Morphology and transport using the Ising lattice as a morphology description

One of the simplest and most commonly studied models of transport in disordered media is the random percolation model. Although this model has been of great value in developing our fundamental understanding of the problem, the morphologies generated seldom mimic the features of real disordered composites. For example, the morphologies predicted from the random percolation model are strictly topologically equivalent over the composition range, a feature that rarely occurs in real systems. In this study we expand the range of lattice based morphologies to include ramified/compact cluster shapes with a variable percolation threshold by incorporating nearest neighbor interactions on a square lattice, i.e. the Ising model. We investigate cluster shape, size and number, and percolation characteristics-morphological features that in part determine the effective transport properties-over the Ising state space. A comparison is made between the transport properties arising from random percolation and this model using two conductivity ratios. We show that overall behavior of simple transport processes is sensitive to structural correlations.