Pierre Huyskens

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.

Solvent dependence of the first hyperpolarizability of p-nitroanilines: Differences between nonspecific dipole–dipole interactions and solute–solvent H-bonds

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...

A new expression for the combinatorial entropy of mixing in liquid mixtures

Abstract In the classic expression for the combinatorial entropy in terms of the mole fractions xA and xB′ the space unoccupied by the B molecules appears for them as divided in numerable parts, each belonging to an A molecule. In the Flory-Huggins expression based on the volume fractions φA and φB the space unoccupied by the B molecules is for them a continuum, not parcelled out in portions based on A standards. However in a solution containing nB moles of B for a total number of moles n, the border of a B molecule is separated from that of the nearest B on the average by a distance equal to ((n/nB)1/2−1) times the mean diameter of the A molecules. Thus, there exists still in the liquid, directions for the B molecules which can be divided according to A standards. Based on this consideration, a new expression is derived for the combinatorial entropy of liquid mixtures which contains a “numerable” part besides a “continuous” part. on applying this equation for the prediction of the solubility of solid n-alkanes in liquid alkanes and neglecting non-ideality effects, the predicted values agree much better with the experimental ones than those deduced from the classic or from the Flory-Huggins expression.

Mobile and static molecular disorder in liquids

Abstract The fraction of time during which a molecule of a pure alcohol does not undergo H-bonding, estimated from the vapor pressure, is two orders of magnitude larger than the fraction of molecules that at a given time are not bound by an H-bond to their neighbors, as deduced from IR spectroscopic data. This obviously “anti-ergodic” statement renders questionable all the thermodynamic treatments of H-bonding in liquids, which are based on the usual Boltzmann expression. This expression equates the thermodynamic probability of a system with the static probability of distribution of the various states and, as outlined by Einstein, does not hold for non-ergodic systems. As pointed out by Pais (A. Pais, Subtle is the Lord. The Science and the Life of Albert Einstein, Oxford University Press, 1982), another Boltzmann relation relates the thermodynamic probability of a state to the fraction of time during which the system is found in that state. The latter definition was used by Einstein in his treatment of the ergodic problem. Similarly, the theory of the thermodynamics of mobile order in H-bonded liquids, of Huyskens and Siegel (P.L. Huyskens and G.G. Siegel, Bull. Soc. Chim. Belg., 97 (1988) 821), considers not the static configurations of the liquid, but the fraction of time during which an OH proton follows the oxygen atom of one or another neighboring molecules in its motion through the liquid. This coordination lowers the entropy and this reduction can be evaluated quantitatively. The present paper establishes a distinction between the static disorder, which is due to the possibility of exchange between the positions of the molecules and exists in mixed crystals, and the mobile disorder, which is due to the enlargement of the domain available for the motions of a given molecule, provoked by the mixing of two real gases. The mixing of two liquids allows an exchange in the positions, but also an expansion of the individual domains available for the motions. Thus, the disorder in liquid mixtures always has a hybrid character, partly static and partly mobile, and H-bonds in the liquid reduce the mobile part. From a quantitative point of view, this hybrid character can only be detected without ambiguity when the molar volumes of the components differ by a factor greater than two. The quantitative equations deduced from this new approach are completely confirmed by the solubilities of solid alkanes in liquid alkanes and in alcohols, and allow the correct prediction of the order of magnitude of the solubilities of liquid alkanes in water.

Molecular structure of liquid alcohols

Abstract A new thermodynamic treatment of continuous association is presented, where the various equilibria between i -mers are replaced by a single equilibrium between an OH groups in the bonded and the non-bonded states, linked in both cases to an indefinite ensemble of molecules. The treatment leads to an association constant K which differs from those considered in the theories of Kretschmer and Wiebe and of Wiehe and Bagley. For pure alcohols the association constant can be estimated from the vapor pressure of the alcohol and that of the homomorphous hydrocarbon. The fraction γ of free OH groups determined in this way is markedly smaller than those calculated from the other theories. For the normal alcohols the product K V A is approximately constant at a given temperature, V A being the molar volume. This can be expected from the increasing of the standard entropy of the non-bonded molecules when the molecular volume increases. For secondary and tertiary alcohols the product K V A is significantly lower due to steric hindrances. However for all the alcohols considered here the enthalpy of the hydrogen bond remains nearly constant — δ H being equal to 24.8 ± 2 kJ mol −1 .

IUPAC-NIST solubility data series. 81. Hydrocarbons with water and seawater - Revised and updated. Part 9. C10 hydrocarbons with water

The mutual solubilities and related liquid–liquid equilibria of C10 hydrocarbons with water are exhaustively and critically reviewed. Reports of experimental determination of solubility in 20 chemically distinct binary systems that appeared in the primary literature prior to end of 2002 are compiled. For ten systems sufficient data are available to allow critical evaluation. All data are expressed as mass percent and mole fraction as well as the originally reported units. In addition to the standard evaluation criteria used throughout the Solubility Data Series, a new method based on the evaluation of the all experimental data for a given homologous series of aliphatic and aromatic hydrocarbons was used.

Solubilities of p-nitroanilines in various classes of solvents. Specific solute-solvent interactions

Abstract The solubilities ф B in volume fractions of p-nitroaniline (PNA) and N,N-dimethyl p-nitroaniline (N,N-PNA) were determined near 25°C in some 40 solvents belonging to different classes using a thermoturbidimetric method. The ratio between the solubilities of the two compounds can be corrected for the differences in the melting characteristics determined from DSC measurements. The solubilities at 25°C of N,N-PNA have then to be multiplied by the factor 2.72. The corrected ratios ф PNA ф∗ N,N-PNA give indications on the formation of H-bonds between the solvent molecules and the NH groups of PNA. This is observed in solvent classes with electron donor oxygens like sulfoxides, ketones, esters and cyclic ethers. However, the ratio ф PNA ф∗ N,N-PNA decreases in an homologous series when the molar volume of the solvent increases, indicating that the formation of H-bonds by PNA depends also on the concentration of the active sites in the solvent and that not all the PNA molecules are involved in H-bonding. ф PNA ф∗ N,N-PNA is also markedly larger than 2 in the lower alcohols demonstrating the formation of N-HO hydrogen bonds at the end of the self-association chains. The fraction γ of the PNA molecules escaping from H-bonding in the electron donor solvents and in alcohols is quantitatively estimated from the solubility using the equations of the theory of the mobile order and disorder of Huyskens and Ruelle. In nitriles a weak formation of N-HHC bonds is observed. In contrast H-bonds are not observed in nitroalkanes. Unexpectedly the ratios ф PNA ф∗ N,N-PNA are much smaller than 1 in chloro alkanes. The formation of EDA bonds between N,N-PNA and these solvents acting as Lewis acids is therefore probable.

Influence of proton transfer on the formation of hydrogen-bonded complexes of higher stoichiometry and on their dissociation into free ions

Proton transfer in a given H-bond ⊂A—H—B—(H)→⊂A−— H+—B—(H) considerably enhances the strength of the electron donor sites of the first partner and that of proton donor sites possibly present in the second one. This leads to the formation of complexes of higher stoichiometry of the type B— H+—(A−—H—A--H—A--H--)or A−---(H—B+—H----B—H—B—H----) where the self-association bonds are much strengthened. This is due to the high stability of the homoconjugated anions or cations in the corresponding ion pairs. In polar solvents like acetonitrile, the ion pairs may dissociate into free ions. The variety of the entities that can be formed necessitates a diversification of the quantitative concepts connected with the proton transfer process. Besides the average value 〈x1〉 of the fractions of the various complexes in the ionized form, other quantities are defined that can also be used in the case of partial dissociation: (1) the percentage of ionized base molecules and (2) the fraction of donor molecules AH ionized after direct interaction with B. A further characteristic used in this generalized treatment is the average number 〈n〉 of proton donor molecules perturbed by one base molecule. Examples of determinations of these various parameters from calorimetric, infrared, or NMR data from the literature are presented and new quantitative correlations established.

Thermodynamic and spectroscopic entities

Abstract The idea of W. Luck to consider, in H bonded self-association, the equilibrium of the hydroxylic proton between a bonded and a non bonded state, irrespective of the situation of the lone pairs of electrons of the OH group is not an approximation but a necessity, when one takes into account that this situation is always changing in the liquid. The mobility and transferability of the H bonds in a liquid phase reduces the entropy with respect to a situation where this bond would be attributed to fixed partners. The direct consequence of this mobility is that the fraction γ of vapourizable molecules in an alcohol is not equal to the fraction γ:Ah of molecules a spectroscopist would recognize as completely free of H bonds, namely with both electron pairs and hydroxylic proton free. It is that γAh of the molecules with free protons irrespective the situation of the lone pairs. This is demonstrated by the comparison of the vapour pressure of ethanol at various temperatures and the spectroscopic determinations of γAh made by Luck. The fraction of time during which an alcohol molecule is vapourizable is thus not the fraction of molecules that a spectroscopist finds in the monomeric state. The mobility of the H bonds renders therefore void the rule that the time average and the ensemble average are the same.

On a hard/soft hydrogen bond interaction

Abstract Various physical properties of AH⋯B hydrogen bonded complexes are analyzed from the point of view of possible proton transfer processes. As a general parameter of the proton-donor–acceptor ability of interacting components the normalized ΔpKN=ΔpKa−ΔpKa(crit) parameter was assumed, where ΔpKa=pKa(B+H)−pKa(AH). ΔpKa(crit) refers to the range where the proton transfer degree reaches 50%. Two kinds of correlations between the given physical property and ΔpKN can be distinguished: of sigma and delta type. To the first one belong dipole moments, 15N NMR chemical shifts, NQR frequencies and the bond lengths in the solid state, while to the second one infra-red protonic band positions, their intensities and 1H NMR chemical shift. A general equation expressing the relationship between any physical property and ΔpKN was derived in which the central factor exp(2.303ξΔpKN) describes the behavior in the critical region. It has been shown that the ξ parameter can be used for the expression of the hardness. The value of this parameter is the higher the harder is interaction its maximum being equal 1. This measure very well correlates with the polarizability in transition state of hydrogen bonds. The detailed analysis of data in literature collected so far shows a good agreement of estimated ξ values by using different physical properties. The influence of various factors on the ξ value is discussed. Most important are chemical properties of interacting components but it was clearly shown the importance of the environment. With increasing permittivity a marked augmentation of the ξ parameter is generally observed.