Orientational order and glassy states in networks of semiflexible polymers

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-02, Vol.83 (2 Pt 1), p.021905-021905, Article 021905
• Main Authors: Kiemes, Martin, Benetatos, Panayotis, Zippelius, Annette
• Format: Article
• Language: English
• Subjects: Computer Simulation; Cytoskeletal Proteins - chemistry; Cytoskeletal Proteins - ultrastructure; Cytoskeleton - chemistry; Cytoskeleton - ultrastructure; Elastic Modulus; Models, Chemical; Models, Molecular; Phase Transition
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/PhysRevE.83.021905

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study 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 semimicroscopic 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 cross-link concentration, and the stiffness of the polymers. A crossing angle θ~2π/M leads to long-range M-fold orientational order, for example, "hexatic" or "tetratic" for θ=60° or 90°, respectively. The transition to the orientationally ordered state is discontinuous and the critical cross-link density, which is higher than that of the gelation transition, depends on the bending stiffness of the polymers and the cross-link angle: The higher the stiffness and the lower the M, the lower is the critical number of cross-links. In between the sol and the long-range ordered state, we always expect a gel which is a statistically isotropic amorphous solid with random positional and random orientational localization of the participating polymers.