Free volume in the hard sphere liquid

S. Sastry; T. M. Truskett; P. G. Debenedetti; S. Torquato; F. H. Stillinger

doi:10.1080/00268979809483161

Free volume in the hard sphere liquid

S. Sastry, T. M. Truskett, P. G. Debenedetti, S. Torquato, F. H. Stillinger

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Abstract

A method is developed for the efficient calculation of free volumes and corresponding surface areas in the hard sphere system by extending a previous method for calculating, exactly, cavity volumes in sphere packings. This method is used for the first time to evaluate the free-volume distribution of the hard sphere liquid over a range of densities near the freezing transition. From the distribution of free volumes, the equation of state can be obtained from a purely geometric analysis, which permits the calculation of pressure in Monte Carlo simulations where the dynamic definition cannot be employed. Furthermore, the cavity-volume distributions are obtained indirectly from the free-volume distributions in a density range where direct measurement is inadequate. Direct measurement of the first moment of the cavity-volume distribution makes it possible to calculate the chemical potential in the vicinity of the freezing transition.

Original language	English (US)
Pages (from-to)	289-297
Number of pages	9
Journal	Molecular Physics
Volume	95
Issue number	2
DOIs	https://doi.org/10.1080/00268979809483161
State	Published - Oct 1998

All Science Journal Classification (ASJC) codes

Biophysics
Molecular Biology
Condensed Matter Physics
Physical and Theoretical Chemistry

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10.1080/00268979809483161

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@article{a9bfa1dccd8447639cc6dd05f1ed7ed7,

title = "Free volume in the hard sphere liquid",

abstract = "A method is developed for the efficient calculation of free volumes and corresponding surface areas in the hard sphere system by extending a previous method for calculating, exactly, cavity volumes in sphere packings. This method is used for the first time to evaluate the free-volume distribution of the hard sphere liquid over a range of densities near the freezing transition. From the distribution of free volumes, the equation of state can be obtained from a purely geometric analysis, which permits the calculation of pressure in Monte Carlo simulations where the dynamic definition cannot be employed. Furthermore, the cavity-volume distributions are obtained indirectly from the free-volume distributions in a density range where direct measurement is inadequate. Direct measurement of the first moment of the cavity-volume distribution makes it possible to calculate the chemical potential in the vicinity of the freezing transition.",

author = "S. Sastry and Truskett, {T. M.} and Debenedetti, {P. G.} and S. Torquato and Stillinger, {F. H.}",

note = "Funding Information: We thank Robin Speedy and David Corti for helpful discussions. P.G.D. gratefully acknowledges support of the US Department of Energy, Division of Chemical Sciences, Office of Basic Energy Sciences (Grant DE-FG02-87ER13714), and of the donors of the Petroleum Research Fund, administered by The American Chemical Society. T.M.T. gratefully acknowledges The National Science Foundation for a graduate research fellowship. S.T. acknowledges the support of the US Department of Energy, Office of Basic Energy Sciences (Grant DE-FG02-92ER14275).",

year = "1998",

month = oct,

doi = "10.1080/00268979809483161",

language = "English (US)",

volume = "95",

pages = "289--297",

journal = "Molecular Physics",

issn = "0026-8976",

publisher = "Taylor and Francis Ltd.",

number = "2",

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TY - JOUR

T1 - Free volume in the hard sphere liquid

AU - Sastry, S.

AU - Truskett, T. M.

AU - Debenedetti, P. G.

AU - Torquato, S.

AU - Stillinger, F. H.

N1 - Funding Information: We thank Robin Speedy and David Corti for helpful discussions. P.G.D. gratefully acknowledges support of the US Department of Energy, Division of Chemical Sciences, Office of Basic Energy Sciences (Grant DE-FG02-87ER13714), and of the donors of the Petroleum Research Fund, administered by The American Chemical Society. T.M.T. gratefully acknowledges The National Science Foundation for a graduate research fellowship. S.T. acknowledges the support of the US Department of Energy, Office of Basic Energy Sciences (Grant DE-FG02-92ER14275).

PY - 1998/10

Y1 - 1998/10

N2 - A method is developed for the efficient calculation of free volumes and corresponding surface areas in the hard sphere system by extending a previous method for calculating, exactly, cavity volumes in sphere packings. This method is used for the first time to evaluate the free-volume distribution of the hard sphere liquid over a range of densities near the freezing transition. From the distribution of free volumes, the equation of state can be obtained from a purely geometric analysis, which permits the calculation of pressure in Monte Carlo simulations where the dynamic definition cannot be employed. Furthermore, the cavity-volume distributions are obtained indirectly from the free-volume distributions in a density range where direct measurement is inadequate. Direct measurement of the first moment of the cavity-volume distribution makes it possible to calculate the chemical potential in the vicinity of the freezing transition.

AB - A method is developed for the efficient calculation of free volumes and corresponding surface areas in the hard sphere system by extending a previous method for calculating, exactly, cavity volumes in sphere packings. This method is used for the first time to evaluate the free-volume distribution of the hard sphere liquid over a range of densities near the freezing transition. From the distribution of free volumes, the equation of state can be obtained from a purely geometric analysis, which permits the calculation of pressure in Monte Carlo simulations where the dynamic definition cannot be employed. Furthermore, the cavity-volume distributions are obtained indirectly from the free-volume distributions in a density range where direct measurement is inadequate. Direct measurement of the first moment of the cavity-volume distribution makes it possible to calculate the chemical potential in the vicinity of the freezing transition.

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DO - 10.1080/00268979809483161

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VL - 95

SP - 289

EP - 297

JO - Molecular Physics

JF - Molecular Physics

IS - 2

ER -

Free volume in the hard sphere liquid

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