Kumar, Senthil V and Kumaran, V (2005) Voronoi neighbor statistics of harddisks and hardspheres. In: Journal of Chemical Physics, 123 (7).

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Abstract
The neighbor distribution in hardsphere and harddisk 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 harddisk freezing transition, and $C_{n}$ decreases sharply to the hexagonal lattice values. In harddisk random structures the pentagon and heptagon populations remain significant even at high volume fraction. In dense hardsphere (threedimensional) structures at the freezing transition, $C_{1}$ is close to 14, instead of the value of 12 expected for a facecenteredcubic 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 equationofstate obtained from Voronoi tessellation are equal to those obtained from thermodynamic calculations. In hardsphere random structures, the dodecahedron population decreases with increasing density. To demonstrate the utility of the neighbor analysis, we estimate the effective hardsphere diameter of the LennardJones fluid by identifying the diameter of the spheres in the hardsphere fluid which has $C_{1}$ equal to that for the LennardJones fluid. The estimates are within 2% deviation from the theoretical results of BarkerHenderson and WeeksChandlerAndersen.
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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