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Journal Article

Random networks of cross-linked directed polymers


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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Ulrich, S., Zippelius, A., & Benetatos, P. (2010). Random networks of cross-linked directed polymers. Physical Review E, 81, 021802-1-021802-6. Retrieved from http://pre.aps.org/abstract/PRE/v81/i2/e021802.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-1283-4
We explore the effect of random permanent cross-links on a system of directed polymers confined between two planes with their end points free to slide on them. We treat the cross-links as quenched disorder and we use a semimicroscopic replica field theory to study the structure and elasticity of this system. Upon increasing the cross-link density, we get a continuous gelation transition signaled by the emergence of a finite in-plane localization length. The distribution of localization length turns out to depend on the height along the preferred direction of the directed polymers. The gelation transition also gives rise to a finite in-plane shear modulus which we calculate and turns out to be universal, i.e., independent of the energy and length scales of the polymers and the cross-links. Using a symmetry argument, we show that cross-links of negligible extent along the preferred axis of the directed polymers do not cause any renormalization to the tilt modulus of the uncross-linked system.