Cavities and free volume in hard-disc and hard-sphere systems
- 1 January 1981
- journal article
- research article
- Published by Royal Society of Chemistry (RSC) in Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics
- Vol. 77 (2) , 329-335
- https://doi.org/10.1039/f29817700329
Abstract
The pressure of a hard-sphere system (in 1, 2 and 3 dimensions and at all densities) can be expressed in terms of the surface area 〈si〉 and volume 〈vi〉 of an average cavity. In contrast, the analogous expression for the pressure in terms of free volume requires the average 〈sf/vf〉 over the free volume of each sphere, which is not expressible in terms of an average free volume. We show that 〈si〉/〈vi〉=〈sf/vf〉. Numerical values for the number, size and variance of cavities in the hard-disc fluid and solid are calculated. An incidental finding is that deviations from the ideal gas equation are given to a good approximation by p/ρkT–1 =⅕ exp 5z for discs and by p/ρkT–1 =⅖ exp 5z for spheres, between the low density percolation transition and the freezing density.Keywords
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