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 T c of the ideal modecoupling 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 T g (or T c in our case) relative to the bulk. We compare our and other simulation results for the T g 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.

The stress-strain relations and the yield behavior of a model glass (a 80:20 binary Lennard-Jones mixture) is studied by means of molecular dynamics simulations. In a previous paper it was shown that, at temperatures below the glass transition temperature, Tg, the model exhibits shear banding under imposed shear. It was also suggested that this behavior is closely related to the existence of a (static) yield stress (under applied stress, the system does not flow until the stress sigma exceeds a threshold value sigmay). A thorough analysis of the static yield stress is presented via simulations under imposed stress. Furthermore, using steady shear simulations, the effect of physical aging, shear rate and temperature on the stress-strain relation is investigated. In particular, we find that the stress at the yield point (the "peak"-value of the stress-strain curve) exhibits a logarithmic dependence both on the imposed shear rate and on the "age" of the system in qualitative agreement with experiments on amorphous polymers, and on metallic glasses. In addition to the very observation of the yield stress which is an important feature seen in experiments on complex systems like pastes, dense colloidal suspensions and foams, further links between our model and soft glassy materials are found. An example is the existence of hysteresis loops in the system response to a varying imposed stress. Finally, we measure the static yield stress for our model and study its dependence on temperature. We find that for temperatures far below the mode coupling critical temperature of the model (Tc = 0.435 in Lennard-Jones units), sigmay decreases slowly upon heating followed by a stronger decrease as Tc is approached. We discuss the reliability of results on the static yield stress and give a criterion for its validity in terms of the time scales relevant to the problem.

a b s t r a c tThe deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthés-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.

Using molecular dynamics simulations, we show that a simple model of a glassy material exhibits the shear localization phenomenon observed in many complex fluids. At low shear rates, the system separates into a fluidized shear band and an unsheared part. The two bands are characterized by a very different dynamics probed by a local intermediate scattering function. Furthermore, a stick-slip motion is observed at very small shear rates. Our results, which open the possibility of exploring complex rheological behavior using simulations, are compared to recent experiments on various soft glasses.

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.

Polymeric thin films of various thicknesses, confined between two repulsive walls, have been studied by molecular dynamics simulations. Using the anisotropy of the perpendicular, P N (z), and parallel components, P T (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 P T (z) (z denotes the distance from the wall), but yield the same formula for the normal component P N (z). When evaluated by MD (or MC)-simulations P N (z) is constant, as required by mechanical stability. Contrary to that, the IK1-method leads to strong oscillations of P N (z). However, all methods give the same expression for the total pressure when integrated over the whole system, and thus the same surface tension, whereas the so-called surface of tension, z s , depends on the applied method. The difference is small for the IK-and H-methods, while the IK1-method leads to values that are in conflict with the interpretation of z s as the effective position of the interface.

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 variations. We will show why a detailed distinction between competing theories on these cooling rate effects would need an excessive amount of computer time. To estimate also the melting transition temperature Tm of this model, the sytem was prepared in a crystalline configuration as an initial state and heated up. The onset of diffusion, accompanied by an isotropization of the pressure tensor was observed for Tm≈0.77. This implies that the model is suitable for studying deeply supercooled melts.

Glass forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro-and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in-line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition. A thorough understanding of the slowing down of transport by orders of magnitude upon approaching the glass transition is one of the grand challenges of condensed matter theory [1][2][3][4][5]. A recent focus in the study of glasses has been to introduce competing mechanisms that lead to glass transition phase diagrams exhibiting non-monotonic behaviour. Reentrant scenarios have been uncovered, for example, upon adding a short-range attraction to colloidal particles [6][7][8], by competing near ordering in binary mixtures [9,10], or by inserting the liquid in a frozen disordered host structure [11][12][13]. However, instead of changing the structure of the liquid directly, one may also affect its properties by purely geometric means, via an increase of its confinement [14][15][16][17][18][19][20][21][22][23][24]. Depending on the ratio of the characteristic confinement length (e.g., the wall separation) to particle diameter, this can either lead to an increase or decrease of the first peak of the pair distribution function-the latter being a measure of the "stiffness" of the local packing structure [18]. As long as crystallization is kinetically hindered, this is expected to have a strong impact on the dynamics of the liquid and the glass transition. Earlier simulation studies and experiments of the confinement effects on the glass transition were mainly concerned with wall-to-wall separations of the order of several particle diameters or larger (see, e.g., [14][15][16][17][18][19] and references therein). Recently, however, the case of stronger confinement has received growing attention [20][21][22][23]. Here we focus on this latter regime of strong confinement, where only a few particle layers fit into the space between the walls. The problem of crystallization is circumvented by introducing size-dispersity [25] into our simulations, which leads to a geometric frustration. We evaluate the diffusion coefficient to assess the slowing-down of the dynamics and to establish a glass-transition state diag...