Entropy Crisis, Ideal Glass Transition and Polymer Melting: Exact Solution on a Husimi Cactus

TL;DR

This paper presents an exact solution for a lattice model of polymer melting on a Husimi cactus, revealing a first-order melting transition, supercooled liquid phase, and a metastable liquid with features akin to mode-coupling theory predictions.

Contribution

The study extends a polymer melting model by including new interactions and provides an exact solution on a Husimi cactus, uncovering complex phase behavior.

Findings

First-order melting transition between liquid and crystalline phases.

Existence of a supercooled liquid phase below melting temperature.

Observation of a metastable liquid with features similar to mode-coupling theory.

Abstract

We introduce an extension of the lattice model of melting of semiflexible polymers originally proposed by Flory. Along with a bending penalty, present in the original model and involving three sites of the lattice, we introduce an interaction energy that corresponds to the presence of a pair of parallel bonds and a second interaction energy associated with the presence of a hairpin turn. Both these new terms represent four-site interactions. The model is solved exactly on a Husimi cactus, which approximates a square lattice. We study the phase diagram of the system as a function of the energies. For a proper choice of the interaction energies, the model exhibits a first-order melting transition between a liquid and a crystalline phase. The continuation of the liquid phase below this temperature gives rise to a supercooled liquid, which turns continuously into a new low-temperature phase, called metastable liquid. This liquid-liquid transition seems to have some features that are characteristic of the critical transition predicted by the mode-coupling theory.