SOME INTEGRAL RELATIONSHIPS FOR DISTRIBUTION-FUNCTIONS OF FLUIDS IN DISORDERED MEDIA

The Yvon-Born-Green, Kirkwood and Kirkwood-Salsburg integral equation hierarchies have been obtained for the case of a fluid adsorbed into a host medium made up of immobile particles. Despite earlier work which showed that the Ornstein-Zernicke equations for this situation were f undamentally different from those of a binary equilibrium fluid mixtur e, the pure-fluid and mixed-fluid-matrix Yvon-Born-Green and Kirkwood- Salsburg equations for the matrix-averaged distribution functions, g(f )((n)) and for g(mf)((n)), are found to be identical to those for the equilibrium mixture. However, the equilibrium mixture equations for g( m)((n)) do not apply. At present, the Kirkwood equation does not appea r in a matrix-averaged form suitable for numerical work. The Kirkwood- Salsburg equations can be used to generate the fundamental graph theor y for the problem. In practical calculations, the special role of the matrix enters principally in the closures used to truncate the hierarc hy of equations. The standard Kirkwood superposition approximation is appropriate in this application, and circumstances in which practical corrections to the superposition approximation can be employed are con sidered. (C) 1995 American Institute of Physics.