The effect of chain polydispersity on the elasticity of disordered polymer networks

TL;DR

This study investigates how chain polydispersity and network preparation influence the elasticity of disordered polymer networks, revealing the importance of chain length distribution and preparation protocol on shear modulus.

Contribution

The paper introduces a generic stress-strain relation that accounts for chain length distribution effects without relying on specific end-to-end distance models.

Findings

Shear modulus depends strongly on network preparation protocol.

The shear modulus is a non-monotonic function of elastically-active strand density.

Short chains significantly impact the elastic properties and must be accurately characterized.

Abstract

Due to their unique structural and mechanical properties, randomly-crosslinked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (\textit{e.g.} chain-length and end-to-end distributions), we generate disordered phantom networks with different crosslinker concentrations $C$ and initial density $\rho_{\rm init}$ and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same $C$, which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by $\rho_{\rm init}$. We rationalise this dependence by employing a generic stress-strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a non-monotonic function of the density of elastically-active strands, and that this behaviour has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly-crosslinked polymer networks, the knowledge of the exact chain conformation distribution is essential for predicting correctly the elastic properties. Finally, we apply our theoretical approach to published experimental data, qualitatively confirming our interpretations.