Thermodynamics of the hydration shell .2. Excess volume and compressibility of a hydrophobic solute

The hydration shell model for the excess volume and compressibility is examined. A modified Kirkwood-Buff formula for the excess volume, which is appropriate for use in the canonical ensemble, is presented. Its pressure derivative is shown to be the excess compressibility, which can be expressed as an integral of the local solvent compressibility over the hydration shell. For methane in water,which is chosen as the first application, the local solvent density and compressibility around the solute are calculated from a Monte Carlo simulation as continuous functions of the distance from the solute, The localization of the excess volume and compressibility within the hydration shell is then analyzed in terms of the deviation of the local solvent density and compressibility from their bulk values, respectively. The effect of the exclusion of solvent molecules by the solute is also described for the excess volume. About 80% of the total excess volume is accounted for/by the excluded volume effect of the solute plus the deviation of the volume per water molecule in the first hydration shell from that in the bulk, whereas the hydration shell model is not even qualitatively successful for describing the excess compressibility. A condition for the qualitative validity of the hydration shell model is identified, This involves the phase relationship between the local excess quantity and the solute-solvent radial distribution function. On the basis of an analysis of the pressure dependence of the chemical potential, the excess compressibility of the model methane-water solution is found to have a positive sign, This apparent ''softness'' of the ''hydrophobic water'', however, is not simply related to the properties of the first hydration shell.