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, whi ch 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 o ver the hydration shell. For methane in water,which is chosen as the f irst 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 ex cess volume and compressibility within the hydration shell is then ana lyzed in terms of the deviation of the local solvent density and compr essibility from their bulk values, respectively. The effect of the exc lusion of solvent molecules by the solute is also described for the ex cess volume. About 80% of the total excess volume is accounted for/by the excluded volume effect of the solute plus the deviation of the vol ume per water molecule in the first hydration shell from that in the b ulk, whereas the hydration shell model is not even qualitatively succe ssful for describing the excess compressibility. A condition for the q ualitative validity of the hydration shell model is identified, This i nvolves the phase relationship between the local excess quantity and t he solute-solvent radial distribution function. On the basis of an ana lysis 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 hydr ation shell.