  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.
