Cell Theories for Hard Particles

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Abstract
The consequences of each of the three approximations made by Kirkwood in deriving the Lennard-Jones—Devonshire cell theory are elucidated by a comparison with exact results in the one-dimensional case of hard rods. This comparison gives an explicit calculation of the one-dimensional communal entropy and shows that the single-occupancy approximation is exact at close packing, although it does not lead to thermodynamic properties which are analytic functions of density. For two- and three-dimensional systems, numerical results show that the cell-theory entropy predictions are more accurate than in one dimension because the particles are more localized. The more-than-one-particle-per-cell theories provide simple and rigorous lower bounds on the entropy, but the convergence to the thermodynamic limit by considering more and more particles is slow.

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