Effect of lattice inhomogeneity on collapsed phases of semi-stiff ISAW polymers

TL;DR

This study explores how random lattice impurities influence the phase behavior of semi-stiff self-avoiding walks, revealing that impurities cause swelling and can eliminate the crystalline phase in long polymers.

Contribution

It introduces a detailed analysis of impurity effects on polymer phases using simulations, highlighting the disappearance of the crystal phase with increasing disorder.

Findings

Impurities cause polymer swelling across all phases.

The crystalline phase vanishes with sufficient impurities in long walks.

A crossover between homogeneous and impurity-dominated regimes is demonstrated.

Abstract

We investigate semi-stiff interacting self-avoiding walks on the square lattice with random impurities. The walks are simulated using the flatPERM algorithm and the inhomogeneity is realised as a random fraction of the lattice that is unavailable to the walks. 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. On a homogeneous lattice this model has an extended phase and two distinct collapsed phases, globular and crystalline, which differ in the anisotropy of the walks. By adding impurities to the lattice we notice a degree of swelling of the walks for all phases that is commensurate with the fraction of the lattice that is removed. Importantly, the crystal phase disappears with the addition of impurities for sufficiently long walks. For finite length walks we demonstrate that competition between the size of the average spaces free of impurities and the size of the collapsed polymer describes the crossover between the homogeneous lattice and the impurity dominated situation.