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Using Monte Carlo simulation, we studied the electrical conductance oftwo-dimensional films. The films consisted of a poorly conductive host matrixand highly conductive rodlike fillers (rods). The rods were of various lengths,obeying a log-normal distribution. They were allowed to be aligned along agiven direction. The impacts of length dispersity and the extent of rodalignment on the insulator-to-conductor phase transition were studied. Twoalternative computational approaches were compared. Within Model I, the filmswere transformed into resistor networks with regular structures and randomlydistributed conductances. Within Model II, the films were transformed intoresistor networks with irregular structures but with equal conductivities ofthe conductors. Comparison of the models evidenced similar behavior in bothmodels when the concentration of fillers exceeded the percolation threshold.Some analytical results were obtained: (i) the relationship between the numberof fillers per unit area and the transmittance of the film within Model I, (ii)the electrical conductance of the film for dense networks within Model II.

journal of applied physics

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