Monte Carlo calculations of the number of ways to pack nonoverlapping rods on a square lattice

Abstract

The number of configurations of nonoverlapping rods on a square lattice is computed for various packing fractions and orientations of the rods. From the number of configurations, the entropies of the configurations are computed and compared with the results of approximate formulas of DiMarzio that are much used in statistical–mechanical theories of liquid crystals. For rods of three lattice sites, our calculations and Dimarzio’s formulas agree to within 0.5% for packing fractions less than 0.5. Some calculations for rods of ten lattice sites also showed good agreement.