Effective electrical conductivity of microstructural patterns of binary mixtures on a square lattice in the presence of nearest-neighbour interactions

The effective conductivity and percolative behaviour of microstructural patterns of binary mixtures are studied. Microstructure patterns are not entirely random, but result from the presence of attractive or repulsive interactions and thermal fluctuations. The interactions of the particles with one another lead to the formation of correlations between particle positions, while thermal fluctuations weaken these correlations. A simple lattice model is used, where each site is occupied by a single particle, and interactions can occur only between the nearest neighbours. The Kawasaki algorithm is adopted to create 2D microstructure samples. The microstructure is treated as a continuous medium, which means that the contribution from the flow through 'choke points' is taken into account in the calculation of the effective conductivity. We studied the thermodynamics of the system and its effective conductivity in a wide range of parameters. A change in the percolation threshold when the temperature changed was observed. The direction of the threshold shift depends on the sign of the interaction between the particles. In the high temperature range, we obtained a formula describing the dependence of the percolation threshold on temperature, as well as on the critical exponent.