Finite-size effects in nanocomposite thin films and fibers.

Monte Carlo simulations of finite-size effects for continuum percolation in three-dimensional, rectangular sample spaces filled with spherical particles were performed. For samples with any dimension less than 10-20 times the particle diameter, finite-size effects were observed. For thin films in the finite-size regime, percolation across the thin direction of the film gave critical volume fraction (p(c)) values that differed from those along the plane of the film. Simulations perpendicular to the film for very thin samples resulted in p(c) values lower than the classical limit of ∼29% (for spheres in a three-dimensional matrix) which increased with film thickness. For percolation along thin films, while holding film thickness constant, p(c) increased with increasing sample size, which is a modification of the finite-sized scaling effect for cubic samples. For samples with a large aspect ratio (fibers) and a finite-sized cross-sectional area, the critical volume fraction increased with sample length, as the sample became quasi-one-dimensional. The results are discussed in the context of adding volume along or perpendicular to the percolation direction. From an experimental perspective, these findings indicate that sample shape, as well as relative size, influences percolation in the finite-size regime.