Affine model of stress stiffening in semiflexible filament networks

TL;DR

This paper develops a refined affine model for semiflexible filament networks that incorporates crosslink distribution effects, enabling accurate predictions of elastic properties and explaining experimental data across different filament types.

Contribution

The study introduces a comprehensive affine model accounting for crosslink separation distribution, improving predictions of network elasticity and fitting experimental data more accurately.

Findings

Accounting for crosslink distribution alters the stress-modulus scaling.

The model fits experimental data for various filament networks.

Stiffer filaments like F-actin may have reduced effective rigidity in networks.

Abstract

We present a revised theoretical study of the affine assumption applied to semiflexible networks. Drawing on simple models of semiflexible worm-like chains we derive an expression for the probability distribution of crosslink separations valid at all separations. This accounts for both entropic and mechanical filament stretching. From this we obtain the free energy density of such networks explicitly as a function of applied strain. We are therefore able to calculate the elastic moduli of such networks for any imposed strain or stress. We find that accounting for the distribution of cross-link separations destroys the simple scaling of modulus with stress that is well known in single chains, and that such scaling is sensitive to the mechanical stretch modulus of individual filaments. We compare this model to three experimental data sets, for networks of different types of filaments, and find that a properly treated affine model can successfully account for the data. We find that for networks of stiffer filaments, such as F-actin, to fit data we require a much smaller effective persistence length than usually assumed to be characteristic of this filament type. We propose that such an effectively reduced rigidity of filaments might be a consequence of network formation.