Model for dynamic shear modulus of semiflexible polymer solutions

We discuss a dynamical model for the frequency-dependent shear modulus of an entangled solution of semiflexible polymers, based on longitudinal fluctuations in filaments between entanglement points or crosslinks. The goal is to explain non-Rouse, power-law scaling of the bulk shear modulus that is found via microscopic rheology of highly entangled F-actin solutions. This generalizes a previous model for the static modulus. Hydrodynamic effects, and the validity of a local drag approximation below the scale of the mesh size, are discussed. We test aspects of our model via a molecular dynamics simulation, and also present for comparison experimental results from microrheology on F-actin.