Chain motion and viscoelasticity in highly entangled solutions of semiflexible rods

Brownian dynamics simulations are used to study highly entangled solutions of semiflexible polymers. Bending fluctuations of semiflexible rods are signficantly affected by entanglement only above a concentration $c^{**}$, where $c^{**}\sim 10^{3}L^{-3}$ for chains of similar length $L$ and persistence length. For $c > c^{**}$, the tube radius $R_{e}$ approaches a dependence $R_{e} \propto c^{-3/5}$, and the linear viscoelastic response develops an elastic contribution that is absent for $c < c^{**}$. Experiments on isotropic solutions of $F$-actin span concentrations near $c^{**}$ for which the predicted asymptotic scaling of the plateau modulus $G \propto c^{7/5}$ is not yet valid.