Paul Ruelle

A New Predictive Equation for the Solubility of Drugs Based on the Thermodynamics of Mobile Disorder

The thermodynamics of mobile disorder rejects the static model of the quasi-lattice for liquids. Because 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.

Aqueous solubility prediction of environmentally important chemicals from the mobile order thermodynamics

Applied to the aqueous solubility of only-sligthly polar compounds with no hydrogen bond donor capacity, the quantitative development of the thermodynamics of mobile order results in a very simple nearly linear predictive solubility equation requiring only the molar volume of the solute and its melting properties in the case of solids. Enhancement of the solubility by weak solvation effects associated to the proton-acceptor ability of the solute towards water is taken into account through standard stability constants reflecting the functionality, the degree of unsaturation and cyclization of the molecule. Accordingly, the molar aqueous solubility of a diverse set of 531 chemicals of environmental relevance is predicted with an average absolute error of 0.37 log units though the solubilities span over more than 12 orders of magnitude. The analysis of the relative importance of the terms contributing to the solubility demonstrates that the poor solubility of low-polarity compounds in water is merely the result of the hydrophobic effect and of its extremely rapid increase with the size of the solute. The mobile order thermodynamics also provides explanations for the empirically deduced solubility-volume linear relationships.

Comparison of the solubility of polycyclic aromatic hydrocarbons in non-associated and associated solvents: The hydrophobic effect

Abstract A remarkable improvement of the predictions of the solubility, Φ B , of a solute B in a solvent S is achieved by the theory of the mobile order of Huyskens. In this theory, the hydrophobic effect of the associated solvents like alcohols against inert substances is no longer considered as a result from a change in the energy of the molecular interactions, but as a decrease of the entropy due to temporary correlated displacements of two or more hydroxylic groups of solvent molecules. Such correlated displacements create a kind of mobile order. Quantitatively, the hydrophobic effect reduces ln Φ B by an amount of r S Φ S V B / V S . A direct consequence of this effect is that an increase in the ratio V B / V S of the molar volumes, which in non-H-bonded solvents is favourable for the solubility, becomes unfavourable in alcohols. For polycyclic aromatic hydrocarbons, the prediction of the solubilities in apolar, polar and associated solvents by the mobile order theory necessitates the knowledge of a single parameter only which can be deduced from one experimental solubility.

The n-octanol and n-hexane/water partition coefficient of environmentally relevant chemicals predicted from the mobile order and disorder (MOD) thermodynamics.

The quantitative thermodynamic development of the mobile order and disorder theory in H-bonded liquids is extended in order to predict the partition coefficient. With respect to the classical predictive methods, the great advantage of the present approach resides in the possibility of predicting partition coefficient not only in the reference n-octanol/water partitioning system, but also in any mutually saturated two-phase system made up of two largely immiscible solvents. Constructed from the various free energy contributions encoded in the distribution process, the model furthermore provides a useful tool to understand both the origin and the factors, like the solute molar volume, that determine the partitioning of non-electrolytes between two immiscible liquid phases. From the comparison of the relative magnitude of the terms which contribute to the overall log P value, much information can also be gained concerning the variation of the partition coefficients of the same substances in different distribution systems. For example, the model has successfully been applied to the log P prediction of a number of environmentally important chemicals of varying structure, size and chemical nature in the n-octanol/water and n-hexane/water systems. Whatever the complexing or non-complexing substances studied, the hydrophobic effect always represent the driving force that rules distribution processes in the aqueous environments. As the dominant contribution to the partition coefficient in any organic/aqueous binary system, it is evidenced why hydrophobicity is usually considered to be a good measure of lipophilicity.

Prediction of carbazole solubility and its dependence upon the solvent nature

Abstract On the basis of at most three parameters, the solubility of carbazole is predicted in 33 nonelectrolyte solvents by means of the general solubility equation derived from the thermodynamics of mobile order. Particular attention is focussed on the influence of the formation of solute-solvent stoechiometrical hydrogen bonds on the treatment of the non-specific dipole-dipole and dispersion interactions. Three classes of solvents can be distinguished according to their solubilizing potential towards carbazole: non-complexing solvents, complexing non-associated solvents and complexing amphiphilic solvents. The analysis of the relative importance of the different terms contributing to the solubility allows one to quantitatively understand its variation between the different classes as well as within each class of solvents.

The effect of proton-acceptor sites of the solute on its solubility in proton-donor solvents

Abstract The solubilities of five solid ketones and two esters are predicted in common organic nonelectrolyte solvents using the solubility equation derived from the mobile order theory. In the framework of this theory, the formation of solute-solvent hydrogen bonds is treated on the basis of standard stability constants. Two different values characterizing the ketone-alcohol and the ester-alcohol hydrogen bonds, respectively 170 and 110 cm 3 /mol, have been determined. The formation of specific molecular interactions brings about a net increasing of the solubility without modifying the values of the other contributions relevant to the solution process. Using the predetermined values of the stability constants, the solubility equation is then successfully applied to predict the solubility of testosterone propionate in 28 solvents including alcohols and water from the sole knowledge of its solubility in hexane.

Enhancement of the solubilities of polycyclic aromatic hydrocarbons by weak hydrogen bonds with water

SummaryThe thermodynamics of mobile order is applied to predict the aqueous solubility of liquid and solid aliphatic and polycyclic aromatic hydrocarbons. The solubility values are mainly determined by the magnitude of the hydrophobic effect. However, contrary to the solubilities of the alkanes, the solubilities of polycyclic aromatic hydrocarbons in water predicted in absence of solute-solvent hydrogen (H) bonds are systematically too low. This shows the contribution of weak specific interactions between the OH groups and the π electrons of the aromatic substances. According to the theory, these interactions are characterized by a stability bility constant Ko which can be derived from solubility data. At 25°C, this constant amounts to 80 cm3/mol, the order of magnitude of which can be explained by the competition of these intermolecular bonds with the rather weak self-association bonds in the secondary chains of water.

Solubility Predictions for Solid Nitriles and Tertiary Amides Based on the Mobile Order Theory

The solubilities of hexadecanenitrile, octadecanenitrile, N,N-diphenyl capramide, and N.N-diphenyl lauramide are predicted in common organic nonelectrolyte solvents using the solubility equation derived from the mobile order theory. In the framework of this theory, the formation of hydrogen bonds is treated on the basis of stability constants. Two values characterizing the nitrile–alcohol and the tertiary amide–alcohol hydrogen bonds, 175 and 600 cm3 mol−1, respectively, are determined. Although the formation of solute–solvent specific molecular interactions brings about a net increase in the solubility, the solubilities of the nitriles and amides in alcohols remain lower than those measured in nonassociated solvents because of the large negative hydrophobic effect of the alcohol molecules.

Ab initio quantum-chemical study of the unimolecular pyrolysis mechanisms of acetic acid☆

Abstract The mechanisms of unimolecular dehydration and decarboxylation reactions occurring during the pyrolysis of acetic acid above 700°C have been investigated by ab initio methods. The atomic basis set influence as well as the electron correlation effects are analyzed by using a variety of basis sets, ranging from minimal to polarized split-valence, and by introducing the Moller-Plesset (MP) perturbation theory. With an activation barrier of 76.0 kcal mol −1 , the concerted dehydration process occurs via a four-centre transition state. On the other hand, the decarboxylation process could be described by two different mechanisms depending on the nature of the kinetic experiments. While in flow systems, the decarboxylation of acetic acid takes place by a concerted mechanism via a four-centre transition state with an activation energy of 77.3 kcal mol − , the results suggest rather a water-catalyzed concerted mechanism via a six-membered transition state for the reaction carried out in batch systems, the activation barrier amounting to 64.0 kcal mol −1 .

Structure and properties of phosphaketene (H?P?C?O): phosphorus versus oxygen protonation?

Phosphaketenes carrying bulky substituents to limit dimerization have recently been reported and for comparison the simple model phosphaketene (1) was investigated using ab initio methods. It has an E-bent structure with a CP bond length of 1.728A; and a CPH bond angle of 90.6°(using the 4-31 G basis set). This is rationalized in terms of stabilizing interactions between the PH and CO fragments so that the C–P bond is essentially a dative single bond enforced by π-back-donation. Both P and O centres carry an overall negative charge; of five possible structures of protonated HPCO considered, phosphorus protonation is unambiguously preferred and the perpendicular structure (11) calculated to be the most stable. Inclusion of polarization functions and correlation energies favours phosphorus protonation further. Also reported are the vibrational frequencies, dissociation energies of the protonated and neutral phosphaketene, and the predicted reactivity in both cycloadditions and additions of HX; comparison is made with reported experimental data where available.