Orientational order and glassy states in networks of semiflexible polymers

Abstract

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, the orientationally ordered phases in networks of randomly cross-linked semiflexible polymers are studied in two dimensions. We consider permanent cross-links prescribing a finite angle, and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of single polymers and small polymer clusters (sol), and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains display either long-range orientational order or are frozen in random directions. The phase behavior is categorized depending on the value of the crossing angle, the degree of thermal fluctuations about the crossing angle, the cross-link 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. a hexatic phase for $\theta = 60^\circ$ or a tetratic phase for $\theta = 90^\circ$. 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). The SIAS is characterized by random positional and random orientational localization of the participating polymers.