Structure and elasticity of model disordered, polydisperse and defect-free polymer networks

TL;DR

This study uses simulations to analyze the structure and elasticity of disordered, polydisperse, defect-free polymer networks, revealing how assembly density influences network topology and linking microscopic localization lengths to macroscopic shear modulus.

Contribution

It introduces a simulation-based approach to model disordered polymer networks with exponential strand length distribution and explores the relationship between network structure, dynamics, and elasticity.

Findings

Network fractal structure depends on assembly density.

Long strand dynamics are described by the tube model.

Crosslink localization length relates to shear modulus.

Abstract

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly crosslinked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the crosslinks and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density, and connect the crosslink localization length to the shear modulus of the system.