Mechanical Properties of End-crosslinked Entangled Polymer Networks using Sliplink Brownian Dynamics Simulations

TL;DR

This study uses Brownian dynamics simulations to analyze the mechanical behavior of entangled polymer networks with crosslinks and sliplinks, revealing how sliplinks influence stress response and shear modulus.

Contribution

It introduces a detailed simulation approach for entangled networks, demonstrating sliplink contributions and validating additivity assumptions for long chains.

Findings

Sliplinks contribute about half the shear modulus of crosslinks.

Additivity of sliplink and crosslink effects holds for chains with two or more entanglements.

Simulation captures normal stress differences in shear.

Abstract

The mechanical properties of a polymeric network containing both crosslinks and sliplinks (entanglements) are studied using a multi-chain Brownian dynamics simulation. We coarse-grain at the level of chain segments connecting consecutive nodes (cross- or sliplinks), with particular attention to the Gaussian statistics of the network. Affine displacement of nodes is not imposed: their displacement as well as sliding of monomers through sliplinks is governed by force balances. The simulation results of stress in uniaxial extension and the full stress tensor in simple shear including the (non-zero) second normal stress difference are presented for monodisperse chains with up to 18 entanglements between two crosslinks. The cases of two different force laws of the subchains (Gaussian chains and chains with finite extensibility) for two different numbers of monomers in a subchain (no = 50 and no = 100) are examined. It is shown that the additivity assumption of slip- and crosslink contribution holds for sufficiently long chains with two or more entanglements, and that it can be used to construct the strain response of a network of infinitely long chains. An important consequence is that the contribution of sliplinks to the small-strain shear modulus is about ⅔ of the contribution of a crosslink.