Stretching Semiflexible Filaments and Their Networks

Arguments are put forward that mean inextensibility is a valid approximation for semiflexible filaments. Using mean inextensibility, a simple analytical expression for the free energy for single filaments as a function of their end-to-end separation is obtained. This expression contains a term that explicitly represents the internal energy of the filament as well as nonzero temperature effects. Using this free energy, the force-extension relationships of semiflexible filaments and the corresponding nonlinear elasticity of their networks are investigated. Accounting for finite longitudinal compliance of filaments, we identify three distinct scaling regimes in the effective modulus of both single filaments and networks. We find the explicit expressions for crossovers between these scaling regimes; dramatic nonlinear elasticity will only be observed if there is a wide separation between the two crossovers.