Expanded solubility parameter approach. II: p-Hydroxybenzoic acid and methyl p-hydroxybenzoate in individual solvents

Solubility prediction, solvate and cocrystal screening as tools for rational crystal engineering

OBJECTIVES

The fact that novel drug candidates are becoming increasingly insoluble is a major problem of current drug development. Computational tools may address this issue by screening for suitable solvents or by identifying potential novel cocrystal formers that increase bioavailability. In contrast to other more specialized methods, the fluid phase thermodynamics approach COSMO-RS (conductor-like screening model for real solvents) allows for a comprehensive treatment of drug solubility, solvate and cocrystal formation and many other thermodynamics properties in liquids. This article gives an overview of recent COSMO-RS developments that are of interest for drug development and contains several new application examples for solubility prediction and solvate/cocrystal screening.

METHODS

For all property predictions COSMO-RS has been used. The basic concept of COSMO-RS consists of using the screening charge density as computed from first principles calculations in combination with fast statistical thermodynamics to compute the chemical potential of a compound in solution.

KEY FINDING

The fast and accurate assessment of drug solubility and the identification of suitable solvents, solvate or cocrystal formers is nowadays possible and may be used to complement modern drug development. Efficiency is increased by avoiding costly quantum-chemical computations using a database of previously computed molecular fragments.

SUMMARY

COSMO-RS theory can be applied to a range of physico-chemical properties, which are of interest in rational crystal engineering. Most notably, in combination with experimental reference data, accurate quantitative solubility predictions in any solvent or solvent mixture are possible. Additionally, COSMO-RS can be extended to the prediction of cocrystal formation, which results in considerable predictive accuracy concerning coformer screening. In a recent variant costly quantum chemical calculations are avoided resulting in a significant speed-up and ease-of-use.

The solubility of liquid and solid compounds in dry octan-1-ol

Using literature data on solubilities, equations have been constructed for the correlation of solubilities of liquids and solids in dry octanol, as log Soct (M). The best equation statistically uses Abraham descriptors together with the compound melting point. For 282 compounds the equation standard deviation is no more than 0.47 log units. If the melting point term is omitted the standard deviation rises to 0.63 log units. It is suggested that if Abraham descriptors are available, these equations represent the most satisfactory equations for the correlation and estimation of solubilities in dry octanol. If these descriptors are not available, then the simple equation of Yalkowsky can be used, although for 223 compounds the equation standard deviation rises to 0.71 log units.

Thermodynamics of solubility, sublimation and solvation processes of parabens

Saturated vapor pressures for a number of parabens (methyl- (MePB); ethyl- (EtPB), n-propyl- (PrPB) and n-butyl- (BuPB)) were obtained and from their respective temperature dependences the sublimation enthalpy, DeltaH(sub)( degrees ), and sublimation entropy, DeltaS(sub)(degrees), as well as their respective relative fractions in the process calculated. The sublimation enthalpies are: DeltaH(sub)(degrees)(MePB)=98.8+/-0.8; DeltaH(sub)(degrees)(EtPB)=100.9+/-0.7; DeltaH(sub)(degrees)(PrPB)=123.7+/-0.6; DeltaH(sub)(degrees)(BuPB)=108.4+/-0.8 kJmol(-1). The obtained values are discussed with regard to X-ray data from the literature. Theoretical calculations of the respective crystal lattice energies were carried out and compared to the experimental data. The following parameters were analyzed: (a) energetic contribution of van der Waals forces and hydrogen bonding to the total packing energy of the crystals; (b) contributions of the different fragments of the paraben molecules to the packing energy; (c) influence of bias of the supposed C-H distances on the result of the calculation procedure. Enthalpies of evaporation were estimated from the measured enthalpies of sublimation and enthalpies of fusion, and compared with literature data. Moreover, the thermodynamic functions of solvation of the molecules in water and in a number of n-alcohols were evaluated. The thermodynamic terms (Gibbs energy, enthalpy and entropy) of the solvation process were split up in their respective specific and nonspecific fraction, and these values compared for all combinations of parabens and solvents. The influence of mutual saturation of the phases in the water-octanol system on the partitioning process of the molecules is also discussed.

A new method to determine the partial solubility parameters of polymers from intrinsic viscosity

A modification of the extended Hansen method, formerly used to determine the partial solubility parameters of drugs and non-polymeric excipients is tested with a polymer for the first time. The proposed method relates the logarithm of the intrinsic viscosities of the polymer in a series of solvents and solvent mixtures with the Hansen (three parameter model) and Karger (four parameter model) partial solubility parameters. The viscosity of diluted solutions of hydroxypropyl methylcellulose (HPMC) was determined in pure solvents and binary mixtures of varying polarity. The intrinsic viscosity was obtained from the common intercept of the Huggins and Kraemer relationships. The intrinsic viscosity tends to increase with increasing the solubility parameter of the medium. The results show that hydrogen bonding and polarity of the polymer largely determine polymer-solvent interactions. The models proposed provided reasonable partial and total solubility parameters for the polymer and enable one to quantitatively characterize, for the first time, the Lewis acid-base ability of a polymer thus, providing a more realistic picture of hydrogen bonding for solvent selection/compatibility and to predict drug-polymer interactions. Combination of the dispersion and polar parameters into a single non-specific solubility parameter was also tested. The results extend earlier findings and suggest that the models are quite versatile and may be applied to drugs, non-polymeric and polymeric excipients.

Determination of partial solubility parameters of five benzodiazepines in individual solvents

Three and four component partial solubility parameters for diazepam, lorazepam, oxazepam, prazepam and temazepam were determined using the extended and expanded Hansen regression models. A comparison was made also with solubility parameters calculated by the group contribution method proposed by Van Krevelen. Although a limited number of solvents was used, the results from the present study indicate that the partial solubility parameters obtained from the experimental regression models clearly reflect the structural differences in these five structurally related molecules. High R(2)-values were observed in the regression models (0.932 < or =R(2)< or =0.984), except for lorazepam (0.606 < or =R(2)< or =0.825). This was attributed to difficulties in obtaining reliable values of the temperature and heat of fusion due to thermal decomposition of this compound. Introduction of the Flory-Huggins size correction parameter did not improve the R(2)- and F-values in any of the regression models used.

Solubility predictions for crystalline nonelectrolyte solutes dissolved in organic solvents based upon the Abraham general solvation model

The Abraham general solvation model is used to predict the saturation solubility of crystalline nonelectrolyte solutes in organic solvents. The derived equations take the form of log (CS/CW) = c + rR2 + sπ2H + aΣα2H + bΣβ2H + vVx and log (CS/CG) = c + rR2 + sπ2H + aΣα2H + bΣβ2H + l log L(16) where CS and CW refer to the solute solubility in the organic solvent and water, respectively, CG is a gas-phase concentration, R2 is the solute's excess molar refraction, Vx is McGowan volume of the solute, Σα2H and Σβ2H are measures of the solute's hydrogen-bond acidity and hydrogen-bond basicity, π2H denotes the solute's dipolarity and (or) polarizability descriptor, and log L(16) is the solute's gas-phase dimensionless Ostwald partition coefficient into hexadecane at 298 K. The remaining symbols in the above expressions are known equation coefficients, which have been determined previously for a large number of gas–solvent and water–solvent systems. Computations show that the Abraham general solvation model predicts the observed solubility behavior of anthracene, phenanthrene, and hexachlorobenzene to within an average absolute deviation of about ±35%.Key words: solubility predictions, organic solvents, nonelectrolyte solutes, partition coefficients.

The solubility of gases and vapours in dry octan-1-ol at 298 K

Ostwald solubility coefficients of 74 compounds in dry octan-1-ol at 298 K have been determined, and have been combined with literature values and additional values we have calculated from solubilities in dry octan-1-ol and vapour pressures to yield a total of 161 log L(OctOH) values at 298 K. These L(OctOH) values are identical to gas-to-dry octan-1-ol partition coefficients, often denoted as K(OA). Application of the solvation equation of Abraham to 124 values as a training set yielded a correlation equation with n = 124, S.D. = 0.125, r2 = 0.9970 and F = 7731. This equation was then used to predict 32 values of log L(OctOH) as a test set, giving a standard deviation, S.D. of 0.131, an average absolute deviation of 0.085 and an average deviation of -0.009 log units. The solvation equation for the combined 156 log L(OctOH) values was log L(OctOH) = -0.120 - 0.203R2 + 0.560pi2(H) + 3.560 sum(alpha2(H)) + 0.702 sum(beta2(H)) + 0.939 logL16, n =156, r2 = 0.9972, S.D. = 0.125, F = 10573, where, n is the number of data points (solutes), r the correlation coefficient, S.D. the standard deviation and F is the F-statistic. The independent variables are solute descriptors as follows: R2 is an excess molar refraction, pi2(H) the dipolarity/polarisability, sum(alpha2(H)) the overall or summation hydrogen-bond acidity, sum(beta2(H)) the overall or summation hydrogen-bond basicity and L16 is the Ostwald solubility coefficient on hexadecane at 298 K. The equation is consistent with similar equations for the solubility of gases and vapours into methanol, ethanol and propan-1-ol. It is suggested that the equation can be used to predict further values of log L(OctOH), for which the solute descriptors are known, to within 0.13 log units.

Proposition of group molar constants for sodium to calculate the partial solubility parameters of sodium salts using the van Krevelen group contribution method

The aim of this study is to propose, for the first time, a set of group molar constants for sodium to calculate the partial solubility parameters of sodium salts. The values were estimated using the few experimental partial solubility parameters of acid/sodium salt series available either from the literature (benzoic acid/Na, ibuprofen acid/Na, diclofenac Na) or determined in this work (salicylic acid/Na, p-aminobenzoic acid/Na, diclofenac), the group contribution method of van Krevelen to calculate the partial parameters of the acids, and three reasonable hypothesis. The experimental method used is a modification of the extended Hansen approach based on a regression analysis of the solubility mole fraction of the drug lnX(2) against models including three- or four-partial solubility parameters of a series of pure solvents ranging from non-polar (heptane) to highly polar (water). The modified method combined with the four-parameter model provided the best results for both acids and sodium derivatives. The replacement of the acidic proton by sodium increased the dipolar and basic partial solubility parameters, whereas the dispersion parameter remained unaltered, thus increasing the overall total solubility parameter of the salt. The proposed group molar constants of sodium are consistent with the experimental results as sodium has a relatively low London dispersion molar constant (identical to that of -OH), a very high Keesom dipolar molar constant (identical to that of -NO(2), two times larger than that of -OH), and a very high hydrogen bonding molar constant (identical to that of -OH). The proposed values are: F((Na)d)=270 (J cm(3))(1/2) mol(-1); F((Na)p)=1030 (J cm(3))(1/2) mol(-1); U((Na)h)=17000 J mol(-1). Like the constants for the other groups, the group molar constants proposed for sodium are certainly not the exact values. However, they are believed to be a fair approximation of the impact of sodium on the partial solubility parameters and, therefore, can be used as such in the group contribution method of van Krevelen.

The modified extended Hansen method to determine partial solubility parameters of drugs containing a single hydrogen bonding group and their sodium derivatives: benzoic acid/Na and ibuprofen/Na

Sodium salts are often used in drug formulation but their partial solubility parameters are not available. Sodium alters the physical properties of the drug and the knowledge of these parameters would help to predict adhesion properties that cannot be estimated using the solubility parameters of the parent acid. This work tests the applicability of the modified extended Hansen method to determine partial solubility parameters of sodium salts of acidic drugs containing a single hydrogen bonding group (ibuprofen, sodium ibuprofen, benzoic acid and sodium benzoate). The method uses a regression analysis of the logarithm of the experimental mole fraction solubility of the drug against the partial solubility parameters of the solvents, using models with three and four parameters. The solubility of the drugs was determined in a set of solvents representative of several chemical classes, ranging from low to high solubility parameter values. The best results were obtained with the four parameter model for the acidic drugs and with the three parameter model for the sodium derivatives. The four parameter model includes both a Lewis-acid and a Lewis-base term. Since the Lewis acid properties of the sodium derivatives are blocked by sodium, the three parameter model is recommended for these kind of compounds. Comparison of the parameters obtained shows that sodium greatly changes the polar parameters whereas the dispersion parameter is not much affected. Consequently the total solubility parameters of the salts are larger than for the parent acids in good agreement with the larger hydrophilicity expected from the introduction of sodium. The results indicate that the modified extended Hansen method can be applied to determine the partial solubility parameters of acidic drugs and their sodium salts.

Partial-solubility parameters of naproxen and sodium diclofenac

The expanded Hansen method was tested for determination of the solubility parameters of two non-steroidal anti-inflammatory drugs, naproxen and sodium diclofenac. This work describes for the first time the application of the method to the sodium salt of a drug. The original dependent variable of the expanded Hansen method, involving the activity coefficient of the drug, was compared with the direct use of the logarithm of the mole fraction solubility 1nX2 in the solubility models. The solubility of both drugs was measured in pure solvents of several chemical classes and the activity coefficient was obtained from the molar heat and the temperature of fusion. Differential scanning calorimetry was performed on the original powder and on the solid phase after equilibration with the pure solvents, enabling detection of possible changes of the thermal properties of the solid phase that might change the value of the activity coefficient. The molar heat and temperature of fusion of sodium diclofenac could not be determined because this drug decomposed near the fusion temperature. The best results for both drugs were obtained with the dependent variable 1nX2 in association with the four-parameter model which includes the acidic and basic partial-solubility parameters delta(a) and delta(b) instead of the Hansen hydrogen bonding parameter delta(h). Because the dispersion parameter does not vary greatly from one drug to another, the variation of solubility among solvents is largely a result of the dipolar and hydrogen-bonding parameters, a fact that is being consistently found for other drugs of small molecular weight. These results support earlier findings with citric acid and paracetamol that the expanded Hansen approach is suitable for determining partial-solubility parameters. The modification introduced in the expanded Hansen method, i.e. the use of 1nX2 as the dependent variable, provides better results than the activity coefficient used in the original method. This is advantageous for drugs such as sodium diclofenac for which the ideal solubility cannot be estimated. This paper shows for the first time that the method is suitable for determination of the partial-solubility parameters of a sodium salt of a drug, sodium diclofenac.

The hydrophobic effect. 2. Relative importance of the hydrophobic effect on the solubility of hydrophobes and pharmaceuticals in H-bonded solvents

The quantitative development of the nonergodic mobile order thermodynamics involving the new interpretation of the hydrophobic effect leads to a general solubility equation. This equation is applied to predict the aqueous and alcohol solubility of chemicals ranging from nonpolar or slightly polar with no H-bonding capacity to polyfunctional polar compounds including pharmaceuticals. The analysis of the relative importance of the contributions involved in the solubility model [i.e., the fluidization of the solute (for solids), the correction for the mixing entropy, the change of the nonspecific cohesion forces, and the formation of solvent-solvent (hydrophobic effect), solute-solute, and solute-solvent H-bonds] unambiguously demonstrates that the hydrophobic effect is essential for predicting the aqueous or alcohol solubility of any substance in general, and of nonpolar compounds in particular. The difference between the origin of the solubility of hydrocarbons in water and of water in hydrocarbons is furthermore presented. In both cases, the quasilinear solubility dependence on the molar volume of the hydrocarbon is of an entropic nature.

The hydrophobic effect. 1. A consequence of the mobile order in H-bonded liquids

The hydrophobic effect has an entropic nature that cannot be explained by classical multicomponent treatments that do not explicitly take into account both the mobility and the nonergodicity of the H-bonds in amphiphilic liquids. The nonergodic thermodynamics of mobile order in H-bonded liquids based on time fractions rather than on concentrations provides a novel qualitative and quantitative explanation for the molecular origin of the hydrophobic effect. Chiefly, this effect corresponds to the loss of the mobile order entropy of associated molecules by dilution with foreign substances. Not being a unique property of water, the propensity of an amphiphilic solvent to induce a solvophobic effect increases primarily as its structuration factor increases, and secondarity as the solute/solvent molar volume ratio increases. On this basis, it can be expected that in the absence of strong solute-solvent specific interactions, the solubility of nonelectrolytes will generally decrease in the following order: butanol > propanol > ethanol > methanol > propylene glycol > ethylene glycol > formamide > water.

Article

The volume fraction solubilities of a number of solid n-fatty alcohols and sterols are predicted in neat organic nonpolar, polar, and hydrogen-bonded solvents including water. In the frame of the mobile order thermodynamics, the predictions are based on the knowledge (a) of the melting properties of the alcohols, which affect the fluidization process, (b) of their molar size, which mainly rules the exchange entropy and the hydrophobic effect, and (c) of the group interaction stability constants, which are responsible for the balance between the competing self-association and strong intermolecular interactions of the alcohols in solution. Owing to its ability to deal properly with these various elementary processes, the proposed thermodynamic solubility model derived from the mobile order theory in H-bonded liquids represents an advance towards reliable and comprehensive estimates of the solubilizing capacity of common solvents for nonideal complexing systems, i.e., the solid alcohols.Key words: solubility prediction, solution thermodynamics, mobile order theory, n-fatty alcohols, sterols.

The expanded Hansen approach to solubility parameters. Paracetamol and citric acid in individual solvents

In this study two solubility-parameter models have been compared using as dependent variables the logarithm of the mole fraction solubility, lnX2e, and ln(alpha)/U (originally used in the extended Hansen method), where alpha is the activity coefficient and U is a function of the molar volume of the solute and the volume fraction of the solvent. The results show for the first time the proton-donor and -acceptor hydrogen-bonding capacities of paracetamol, as measured by the acidic and basic partial-solubility parameters. The influence of solvents on the differential scanning calorimetry (DSC) pattern of the solid phases was also studied in relation to the solubility models tested. Citric acid was chosen as a test substance because of its high acidity and its proton donor capacity to form hydrogen bonds with basic solvents. The partial acidic and basic solubility parameters obtained from multiple regression were consistent with this property, validating the model chosen. The results show that the more direct lnX2e variable was more suitable for fitting both models, and the four-parameter model seemed better for describing the interactions between solvent and solute.

Partial solubility parameters and solvatochromic parameters for predicting the solubility of single and multiple drugs in individual solvents

A modification of the extended Hansen method is used for estimating the solubility of sulfadiazine and other organic drug molecules in a number of individual solvents ranging from nonpolar to highly polar. The equations obtained for each drug involve the partial solubility parameters of the solvents and allow the prediction of solubility of these drugs in a new solvent. Furthermore, a number of drugs (e.g., sulfadiazine, sulfamethoxypyridazine, naphthalene, and some benzoic acid derivatives) are combined in a single expression including the ideal solubility of the drugs and the partial solubility parameters of the solvents. The equation fits the solubilities of these drugs in a wide variety of solvents and may be used to predict the solubility of other sulfonamides and benzoic acid derivatives in semipolar and highly polar solvents. The solvatochromic parameter approach is also used in models for predicting the solubility of single drugs in individual solvents. It was tested with multiple solutes as was the partial solubility parameter approach. However, the latter approach is superior; the parameters of the solubility parameter method are all statistically significant for drugs tested individually or together in a single equation, a condition that is not obtained with the solvatochromic model.

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 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.

Determination of partial and total cohesion parameters of caffeine, theophylline, and methyl p-hydroxybenzoate by gas-solid chromatography

For the first time, the total and partial solubility parameters, delta t, delta d, and delta s, of caffeine, theophylline, and methyl p-hydroxybenzoate were obtained by gas-solid chromatography (from the adsorption internal energy), by using the Keller, Karger, and Snyder equation. In comparison with the solubilization techniques, this method has the advantage of giving single solubility parameter values. The experimental work has been reduced to a minimum by the optimization of the matrix of experiments, according to the D-criterion, without any diminution in the quality of the results.

Expanded solubility parameter approach. I: Naphthalene and benzoic acid in individual solvents

An expanded solubility parameter system was tested in conjunction with the extended Hansen solubility approach and the UNIFAC method to calculate the solubilities of naphthalene and benzoic acid in polar and nonpolar solvents. The expanded parameter system is characterized by delta d for the dispersion force, delta p for dipolar forces, a basic or electron-donor parameter, delta b, and an acidic or electron-acceptor parameter delta a. The correlation between the calculated and observed solubilities of benzoic acid was increased by use of the four-parameter system. An indicator variable was required to bring the solubilities into line in strongly dipolar solvents such as N,N-dimethylformamide. For naphthalene, use of the four-parameter approach proved not to be an improvement over the three-parameter extended Hansen solubility approach. The UNIFAC method was not successful in calculating solubilities of benzoic acid in the 40 polar and nonpolar solvents. A triangular plot of the three Hansen parameters for benzoic acid, p-hydroxybenzoic acid, and methyl p-hydroxybenzoate illustrated the contributions of dispersion, dipolar, and Lewis acid-base (hydrogen bonding) interaction forces among the three benzoic acid compounds and the various classes of solvents. A multiple regression procedure for calculating the four partial solubility parameters of drug solutes was developed.