk shows an acceleration of the dynamics due to the presence of the walls. This leads to a reduction of the critical temperature T(c) of the mode coupling theory with decreasing film thickness. Analyzing the same data by the Vogel-Fulcher-Tammann (VFT) equation, we also estimate the VFT temperature T0(D). The ratio T0(D)/T(bulk)(0) decreases for smaller D similarly to T(c)(D)/T(bulk)(c). These results are in qualitative agreement with that of the glass transition temperature observed in some experiments on supported polymer films.

Molecular dynamics results on the pressure tensor of polymer films

Polymeric thin films of various thicknesses, confined between two repulsive walls, have been studied by molecular dynamics simulations. Using the anisotropy of the perpendicular, PN(z), and parallel components, PT(z), of the pressure tensor the surface tension of the system is calculated for a wide range of temperature and for various film thicknesses. Three methods of determining the pressure tensor are compared: the method of Irving and Kirkwood (IK), an approximation thereof (IK1), and the method of Harasima (H). The IK- and the H-methods differ in the expression for PT(z) (z denotes the distance from the wall), but yield the same formula for the normal component PN(z). When evaluated by molecular dynamics (or Monte Carlo)-simulations PN(z) is constant, as required by mechanical stability. Contrary to that, the IK1-method leads to strong oscillations of PN(z). However, all methods give the same expression for the total pressure when integrated over the whole system, and thus the same surface tension, w...

Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method

The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J.M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Strain energy function of red blood cell membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.

Cooling rate dependence of the glass transition temperature of polymer melts: Molecular dynamics study

A coarse-grained bead spring model of short polymer chains is studied by constant pressure molecular dynamics (MD) simulations. Due to two competing length scales for the length of effective bonds and the energetically preferred distance between nonbonded beads, one observes a glass transition when dense melts are cooled down (as shown in previous work, at a pressure p=1 the mode coupling critical temperature is at Tc≈0.45 and the Vogel–Fulcher temperature is T0≈0.33, in Lennard-Jones units). The present work extends these studies, estimating a cooling-rate-dependent glass transition temperature Tg(Γ) by cooling the model system from T=0.6 down to T=0.3, applying cooling rates from Γ≈10−3 to Γ≈10−6 (in MD time units), and attempting to identify Tg(Γ) from a kink in the volume versus temperature or potential energy versus temperature curves. It is found that Tg(Γ) lies in the range 0.43⩽Tg(Γ)⩽0.47, for the cooling rates quoted, and the variation of Tg(Γ) for Γ is compatible with the expected logarithmic va...

Molecular Dynamics Simulations

A tutorial introduction to the technique of molecular dynamics (MD) is given, and some characteristic examples of applications are described. The purpose and scope of these simulations and the relation to other simulation methods is discussed, and the basic MD algorithms are described. The sampling of intensive variables (temperature T, pressure p) in runs carried out in the microcanonical (NV E) ensemble (N = particle number, V = volume, E = energy) is discussed, as well as the realization of other ensembles (e.g. the NV T ensemble). For a typical application example, molten SiO2, the estimation of various transport coefficients (self-diffusion constants, viscosity, thermal conductivity) is discussed. As an example of non-equilibrium molecular dynamics, a study of a glass-forming polymer melt under shear is mentioned.

Shear stress in lattice Boltzmann simulations

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second-order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also investigated which value of the relaxation parameter minimizes the error. Furthermore, for simulations using velocity boundary conditions, an artificial mass increase is often observed. This is a consequence of the compressibility of the lattice Boltzmann fluid. We investigate this issue and derive an analytic expression for the time dependence of the fluid density in terms of the Reynolds number, Mach number, and a geometric factor for the case of a Poiseuille flow through a rectangular channel in three dimensions. Comparison of the analytic expression with results of lattice Boltzmann simulations shows excellent agreement.

Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells

Via computer simulations, we provide evidence that the shear rate induced red blood cell tumbling-to-tank-treading transition also occurs at quite high volume fractions, where collective effects are important. The transition takes place as the ratio of effective suspension stress to the characteristic cell membrane stress exceeds a certain value and does not explicitly depend on volume fraction or cell deformability. This value coincides with that for a transition from an orientationally less ordered to a highly ordered phase. The average cell deformation does not show any signature of transition, but rather follows a simple scaling law independent of volume fraction.

Roughness-gradient–induced spontaneous motion of droplets on hydrophobic surfaces: A lattice Boltzmann study

The effect of a step-wise change in the pillar density on the dynamics of droplets is investigated via three-dimensional lattice Boltzmann simulations. For the same pillar density gradient but different pillar arrangements, both motion over the gradient zone as well as complete arrest are observed. In the moving case, the droplet velocity scales approximately linearly with the texture gradient. A simple model is provided reproducing the observed linear behavior. The model also predicts a linear dependence of droplet velocity on surface tension. This prediction is clearly confirmed via our computer simulations for a wide range of surface tensions.

Computer Simulations of Polymers Close to Solid Interfaces: Some Selected Topics

This paper presents a topical overview of molecular-dynamics and Monte Carlo simulations for polymer systems close to solid interfaces. The simulations utilize simplified coarse-grained models: The polymers are represented by bead-spring chains, and the walls by a crystalline layer of Lennard-Jones particles or by a smooth impenetrable barrier. This approach has two advantages. First, it reduces the complexity of the simulation. Often, it is only then possible that the interesting length and time scales can be studied at all. Second, the approach concentrates on generic features that are believed to determine the physics of the problem under consideration. The results of the simulation can thus help to single out those features which should be incorporated in an analytical treatment. In this paper, we want to illustrate the versatility of these models by applying them to a broad spectrum of different problems. The situations considered range from the adsorption of a polymer from dilute solution onto a wall, over the importance of sub-monolayer monomeric or polymeric lubricants for kinetic friction, to the crystallization or glass transition of dense polymer films.