Polymer films in the normal-liquid and supercooled state: a review of recent Monte Carlo simulation results

Characterization of Monte Carlo Dynamic/Kinetic Properties of Local Structure in Bond Fluctuation Model of Polymer System

We report the results of the characterization of local Monte Carlo (MC) dynamics of an equilibrium bond fluctuation model polymer matrix (BFM), in time interval typical for MC simulations of non-linear optical phenomena in host-guest systems. The study contributes to the physical picture of the dynamical aspects of quasi-binary mosaic states characterized previously in the static regime. The polymer dynamics was studied at three temperatures (below, above and close to the glass transition), using time-dependent generalization of the static parameters which characterize local free volume and local mobility of the matrix. Those parameters play the central role in the kinetic MC model of host-guest systems. The analysis was done in terms of the probability distributions of instantaneous and time-averaged local parameters. The main result is the characterization of time scales characteristic of various local structural processes. Slowing down effects close to the glass transition are clearly marked. The approach yields an elegant geometric criterion for the glass transition temperature. A simplified quantitative physical picture of the dynamics of guest molecules dispersed in BFM matrix at low temperatures offers a starting point for stochastic modeling of host-guest systems.

Modeling of Nonlinear Optical Phenomena in Host-Guest Systems Using Bond Fluctuation Monte Carlo Model: A Review

We review the results of Monte Carlo studies of chosen nonlinear optical effects in host-guest systems, using methods based on the bond-fluctuation model (BFM) for a polymer matrix. In particular, we simulate the inscription of various types of diffraction gratings in degenerate two wave mixing (DTWM) experiments (surface relief gratings (SRG), gratings in polymers doped with azo-dye molecules and gratings in biopolymers), poling effects (electric field poling of dipolar molecules and all-optical poling) and photomechanical effect. All these processes are characterized in terms of parameters measured in experiments, such as diffraction efficiency, nonlinear susceptibilities, density profiles or loading parameters. Local free volume in the BFM matrix, characterized by probabilistic distributions and correlation functions, displays a complex mosaic-like structure of scale-free clusters, which are thought to be responsible for heterogeneous dynamics of nonlinear optical processes. The photoinduced dynamics of single azopolymer chains, studied in two and three dimensions, displays complex sub-diffusive, diffusive and super-diffusive dynamical regimes. A directly related mathematical model of SRG inscription, based on the continuous time random walk (CTRW) formalism, is formulated and studied. Theoretical part of the review is devoted to the justification of the a priori assumptions made in the BFM modeling of photoinduced motion of the azo-polymer chains.

Molecular dynamics simulation of the capillary leveling of viscoelastic polymer films

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 most experimental approaches.

Effects of nanoscopic-confinement on polymer dynamics

The static and dynamic behavior of polymers in confinement close to interfaces can be very different from that in the bulk. Among the various geometries, intercalated nanocomposites, in which polymer films of ∼1 nm thickness reside between the parallel inorganic surfaces of layered silicates in a well-ordered multilayer, offer a unique avenue for the investigation of the effects of nanoconfinement on polymer structure and dynamics by utilizing conventional analytical techniques and macroscopic specimens. In this article, we provide a review of research activities mainly in our laboratory on polymer dynamics under severe confinement utilizing different polymer systems: polar and non-polar polymers were mixed with hydrophilic or organophilic silicates, respectively, whereas hyperbranched polymers were studied in an attempt to probe the effect of polymer-surface interactions by altering the number and the kinds of functional groups in the periphery of the branched polymers. The polymer dynamics was probed by quasielastic neutron scattering and dielectric relaxation spectroscopy and was compared with that of the polymers in the bulk. In all cases, very local sub-Tg processes related to the motion of side and/or end groups as well as the segmental α-relaxation were identified with distinct differences recorded between the bulk and the confined systems. Confinement was found not to affect the very local motion in the case of the linear chains whereas it made it easier for hyperbranched polymers due to modifications of the hydrogen bond network. The segmental relaxation in confinement becomes faster than that in the bulk, exhibits Arrhenius temperature dependence and is observed even below the bulk Tg due to reduced cooperativity in the confined systems.

Chain end mobilities in polymer melts--a computational study

The Rouse model can be regarded as the standard model to describe the dynamics of a short polymer chain under melt conditions. In this contribution, we explicitly check one of the fundamental assumptions of this model, namely, that of a uniform friction coefficient for all monomers, on the basis of MD simulation data of a poly(ethylene oxide) (PEO) melt. This question immediately arises from the fact that in a real polymer melt, the terminal monomers have on average more intermolecular neighbors than the central monomers, and one would expect that exactly these details affect the precise value of the friction coefficient. The mobilities are determined by our recently developed statistical method, which provides detailed insights into the local polymer dynamics. Moreover, it yields complementary information to that obtained from the mean square displacement (MSD) or the Rouse mode analysis. It turns out that the Rouse assumption of a uniform mobility is fulfilled to a good approximation for the PEO melt. However, a more detailed analysis reveals that the underlying microscopic dynamics are highly affected by different contributions from intra- and intermolecular excluded volume interactions, which cannot be taken into account by a modified friction coefficient. Minor deviations occur only for the terminal monomers on larger time scales, which can be attributed to the presence of two different escape mechanisms from their first coordination sphere. These effects remain elusive when studying the dynamics with the MSD only.

Analysis of local properties during a scratch test on a polymeric surface using molecular dynamics simulations

This work demonstrates a possible route to connect a particle (chain) based understanding with continuum mechanical questions about contact mechanics. The bond orientation, chain conformation and stress field of a polymer film were analyzed during scratch tests (tangential contact) using a molecular dynamics (MD) simulation approach. Scratch tests with a conical tip at constant scratching velocity were simulated on linear amorphous polymer surfaces at various temperatures and roughnesses of the tip and for various interactions between the tip and the particles of the polymer chains. The second Legendre polynomial (computed for small domains around the tip) gave the bond orientation inside the polymer film during sliding of the tip. The gyration tensor (layer-resolved in the direction of the polymer film thickness) provided information about the conformation of the polymer chains. These results allowed us to argue in favor of Briscoe's hypothesis (thin film sheared vs. "bulk" compressive behavior) concerning the friction properties of the polymer surfaces. Finally, the first stress measurements of the virial stress tensor (in sub-boxes placed in the MD cell) revealed a complex combination between compressive hydrostatic pressure and shear stress, which may be interpreted as a complex sheared domain at the interface.

Mechanical properties of thin confined polymer films close to the glass transition in the linear regime of deformation: theory and simulations

Over the past twenty years experiments performed on thin polymer films deposited on substrates have shown that the glass transition temperature T(g) can either decrease or increase depending on the strength of the interactions. Over the same period, experiments have also demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. A model for the dynamics of non-polar polymers, based on percolation of slow subunits, has been proposed and developed over the past ten years. It proposes a unified mechanism regarding these two features. By extending this model, we have developed a 3D model, solved by numerical simulations, in order to describe and calculate the mechanical properties of polymers close to the glass transition in the linear regime of deformation, with a spatial resolution corresponding to the subunit size. We focus on the case of polymers confined between two substrates with non-negligible interactions between the polymer and the substrates, a situation which may be compared to filled elastomers. We calculate the evolution of the elastic modulus as a function of temperature, for different film thicknesses and polymer-substrate interactions. In particular, this allows to calculate the corresponding increase of glass transition temperature, up to 20 K in the considered situations. Moreover, between the bulk T(g) and T(g) + 50 K the modulus of the confined layers is found to decrease very slowly in some cases, with moduli more than ten times larger than that of the pure matrix at temperatures up to T(g) + 50 K. This is consistent with what is observed in reinforced elastomers. This slow decrease of the modulus is accompanied by huge fluctuations of the stress at the scale of a few tens of nanometers that may even be negative as compared to the solicitation, in a way that may be analogous to mechanical heterogeneities observed recently in molecular dynamics simulations. As a consequence, confinement may result not only in an increase of the glass transition temperature, but in a huge broadening of the glass transition.

Crystal nucleation enhanced at the diffuse interface of immiscible polymer blends

We report dynamic Monte Carlo simulations of immiscible binary polymer blends, which exhibit weakly enhanced crystal nucleation near interfaces between two phase-separated polymers. We found that this enhancement is not accompanied by any preferred crystal orientation, implying its origin is mainly of enthalpic rather than entropic nature. Mean-field theory of polymer blends predicts that for immiscible polymers the melting point of the crystallizable component increases upon dilution in the other component, while it normally decreases for miscible blends. A local dilution is forced to occur at the diffuse interface of immiscible polymers; therefore the melting point of crystallizable polymers rises, which, in turn, enhances the thermodynamic driving force for crystal nucleation near the interface.

Understanding crystal orientation in quasi-one-dimensional polymer systems

We performed molecular simulations of polymer crystallization confined in rigid nanotubes. We found that the neutrally repulsive walls of nanotubes enhance the crystal nucleation. This enhancement gives uniform crystal orientation parallel to the tube axis at high temperatures. However, the nanotube walls that are wetted by the polymer, i.e. 'sticky' walls, switch the dominant crystal orientation from parallel to perpendicular. Since only perpendicularly oriented crystals can grow along the tube to give high crystallinities, the sticky walls provide a promising route towards the mass production of uniformly oriented nanocrystals in quasi-one-dimensional polymer systems.

Computer simulation of adsorption kinetics of surfactants on solid surfaces

Adsorption kinetics of surfactants on solid surfaces has been studied by using computer simulation. Both bulk surfactant concentration and diffusion region are explicitly integrated in our model. Depending on the head-surface interaction, our simulation results indicate that there exist two different kinetic modes in adsorption process of surfactants on solid surfaces. One is the four-regime mode and the other is step-wise mode. For the strongly attractive head-surface interaction, four distinct regimes of surfactant adsorption are found: a diffusion-controlled regime, a self-assembly controlled regime, an intermediate coverage regime and a saturated regime. In particular, the adsorption in second regime displays a power-law time dependence with an exponent unrelated to bulk concentrations and diffusion coefficients. While for the weaker adsorption surfaces, the step-wise mode is found. The mode includes a low-coverage nucleation regime and the saturated regime after a sudden aggregation of surfactants on the substrates which occurs stochastically. Besides the head-surface interaction, in this work, the effects of surfactant diffusivity, bulk concentration, the length of diffusion zone and surfactant architecture on the adsorption kinetics are also considered. The simulated adsorption kinetics is compared qualitatively with experimental results.

Coarse grained model of entangled polymer melts

A coarse graining procedure aimed at reproducing both the chain structure and dynamics in melts of linear monodisperse polymers is presented. The reference system is a bead-spring-type representation of the melt. The level of coarse graining is selected equal to the number of beads in the entanglement segment, Ne. The coarse model is still discrete and contains blobs each representing Ne consecutive beads in the fine scale model. The mapping is defined by the following conditions: the probability of given state of the coarse system is equal to that of all fine system states compatible with the respective coarse state, the dissipation per coarse grained object is similar in the two systems, constraints to the motion of a representative chain exist in the fine phase space, and the coarse phase space is adjusted such to represent them. Specifically, the chain inner blobs are constrained to move along the backbone of the coarse grained chain, while the end blobs move in the three-dimensional embedding space. The end blobs continuously redefine the diffusion path for the inner blobs. The input parameters governing the dynamics of the coarse grained system are calibrated based on the fine scale model behavior. Although the coarse model cannot reproduce the whole thermodynamics of the fine system, it ensures that the pair and end-to-end distribution functions, the rate of relaxation of segmental and end-to-end vectors, the Rouse modes, and the diffusion dynamics are properly represented.

Theory of glassy dynamics in conformationally anisotropic polymer systems

A mode coupling theory for the ideal glass transition temperature, or crossover temperature to highly activated dynamics in the deeply supercooled regime, T(c), has been developed for anisotropic polymer liquids. A generalization of a simplified mode coupling approach at the coarse-grained segment level is employed which utilizes structural and thermodynamic information from the anisotropic polymer reference interaction site model theory. Conformational alignment or/and coil deformation modifies equilibrium properties and constraining interchain forces thereby inducing anisotropic segmental dynamics. For liquid-crystalline polymers a small suppression of T(c) with increasing nematic or discotic orientational order is predicted. The underlying mechanism is reduction of the degree of coil interpenetration and intermolecular repulsive contacts due to segmental alignment. For rubber networks chain deformation results in an enhanced bulk modulus and a modest elevation of T(c) is predicted. The theory can also be qualitatively applied to systems that undergo nonuniversal local deformation and alignment, such as polymer thin films and grafted brush layers, and large elevations or depressions of T(c) are possible. Extension to treat directionally dependent collective barrier formation and activated hopping is possible.

Structure of an Associating Polymer Melt in a Narrow Slit by Molecular Dynamics Simulation

Molecular dynamics simulation has been used to study the equilibrium properties of a generic coarse-grained polymer melt with associating terminal groups, confined in a narrow slit by two atomically smooth walls. Simulations were carried out as a function of wall separation and attracting strength as well as polymer end-end interaction strength. We find that confinement has an important effect on the melt properties. In particular, strongly attracting walls can produce radical changes in chain conformation, the nature of the transient network, and the structure of the aggregates formed by the associating terminals.

Heterogeneous nature of the dynamics and glass transition in thin polymer films

Recent experiments have demonstrated that the dynamics in liquids close to and below the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. We use here a model proposed recently for explaining these features, and show that the heterogeneous nature of the dynamics has important consequences when considering the dynamics of thin films. We show how the dominant relaxation time in a thin film is changed as compared to the bulk, as a function of the thickness, the interaction energy with the substrate, and the temperature. The corresponding time scales cover the so-called VFT (or WLF) regime and vary between 10(-8) s to 10(4) s typically. In the absence of interaction, our model allows for interpreting suspended films experiments, in the case of small polymers for which the data do not depend on the polymer weight. The interaction leads to an increase of T(g) for an interaction per monomer of the order of the thermal energy T. This increase saturates at the value corresponding to strongly interacting films for adsorption energies slightly larger and still of order T. In particular, we predict that the T(g) shift can be non-monotonous as a function of the film thickness, in the case of intermediate interaction strength.

Glass transition temperature of freely-standing films of atactic poly(methyl methacrylate)

We have used ellipsometry to measure the glass transition temperature T(g) of high molecular weight (M(w)=790 x 10(3)), freely-standing films of atactic poly(methyl methacrylate) (a-PMMA), as well as films of the same polymer supported on two different substrates: the native oxide layer of silicon (Si) and gold-covered Si. We observe linear reductions in T(g) with decreasing film thickness h for the freely-standing PMMA films with 30 nm < h<100 nm, which is qualitatively similar to previous results obtained for freely-standing polystyrene (PS) films. However the magnitude of the T(g) reductions for PMMA is much less than for freely-standing films of PS of comparable molecular weight and thickness. We also find that for films supported on either substrate, with thicknesses as small as 30 nm, the T(g) values do not deviate substantially from the value measured for thick films.

Confinement effects on the slow dynamics of a supercooled polymer melt: Rouse modes and the incoherent scattering function

Results of large-scale molecular-dynamics simulations of a supercooled polymer film are presented (F. Varnik, J. Baschnagel, K. Binder, J. Phys. IV 10, 239 (2000)). The dynamic and static properties of the system are studied for a wide range of film thicknesses (from 3 to about 55 times the bulk radius of gyration) and temperatures (from the normal liquid state to the supercooled region). The system is confined between two completely smooth and purely repulsive walls. Motivated by the previous results on the enhancement of the local relaxation dynamics due to the confinement (F. Varnik, J. Baschnagel, K. Binder, Eur. Phys. J. E 8, 175 (2002); Phys. Rev. E. 65, 021507 (2002)), we now study the effect of the walls on the dynamics of the Rouse modes. It has been reported from Monte Carlo studies of the Bond Fluctuation Model (BFM) that, contrary to the enhancement of the "cage dynamics" (exemplified by a faster relaxation of the incoherent scattering function in the film), Rouse modes exhibit a slower relaxation in the confined system (C. Mischler, J. Baschnagel, K. Binder, Adv. Colloid Interface Sci. 94, 197 (2001)). However, we do not observe such a discrepancy for our continuum model: At a given temperature, the relaxation of a given Rouse mode is faster in the film than in the bulk in accordance with the acceleration of the dynamics around the cage.

Viscoelastic dynamics of polymer thin films and surfaces

The strain relaxation behavior in a viscoelastic material, such as a polymer melt, may be strongly affected by the proximity of a free surface or mobile interface. In this paper, the viscoelastic surface modes of the material are discussed with respect to their possible influence on the freezing temperature and dewetting morphology of thin polymer films. In particular, the mode spectrum is connected with mode coupling theory assuming memory effects in the melt. Based on the idea that the polymer freezes due to these memory effects, surface melting is predicted. As a consequence, the substantial shift of the glass transition temperature of thin polymer films with respect to the bulk is naturally explanied. The experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. Finally, a simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid polymer films. It demonstrates that by taking into account the viscoelastic properties of the film, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.

The effects of changes of intermolecular coupling on glass transition dynamics in polymer thin films and glass-formers confined in nanometer pores

Intermolecular coupling plays an important role in determining the dynamics and the mobility of polymeric and non-polymeric glass-formers. The breadth of the dispersion is an indicator of the intermolecular coupling strength. The coupling model relates intermolecular coupling through the breadth of the dispersion to the dynamics of bulk glass-formers. When a glass-former is confined in nanometer pores or in thin films and if there is absence of chemical and physical interactions with the wall, intermolecular coupling is reduced, resulting in an increase of mobility. The coupling model is used to account for such changes of relaxation time of 1) ortho-terphenyl and poly(dimethyl siloxane) confined in nanometer pores, 2) polymer thin film confined between two impenetrable walls from Monte Carlo simulation, and 3) polymer film confined by perfectly smooth and purely repulsive potential acting on the repeat units from molecular-dynamics simulation. The model continues to explain the opposite effects observed when there is an increase of intermolecular coupling due to the presence of chemical or physical interaction with the walls.