Systematic bottom-up theory for the viscoelastic response of worm-like chain networks

Abstract

Using the frequency-dependent force-extension response functions of single worm-like chains as the only input, the linear complex viscoelastic modulus $G(\omega)$ of a polymeric network with given connectivity is derived from a systematic bottom-up theory via iterative coarse-graining. Choosing a cubic connectivity and accounting for random network orientation, we find excellent agreement with experimental data for actin networks under shear over the entire frequency range with the strength of the osmotic pressure that acts within the polymeric network as the only fitting parameter. In particular, we obtain a viscoelastic plateau regime at low frequencies and a crossover to an intermediate-frequency regime characterized by a power law behavior $G(\omega) \propto \omega^{1/2}$ and an inhomogeneous shear deformation field.