Mean-Field Treatment of the Many-Body Fokker-Planck Equation

We review some properties of the stationary states of the Fokker - Planck equation for N interacting particles within a mean field approximation, which yields a non-linear integrodifferential equation for the particle density. Analytical results show that for attractive long range potentials the steady state is always a precipitate containing one cluster of small size. For arbitrary potential, linear stability analysis allows to state the conditions under which the uniform equilibrium state is unstable against small perturbations and, via the Einstein relation, to define a critical temperature Tc separating two phases, uniform and precipitate. The corresponding phase diagram turns out to be strongly dependent on the pair-potential. In addition, numerical calculations reveal that the transition is hysteretic. We finally discuss the dynamics of relaxation for the uniform state suddenly cooled below Tc.Comment: 13 pages, 8 figure

Multiscale Effects of Interfacial Polymer Confinement in Silica Nanocomposites

Dispersing hydrophilic nanofillers in highly hydrophobic polymer matrices is widely used to tune the mechanical properties of composite material systems. The ability to control the dispersion of fillers is closely related to the mechanical tunability of such composites. In this work, we investigate the physical–chemical underpinnings of how simple end-group modification to one end of a styrene–butadiene chain modifies the dispersion of silica fillers in a polymer matrix. Using surface-sensitive spectroscopies, we directly show that polymer molecular orientation at the silica surface is strongly constrained for silanol functionalized polymers compared to nonfunctionalized polymers because of covalent interaction of silanol with silica. Silanol functionalization leads to reduced filler aggregation in composites. The results from this study demonstrate how minimal chemical modifications of polymer end groups are effective in modifying microstructural properties of composites by inducing molecular ordering of polymers at the surface of fillers

Nonlinear Mori-Zwanzig theory and quadratic coarse-grained coordinates for complex molecular systems

International audienceAbstract We first introduce the Zwanzig-Kawasaki version of the Generalized
Langevin Equation (GLE) and show as a preamble and under some hy-
pothesis about the relaxation of the fluctuations in the orthogonal sub-
space, that the commonly used term for the Markovian approximation
of the dissipation is rigorously vanishing, necessitating the use of the
next-order term, in an integral series we introduce. Independently, we
provide thereafter a comprehensive description of complex coarse-grained
molecules which, in addition to the classical positions and momenta of
their centers of mass, encompasses their shapes, angular momenta and
internal energies. The dynamics of these quantities is then derived as
the coarse-grained forces, torques, microscopic stresses, energy transfers,
from the coarse-grained potential built with their Berne-like anisotropic
interactions. By incorporating exhaustively the quadratic combinations of
the atomic degrees of freedom, this novel approach enriches considerably
the dynamics at the coarse-grained level and could serve as a foundation
for developing numerical models more holistic and accurate than Dissi-
pative Particle Dynamics (DPD) for the simulation of complex molecular
systems. This advancement opens up new possibilities for understand-
ing and predicting the behavior of such systems in various scientific and
engineering applications

Diffusion de particules classiques en interaction (équation de Fokker-Planck en champ moyen)

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Grain Shape Dynamics for Molecular Simulations at the Mesoscale

International audienc

Development of anisotropic force fields for homopolymer melts at the mesoscale

International audienceWith the aim of producing realistic coarse-grained models of homopolymers, we introduce a tabulated backbone-oriented anisotropic potential. The parameters of the model are optimized using statistical trajectory matching. The impact of grain anisotropy is evaluated at different coarse-graining levels using cis-polybutadiene as a test case. We show that, at the same time, tuning the aspect ratio of the grains can lead to a better density and structure and may reduce the unphysical bond crossings by up to 90%, without increasing the computation time too much and thereby jeopardizing the main advantage of coarse-grained models

Backbone oriented anisotropic coarse grains for efficient simulations of polymers

International audienc

Assessing the derivation of time parameters from branched polymer coarse-grain model

International audienc

Heterogeneity Effects in Highly Cross-Linked Polymer Networks

International audienceDespite their level of refinement, micro-mechanical, stretch-based and invariant-based models, still fail to capture and describe all aspects of the mechanical properties of polymer networks for which they were developed. This is for an important part caused by the way the microscopic inhomogeneities are treated. The Elastic Network Model (ENM) approach of reintroducing the spatial resolution by considering the network at the level of its topological constraints, is able to predict the macroscopic properties of polymer networks up to the point of failure. We here demonstrate the ability of ENM to highlight the effects of topology and structure on the mechanical properties of polymer networks for which the heterogeneity is characterised by spatial and topological order parameters. We quantify the macro- and microscopic effects on forces and stress caused by introducing and increasing the heterogeneity of the network. We find that significant differences in the mechanical responses arise between networks with a similar topology but different spatial structure at the time of the reticulation, whereas the dispersion of the cross-link valency has a negligible impact