The mechanics of phantom Mikado networks

Abstract

The elasticity of networks comprised of semi-flexible polymers plays a vital role in regulating the mechanics of both intra-and extra-cellular matrices. The behaviour of this polymer scaffold will depend on the nature and density of cross-linking between constituent fibres. While modelling efforts have investigated the effects of cross-link density in biopolymer networks, this is often accompanied by changes in both the fibre density and the network structure. We investigate the elasticity of a quasi two-dimensional Mikado network of elastic rods, in which cross-link density is allowed to vary while polymer density is held constant. In particular, this model is extended by allowing constituent rods to cross without forming cross-links, while polymer density and network geometry are preserved. In doing so, the competing contributions to the shear modulus from cross-link density, mesh size, geometry and polymer density are decoupled. We find that previous scaling laws fail to capture the well-studied transition from bend-to stretch-dominated elasticity as cross-link density is varied. We identify a length scale which relates cross-link density to the transition between affine and nonaffine regimes, and which provides a collapse of simulation data curves for varying cross-link densities.