Drug molecules with low aqueous solubility can be solubilized by a class of cosolvents, known as hydrotropes. Their action has often been explained by an analogy with micelle formation, which exhibits critical micelle concentration (CMC). Indeed, hydrotropes also exhibit "minimum hydrotrope concentration" (MHC), a threshold concentration for solubilization. However, MHC is observed even for nonaggregating monomeric hydrotropes (such as urea); this raises questions over the validity of this analogy. Here we clarify the effect of micellization on hydrotropy, as well as the origin of MHC when micellization is not accompanied. On the basis of the rigorous Kirkwood-Buff (KB) theory of solutions, we show that (i) micellar hydrotropy is explained also from preferential drug-hydrotrope interaction; (ii) yet micelle formation reduces solubilization effeciency per hydrotrope molecule; (iii) MHC is caused by hydrotrope-hydrotrope self-association induced by the solute (drug) molecule; and (iv) MHC is prevented by hydrotrope self-aggregation in the bulk solution. We thus need a departure from the traditional view; the structure of hydrotrope-water mixture around the drug molecule, not the structure of the aqueous hydrotrope solutions in the bulk phase, is the true key toward understanding the origin of MHC.

How do osmolytes affect the conformation and configuration of supramolecular assembly, such as ion channel opening and actin polymerization? The key to the answer lies in the excess solvation numbers of water and osmolyte molecules; these numbers are determinable solely from experimental data, as guaranteed by the phase rule, as we show through the exact solution theory of Kirkwood and Buff (KB). The osmotic stress technique (OST), in contrast, purposes to yield alternative hydration numbers through the use of the dividing surface borrowed from the adsorption theory. However, we show (i) OST is equivalent, when it becomes exact, to the crowding effect in which the osmolyte exclusion dominates over hydration; (ii) crowding is not the universal driving force of the osmolyte effect (e.g., actin polymerization); (iii) the dividing surface for solvation is useful only for crowding, unlike in the adsorption theory which necessitates its use due to the phase rule. KB thus clarifies the true meaning and limitations of the older perspectives on preferential solvation (such as solvent binding models, crowding, and OST), and enables excess number determination without any further assumptions.

Adsorbate–adsorbate interaction can be determined directly from an adsorption isotherm via a rigorous statistical thermodynamic theory.

The energetic representation of the molecular configuration in a dilute solution is introduced to express the solvent distribution around the solute over a one-dimensional coordinate specifying the solute-solvent interaction energy. In this representation, the correspondence is shown to be one-to-one between the set of solute-solvent interaction potentials and the set of solvent distribution functions around the solute. On the basis of the one-to-one correspondence, the Percus-Yevick and hypernetted-chain integral equations are formulated over the energetic coordinate through the method of functional expansion. It is then found that the Percus-Yevick, hypernetted-chain, and superposition approximations in the energetic representation determine the solvent distribution functions correctly to first-order with respect to the solute-solvent interaction potential and to the solvent density. The expressions for the chemical potential of the solute are also presented in closed form under these approximations and are shown to be exact to second-order in the solute-solvent interaction potential and in the solvent density.

In order to understand the origin of the Hofmeister series, a statistical-mechanical analysis, based upon the Kirkwood-Buff (KB) theory, has been performed to extract information regarding protein hydration and water-mediated protein-salt interactions from published experimental data-preferential hydration and volumetric data for bovine serum albumin in the presence of a wide range of salts. The analysis showed a linear correlation between the preferential hydration parameter and the protein-cosolvent KB parameter. The same linear correlation holds even when nonelectrolyte cosolvents, such as polyethelene glycol, have been incorporated. These results suggest that the Hofmeister series is due to a wide variation of the water-mediated protein-cosolvent interaction (but not the change of protein hydration) and that this mechanism is a special case of a more general scenario common even to the macromolecular crowding.

Can the sorption mechanism be proven by fitting an isotherm model to an experiment? Such a question arises because (i) multiple isotherm models, with different assumptions on sorption mechanisms, often fit an experimental isotherm equally well, (ii) some isotherm models [such as Brunauer−Emmett−Teller (BET) and Guggenheim− Anderson−de Boer (GAB)] fit experimental isotherms that do not satisfy the underlying assumptions of the model, and (iii) some isotherms (such as Oswin and Peleg) are empirical equations that do not have a well-defined basis on sorption mechanisms. To overcome these difficulties, we propose a universal route of elucidating the sorption mechanism directly from an experimental isotherm, without an isotherm model, based on the statistical thermodynamic fluctuation theory. We have shown that how sorbate−sorbate interaction depends on activity is the key to understanding the sorption mechanism. Without assuming adsorption sites and planar layers, an isotherm can be derived, which contains the Langmuir, BET, and GAB models as its special cases. We have constructed a universal approach applicable to adsorption and absorption, solid and liquid sorbents, and vapor and liquid sorbates and demonstrated its efficacy using the humidity sorption isotherm of sucrose from both the solid and liquid sides.

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.

An approximate functional for the chemical potential of a solute in solution is presented in the energy representation. This functional is constructed by adopting the Percus-Yevick-like approximation in the unfavorable region of the solute-solvent interaction and the hypernetted-chain-like approximation in the favorable region. The chemical potential is then expressed in terms of energy distribution functions in the solution and pure solvent systems of interest, and is given exactly to second order with respect to the solvent density and to the solutesolvent interaction. In the practical implementation, computer simulations of the solution and pure solvent systems are performed to provide the energy distribution functions constituting the approximate functional for the chemical potential. It is demonstrated that the chemical potentials of nonpolar, polar, and ionic solutes in water are evaluated accurately and efficiently from the single functional over a wide range of thermodynamic conditions.