The mechanics and affine–nonaffine transition in polydisperse semiflexible networks

Abstract

Semiflexible gels are composed of a crosslinked network of filaments that can support both bending and extensional forces. We study numerically the mechanical effect of adding a low density of highly incompliant semiflexible filaments to a random network of softer semiflexible filaments. Such heterogeneous networks form simple models of the mechanics of cytoskeletal networks composed primarily of F-actin but containing a low density of significantly stiffer microtubules. Networks composed solely of these two filament types were recently studied in the in vitro experiments of Lin et al. Here we determine the effect of the stiffer impurity filaments generally on the collective mechanics of the heterogeneous filament network and, more specifically, on the affine to non-affine (A/NA) crossover in the softer filament matrix, which occurs in semiflexible networks as a function of their network density. We show that the addition of a small fraction of longer and stiffer filaments to a nonaffine network leads to a significant increase in its collective elastic moduli, even though the stiff filaments do not themselves form a stress bearing network. We also determine the relationship between the density of the stiff filaments and the geometric measure of nonaffinity for the network. Here the effect of the stiffer impurity filaments is complex: their addition makes affine networks slightly more affine, but highly nonaffine networks even more nonaffine. Moreover, there is a strong negative spatial correlation between density of the stiff filaments and local geometric measure of nonaffinity. Taken together, these two observations show that the stiffer filaments serve to locally suppress nonaffine deformation but redistribute it to regions of the network where the stiffer filaments are sparse.