Anisotropic Random Networks of Semiflexible Polymers

TL;DR

This paper develops a theoretical framework to understand how semiflexible polymers form anisotropic networks with various phase transitions, including gelation, isotropic-nematic, and orientational glass states, influenced by polymer stiffness and crosslink density.

Contribution

It introduces a semimicroscopic replica field theory capturing the formation and phase behavior of anisotropic networks of semiflexible polymers, including novel insights into the transitions involved.

Findings

Continuous gelation transition with increasing crosslink density.

Synchronous isotropic-nematic transition for stiff polymers.

Emergence of an orientational glass state as polymer stiffness decreases.

Abstract

Motivated by the organization of crosslinked cytoskeletal biopolymers, we present a semimicroscopic replica field theory for the formation of anisotropic random networks of semiflexible polymers. The networks are formed by introducing random permanent crosslinks which fix the orientations of the corresponding polymer segments to align with one another. Upon increasing the crosslink density, we obtain a continuous gelation transition from a fluid phase to a gel where a finite fraction of the system gets localized at random positions. For sufficiently stiff polymers, this positional localization is accompanied by a {\em continuous} isotropic-to-nematic (IN) transition occuring at the same crosslink density. As the polymer stiffness decreases, the IN transition becomes first order, shifts to a higher crosslink density, and is preceeded by an orientational glass (statistically isotropic amorphous solid) where the average polymer orientations freeze in random directions.