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In this paper, the influence of solvents on the first hyperpolarizability β of nonlinear optical (NLO) molecules is studied at 25 °C for solutions of p-nitroaniline and N,N-dimethyl paranitroaniline in some 50 solvents belonging to different classes. The hyperpolarizabilities deduced from measured hyper-Rayleigh scattering are the relative ones with as reference that of paranitroaniline in 1,4-dioxane. Taking for the latter the literature value of 16.9 10−30 esu, the β values vary from 14.4 to 29.9 10−30 esu for paranitroaniline and from 28.7 to 46.2 10−30 esu for N,N-dimethyl paranitroaniline. A selection of the solvents is made on the basis of the fraction of the time γ0 during which the NLO molecule is not involved in H-bonding with the solvent molecules. γ0 can be determined from the solubility in the given solvent. The formation of specific solute–solvent interactions as H-bonds always increases the hyperpolarizability β. In the absence of such interactions, the hyperpolarizability increases with the square root of the gaseous dipole moment of the solvent molecule and decreases when the mean interdistance between the center of the NLO molecule and the closest solvent dipole increases. A statistical study of a large number of solvents leads indeed to the correlation β=βgas+aμS/VS where a is a constant for a given NLO molecule. When H-bonds are formed the correlation becomes: β=βgas+γ0aμS/VS+(1−γ0)bμS, where b is a constant for a given NLO molecule. H-bond formation enhances the hyperpolarizability because it reduces the distance between the neighboring solvent dipole and the center of the NLO molecule to a constant value, independent of VS.

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The thermodynamics of mobile disorder rejects the static model of the quasi-lattice for liquids. Because cause of the perpetual change of neighbors, during the observation time of thermodynamics of the order of seconds, each molecule of a given kind in a solution has experienced the same environment and had at its disposal the same mobile volume. This domain is not localizable and not orientable. Each molecular group perpetually "visits" successively all parts of this domain. The highest entropy is obtained when the groups visit all the parts of the domain without preference. H-bonds are preferential contacts with given sites of the neighbors that cause deviations with respect to such "random" visiting, thereby decreasing the entropy. The quantitative development of these ideas leads to equations describing the effect of solvent-solvent, solute-solvent, and solute-solute hydrogen bonds on the chemical potential of the solute. A universal equation predicting the solubility of drugs in a given solvent is derived. The effect of H-bonds is governed not by "solubility parameters" but by stability constants from which the order of magnitude can be estimated. From the sole knowledge of the solubility of methylparaben in pentane, the method predicts correctly the order of magnitude of its solubility in 26 other solvents, including alcohols and water.

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