Hard rods on lattices

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Abstract
Exact calculations and enumerations of systems of hard rigid rods distributed at closed packed density on L x L square lattices, where each rod occupies N < 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 < | s | > ≤ 11/36 for L/N > 2 and decreases continuously with increasing size of the system L/N for all N. The entropy per rod of our systems behaves as SN ∝ N -1 × In N as N → ∞. 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

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