Excluded volume interactions and packing in liquids

We now consider packing issues associated with the reference term of van der Waals approaches exemplified by Eq. (4.1), p. 61. As noted there, the simplest interaction model appropriate for those terms is a hard-core model. The distinguished molecule considered will perfectly repel solvent molecules from an overlap, or excluded, volume. The general issues we develop will apply to such molecules in general solvents, i.e., the solvent need not be simple in the same sense as the hard-core solute we treat. But we will exemplify our general conclusions with results on the hard-sphere solvent system. The notation here, however, continues to use the tilde, as /i (i ), to indicate that the distinguished solute might serve as a reference case for subsequent treatment of other interactions. 

Eor such models the interaction part of the chemical potential of the solute is obtained as 

The operation of this formula can be viewed alternatively imagine identifying a molecular-scale volume at an arbitrary position in the liquid system by, first, hypothetical placement of the solute, and, second, determination of those positions 

Pa k 0l ), and to extract the extreme member p Q Oi ). We model the probabilities Pa k 0i ) on an information theory basis. We consider a relative or cross-information entropy (Shore and Johnson, 1980), 

An appropriate quahtative view of such maximum-entropy modeling is that it is a betting strategy. More specifically, this procedure identifies an assignment of probabilities that corresponds to the sampling experiment that, relative to Pa is maximally degenerate consistent with the constraint of the provided 

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Excluded volume interactions and packing in liquids coupled system. Explain why... 

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