Percolation of sticks: effect of stick alignment and length dispersity

Abstract

Using Monte Carlo simulation, we studied the percolation of sticks, i.e. zero-width rods, on a plane paying special attention to the effects of stick alignment and their length dispersity. The stick lengths were distributed in accordance with log-normal distributions, providing a constant mean length with different widths of distribution. Scaling analysis was performed to obtain the percolation thresholds in the thermodynamic limits for all values of the parameters. Greater alignment of the sticks led to increases in the percolation threshold while an increase in length dispersity decreased the percolation threshold. A fitting formula has been proposed for the dependency of the percolation threshold both on stick alignment and on length dispersity.