Numerical study of a slip-link model for polymer melts and nanocomposites

We present a numerical study of the slip link model introduced by Likhtman for describing the dy- namics of dense polymer melts. After reviewing the technical aspects associated with the implemen- tation of the model, we extend previous work in several directions. The dependence of the relaxation modulus with the slip link density and the slip link stiffness is reported. Then the nonlinear rheolog- ical properties of the model, for a particular set of parameters, are explored. Finally, we introduce excluded volume interactions in a mean field such as manner in order to describe inhomogeneous systems, and we apply this description to a simple nanocomposite model. With this extension, the slip link model appears as a simple and generic model of a polymer melt, that can be used as an alternative to molecular dynamics for coarse grained simulations of complex polymeric systems

Polymer blend and polymer-solvent blend : thermodynamics and dynamics close to the glass transition

L’objet de ce travail est la description de la dynamique de diffusion dans les polymères à l’approche de la transition vitreuse et notamment les processus de relaxation hors équilibre. Nous développons, pour les mélanges compressibles de polymères et polymère-solvant, un modèle thermodynamique qui permet de calculer les forces thermodynamiques dans des situations hors d’équilibre (formalisme général d’Onsager). La dynamique correspondante repose sur l’existence d’hétérogénéités dynamiques près de Tg dues aux fluctuations de concentration (modèle de Long et Lequeux). Nous avons développé deux méthodes. La première est basée sur une équation de Fokker-Planck décrivant, à l’échelle des hétérogénéités (quelques nm), la distribution des fluctuations de concentration de polymère et de solvant. Après l’étude des mécanismes de relaxation à cette échelle, nous étudions l’échelle macroscopique, pour rendre compte de la pénétration du solvant dans un matériau vitreux ou du séchage d’un mélange polymère-solvant près de Tg. La deuxième méthode consiste en la simulation de ces mécanismes de relaxation par une description spatiale. Celle-ci est basée sur une discrétisation de l’espace, chaque site pouvant échanger du solvant ou des monomères selon une dynamique décrite par des équations de Langevin non-linéaires couplées. Cette dernière méthode est plus générale mais plus coûteuse en temps de calculs. Nous montrons que les résultats obtenus des deux façons sont cohérents. Il s’agit de la première méthode permettant de décrire microscopiquement et quantitativement la diffusion de solvant près et en dessous de la transition vitreuseThe aim of this work is to describe the diffusion dynamics in polymers close to the glass transition (relaxation processes at non equilibrium states). A thermodynamic model for polymer-polymer and polymer-solvent blends is developed. It is able to compute the thermodynamic forces existing at non equilibrium for the mentioned blends (Onsagers formalism). The correspondent dynamic are based upon the existence of thermodynamic heterogeneities close to Tg due to concentration's fluctuations (Long-Lequeux model). Two methods were developed. The first is based on a Fokker-Planck equation which describes, at the heterogeneity scale (i.e. nanometric scale), the distribution of fluctuations of polymer and solvent. Following the study on the relaxation mechanism in the nanometric scale, a microscopic scale was then considered, in order to take in account either the solvent penetration within a glassy material or the drying of a polymer-solvent blend close to Tg. The second method consists in the simulation of the mentionned relaxation mechanisms using a spatial approach. This approach is based on a special discretization, each site being able to exchange solvent molecules or monomers according to the dynamics described by coupled non-linear Langevin equations. This second method is a more general approach. However the calculations related to it are more time-consuming. The results obtained by both methods are in good agreement. This is the very first method able to describe microscopically and quantitatively the solvents diffusion close to or below T

Entanglement-induced reinforcement in polymer nanocomposites

International audienceWe propose a coarse-grained model able to describe filled entangled polymer melts. Our purpose is to study the reinforcement caused by the effect of fillers on the entanglement network, as speculated in previous experimental work, and also observed in molecular dynamics studies. In this work, the filler volume fraction effect, the distribution of the fillers (cubic lattice, randomly dispersed, and small clusters randomly dispersed) and the presence or absence of grafted chains on the fillers are investigated. Our model is based on a “slip-link” model initially developed to study the entanglements in pure polymer melts and offers a less costly computational method than molecular dynamics simulations for the study of entangled polymer melts. The polymer chains are described as Rouse chains of Brownian particles connected by Hookean springs, and are subject to friction and random forces. Entanglements are artificially imposed by objects (slip-links) exhibiting statistical fluctuations that do not modify the equilibrium statistics of the melt. In addition we introduced excluded volume interactions between chain segments, to take into account the incompressibility of the melt. These excluded volume interactions do not perturb the dynamics of the chains in the homogeneous limit as expected from theoretical considerations on short range interactions. Finally, the fillers are modeled by immobile spherical objects, with or without grafted chains, which interact with a repulsive potential with the chain monomers. The chains grafted onto the fillers are represented by “additional slip links” confined in the vicinity of each filler. We first present the effect of the filler distribution and filler volume fraction, considering only bare fillers. Then, the effect of grafted chains via the additional slip-links is also shown as a function of the same parameters. Our results show that the presence of grafted chains induces an important change in the viscosity, calculated by integrating the stress autocorrelation function. Both the plateau value and the terminal relaxation time depend on the density of fillers and on the number of grafted chains. Moreover, we find that a disordered filler configuration induces confinement effects that amplify reinforcement compared to the case of a perfectly ordered configuration