Onset of entanglement

TL;DR

This paper develops a theoretical model for polymer entanglement using an extended Cahn-Hilliard functional, revealing a crossover to entangled states characterized by critical slowing down and increased tensile modulus.

Contribution

It introduces a novel extended functional derived from gauge theory to describe polymer entanglement beyond Gaussian approximation.

Findings

Crossover to entanglement occurs as chain length decreases.

Critical slowing down is observed at the entanglement transition.

Tensile modulus increases significantly in the entangled regime.

Abstract

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.