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Voronoi neighbor statistics of hard-disks and hard-spheres

Kumar, Senthil V and Kumaran, V (2005) Voronoi neighbor statistics of hard-disks and hard-spheres. In: Journal of Chemical Physics, 123 (7).


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The neighbor distribution in hard-sphere and hard-disk fluids is analyzed using Voronoi tessellation. The statistical measures analyzed are the nth neighbor coordination number $(C_{n})$, the nth neighbor distance distribution $[f_{n}(r)]$, and the distribution of the number of Voronoi faces $(P_{n})$. These statistics are sensitive indicators of microstructure, and they distinguish thermodynamic and annealed structures. A sharp rise in the hexagon population marks the on set of hard-disk freezing transition, and $C_{n}$ decreases sharply to the hexagonal lattice values. In hard-disk random structures the pentagon and heptagon populations remain significant even at high volume fraction. In dense hard-sphere (three-dimensional) structures at the freezing transition, $C_{1}$ is close to 14, instead of the value of 12 expected for a face-centered-cubic lattice. This is found to be because of a topological instability, where a slight perturbation of the positions in the centers of a pair of particles transforms a vertex in the Voronoi polyhedron into a Voronoi surface. We demonstrate that the pair distribution function and the equation-of-state obtained from Voronoi tessellation are equal to those obtained from thermodynamic calculations. In hard-sphere random structures, the dodecahedron population decreases with increasing density. To demonstrate the utility of the neighbor analysis, we estimate the effective hard-sphere diameter of the Lennard-Jones fluid by identifying the diameter of the spheres in the hard-sphere fluid which has $C_{1}$ equal to that for the Lennard-Jones fluid. The estimates are within 2% deviation from the theoretical results of Barker-Henderson and Weeks-Chandler-Andersen.

Item Type: Journal Article
Publication: Journal of Chemical Physics
Publisher: American Institute of Physics
Additional Information: Copyright for this article belongs to American Institute of Physics.
Department/Centre: Division of Mechanical Sciences > Chemical Engineering
Date Deposited: 27 Sep 2005
Last Modified: 19 Sep 2010 04:20
URI: http://eprints.iisc.ac.in/id/eprint/3731

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