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Orientational order and glassy states in networks of semiflexible polymers

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Kiemes,  Martin
Fellow Group Polymers, complex fluids and disordered systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Zippelius,  Annette
Fellow Group Polymers, complex fluids and disordered systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Kiemes, M., Benetatos, P., & Zippelius, A. (2011). Orientational order and glassy states in networks of semiflexible polymers. Physical Review E, 83: 021905. doi:10.1103/PhysRevE.83.021905.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-11E1-9
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.