Force-extension relation of cross-linked anisotropic polymer networks

TL;DR

This paper analytically investigates how cross-links affect the nonlinear force-extension behavior of aligned semiflexible polymer bundles, revealing entropic effects and scaling laws near gelation.

Contribution

It provides a theoretical analysis of the force-extension relation in anisotropic, cross-linked polymer networks, highlighting entropic effects and scaling near gelation.

Findings

Cross-links increase the differential stiffness of polymer bundles.

Cross-link contribution scales inversely with force for hard cross-links.

Behavior near gelation matches shear modulus scaling.

Abstract

Cross-linked polymer networks with orientational order constitute a wide class of soft materials and are relevant to biological systems (e.g., F-actin bundles). We analytically study the nonlinear force-extension relation of an array of parallel-aligned, strongly stretched semiflexible polymers with random cross-links. In the strong stretching limit, the effect of the cross-links is purely entropic, independent of the bending rigidity of the chains. Cross-links enhance the differential stretching stiffness of the bundle. For hard cross-links, the cross-link contribution to the force-extension relation scales inversely proportional to the force. Its dependence on the cross-link density, close to the gelation transition, is the same as that of the shear modulus. The qualitative behavior is captured by a toy model of two chains with a single cross-link in the middle.