Fiber Network Elasticity as Function of Crosslinker Density

Abstract

Crosslinkers determine the architecture of polymer networks and thus are of great importance for the resulting mechanical properties. A simple morphological model is proposed for the investigation of the linear elastic response of 3D fiber networks to randomly disconnecting network nodes. Isotropic ordered and disordered, 4-coordinated networks are modeled as homogeneous bodies in the shape of a network with a given volume fraction with locally isotropic elastic moduli. The 4-coordinated nodes are randomly split into two locally unconnected fibers representing a morphology change of the network at constant volume fraction. The effective shear modulus is studied using a voxel-based finite element method. Our results show a strong, continuous decrease of the shear modulus with decreasing number of nodes in the network without a percolation transition. The morphology of the networks is characterized by the Euler number that linearly depends on the fraction of split nodes, and that is easily extracted from 3D confocal microscopy data. Associating all network nodes with fiber junctions connected by a crosslinking molecule, this approach is a first order model for elasticity of biological networks with varying crosslinker density.