Relation to Other Molecular Properties

Since log/3 reflects the difference in solvation energy between water and the lipid phase, it is to be expected that correlation would be found between log/3 and water solubility. Hansch, Quinlan and Lawrence in 1968 found linear relationships with logS*, for a wide range of liquids [58]. In 1980, Yalkowsky and Valvani extended this to solids, by including melting point in a linear relationship [59]. By 1991, Suzuki [60] had developed an estimating system for both partition coefficient and solubility. Eq. (15) covers a wide range of log/' and molar solubility, S, values in a set of 348 liquids and 149 solids. Tm is the melting point in °C; for liquids Tm is set equal to 25.

logl/S = 1.050 logP + 0.00956(rm - 25) - 0.515 (15)

If the important feature of the partitioning process is the formation of "iceberg" or "ordered" water about a solute, one would expect linear relationships between the "bulk" of the solute (surface area, see section 2.3.5, or volume) and free energy of partitioning, with corrections for polar interactions between the solute and water. Many correlations with volume have been presented, often being given in support of the "iceberg" theory of the hydrophobic effect [61]. In a seminal paper published in 1977, Cramer [62] looked in detail at volume/solvation relationships for hydrocarbons and for rare gases. He pointed out that whereas solubility of hydrocarbons in water decreased linearly with molecular volume, the solubility of rare gases in water actually increases with volume, in direct contradiction to the then current views of "hydrophobic" bonding. He discussed some other discrepancies in the popular "iceberg" theory of hydrophobic bonding, pointing also to the oft-overlooked importance of interaction with the lipid phase in determining logP. In the partitioning of a methylene moiety from water into octanol, Cramer gave the values of AG = — 0.54 kcal/mol for favorable solvation by octanol, and only AG = + 0.18 for unfavorable solvation by water. The overall process of transfer of a methylene is thus much better characterized energetically as lipophilic, than as hydrophobic - whatever the nature of hydrophobic forces might be.

Cramer offered an explanation of his results in terms of a cavity model of solvation. In a cavity model, energies are calculated first to create a solvent cavity, and then for interactions between the solvent and the solute molecule within the cavity. The first component is always a repulsive energy, which increases directly with solvent bulk (surface area or volume). This repulsive component is opposed by an attractive solvation energy which is proportional to solute polarizability, and polarizability in turn is proportional to molecular volume. Hence, it is possible to have both positive and negative slopes for a relationship between partition coefficient and volume.

The cavitation model is very attractive, and the focus on polarizability has been renewed recently by the "solvatochromic" approach to logP, first proposed by Kamlet and coworkers in 1977 [63-65] and discussed in the review by Leo [32] in 1993. Eq. (16) expresses the relationship between log/5 and a solute volume term, V, a polarity/pola-rizability term tc*. and independent measures of solute hydrogen-bond acceptor strength fi¡i and hydrogen-bond donor strength aH.

Leo has commented that once Eq. (16) has been well established, its real value will not be in calculating logP, but in the understanding it affords us of the relative contributions of solute size, polarizability/polarity and H-bond acceptor strength. Solute H-bond donor strength does not seem important for the octanol/water system, since the H-bond acceptor strength of water and octanol are about equal.

Honig, Sharp and An-Suei Yang in 1993 reviewed macroscopic models of aqueous solutions [66], Their discussion was in terms of the free energy of formation of cavity interfaces, which will be governed by the cohesive forces of the solvent. In this sense, all aqueous interfaces (solute-water interfaces), whether the solute is nonpolar or polar, are "hydrophobic" in that there will always be some force, surface tension, acting to minimize this interfacial area. This begs the question, what is the origin of surface tension?

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