Force–extension relation of cross-linked anisotropic polymer networks

Benetatos, Panayotis; Ulrich, Stephan; Zippelius, Annette

doi:10.1088/1367-2630/14/11/115011

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Force–extension relation of cross-linked anisotropic polymer networks

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Zippelius, Annette
Fellow Group Polymers, complex fluids and disordered systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Benetatos, P., Ulrich, S., & Zippelius, A. (2012). Force–extension relation of cross-linked anisotropic polymer networks. New Journal of Physics, 14: 115011, pp. 115011-115023. doi:10.1088/1367-2630/14/11/115011.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-105B-1

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 behaviour is captured by a toy model of two chains with a single cross-link in the middle.