HARD-RODS ON LATTICES

Exact calculations and enumerations of systems of hard rigid rods distributed at closed packed density on L multiplied by L square lattices, where each rod occupies N less than L nearest neighbour lattice sites, have been performed. In contrast to mean-field theories our results though restricted to finite L and N provide evidence against long-range orientational order: the absolute magnitude of the orientational order parameter is LT AN BR vertical s vertical RT AN BR less than equivalent to 11/36 for L/N greater than 2 and decreases continuously with increasing size of the system L/N for all N. The entropy per rod of our systems behaves as S//N varies directly as N** minus **1 multiplied by ln N as N yields infinity . Hard rods on cubic lattices are also briefly considered. Some implications of our results are discussed with respect to liquid crystals, polymeric liquid crystals and current theories of polymer melting.