Abstract
A statistical mechanical treatment is given of the confinement of a wormlike polymer in an entangled solution to a tube, yielding quantitative predictions for the average tube diameter and macroscopic plateau modulus G, in the tightly entangled regime in which is much less than the persistence length Three approaches are pursued. A self-consistent binary collision approximation, which explicitly describes the topological constraints imposed by neighboring chains, yields predictions consistent with the scaling laws and proposed previously, where is the contour length per unit volume. An effective medium approximation, which treats the network as a continuum with a modulus G, instead yields and which is found to be the correct scaling in the limit An elastic network approximation treats the displacement 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 treated in a binary collision approximation. Predictions are compared to measurements of both and G in actin protein filament (F-actin) solutions.
- Received 27 December 1999
DOI:https://doi.org/10.1103/PhysRevE.63.031502
©2001 American Physical Society