  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 length dispersity and the extent of 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. Comparison of the models evidenced similar behavior in both
models when the concentration of fillers exceeded the percolation threshold.
Some analytical results were obtained: (i) the relationship between the number
of 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.
