Electrical conductance of two-dimensional composites with embedded rodlike fillers: An analytical consideration and comparison of two computational approaches

Using Monte Carlo simulation, we studied the electrical conductance of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rodlike fillers (rods). The rods were of various lengths, obeying a log-normal distribution. They were allowed to be aligned along a given direction. The impacts of the length dispersity and the extent of the rod alignment on the insulator-to-conductor phase transition were studied. Two alternative computational approaches were compared. Within Model I, the films were transformed into resistor networks with regular structures and randomly distributed conductances. Within Model II, the films were transformed into resistor networks with irregular structures but with equal conductivities of the conductors. A comparison of the models evidenced similar behavior in both models when the concentration of fillers exceeded the percolation threshold. However, a fairly fine mesh should be used in Model I to obtain a reasonable estimation of the electrical conductance. The electrical conductance is slightly overestimated in Model I. In anisotropic systems, the length dispersity of fillers has a more pronounced effect on the electrical conductance along the direction of the rod alignment. Some analytical results were obtained: (i) the relationship between the number of fillers per unit area and the transmittance of the films within Model I and (ii) the electrical conductance of the films for dense networks within Model II.