Orientational order and glassy states in networks of semiflexible polymers

TL;DR

This paper investigates how networks of cross-linked semiflexible polymers develop various orientational orders and glassy states, revealing the influence of crossing angles, stiffness, and cross-link density on phase transitions.

Contribution

It introduces a semi-microscopic replica field theory to analyze orientational ordering and gelation in cross-linked semiflexible polymer networks, highlighting the role of crossing angles and stiffness.

Findings

Long-range orientational order depends on crossing angle and polymer stiffness.

Gelation transition is continuous and influenced by cross-link density.

Presence of a statistically isotropic amorphous solid (SIAS) phase between sol and ordered states.

Abstract

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order or are frozen in random directions depending on the value of the crossing angle, the crosslink concentration and the stiffness of the polymers. A crossing angle $\theta\sim 2\pi/M$ leads to long range $M$-fold orientational order, e.g., "hexatic" or "tetratic" for $\theta=60^{\circ}$ or $90^{\circ}$, respectively. The transition is discontinuous and the critical cross-link density depends on the bending stiffness of the polymers and the cross-link geometry: the higher the stiffness and the lower $M$, the lower the critical number of cross-links. In between the sol and the long range ordered state, we always observe a gel which is a statistically isotropic amorphous solid (SIAS) with random positional and random orientational localization of the participating polymers.