Tube diameter in tightly entangled solutions of semiflexible polymers - art. no. 031502

A statistical mechanical treatment is given of the confinement of a wormlik e polymer in an entangled solution to a tube, yielding quantitative predict ions for the average tube diameter D-e and macroscopic plateau modulus G, i n the tightly entangled regime in which D-e is much less than the persisten ce length L-p. Three approaches an pursued. A self-consistent binary collis ion approximation, which explicitly describes the topological constraints i mposed by neighboring chains, yields predictions consistent with the scalin g laws D-e proportional to rho (-3/5) and G proportional to rho (7/5) propo sed previously, where rho is the contour length per unit volume. An effecti ve medium approximation, which treats the network as a continuum with a mod ulus G, instead yields D-e proportional to rho (-1/3) and G proportional to rho (4/3), which is found to be the correct scaling in the limit rhoL(p)(2 ) much greater than 1. An elastic network approximation treats the displace ment of a test chain as the sum of a collective displacement of the network , which is treated as a continuum, plus a local displacement, which is trea ted in a binary collision approximation. Predictions are compared to measur ements of both D-e and G in actin protein filament (F-actin) solutions.