Polydispersity controls the strength of semi-flexible polymer networks

The classical theory of polymer elasticity is built upon the assumption of network monodispersity-the premise that polymer networks are comprised of sub-chains of equal length. The crosslinking of biopolymers, however, is a random process and the resultant networks are likely to be polydisperse. The effect of structural polydispersity on the mechanical behavior of biopolymer networks is not well understood. The purpose of this contribution is to show how network polydispersity controls mechanical behavior and the ultimate properties of crosslinked semi-flexible filaments at finite deformations. The proposed micromechanical continuum model is based on the force-elongation relation of individual chains of different lengths. It is shown that the mechanical strength of the network is controlled by the finite-extensibility of filaments and the degradation of shorter filaments at relatively small stretches. The progressive failure of filaments continues and eventually determines the ultimate strength of the network. The predicted stress-stretch behaviors are in reasonable agreement with the experimental data for connective tissues.