An investigation of the influence of solute size and insertion conditions on solvation thermodynamics

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Abstract
In this paper we examine the influence of solute size and insertion conditions on solvent structural changes and excess thermodynamic properties in the infinite dilution limit. A general integral equation approach which can be applied under arbitrary conditions is given and isothermal-isochoric and isothermal-isobaric insertions are discussed in detail. Scaling relationships valid in the large solute limit are determined for both structural and thermodynamic properties. This is done by considering macroscopic thermodynamic relationships and explicit evaluation of low solvent density expansions of pair correlation functions. The hypernetted-chain and reference hypernetted-chain closure approximations are used to obtain numerical results for the insertion of hard sphere solutes of varying diameter into hard sphere, dipolar hard sphere and water-like solvents. The results obtained give a good deal of insight into the nature of solvation of inert solutes. It is shown that for all three solvents the excess properties are very well represented by a function obtained by summing terms proportional to the solute volume, surface area and diameter. One would expect such a result for large solutes, but here we show that this expression extrapolates all the way down to solutes comparable in size to the solvent particles. Further, it is shown that both the numerical value, and, more importantly, the physical interpretation of the excess thermodynamic properties strongly depend on the insertion conditions. Under all insertion conditions the chemical potential is a local property in the sense that it is completely determined by solute-solvent correlations which are important only in the immediate vicinity of the solute. However, this is not true of the excess energy, enthalpy and entropy which all contain nonlocal contributions arising essentially from changes in the actual or effective solvent density depending on the insertion conditions. We demonstrate that the nonlocal contributions can be very significant and therefore the excess energies, enthalpies and entropies often cannot provide useful information about solvent structure near solutes. This has significant implications for models which attempt to rationalize excess thermodynamics in terms of local solvent structure in the vicinity of solute particles.