Materials Chemistry Research Dept. Bl011178 Technical Memorandum

Frank H. Stillinger

Free Volume in the Hard­Sphere Liquid

Srikanth Sastry (1) , Thomas M. Truskett (1) , Pablo G. Debenedetti
(1)*, 
Salvatore Torquato (2;3) , and Frank H. Stillinger (4;2)
 
(1) Department of Chemical Engineering 
Princeton University, Princeton, NJ 08544 
(2) Princeton Materials Institute 
Princeton, University, Princeton, NJ 08544 
(3) Department of Civil Engineering and Operations Research, 
Princeton, University, Princeton, NJ 08544 
(4) Bell Laboratories, Lucent Technologies 
Murray Hill, NJ 07974 
* Electronic address: pdebene@pucc.princeton.edu 
BL0111780-971223-15-TM

Abstract We present a method for the efficient calculation of free volumes and corresponding surface areas in the hard­sphere system by extending a previous method for calculating, exactly, cavity volumes in sphere packings. Using this method, we evaluate, for the first time, the free­volume distribution of the hard­sphere 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, we obtain the cavity­volume distributions indirectly from the free­volume distributions in a density range where direct measurement is inadequate. Direct measurement of the first moment of the cavity­volume distribution enables us to calculate the chemical potential in the vicinity of the freezing transition.

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