Onset of entanglement

Details Onset of entanglement Onset of entanglement

1998-01-09

arxiv.org/abs/cond-mat/9801082v1

Physics

Condensed Matter

Soft Condensed Matter

18 pages, with 4 figures

Scientific paper

10.1103/PhysRevE.58.3469

We have developed a theory of polymer entanglement using an extended Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive term, operating over mesoscales, which is interpreted as giving rise to entanglement, and the other a local repulsive term indicative of excluded volume interactions. We show how such a functional can be derived using notions from gauge theory. We go beyond the Gaussian approximation, to the one-loop level, to show that the system exhibits a crossover to a state of entanglement as the average chain length between points of entanglement decreases. This crossover is marked by critical slowing down, as the effective diffusion constant goes to zero. We have also computed the tensile modulus of the system, and we find a corresponding crossover to a regime of high modulus.

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