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

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 but not ordered anisotropically and so may be affected differently by a disorderd lattice. The trails are simulated using the flatPERM algorithm and the inhomogeneity is realised by making a random fraction of the lattice 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 displays no more than one true thermodynamic collapsed phase.