First Order Phase Transition of a Long Polymer Chain

TL;DR

This paper investigates a lattice model of a self-avoiding polygon with bending energy, demonstrating through Monte Carlo simulations that it exhibits a first-order nematic phase transition controlled by density and energy parameters.

Contribution

It introduces a lattice polygon model with bending energy and shows the existence of a first-order phase transition using Monte Carlo methods.

Findings

Identification of a first-order nematic phase transition.

Phase transition occurs across a curve in the parameter plane.

Model links polymer conformation to phase behavior.

Abstract

We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\circ$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\mu$ and $\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\beta$-$\mu$ plane.