Force-extension relation of cross-linked anisotropic polymer networks

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.

7 pages, 4 figures

References in corpus (5)

• Elasticity of Stiff Polymer Networks
• Mechanics of bundled semiflexible polymer networks
• Mechanical response of active gels
• Anisotropic Random Networks of Semiflexible Polymers
• Orientational order and glassy states in networks of semiflexible polymers

Cited by in corpus (6)

• Tension-induced binding of semiflexible biopolymers
• Bundling in brushes of directed and semiflexible polymers
• Elasticity of a semiflexible filament with a discontinuous tension due to a cross-link or a molecular motor
• Elasticity of cross-linked semiflexible biopolymers under tension
• Tensile elasticity of semiflexible polymers with hinge defects
• Cross-linked pair of polymer chains under strong tension