Statistical thermodynamics of aqueous solutions. I. Water structure, solutions with non-polar solutes, and hydrophobic interactions

Abstract

A statistical thermodynamic theory of the structure and thermodynamic properties of liquid water is needed for a description of the thermodynamics properties of aqueous salt solutions. For this purpose, such a theory, developed earlier by Némethy and Scheraga, has been modified by removing an empirical cluster restriction, by using a different form of the partition function for unbonded water, by treating the librational and translational frequencies differently, and by removing the restriction that the energy levels are equally spaced. These modifications improved the computed thermodynamic properties of liquid H 2O and D 2O, and provide a basis to treat aqueous solutions of non-polar molecules and, subsequently, salts. The presence of a non-polar solute leads to shifts of the energy levels of the variously bonded species in the first layer of the surrounding water molecules, and a resulting increase in the fraction of hydrogen bonds between water molecules; i.e. non-polar solutes in aqueous solutions can be characterized as ‘structure making’. Theoretical, Monte Carlo and molecular dynamics calculations, and also simplified models, in the literature, support the assumption in the model used here of a partial cage-like (hydrogen-bonded) structure around a hydrocarbon molecule (hydrophobic hydration). The computed thermodynamic parameters for the transfer of hydrocarbons from a non-polar medium to an aqueous environment, based on a statistical thermodynamic treatment, are reproduced very well by the theory. With no additional parameters, the theory accounts qualitatively for the transfer of argon, propane and butane, respectively, from H 2O to D 2O, better than the original theory. The strengths of pairwise hydrophobic interactions, computed by Némethy and Scheraga, and subsequently verified experimentally, are not altered by the modification of the earlier theory for liquid water.