Solvation theory to provide a molecular interpretation of the hydrophobic entropy loss ofnoble-gas hydration

Abstract

An equation for the chemical potential of a dilute aqueous solution of noble gases is derivedin terms of energies, force and torque magnitudes, and solute and water coordinationnumbers, quantities which are all measured from an equilibrium molecular dynamicssimulation. Also derived are equations for the Gibbs free energy, enthalpy and entropy ofhydration for the Henry’s law process, the Ostwald process, and a third proposed processgoing from an arbitrary concentration in the gas phase to the equivalent mole fraction inaqueous solution which has simpler expressions for the enthalpy and entropy changes. Goodagreement with experimental hydration free energies is obtained in the TIP4P andSPC/E water models although the solute’s force field appears to affect the enthalpies and entropiesobtained. In contrast to other methods, the approach gives a complete breakdown of theentropy for every degree of freedom and makes possible a direct structural interpretation ofthe well-known entropy loss accompanying the hydrophobic hydration of small non-polarmolecules under ambient conditions. The noble-gas solutes experience only a smallreduction in their vibrational entropy, with larger solutes experiencing a greater loss. Thevibrational and librational entropy components of water actually increase but onlymarginally, negating any idea of water confinement. The term that contributes the most tothe hydrophobic entropy loss is found to be water’s orientational term which quantifies thenumber of orientational minima per water molecule and how many ways the wholehydrogen-bond network can form. These findings help resolve contradictory deductionsfrom experiments that water structure around non-polar solutes is similar tobulk water in some ways but different in others. That the entropy loss lies inwater’s rotational entropy contrasts with other claims that it largely lies in water’stranslational entropy, but this apparent discrepancy arises because of differentcoordinate definitions and reference frames used to define the entropy terms.