Polymer collapse of a self-avoiding trail model on a two-dimensional inhomogeneous lattice

TL;DR

This paper investigates how random impurities affect the collapse behavior of a self-avoiding trail model on a two-dimensional triangular lattice, revealing that impurities reduce the number of distinct collapsed phases.

Contribution

It introduces a study of self-avoiding trails with impurities on a triangular lattice, showing the disruption of the maximally dense phase and the reduction to a single collapsed phase.

Findings

Impurities diminish the anisotropic ordered collapsed phase.

The maximally dense phase becomes a denser globule phase with impurities.

Only one true thermodynamic collapsed phase remains in the presence of disorder.

Abstract

The study of the effect of random impurities on the collapse of a flexible polymer in dilute solution has had recent attention with consideration of semi-stiff interacting self-avoiding walks on the square lattice. In the absence of impurities the model displays two types of collapsed phase, one of which is both anisotropically ordered and maximally dense (crystal-like). In the presence of impurities the study showed that the crystal type phase disappears. Here we investigate extended interacting self-avoiding trails on the triangular lattice with random impurities. Without impurities this model also displays two collapsed phases, one of which is maximally dense. However, this maximally dense phase is not ordered anisotropically. The trails are simulated using the flatPERM algorithm and the inhomogeneity is realised as a random fraction of the lattice that is unavailable to the trails. We calculate several thermodynamic and metric quantities to map out the phase diagram and look at how the amount of disorder affects the properties of each phase but especially the maximally dense phase. Our results indicate that while the maximally dense phase in the trail model is affected less than in the walk model it is also disrupted and becomes a denser version of the globule phase so that the model with impurities only displays no more than one true thermodynamic collapsed phase.