Viscoelasticity of tightly entangled solutions of semiflexible polymers

Abstract

A molecular model is introduced to describe the linear viscoelasticity of tightly entangled solutions of semiflexible polymers. An expression for the stress of a solution of wormlike chains is derived, and a tube model is used to describe the effects of entanglement. Consideration of the Brownian dynamics of the polymer within its tube yields a dynamic modulus ${G}^{*}(\ensuremath{\omega})\ensuremath{\propto}(i\ensuremath{\omega}{)}^{3/4}$ at high frequencies, in agreement with the results of recent microrheology experiments on actin solutions.