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Spin coating yields thin films of non-equilibrated polymers, with severe consequences, observable by the naked eye, in creep experiments on molten filamentlike samples derived from these films. While filaments from annealed films showed the expected monotonic elongation, filaments made from as-cast films initially showed the opposite behavior: They contracted and thereby lifted loads up to a thousand times the weight of the filament over a distance of almost up to $40%$ its initial length. We discuss the molecular origin of such large macroscopic manifestations of deviations from equilibrium in terms of reduced conformational entropy.

Conditions of rapid processing often drive polymers to adopt nonequilibrium molecular conformations, which, in turn, can give rise to structural, dynamical, and mechanical properties that are significantly different from those in thermodynamic equilibrium. However, despite the possibility to control the desired nonequilibrium properties of polymers, a rigorous microscopic understanding of the processing-property relations is currently lacking. In an attempt to stimulate progress along this topical direction, we focus here on three prototypical and apparently different cases: spin-coated polymer films, rapidly drawn polymer fibers, and sheared polymer melts. Inspired by the presence of common observations in the chosen cases, we search for order parameters as, for example, topological correlations and heterogeneities, which may allow characterizing the processing-induced behavior of polymers. We highlight that such approaches, necessitating concerted efforts from theory, simulations, and experiments, can provide a profound understanding leading to predictable and tunable properties of polymers., SCOPUS: re.j, info:eu-repo/semantics/published

Understanding the consequences of the noncrossing constraint is one of the remaining challenges in the physics of walks and polymers. To address this problem, we performed molecular simulations for the separation of only two initially connected, overlapping polymer chains with interactions tuned such that they are nearly random walks. The separation time for a configuration strongly correlates with the number of monomer contacts between both chains. We obtain a broad distribution of separation times with a slowly decaying tail. Knots only play a role for those configurations that contribute to the tail of the distribution. In contrast, when starting from the same initial configuration but allowing for chain crossings, separation is qualitatively faster and the time distribution narrow. The simulation results are rationalized by analytical theory. A theory of contacts based on polymer fractality and criticality is presented, along with the expected effects of knots.

We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasi-static and dynamical) shear-stress fluctuations as a function of temperature T and sampling time $\Delta t$. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time-averaged for each shear plane) to the stress-fluctuation relation $\mu_{sf}$ for the shear modulus and the shear-stress relaxation modulus $G(t)$. Using 100 independent configurations we pay attention to the respective standard deviations. While the ensemble-averaged modulus $\mu_{sf}(T)$ decreases continuously with increasing T for all $\Delta t$ sampled, its standard deviation $\delta \mu_{sf}(T)$ is non-monotonous with a striking peak at the glass transition. The question of whether the shear modulus is continuous or has a jump-singularity at the glass transition is thus ill-posed. Confirming the effective time-translational invariance of our systems, the $\Delta t$-dependence of $\mu_{sf}$ and related quantities can be understood using a weighted integral over $G(t)$. This implies that the shear viscosity $\eta(T)$ may be readily obtained from the $1/\Delta t$-decay of $\mu_{sf}$ above the glass transition., Comment: 21 pages, 21 figures, submitted to PRE

Glass formation and glassy behavior remain as the important areas of investigation in soft matter physics with many aspects which are still not completely understood, especially at the nanometer size-scale. In the present work, we show an extension of the "nanobubble inflation" method developed by O'Connell and McKenna [Rev. Sci. Instrum. 78, 013901 (2007)] which uses an interferometric method to measure the topography of a large array of 5 μm sized nanometer thick films subjected to constant inflation pressures during which the bubbles grow or creep with time. The interferometric method offers the possibility of making measurements on multiple bubbles at once as well as having the advantage over the AFM methods of O'Connell and McKenna of being a true non-contact method. Here we demonstrate the method using ultra-thin films of both poly(vinyl acetate) (PVAc) and polystyrene (PS) and discuss the capabilities of the method relative to the AFM method, its advantages and disadvantages. Furthermore we show that the results from experiments on PVAc are consistent with the prior work on PVAc, while high stress results with PS show signs of a new non-linear response regime that may be related to the plasticity of the ultra-thin film.

Copolymers are commonly used as interface modifiers that allow for the compatibilization of polymer components in a blend. For copolymers to function as a compatibilizer, they must diffuse through the matrix of the blend to the interface between the two blend components. The diffusivity of a copolymer in a blend matrix therefore becomes important in determining good candidates for use as compatibilizers. In this work, coarse-grained Monte Carlo simulations using the bond fluctuation model modified with an overlap penalty have been developed to study the diffusive behavior of PS/PMMA random copolymers in a PMMA homopolymer blend. The simulations vary the connectivity between different monomers, the thermodynamic interactions between the monomers which manifest within a chain, and between copolymer and homopolymer matrix and define the monomer friction coefficient of each component independently, allowing for the determination of the combined effect of these parameters on copolymer chain diffusion. The results of this work indicate that PS-r-PMMA copolymer diffusion is not linearly dependent on the copolymer composition on a logarithmic scale, but its diffusion is a balance of the kinetics governed by the dominant motion of the faster styrene monomers and thermodynamics, which are governed by the concentration of styrene monomer within a given monomer's local volume.

Surface tension-driven flow techniques have recently emerged as an efficient means of shedding light into the rheology of thin polymer films. Motivated by experimental and theoretical approaches in films bearing a varying surface topography, we present results on the capillary relaxation of a square pattern at the free surface of a viscoelastic polymer film, using molecular dynamics simulations of a coarse-grained polymer model. Height profiles are monitored as a function of time after heating the system above its glass-transition temperature and their time dependence is fitted to the theory of capillary leveling. Results show that the viscosity is not constant, but time dependent. In addition to providing a complementary insight about the local inner mechanisms, our simulations of the capillary-leveling process therefore probe the viscoelasticity of the polymer and not only its viscosity, in contrast to previous experimental approaches.

Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the intrachain subchain size distribution. Irrespective of the density sufficiently long chains are found to consist of compact packings of blobs of fractal perimeter dimension dp = 5/4.

This work presents a mechanical analysis of tangential contact using molecular dynamics simulations. Scratch tests with a conical tip on amorphous polymer surfaces were simulated at various temperatures, scratching velocities, roughnesses of the tip and with various interactions between the tip and the monomers. The local friction coefficient for the different contact conditions (temperature, tip roughness and scratching velocity) was calculated by studying the apparent friction and the contact asymmetry. The results are in good agreement with experimental data from tests on classical polymer surfaces on a microscopic scale.

By means of molecular dynamics simulations and scaling theory we study the response of opposing polymer brushes to constant shear motion under good solvent conditions. Model systems that contain explicit solvent molecules (Lennard-Jones dimers) are compared to solvent-free systems while varying of the distance between the grafted layers and their molecular parameters, chain length and grafting density. Our study reveals a power-law dependence of macroscopic transport properties on the Weissenberg number, W, beyond linear response. For instance, we find that the kinetic friction constant scales as μ ∼ W0.57 for large values of W. We develop a scaling theory that describes our data and previous numerical data including recent experiments. © 2010 American Chemical Society. Fil: Galuschko, A.. Institut Charles Sadron; Francia Fil: Spirin, L.. Johannes Gutenberg Universitat Mainz; Alemania Fil: Kreer, T.. Institut Charles Sadron; Francia Fil: Johner, A.. Institut Charles Sadron; Francia Fil: Pastorino, Claudio. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigaciones y Aplicaciones no Nucleares. Gerencia de Física (Centro Atómico Constituyentes); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Wittmer, J.. Institut Charles Sadron; Francia Fil: Baschnagel, J.. Institut Charles Sadron; Francia

Conformational properties of regular dendrimers and more general hyperbranched polymer stars with Gaussian statistics for the spacer chains between branching points are revisited numerically. We investigate the scaling for asymptotically long chains especially for fractal dimensions $d_f = 3$ (marginally compact) and $d_f = 2.5$ (diffusion limited aggregation). Power-law stars obtained by imposing the number of additional arms per generation are compared to truly self-similar stars. We discuss effects of weak excluded volume interactions and sketch the regime where the Gaussian approximation should hold in dense solutions and melts for sufficiently large spacer chains., 13 pages, 14 figures

We present results of molecular dynamics simulations for free-standing and supported thin films of a nonentangled polymer melt using a coarse-grained (bead-spring) model. Our discussion is mainly concerned with the equilibrium properties of the films above the critical temperature (Tc) of mode-coupling theory, although we also determine the glass-transition temperature (Tg) by measurements of the film thickness h upon cooling. We explore the influence of confinement on the structure and dynamics of the polymer films. We find that the dynamics in the films is accelerated compared to the bulk, that this enhanced mobility originates from the surfaces, and that the effect is larger at the free than at the supported surface. Thus, the films have lower Tc values relative to the bulk. Tc depends on film thickness h; this dependence can be well parametrized by Tc(h) = T/(1 + h0/h), a function proposed by experiments on supported polystyrene films. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2951–2967, 2006

The behaviour of a flexible polymer chain in solvents of variable quality in dilute solution is discussed both in the bulk and in the presence of an adsorbing wall. Monte Carlo simulations of coarse-grained bead-spring models and of the bond fluctuation model are presented and interpreted in terms of phenomenological theories and scaling concepts. Particular attention is paid to the behaviour of the polymer chain when the temperature of the polymer solution gets lower than the Theta temperature. It is argued that the adsorption transition line at the Theta temperature splits into lines of wetting and drying transitions of polymer globules attached to the wall. In addition, it is shown that the coil-globule transition is followed by a second transition, which in the bond fluctuation model is a crystallization into a regular lattice structure. Performing a finite size scaling analysis on the two transitions it is shown that (for the chosen model) both transitions coincide in the thermodynamic limit, corresponding to a direct collapse of the random coil into the crystal without intermediate coil-globule transition. The implications of this result for the standard mean field or tricritical theory of the coil-globule transition based on a truncated virial expansion are discussed.

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.

We present a comparison between results, obtained from different simulation models, for the static properties of end-tethered polymer layers in good solvent. Our analysis includes data from two previous studies--the bond fluctuation model of Wittmer et al. [J. Chem. Phys. 101, 4379 (1994)] and the off-lattice bead-spring model of Grest and Murat [Macromolecules 26, 3108 (1993)]. Additionally, we explore the properties of a similar off-lattice model simulated close to the Theta temperature. We show that the data for the bond fluctuation and the Grest-Murat model can be analyzed in terms of scaling theory because chains are swollen inside the Pincus blob. In the vicinity of the Theta point the structure of the chains is essentially Gaussian in the Pincus blob. Therefore, the data for the second off-lattice model can be compared quantitatively to the self-consistent field theory. Different ways to determine the parameters of the self-consistent field theory are discussed.

We analyze dynamical heterogeneities in a simulated “bead-spring” model of a nonentangled, supercooled polymer melt. We explore the importance of chain connectivity on the spatially heterogeneous motion of the monomers. We find that when monomers move, they tend to follow each other in one-dimensional paths, forming strings as previously reported in atomic liquids and colloidal suspensions. The mean string length is largest at a time close to the peak time of the mean cluster size of mobile monomers. This maximum string length increases, roughly in an exponential fashion, on cooling toward the critical temperature TMCT of the mode-coupling theory, but generally remains small, although large strings involving ten or more monomers are observed. An important contribution to this replacement comes from directly bonded neighbors in the chain. However, mobility is not concentrated along the backbone of the chains. Thus, a relaxation mechanism in which neighboring mobile monomers along the chain move predominant...

The adsorption of long flexible chains from dilute solution is studied by Monte Carlo simulation of a coarse-grained bead-spring model, and the results are interpreted in terms of phenomenological theories, using both mean field approaches and scaling concepts. It is shown that the surface excess, i.e., the integral of the local density difference of the monomers close to the surface relative to the bulk changes its sign very close to the adsorption transition (that is a sharp transition in the limit where the chain length diverges to infinity) for long chains, and it can be described in terms of the standard scaling description that has previously been tested for polymers with one end anchored on the surface (“polymer mushrooms”). Attention is also paid to the question on how this description changes when the temperature T of the polymer solution approaches the theta temperature Θ. Since the theta point can also be considered as an end point of a line of critical points, where the polymer solution phase ...

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.

A bead-spring model of a polymer chain with one end attached to a wall is studied by Monte Carlo simulations for chain lengths 16 ≤ N ≤ 256. Two types of adsorption potentials, 9-3 and 10-4 Lennard-Jones (LJ) potentials, between the effective monomers and the wall are assumed. For both cases the adsorption transition where the chain changes its asymptotic statistical properties from a three-dimensional to a two-dimensional configuration is located using a scaling analysis. It is shown that the crossover exponent φ = 0.50 ± 0.02 is the same for both LJ potentials. This value is compatible with recent theoretical predictions and simulation results for lattice models with short-range wall potentials. The results of our study support the expectation that the exponents describing the adsorption transition are universal, i.e., they are not influenced by the precise form and the long-range character of the adsorption potentials used. The technical aspects of the simulations (which use configurational bias methods as well as histogram re-weighting) are also carefully discussed.

The influence of a film geometry on the glass transition is investigated via molecular dynamics (MD) simulations of a (non-entangled) polymer melt. The confinement is realized by two identical potential barriers of the form U wall = z -9 , where z denotes the distance of a particle from the wall. Despite the geometric confinement, basic qualitative features of the system dynamics can be well described in the framework of the mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time α-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT β-process. A comparison of the dynamics in the film and in the bulk shows an acceleration of the relaxation processes due to the presence of the walls. This leads to a reduction of the critical temperature, T c , of MCT with decreasing film thickness. A comparison of the quantities like the static structure factor and the mean-square displacements for the bulk and for the film suggests that T - T c (D) is a relevant temperature scale for the dynamics at intermediate times. Furthermore, we also analyze the sharp rise of the relaxation times at low temperatures by the Vogel-Fulcher-Tammann (VFT) equation and thus estimate the VFT-temperature T 0 (D). We observe that, similar to T c (D), also T 0 (D) decreases for smaller D. As T 0 ≤ T g ≤ T c , these results suggest that also the glass transition temperature should decrease for stronger confinement.

A melt of nonentangled polymer chains confined between two smooth and purely repulsive walls is studied for various film thicknesses D and temperatures. The dynamics of the supercooled films is qualitatively identical to that of the bulk, but the walls lead to faster relaxation. To quantify this observation we analyze the data by the mode-coupling theory (MCT) of the glass transition. We find that the critical temperature of MCT, Tc(D), decreases with D and that T - Tc(D) is a relevant temperature scale. The static structure factor and dynamic correlation functions at intermediate times coincide with bulk behavior when compared to the same T - Tc(D).

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular-dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), D, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time alpha-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT beta-process. An analysis of the temperature dependence of the alpha-relaxation time suggests that the critical temperature, T(c), of MCT decreases with D. If the confinement is not too strong ( D>or=10monomer diameter), the static structure factor of the film coincides with that of the bulk when compared for the same distance, T - T(c)( D), to the critical temperature. This suggests that T - T(c)( D) is an important temperature scale of our model both in the bulk and in the films.

We examine the thermodynamics of supercooled liquids focusing on the immediate vicinity of an onset temperature, TA, where system dynamics just begin to experience caging effects. Simulation data from a polymer model and from small molecule mixtures show, in agreement with experiment, that the configurational entropy becomes strongly temperature dependent below TA. Since the diffusion coefficient follows the Adam-Gibbs relationship, our results clearly establish a thermodynamic connection to the localized dynamics of glass-forming liquids.

This paper reports Monte Carlo simulation results of a polymer melt of short, non-entangled chains which are embedded between two impenetrable walls. The melt is simulated by the bond-fluctuation lattice model under athermal conditions, i.e. only excluded volume interactions between the monomers and between the monomers and the walls are taken into account. In the simulations, the wall separation is varied from about one to about 15 times the bulk radius of gyration R g . The confinement influences both static and dynamic properties of the films: Chains close to the walls preferentially orient parallel to it. This parallel orientation decays with increasing distances from the wall and vanishes for distances larger than about 2 R g . Strong confinement effects are therefore observed for film thicknesses D ≲4 R g . The preferential alignment of the chains with respect to the walls suppresses reorientations in perpendicular direction, whereas parallel reorientations take place in an environment of high monomer density. Therefore, they have a relaxation time larger than that of the bulk. On the other hand, the influence of confinement on the translation motion of the chains parallel to the walls is very weak. It almost coincides with the bulk behavior even if D ≈1.5 R g . Despite these differences between translational and reorientational dynamics, their behavior can be well reproduced by a variant of Rouse theory which only assumes orthogonality of the Rouse modes and determines the necessary input from the simulation.

Glass formation and glassy behavior remains an important field of study in condensed matter physics, with many aspects still little understood. The approach used in this work is to observe the changes in behavior of glass-forming materials at the nanometer scale by exploring the viscoelastic properties of ultrathin free-standing glassy polymer films. An experimental measurement cell based on the nanobubble inflation method is used, consisting of inflating a polymer film suspended over an array of 5 µm diameter holes in a Si wafer. Measuring the deformation as a function of time as the material relaxes is used to determine the creep compliance. Both polystyrene (PS) and poly(vinyl acetate) (PVAc) films of a few tens of nm thickness prepared by spin-coating from solution have been studied. Interference microscopy is used to measure the deformation over several hours, which is challenging at the nanoscale due to mechanical deformations and drift. In this paper we present some of the first solutions developed to allow consistent measurements of film deformation using this novel interference nanoscopy technique. Future work will involve the measurements of creep compliance as a function of different film properties so as to be able to compare the results with theoretical predictions.

This paper reports results of molecular dynamics simulations for a glassy polymer melt consisting of short, non-entangled chains. The temperature region studied covers the supercooled state of the melt above the mode-coupling critical temperature. The analysis focuses on the interplay of simple-liquid and polymer-specific effects. One can clearly distinguish two regimes: a regime of small and one of large monomer displacements. The first regime corresponds to motion of a monomer in its local environment. It is dominated by the cage effect and well described by the idealized mode-coupling theory. The second regime is governed by the late-β/early-α process. In this regime the connectivity of the monomers begins to interfere with the cage dynamics and finally becomes dominant. The monomer displacement is compared with simulation results for a binary Lennard-Jones mixture to highlight the differences which are introduced by the connectivity of the particles.

We report results of molecular-dynamics simulations for a glassy polymer melt consisting of short, linear bead-spring chains. It was shown in previous work that this onset of the glassy slowing down is compatible with the predictions of the mode coupling theory. The physical process of `caging' of a monomer by its spatial neighbors leads to a distinct two step behavior in the particle mean square displacements. In this work we analyze the effects of this caging process on the Rouse description of the melt's dynamics. We show that the Rouse theory is applicable for length and time scales above the typical scales for the caging process. Futhermore, the monomer displacement is compared with simulation results for a binary Lennard-Jones mixture to point out the differences which are introduced by the connectivity of the particles., Comment: 19 pages of REVTeX, 11 ps-figures, accepted by Comp.Theo. Poly. Sci

We report results of molecular-dynamics simulations for a glassy polymer melt consisting of short, linear bead-spring chains. It was shown in previous work that this onset of the glassy slowing down is compatible with the predictions of the mode coupling theory. The physical process of `caging' of a monomer by its spatial neighbors leads to a distinct two step behavior in the particle mean square displacements. In this work we analyze the effects of this caging process on the Rouse description of the melt's dynamics. We show that the Rouse theory is applicable for length and time scales above the typical scales for the caging process. Futhermore, the monomer displacement is compared with simulation results for a binary Lennard-Jones mixture to point out the differences which are introduced by the connectivity of the particles.

The dynamical behavior of a supercooled polymer melt is studied by means of Monte Carlo simulation. The simulation uses a version of the bond-fluctuation (lattice) model in which long bond vectors are favored energetically. The expansion on the length scale of a bond also induces an increase of the chains' size and stiffness during supercooling. In a dense melt the tendency of an individual chain to stretch has to compete with that of all others. This competition between the internal energy of a chain and the density of the melt strongly slows down the structural relaxation at low temperatures. In order to analyze the dynamical behavior of this model different relaxation functions were calculated in a temperature region ranging from the normal liquid-like to the supercooled state of the melt. Among these relaxation functions are the end-to-end vector correlation function and the correlation function of the Rouse modes. Both functions exhibit a time-temperature superposition property at all times....

As a first step toward the computer simulation of polydisperse polymeric melts, a lattice model containing two types of chains with lengths N1 = 20 − x and N2 = 20 + 4x (0 ≤ x ≤ 10 ) is studied. This variation of x, together with the fixed composition of 80% of short and 20% of long chains, leads to a polydispersity of 1 ≤ Nw/Nn ≤ 2 (Nw, Nn: weight-, number-average chain lengths). To represent dense melts, the bond-fluctuation model at a volume fraction, φ = 1/2, of occupied lattice sites is used. The simulation treats both the athermal case (chain connectivity and excluded volume interaction only) and a thermal case, where additionally a choice for the bond length and bond angle potentials is made, which has recently been proposed to mimic polyethylene. For both cases number-, mass-, and z-averages of various static and dynamic quantities are calculated and compared with the results of the monodisperse melt. The main results are as follows. Whereas structural properties of the mono- and bidisperse melts...

The bond fluctuation model of polymer chains on sc lattices with an energy that favours long bonds can describe the slowing down of supercooled melts that approach the glass transition in qualitative similarity with various experiments. In this paper we focus on the question of whether there exists a correlation length that increases to large values when the temperature is lowered towards the glass transition. Two types of analysis are presented: firstly density oscillations near hard walls become long range, and the resulting correlation length becomes larger than the gyration radius, secondly oscillations in the pair correlation function in real space also become long range, and a similar correlation length can hence also be deduced in the bulk, without recourse to surface effects. In contrast, a finite-size scaling analysis of the diffusion behaviour of chains in small three-dimensional lattices with periodic boundary conditions does not give evidence for this length, unlike earlier results fo...

We present results on the glass transition in polymer melts using Monte Carlo simulations of the bond fluctuation lattice model. There are two questions we address in this work. What is the temperature dependence of the entropy density in such a model polymer melt and how well is it described by theories like the Gibbs-DiMarzio theory of the glass transition? And to what degree is one able to map the Hamiltonian of such an abstract lattice model onto a specific polymer material and use it to model the large scale and long time properties of a realistic polymer melt?

The bond fluctuation model on the simple cubic lattice with a bond-length dependent potential energy favoring long bonds exhibits a glassy freezing in as the temperature is lowered, many properties being qualitatively similar to experiment. The present paper studies the dynamical properties of the model (as they result from the random hopping algorithm), using configurations of undercooled polymer melts that have been carefully equilibrated by the slithering snake algorithm. In this way quantitatively reliable data can be obtained for distinctly lower temperatures than in the previous work on the dynamics of this model that used the random hopping algorithm for equilibration as well. If various mean-square displacements, the self-diffusion constant, autocorrelation functions of the end-to-end vector, intermediate incoherent scattering functions, and single chain dynamic structure factors are analyzed, it is found that the slowing down of relaxation times occurs according to the Vogel-Fulcher law. Within the uncertainties of the analysis the Vogel-Fulcher temperature of all these times is the same, 0.12 ≤ T 0 ≤ 0.13. Particularly illuminating is an analysis of the Rouse modes, which supports this conclusion and furthermore yields compelling evidence for the time-temperature superposition principle. It is shown that no static cross-correlations develop between different Rouse modes in the undercooled melt.

This paper briefly reviews recent results of extensive Monte Carlo simulations for the glass transition of polymer melts. The simulation used the bond-fluctuation model, a lattice model, which exhibits glassy behaviour due to the development of a competition between packing constraints and chain stiffening at low temperatures. For this model static and dynamic properties were analysed, such as the influence of the cooling rate and of the chain length on the glass transition temperature, physical aging effects, the time-dependences of various mean-square displacements and structural relaxation functions and the temperature-dependences of structural relaxation times and of the diffusion coefficient. Besides an outline of these results we discuss in some detail a quantitative comparison between the incoherent intermediate scattering function and the extended mode-coupling theory and between the entropy of the melt and the Gibbs - Di Marzio theory.

By means of dynamic Monte Carlo simulation the physical aging of a glassy polymer melt is studied. The melt is simulated by a coarse-grained lattice model, the bond-fluctuation model, on a simple cubic lattice. In order to generate glassy freezing an energy is associated with long bonds, which leads to a competition between the energetically favored bond stretching and the local density of the melt at low temperatures. The development of this competition during the cooling process strongly slows down the structural relaxation and makes the melt freeze in an amorphous structure as soon as the internal relaxation time matches the time scale of the cooling rate. Therefore the model exhibits pronounced cooling rate and physical aging effects close to the glass transition. The physical aging of the model occurs on all length scales of a polymer in a self-similar way, which may be expressed by a time-temperature superposition principle for the aging time. For short aging times an Andrade behavior is found for all studied quantities.

Dynamic properties of a dense polymer melt confined between two hard walls are investigated over a wide range of temperatures by dynamic Monte Carlo simulation. The temperature interval ranges from the ordinary liquid to the strongly supercooled melt. The influence of temperature, density and confinement on the polymer dynamics is studied by various mean-square displacements, structural relaxation functions and quantities derived from them (relaxation times, apparent diffusion coefficients, monomer relaxation rates), yielding the following results: The motion of the monomers and polymers close to the walls is enhanced in parallel, but reduced in perpendicular direction. This dynamic anisotropy strongly increases during supercooling and extends into the bulklike inner region of the film over a length scale which is larger than the bulk radius of gyration at low temperatures. However, the absolute freezing of the melt occurs in each layer at the same temperature for both the parallel and the perpendicular direction.

Coarse-grained models of polymer chains interacting with hard walls are introduced and dynamics of the chains is studied in the framework of dynamic Monte Carlo simulations. Lattice models like the bond fluctuation model and off-lattice beadspring model are discussed. The dynamics of single chains at attractive walls in the vicinity of the adsorption transition is studied, with an emphasis on the question of whether the chain motion is described by the two-dimensional version of the Rouse model. For dense polymer systems confined between walls, the slowing down near the glass transition of the model is considered. Simulations are used to test various theoretical concepts and their application to experiment is discussed briefly.

As a coarse-grained model for dense amorphous polymer systems interacting with solid walls (i.e., the fiber surface in a composite), the bond fluctuation model of flexible polymer chains confined between two repulsive surfaces is studied by extensive Monte Carlo simulations. Choosing a potential for the length of an effective bond that favors rather long bonds, the full temperature region from ordinary polymer melts down to the glass transition is accessible. It is shown that in the supercooled state near the glass transition an “interphase” forms near the walls, where the structure of the melt is influenced by the surface. This “interphase” already shows up in static properties, but also has an effect on monomer mobilities and the corresponding relaxation behavior of the polymer matrix. The thickness of the interphase is extracted from monomer density oscillations near the walls and is found to be strongly temperature dependent. It is ultimately larger than the gyration radius of the polymer chains. Effects of shear deformation on this model are simulated by choosing asymmetric jump rates near the moving wall (large jump rate in the direction of motion, and a small rate against it). It is studied how this dynamic perturbation propagates into the bulk of the polymer matrix.

The properties of the interface between a polymer melt and a solid wall are studied over a wide range of temperatures by dynamic Monte Carlo simulations. It is shown that in the supercooled state near the glass transition of the melt an “interphase” forms, the structure of which is influenced by the wall. The thickness of this interphase is determined from the monomer density profile near the surface and is strongly temperature dependent. At low glass-like temperatures it is larger than the bulk radius of gyration of the chains.

The concentration profile of a symmetrical binary (AB) polymer mixture confined between two ‘neutral’ repulsive walls is studied by Monte Carlo simulation of the bond fluctuation model, using a chain length N = N A = N B = 32 and a distance of D = 20 lattice spacings between the walls. Choosing volume fractions and temperatures such that one stays inside the coexistence curve, one has A-rich and B-rich domains coexisting with each other, in each kind of domain the minority component being enriched at the surface. In contrast to simple Ising lattice gas models of mixtures, the steepest gradient in the volume fraction profile does not occur right at the surface, but a few layers away from the wall. Possible reasons for the observed flatness of this concentration profile near walls (which agrees with recent experimental findings) are briefly discussed.

The adsorption process of the single polymer chain in a polymer brush of varying surface coverages is studied by means of Monte Carlo simulations of the bond-fluctuation lattice model. Only the end monomers can adsorb at the grafting surface, whereas inner monomers interact repulsively with it. The brush builds up a steric hindrance which forces the penetrating polymer to stretch strongly and which is responsible for small adsorption probabilities at surface coverages close to the overlap density. The final step of the adsorption process is determined by a fluctuation of the end monomer around its average position, which is comparable to the initial step of the desorption process.

The use of coarse-grained lattice models for the modelling of the glassy freezing in of polymer melts is discussed. The bond-fluctuation model is shown to be a reasonable compromise between simulation efficiency and realistic chemical detail. The potential energy, favoring large values of the length of effective bonds, is at low temperatures in conflict with the tendency for dense packing of the effective monomers and this “geometrical frustration” is responsible for the glass transition of this model. It is shown that many physical properties of the model are in surprisingly close agreement with experiments. Open problems and directions for future research are briefly discussed.

We measure the chemical potential in a polymer melt with a modification of Widom’s insertion method. Our method is based on partial insertion of a testchain by controlling the interaction between the testchain and the melt by means of a control parameter. The chemical potential can be obtained from a single run in a multicanonical‐like simulation over a wide range of temperatures and densities. From the chemical potential the osmotic pressure and the entropy are calculated. We study a variant of the bond fluctuation model of a polymer melt where an energy is gained when the bond vector is taken from the set (±3,0,0) lattice spacings (or permutations thereof). From extensive previous studies it is known that the model exhibits a glass‐like freezing at low temperatures. We show that the configurational entropy decreases strongly when one cools the system through this transition, but it remains distinctly nonzero in the glass phase.

In this paper, we reanalyse the incoherent intermediate scattering function, determined by a Monte Carlo simulation of a polymer melt, in the framework of the extended mode-coupling theory (MCT). A previous analysis with the idealized MCT showed systematic deviations between theory and simulation at low temperatures, which could be qualitatively attributed to the neglect of hopping processes. If these hopping processes are taken into account quantitatively by the application of the extended MCT, the discrepancies at low temperatures disappear, and a (quite) accurate estimate of the critical temperature becomes possible.

This paper reviews the results of a large scale Monte Carlo simulation for the dynamics of a supercooled polymer melt. The dynamics of the melt was studied by means of the time evolution of the incoherent intermediate scattering function φs q(t), which was monitored over seven decades in time. In an intermediate time window it is possible to describe the decay of φs q(t) quantitatively in the framework of mode-coupling theory, provided the extended version of the theory is used.

The bond fluctuation model on square and s.c. lattices is used as a coarse-grained model for flexible polymers in dense melts. Using an energy that favours long bonds, a conflict is created between the tendency of the bonds to stretch at low temperatures and packing constraints. This simple concept of ‘geometric frustration’ leads to glass transition. Both static and dynamic properties of this model are investigated by Monte Carlo simulations, paying attention to effects found by varying the cooling rate and the chain length N of the polymers. In two and three spatial dimensions an effective (cooling-rate dependent) glass transition temperature T g can be defined, where the system falls out of equilibrium. T g varies as T g(N) = T g(∞)—constant/N, consistent with the theory of Gibbs and DiMarzio. Furthermore, we determine the diffusion coefficient, whose temperature dependence is Vogel-Fulcher like in both spatial dimensions with T 2D 0 < T 3D 0 (T 0 is the Vogel-Fulcher temperature), and we prov...

We develop a fluctuating hydrodynamics approach to study the impact of the hydrodynamic and viscoelastic interactions on the motion of the center of mass of a polymer as well as on the relaxation of Rouse modes, either in a Θ solvent or in a melt of identical unentangled chains. We show that this method allows us to describe the effect of hydrodynamic interactions beyond the Zimm (for a single chain in a Θ solvent) or the Rouse models (for an unentangled melt). In the latter case, we recover the same important effect of the viscoelastic hydrodynamic interactions on the center-of-mass diffusion, first described in Farago et al (2011 Phys. Rev. Lett. 107 178301).

This paper summarizes some results of a Monte Carlo simulation for the glass transition in dense two- and three-dimensional polymer melts which are simulated by the bond-fluctuation model on a d -dimensional cubic lattice. Combining this model with a two-level Hamiltonian which favours long bonds, a competition between the energetic and topological constraints in the system is created, which prevents crystallization and makes the melt freeze in an amorphous structure. The results of the two-dimensional simulation deal with the influence of the chain length, N , on the glass transition temperature, T g . A linear relationship between T g and 1/ N is found. The three-dimensional model is used to exemplify the dynamical properties of the model by a quantitative analysis of the incoherent intermediate scattering function in the framework of the idealized mode coupling theory.

An approximate theory, including effects of the density, for the equilibrium properties of a polymer lattice model (bond‐fluctuation model) is presented and compared with Monte Carlo simulations. Effects of the density are taken into account by balancing the volume requirements of the individual bond vectors with the pressure that a melt exerts at a given density. This simple theory yields rather accurate (to within a few percent) estimates for the chain length and temperature dependence of various quantities that scan different length scales of the polymers (bond length, radius of gyration, etc.). With the inclusion of the density, one can also design an improved definition of an internal temperature of the melt, which is distinct from the external temperature of the surrounding heat bath. When the melt falls out of equilibrium during the vitrification process, this internal temperature is expected to measure the temperature that the melt actually experiences, and may thus serve to eliminate the nonequil...