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Abstract

Motivated by the organization of cross-linked 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 cross-links which fix the orientations of the corresponding polymer segments to align with one another. Upon increasing the cross-link 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 continuous isotropic-to-nematic (IN) transition occurring at the same cross-link density. As the polymer stiffness decreases, the IN transition becomes first order, shifts to a higher cross-link density, and is preceded by an amorphous solid where the average polymer orientations freeze in random directions.