Random networks of cross-linked directed polymers

Details Random networks of cross-linked directed polymers Random networks of cross-linked directed polymers

2009-11-16

arxiv.org/abs/0911.3088v2

Phys. Rev. E 81, 021802 (2010)

Physics

Condensed Matter

Soft Condensed Matter

7 pages, 3 figures

Scientific paper

10.1103/PhysRevE.81.021802

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.

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