A simple relationship between dielectric constant of mixed solvents with solvent composition and temperature

A simple computational method for calculating dielectric constants of solvent mixtures based on Redlich-Kister extension was proposed. The model was applied to the experimental dielectric constant of binary and ternary solvent mixtures at fixed and/or various temperatures and showed accurate results. Overall average percentage deviation (OAPD) between calculated and experimental dielectric constants was calculated as an accuracy criterion. The OAPDs for correlative and predictive analyses of dielectric constants in binary solvents at a fixed temperature were 0.56 and 1.42%, respectively. The corresponding values for binary solvents at different temperatures were 1.29 and 1.92%, respectively. The OAPDs for correlative and predictive analyses of dielectric constants of a nonaqueous ternary solvent mixture at various temperatures were 1.61 and 3.05%. The accuracy of the proposed models has also been compared with those of previously published models and results showed that the proposed models were superior and capable of providing more accurate results.     

Determination of solubility profiles of eflucimibe polymorphs: experimental and modeling

This work presents the determination of the phase diagram of two polymorphs of Eflucimibe in pure solvents and solvent mixtures at different temperatures. Solid phase changes were analysed by Differential Scanning Calorimetry. Solubility measurements show that the solubility of the two forms are very similar. Experimental data obtained in ethanol, reported in a Van t'Hoff plot, exhibit a transition temperature around 265 K. A single maximum is observed when solubility is plotted against the solubility parameters of solvents or solvent mixture and it is not related to a solid phase change. This phenomenon, known as a positive synergetic effect, has been explained in term of evolution of solute-solvents polar interactions. Several thermodynamics models (UNIFAC, UNIQUAC, Wilson, Scatchard Hildebrand ... ) were tested in order to predict the Liquid-Solid Equilibrium for this system. The semi empirical model UNIQUAC gives the best fit. The results obtained are in good agreement with the experimental data (mean deviation lower than 5%) and the solubility maximum found experimentally for each polymorph is also well described.     

Solubility prediction of salicylic acid in water-ethanol-propylene glycol mixtures using the Jouyban-Acree model

To show the applicability of a solution model, i.e. the Jouyban-Acree model, for predicting the solubility of a solute in ternary solvent systems based on model constants computed using solubility data of the solute in binary solvent systems, the solubility of salicylic acid in water-ethanol, water-propylene glycol, ethanol-propylene glycol mixtures was determined. A minimum number of three data points from each binary system was used to calculate the binary interaction parameters of the model. Then the solubility in other binary solvent compositions and also in a number of ternary solvents was predicted, and the mean percentage deviation (MPD) was calculated as an accuracy criterion. The overall MPD (+/-SD) was 7.3 (+/-7.3)% and those of a similar predictive model was 15.7 (+/-11.5)%. The mean difference between the proposed and a previous model was statistically significant (paired t-test, p < 0.004).     

Solubility of drugs in aqueous solutions. Part 2: binary nonideal mixed solvent

As in a previous paper [Int. J. Pharm. 258 (2003) 193–201], the Kirkwood–Buff theory of solutions was employed to calculate the solubility of a solid in mixed solvents. Whereas in the former paper the binary solvent was assumed ideal, in the present one it was considered nonideal. A rigorous expression for the activity coefficient of a solute at infinite dilution in a mixed solvent [Int. J. Pharm. 258 (2003) 193–201] was used to obtain an equation for the solubility of a poorly soluble solid in a nonideal mixed solvent in terms of the solubilities of the solute in the individual solvents, the molar volumes of those solvents, and the activity coefficients of the components of the mixed solvent.

The Flory–Huggins and Wilson equations for the activity coefficients of the components of the mixed solvent were employed to correlate 32 experimental data sets regarding the solubility of drugs in aqueous mixed solvents. The results were compared with the models available in literature. It was found that the suggested equation can be used for an accurate and reliable correlation of the solubilities of drugs in aqueous mixed binary solvents. It provided slightly better results than the best literature models but has also the advantage of a theoretical basis.     

A Modification of the Extended Hildebrand Approach to Predict the Solubility of Structurally Related Drugs in Solvent Mixtures

Abstract— A modification of the extended Hildebrand equation is proposed to estimate the solubility of an organic drug in solvent mixtures. The equation accurately reproduces the solubility of four sulphonamides in dioxane-water mixtures without requiring the heat of fusion of the solute. A single equation is obtained for predicting the solubility of related drugs using the solubilities of the drugs in the pure solvents, dioxane and water, and solute-solvent interaction terms consisting of the solubility parameter, δ₂, of the solute and the solubility parameter, δ₁, and basic partial solubility parameter, δ_1b, of the solvent mixture. By this procedure a single equation was obtained to estimate the solubilities of three xanthines in dioxane-water and another equation to obtain the solubilities of four sulphonamides. The equation obtained for sulphonamides is able to predict the experimental solubilities of two parent compounds, sulphasomidine and sulphathiazole, and the solubilities of a drug of different structure, p-hydroxybenzoic acid. This suggests that the intermolecular solute-solvent interaction of sulphonamides and p-hydroxybenzoic acid are similar. The results indicate that the solubility behaviour of drugs having different structures may be modelled using a common equation provided that they show similar solute-solvent interactions.     

Solubility of drugs in aqueous solutions. Part 4. Drug solubility by the dilute approximation

As in our previous publications in this journal [Int. J. Pharm. 258 (2003a) 193; Int. J. Pharm. 260 (2003b) 283; Int. J. Pharm. 267 (2003c) 121], this paper is concerned with the solubility of poorly soluble drugs in aqueous mixed solvents. In the previous publications, the solubilities of drugs were assumed to be low enough for the so-called infinite dilution approximation to be applicable. In contrast, in the present paper, the solubilities are considered to be finite and the dilute solution approximation is employed. As before, the fluctuation theory of solutions is used to express the derivatives of the activity coefficient of a solute in a ternary solution (dilute solute concentrations in a binary solvent) with respect to the concentrations of the solvent and cosolvent. The expressions obtained are combined with a theoretical equation for the activity coefficient of the solute. As a result, the activity coefficient of the solute was expressed through the activity coefficients of the solute at infinite dilution, solute mole fraction, some properties of the binary solvent (composition, molar volume and activity coefficients of the components) and parameters reflecting the nonidealities of binary species. The expression thus obtained was used to derive an equation for the solubility of poorly soluble drugs in aqueous binary solvents which was applied in two different ways. First, the nonideality parameters were considered as adjustable parameters, determined from experimental solubility data. Second, the obtained equation was used to correct the solubilities of drugs calculated via the infinite dilution approximation. It was shown that both procedures provide accurate correlations for the drug solubility.     

Prediction of solubility in nonideal multicomponent systems using the UNIFAC group contribution model

There is a need to identify suitable blends of solvents to dissolve drugs. Empirical approaches, such as trial-and-error and response surface, require several solubility measurements. In this study the UNIFAC method was used to predict solubility in highly nonideal multicomponent systems in which only the solute enthalpy of fusion and melting point must by measured. UNIFAC combines a group contribution approach with the UNIQUAC model for activity coefficients. Parameters characterizing interactions among constituent groups of a molecule have been previously determined from binary vapor pressure data. These tabulated group parameters are used to predict activity coefficients for newly synthesized compounds. These coefficients, together with the ideal solubility, permit a prediction of solubility. The solubility of 4-hexylresorcinol in ethyl acetate, ethyl myristate, and hexane mixtures was both measured and calculated using UNIFAC. The predicted solubilities were within 10% of the experimental solubilities for all but 3 of 21 mixtures. Since the method accounted for positive and negative deviations from ideality in a hydrogen-bonding system of molecules having different sizes, it shows great potential for use in pharmacy.     

Solubility of drugs in aqueous solutions. Part 3: multicomponent mixed solvent

The results obtained previously by Ruckenstein and Shulgin [Int. J. Pharm. 258 (2003a) 193; Int. J. Pharm. 260 (2003b) 283] via the fluctuation theory of solutions regarding the solubility of drugs in binary aqueous mixed solvents were extended in the present paper to multicomponent aqueous solvents. The multicomponent mixed solvent was considered to behave as an ideal solution and the solubility of the drug was assumed small enough to satisfy the infinite dilution approximation.An expression derived for the activity coefficient of a solid solute in a multicomponent solvent was used to obtain an equation for the solubility of a drug in terms of its solubilities in two subsystems of the multicomponent solvent and their molar volumes. Ultimately the solubility can be expressed in terms of those in binary or even in individual solvents and their molar volumes.The method was applied to the solubility of tioconazole and 19-Nor-1alpha,25-dihydrovitamin D(2) in several ternary and in a quaternary aqueous mixed solvents. The predicted solubilities were compared with experimental data and good agreement was found.     

Relationship between swelling of hydroxypropylmethylcellulose and the Hansen and Karger partial solubility parameters

A model that relates the equilibrium swelling of hydroxypropylmethylcellulose to the partial solubility parameters of both the polymer and the solvents is proposed to interpret and correlate the experimental data. The non-specific interactions are expressed as the dispersion delta(d) and polar delta(p) solubility parameters of Hansen, or as a combination of both. Hydrogen bonding is represented by the acidic delta(a) and the basic delta(b) Karger solubility parameters. The results are compared with models including the same parameters for non-specific interactions (delta(d) and delta(p)) and the Hansen hydrogen bonding parameter delta(h). Equilibrium swelling of this hydrophilic polymer that is widely used in drug formulation is measured in pure solvents covering a wide polarity range. In a qualitative way, swelling increases in solvents with higher Hildebrand solubility parameters and stronger hydrogen bonding capability, and it decreases in non-polar solvents. Single polarity indexes, such as the Hildebrand solubility parameter or the partition coefficient (PC), do not fit well the overall experimental data. The best correlations were obtained with the proposed model, providing at the same time an interpretation consistent with the physical meaning of the terms included in the equation. Swelling increases as the non-specific interactions of the polymer and the solvents become alike, and as the Lewis acid-base interactions of the polymer (1) and the solvent (2) represented by the products delta(1a)delta(2b) and delta(1b)delta(2a) become greater. Conversely, hydrogen bonding self association of the solvents (the product delta(1a)delta(1b)) lowers swelling. The results show that the Karger hydrogen bonding parameters provide a better approach than the Hansen hydrogen bonding parameter to correlate the swelling behavior of a hydrophilic polymer.     

Thermodynamic modeling of activity coefficient and prediction of solubility: Part 2. Semipredictive or semiempirical models

The solubility of stearic acid, ranitidine hydrochloride, and stavudine were predicted in selected organic solvents. The experimental solubility data of stearic acid and ranitidine hydrochloride were reported in previous work of the authors and stavudine's solubility was measured in this work. Equilibrium aqueous solubility of crystalline stauvudine was determined at controlled temperatures by stirring and filtration, with spectrophotometric quantification. The new model developed in Part 11 of this communication was modified as a semipredictive model with two adjustable parameters. Predicting the solubility data with the NRTL model using just one experimental point resulted in a big error while the modified new model and the UNIQUAC model showed much smaller errors. A new method was proposed in this work for predicting the solubility data of all polymorphs of a given compound using the experimental solubility data of one of the polymorphs of the same chemical compound. Although in general, the UNIQUAC model predictions were marginally superior, the new model is simpler and does not require the molecular parameters such as Van der Waals area and volume. The solubility prediction in a mixture of solvents using the NRTL and UNIQUAC models was also discussed.     

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, lnX₂^e, and ln(α)/U (originally used in the extended Hansen method), where α 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 lnX₂^e variable was more suitable for fitting both models, and the four-parameter model seemed better for describing the interactions between solvent and solute.     

Determination of Solute–Polymer Interaction Properties and Their Application to Parenteral Product Container Compatibility Evaluations

Kinetic and thermodynamic interaction properties between dialkyl phthalate test compounds and a polyolefin polymer were examined via a permeation-cell experimental design. Disappearance and appearance rates of solute in the receptor and donor solutions, as well as the equilibrium composition of the test system, are used to determine sorption and diffusion coefficients and the solute/polymer equilibrium binding constant. Sorption rate constants and diffusion coefficients exhibit Arrenhius-type behavior. The binding constants obtained correlate well with the solute's octanol–water partition coefficient. The kinetic and thermodynamic data generated combine with proposed interaction models to identify solute/polymer interactions (binding and leaching) pertinent to evaluating container/solution compatibility for parenteral products.     

Prediction of xanthine solubilities using statistical techniques

Mixture response-surface methodology can be used as a technique to predict solubility in mixed solvent systems. The present report shows that if the intent is to predict solubility in nonideal solutions, mixture response-surface methodology is a better technique than one which assumes a particular mechanism to hold true. This is demonstrated by comparing the predictive ability of the mixture response-surface model with that of an extended Hildebrand approach to nonideal solutions. The nonideal systems are those used by Martin and co-workers involving the solubility of theobromine, caffeine, and theophylline in dioxane-water mixtures.     

Dielectric constants of solid-liquid and liquid-liquid systems as a function of composition.

The dielectric constant of a solid substance in the dissolved state may be found by using a solvent with a dielectric constant that remains invariable when the solid substance is dissolved. The slope values obtained from dielectric constant versus concentration plots of the solid substance in two solvents with different dielectric constants are extrapolated or interpolated. The dielectric constant of a solid substance in the dissolved state also can be found directly from the dielectric constants of solutions of the solid in one solvent at two concentrations. The dielectric constants are converted to polarizations, and the two values allow calculations of the polarizations of the solvent and solute separately. From the polarization of the solute, one can calculate its dielectric constant (in dissolved state). Such a procedure is correct only if the dielectric constant is concentration independent.     

Comparison of various cosolvency models for calculating solute solubility in water-cosolvent mixtures

Previously published cosolvency models are critically evaluated in terms of their ability to mathematically correlate solute solubility in binary solvent mixtures as a function of solvent composition. Computational results show that the accuracy of the models is improved by increasing the number of curve-fit parameters. However, the curve-fit parameters of several models are limited. The combined nearly ideal binary solvent/Redlich-Kister, CNIBS/R-K, was found to be the best solution model in terms of its ability to describe the experimental solubility in mixed solvents. Also resented is an extension of the mixture response surface model. The extension was found to improve the correlational ability of the original model.     

Solubility of drugs in aqueous solutions. Part 1. Ideal mixed solvent approximation

The present paper deals with the application of the fluctuation theory of solutions to the solubility of poorly soluble drugs in aqueous mixed solvents. The fluctuation theory of ternary solutions is first used to derive an expression for the activity coefficient of a solute at infinite dilution in an ideal mixed solvent and, further, to obtain an equation for the solubility of a poorly soluble solid in an ideal mixed solvent. Finally, this equation is adapted to the solubility of poorly soluble drugs in aqueous mixed solvents by treating the molar volume of the mixed solvent as nonideal and including one adjustable parameter in its expression. The obtained expression was applied to 32 experimental data sets and the results were compared with the three parameter equations available in the literature.     

Predicting the Solubility of Drugs in Solvent Mixtures: Multiple Solubility Maxima and the Chameleonic Effect

Abstract— An approach to reproduce the solubility profile of a drug in several solvent mixtures showing two solubility maxima is proposed in this work. The solubility of sulphamethoxypyridazine was determined at 25°C in several mixtures of varying polarity (hexane: ethyl acetate, ethyl acetate:ethanol and ethanol: water). Sulphamethoxypyridazine was chosen as a model drug because of its proton-donor and proton-acceptor properties. A plot of the mole fraction of the drug vs the solubility parameter of the solvent mixtures shows two solubility peaks. The two peaks found for sulphamethoxypyridazine demonstrate the chameleonic effect as described by Hoy and suggest that the solute-solvent interaction does not vary uniformly from one mixture to another. The different behaviour of the drug in mixtures of two proton-donor and proton-acceptor solvents (alcohol and water), and in mixtures of one proton acceptor (ethyl acetate) and one proton donor-proton acceptor (ethanol) is rationalized in terms of differences in the proton donor-acceptor ability of the solvent mixtures. An approach based on the acidic and basic partial solubility parameters together with the Hildebrand solubility parameter of the solvent mixtures is developed to reproduce the experimental results quantitatively. The equation predicts the two solubility maxima as found experimentally, and the calculated values closely correspond to the experimental values through the range composition of the solvent mixtures. These results show that the chameleonic effect can be described in a quantitative way in terms of Lewis acid-base interactions; this approach can assist the product formulator to choose the proper solvent mixture for a new drug. A good solvent blend should result in a solubility parameter close to that of the drug; the acidic and basic partial solubility parameter values should provide maximum acid-base interaction of the mixed solvent with the drug. The failure in one of these conditions results in decreased solubility. Solubility parameters as well as the acidic and basic parameters are tabulated or they can be obtained from group contribution methods, making easier the evaluation of the best solvent mixture for a drug.