Nonaffine rubber elasticity for stiff polymer networks

TL;DR

This paper develops a theory for the elasticity of stiff polymer networks that accounts for their anisotropic bending and stretching responses, using a self-consistent approach based on floppy modes, and matches simulation and experimental data.

Contribution

It introduces a novel theoretical framework that incorporates non-affine bending deformations in stiff polymer networks, improving upon previous stretching-based models.

Findings

Shear modulus scaling matches recent 2D simulation results.

Theory explains bulk rheology of actin networks.

Non-affinity length scale is characterized by fiber length.

Abstract

We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces (``stretching''). Unlike in previous approaches, where network elasticity is derived from the stretching mode, our theory properly accounts for the soft bending response. A self-consistent effective medium approach is used to calculate the macroscopic elastic moduli starting from a microscopic characterization of the deformation field in terms of ``floppy modes'' -- low-energy bending excitations that retain a high degree of non-affinity. The length-scale characterizing the emergent non-affinity is given by the ``fiber length'' $l_f$, defined as the scale over which the polymers remain straight. The calculated scaling properties for the shear modulus are in excellent agreement with the results of recent simulations obtained in two-dimensional model networks. Furthermore, our theory can be applied to rationalize bulk rheological data in reconstituted actin networks.