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Orientational order and glassy states in networks of semiflexible polymers.

M. Kiemes,P. Benetatos,A. Zippelius

Published 2010 in Physical review. E, Statistical, nonlinear, and soft matter physics

ABSTRACT

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.

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