Non-universality of elastic exponents in random bond-bending networks

TL;DR

This study reveals that elastic properties in two-dimensional random rod networks near the rigidity transition do not follow universal behavior, contrasting with geometric percolation, which has implications for understanding actin-fiber networks.

Contribution

It demonstrates that elastic exponents in random rod networks are non-universal, differing from geometric exponents, challenging assumptions of universality in percolation theory.

Findings

Elastic modulus vanishes with an exponent of approximately 3.0 near the transition.

Geometric quantities exhibit universal behavior, but elastic properties do not.

Implications for the mechanical behavior of actin-fiber networks are discussed.

Abstract

We numerically investigate the rigidity percolation transition in two-dimensional flexible, random rod networks with freely rotating cross-links. Near the transition, networks are dominated by bending modes and the elastic modulii vanish with an exponent f=3.0\pm0.2, in contrast with central force percolation which shares the same geometric exponents. This indicates that universality for geometric quantities does not imply universality for elastic ones. The implications of this result for actin-fiber networks is discussed.