A thermodynamic analysis of solvation in dipolar liquids

The chemical potential of infinitely dilute dipole solvation is dissected into parts of cavity formation, dispersion forces, and dipolar interactions. It is this latter part whose treatment is improved here over previous models by applying the Padé approximation for the perturbation expansion. In this way allowance is made for local solvent structuring around the solute due to packing effects. The solvent is modelled by spherical hard molecules of spherical polarizability, centered dipole moment, and central dispersion potential. For realistic parameter values, the Padé result of dipole solvation falls between the predictions of the Onsager theory and the mean-spherical approximation (MSA), and approaches the continuum limit faster than the MSA. The latter is demonstrated to be just the low-density limit of the Padé form. Tested on experimental solvation free energies of nitromethane as the solute in select solvents, the Padé form is found to predict the polarity dependence of the chemical potential of dipole solvation far better than MSA and Onsager theories. We also set out to a qualitative analysis of hydration thermodynamics, in particular enthalpies and entropies. The calculated values of both components of the hydration free energy are substantially too negative compared to experiment, with an equality found between excess enthalpies and excess entropies times temperature. This is all the more meaningful as the excess entropy originates chiefly from cavity formation, and the excess enthalpy mainly from dispersion and dipolar forces. Both parts are thus derived from equations that are fully independent of one another. The excess enthalpy is identified with the solvent reorganization energy featuring the solvent-solvent interaction changes induced by the solute. This is the first time as it appears that, by applying the Padé approximation to the solvation problem, solvent reorganization energies for real systems can be extracted from experimental solvation data. The primary factor determining the solvent reorganization energy is found to be solute size. Since the solvent reorganization terms are locked into exact enthalpy-entropy compensation, in line with thermodynamic considerations, a simple solvent model as the present one is adequate to treat solvation free energies. Large negative entropies of hydration at constant pressure arise from the cavity formation term and are traced to two particular properties of water: small molecular size and low expansibility, with the latter being of greater impact. In fact, for all other solvents considered, the entropies of cavity formation at constant pressure are positive due to the high liquid expansibilities. These lead to overall small negative, or even positive, solvation entropies at constant pressure.