The morphology of many porous materials is sponge-like. For describing fluid adsorption in such materials,
we propose here a quite general sponge model which is built by digging spherical cavities in a continuum.
In contrast to the hard-sponge model proposed recently by Zhao et al. [Zhao, S. L.; Dong, W.; Liu, Q. H. J.
Chem. Phys.
2006, 125, 244703], the continuum in the present soft-sponge model is permeable to fluid particles.
Although the general expression of the fluid−matrix interaction potential is not pair additive, we were able
to extend some statistical-mechanics formalism of liquid state to deal with this model. We derived the
diagrammatic expansions of various correlation functions and Ornstein−Zernike equations. Usually, one would
not expect that the thermodynamic quantities (e.g., internal energy) of a system with a nonpair-additive
interaction can be completely determined from the structural information at the two-body level. We found a
remarkable result that for the soft-sponge model considered here, the internal potential energy can be determined
from only two-body correlation functions. In the particular case of a soft-sponge model with nonoverlapping
cavities, we show that the fluid−matrix interaction can be also described by a pair-additive potential. In this
case, the Madden−Glandt formalism applies. The Ornstein−Zernike equations obtained by using the pair-additive fluid−matrix interaction potential look to be quite different from those obtained by starting with the
nonpair-additive potential. We found the relationship between the two descriptions and show how the two
sets of Ornstein−Zernike equations can be transformed from each other for a soft-sponge model with
nonoverlapping cavities.