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Voronoi cell volume distribution and configurational entropy of hard-spheres

Kumar, Senthil V and Kumaran, V (2005) Voronoi cell volume distribution and configurational entropy of hard-spheres. In: Journal of Chemical Physics, 123 (11).

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Abstract

The Voronoi cell volume distributions for hard-disk and hard-sphere fluids have been studied. The distribution of the Voronoi free volume \upsilon f, which is the difference between the actual cell volume and the minimal cell volume at close packing, is well described by a two-parameter (2 \Gamma) or a three-parameter (3\Gamma) gamma distribution. The free parameter m in both the 2\Gamma and 3\Gamma models is identified as the "regularity factor." The regularity factoris the ratio of the square of the mean and the variance of the free volume distribution, and it increases as the cell volume distribution becomes narrower. For the thermodynamic structures, the regularity factor increases with increasing density and it increases sharply across the freezing transition, in response to the onset of order. The regularity factor also distinguishes between the dense thermodynamic structures and the dense random or quenched structures. The maximum information entropy (max-ent) formalism, when applied to the gamma distributions, shows that structures of maximum information entropy have an exponential distribution of \upsilon f. Simulations carried outusing a swelling algorithm indicate that the dense random-packed states approach the distribution predicted by the max-ent formalism, though the limiting case could not be realized in simulations due to the structural in homogeneities introduced by the dense random-packing algorithm. Using the gamma representations of the cell volume distribution, we check the numerical validity of the Cohen-Grest expression [M. H. Cohen and G. S. Grest, Phys. Rev. B 20, 1077 (1979)]for the cellular (free volume) entropy, which is a part of the configurational entropy. The expression is exact for the hard-rod system, and a correction factor equal to the dimension of the system,D, is found necessary for the hard-disk and hard-sphere systems. Thus,for the hard-disk and hard-sphere systems, the present analysis establishes a relationship between the precisely defined Voronoi free volume (information) entropy and the thermodynamic entropy. This analysis also shows that the max-ent formalism, when applied to the free volume entropy, predicts an exponential distribution which is approached by disordered states generated by a swelling algorithm in the dense random-packing limit.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to American Institute of Physics.
Department/Centre: Division of Mechanical Sciences > Chemical Engineering
Date Deposited: 11 Nov 2005
Last Modified: 19 Sep 2010 04:21
URI: http://eprints.iisc.ernet.in/id/eprint/3995

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