Critical packing fraction of rectangular particles on the square lattice

Abstract

The random packing of identical and nonoverlapping rectangular particles of size nxm (1</=n,m</=10) is studied numerically on the square lattice, and the corresponding packing fractions p(f) and percolation probabilities P(infinity) are determined. We find that for randomly oriented particles there is a critical packing fraction p(c)(f)=0.67+/-0.01, such that for all particles sizes nxm for which p(f)<p(c)(f) they do not percolate, i.e., P(infinity)-->0 for L-->infinity, while when p(f)>p(c)(f),P(infinity)-->1 when L-->infinity and an infinite cluster exists. The value for p(c)(f) is found to be consistent with the continuum percolation threshold p(c) congruent with0.67 for overlapping particles in two dimensions.