Microstructure of two-phase random media. II. The Mayer--Montroll and Kirkwood--Salsburg hierarchies

Journal Article · Tue Mar 15 04:00:00 EST 1983 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.445245· OSTI ID:5709687

Torquato, S; Stell, G

It is shown that the Mayer--Montroll (MM) and Kirkwood--Salsburg (KS) hierarchies of equilibrium statistical mechanics for a binary mixture under certain limits become equations for the n-point matrix probability functions S/sub n/ associated with two-phase random media. The MM representation proves to be identical to the S/sub n/ expression derived by us in a previous paper, whereas the KS representation is different and new. These results are shown to illuminate our understanding of the S/sub n/ from both a physical and quantitative point of view. In particular rigorous upper and lower bounds on the S/sub n/ are obtained for a two-phase medium formed so as to be in a state of thermal equilibrium. For such a medium consisting of impenetrable-sphere inclusions in a matrix, a new exact expression is also given for S/sub n/ in terms of a two-body probability distribution function rho/sub 2/ as well as new expressions for S/sub 3/ in terms of rho/sub 2/ and rho/sub 3/, a three-body distribution function. Physical insight into the nature of these results is given by extending some geometrical arguments originally put forth by Boltzmann.

• Research Organization: Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27650GA Technologies Inc., San Diego, California 92121
• OSTI ID: 5709687
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 78:6; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
BINARY MIXTURES
CRYSTAL STRUCTURE
DISPERSIONS
DISTRIBUTION FUNCTIONS
FUNCTIONS
MECHANICS
MICROSTRUCTURE
MIXTURES
PHASE STUDIES
PROBABILITY
STATISTICAL MECHANICS