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.     

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.     

Excess free energy approach to the estimation of solubility in mixed solvent systems I: Theory

An approach is developed by which the solubility of an organic compound in mixed solvents may be estimated. In this approach, an expression for the excess Gibbs free energy of mixing for multicomponent solvent systems was used to obtain parameters characteristic of the interaction between the solvents. A fairly simple equation which predicts the solubility of a solute in a binary solvent system over the entire solvent composition range was then derived. The equation may be partitioned into terms that contain (a) pure solvent solubilities, (b) solvent-solvent interaction contributions, and (c) contributions from the solute-mixed solvent interactions. The required data are the molar volume of the solute, the pure solvent solubilities, and, theoretically, one experimentally determined solubility in a solvent mixture. The equation can be easily extended for systems with three or more solvents.     

Solubility of drugs in aqueous solutions. Part 5. Thermodynamic consistency test for the solubility data

This paper is devoted to the verification of the quality of experimental data regarding the solubility of sparingly soluble solids, such as drugs, environmentally important substances, etc. in mixed solvents. A thermodynamic consistency test based on the Gibbs-Duhem equation for ternary mixtures is suggested. This test has the form of an equation, which connects the solubilities of the solid, and the activity coefficients of the constituents of the solute-free mixed solvent in two mixed solvents of close compositions. The experimental data regarding the solubility of sparingly soluble substances can be verified with the suggested test if accurate data for the activity coefficients of the constituents of the solute-free mixed solvent are available. The test was applied to a number of systems representing the solubilities of sparingly soluble substances in mixed solvents. First, the test was scrutinized for four nonaqueous systems for which accurate solubility data were available. Second, the suggested test was applied to a number of systems representing experimental data regarding the solubility of sparingly soluble substances in aqueous mixed solvents.     

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.     

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.     

Thermodynamic modeling of activity coefficient and prediction of solubility: Part 1. Predictive models

A new activity coefficient model was developed from excess Gibbs free energy in the form G(ex) = cA(a) x(1)(b)...x(n)(b). The constants of the proposed model were considered to be function of solute and solvent dielectric constants, Hildebrand solubility parameters and specific volumes of solute and solvent molecules. The proposed model obeys the Gibbs-Duhem condition for activity coefficient models. To generalize the model and make it as a purely predictive model without any adjustable parameters, its constants were found using the experimental activity coefficient and physical properties of 20 vapor-liquid systems. The predictive capability of the proposed model was tested by calculating the activity coefficients of 41 binary vapor-liquid equilibrium systems and showed good agreement with the experimental data in comparison with two other predictive models, the UNIFAC and Hildebrand models. The only data used for the prediction of activity coefficients, were dielectric constants, Hildebrand solubility parameters, and specific volumes of the solute and solvent molecules. Furthermore, the proposed model was used to predict the activity coefficient of an organic compound, stearic acid, whose physical properties were available in methanol and 2-butanone. The predicted activity coefficient along with the thermal properties of the stearic acid were used to calculate the solubility of stearic acid in these two solvents and resulted in a better agreement with the experimental data compared to the UNIFAC and Hildebrand predictive models.     

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.     

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 pioglitazone hydrochloride in ethanol,N-methyl pyrrolidone,polyethylene glycols and water mixtures at 298.20 °K

Background and the purpose of the study

Solubility of pharmaceuticals is still a challenging subject and solubilization using cosolvents is the most common technique used in the pharmaceutical industry. The purpose of this study was reporting and modeling the experimental molar solubility of pioglitazone hydrochloride (PGZ-HCl) in binary and ternary mixtures of ethanol (EtOH), N-methyl pyrrolidone (NMP), polyethylene glycols (PEGs) 200, 400, 600 and water along with the density of saturated solutions at 298.2 °K.

Methods

To provide a computational method, the Jouyban-Acree model was fitted to the solubilities of the binary solvents, and solubilities of the ternary solvents were back-calculated by employing the solubility data in mono-solvents. In the next step, the ternary interaction terms were added to the model and the prediction overall mean percentage deviation (MPD) of the ternary data was reduced. Also a previously proposed version of the model was used to predict the solubility of PGZ-HCl in binary and ternary mixtures employing the experimental solubility data in mono-solvents.

Results

The overall MPD of the model for fitting the binary data and predicted data of ternary solvents were 2.0 % and 50.5 %, respectively. The overall MPD of the predicted solubilities in ternary solvents using the ternary interaction terms in the model was 34.2 %, and by using the proposed version of the Jouyban-Acree model for binary and ternary data the overall correlation and prediction errors were 18.0 and 15.0 %, respectively.

Conclusion

The solubility of PGZ-HCl was increased by addition of EtOH, NMP, PEGs 200, 400 and 600 to aqueous solutions. The reported data extended the available solubility data of pharmaceuticals which are crucial in formulation of liquid dosage forms. The constants of the Jouyban-Acree model using the generated data are also reported which provides the possibility of solubility prediction in other solvent mixtures and temperatures.     

The effect of temperature on the solubilities of testosterone propionate in low polarity solvents

The solubilities of testosterone propionate have been determined between 25 and 100° in 15 solvents and compared with theoretical values obtained from regular solution theory. Entropy considerations show that solvent-solute interactions occur in some solvents, increasing the solubility and resulting in deviations from regular solution behaviour. “Regular solutions” are obtained only in saturated hydrocarbon solvents, and the solubility is more accurately predicted as the temperature approaches the melting point, and as the molar volumes of solvent approach that of the solute.     

Solubility properties in polymers and biological media. 2. The correlation and prediction of the solubilities of nonelectrolytes in biological tissues and fluids

Solubilities of a range of nonelectrolyte solutes in biological systems, such as blood, plasma, brain, lung, liver, kidney, muscle tissue, and human fat, are correlated and predicted through an equation that takes the form log Ltissue = c + w log Lwater + o log Loil, where L is the Ostwald solubility coefficient (or gas/liquid partition coefficient). The ratio of the constants o and w gives a measure of the "oiliness" of a given biological tissue or fluid. The strong possibility exists that, for many types of nonelectrolyte solutes, simple measurements of solubilities in water and oil (gas/liquid partition coefficients) will allow accurate predictions of solubilities in the above biological solvents, as well as tissue/blood partition coefficients. The solubility of rare gases and the inorganic gases H2, N2, CO, and O2 may be correlated through the simpler equation log Ltissue = l'RG + d', where l' and d' are constants that characterize the phase, and RG is a known parameter, obtained by normalizing and averaging solubilities over a range of solvent systems, that characterizes the solute. Both of the above equations allow prediction of L in biological solvents to within about 20%, which compares well with the precision of the experimental measurements.     

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).     

Influence of solvent composition on the solid phase at equilibrium with saturated solutions of quinolones in different solvent mixtures

The dissolution profiles and solubilities of three quinolonic drugs (oxolinic, pipemidic, and nalidixic acids) in different solvent mixtures were studied. The behavior of the solid phase, during solubility experiments was in-depth investigated with the aim of detecting possible crystalline modifications, such as polymorphic transitions or solvate formations, that might modify drug stability and/or solubility properties. In order to test the influence of both the nature and polarity of the co-solvents, aqueous and non-aqueous binary mixtures have been prepared by using Lewis base (dioxane and ethyl acetate) and amphiprotic co-solvents (ethanol and water). Differential scanning calorimetry (DSC), hot stage microscopy, IR spectroscopy and X-ray powder diffraction were used in combination with solubility and dissolution studies to characterize and investigate the solid state properties of the original powders and the corresponding ones at equilibrium with the different pure solvents and solvent mixtures examined. The solid phases of nalidixic and oxolinic acids did not show any change after equilibration with the various pure solvents or binary solvent mixtures, regardless the chemical nature of the examined solvents. On the contrary, in the case of pipemidic acid, the different analytical techniques used to characterize the drug solid state enabled identification of a solvated form at equilibrium with pure dioxane and a trihydrated form in aqueous mixtures of water with both ethanol (amphiprotic) or dioxane (Lewis base) in a concentration range from 10 to 100% water.     

Solution thermodynamics of alkyl p-aminobenzoates.

Equilibrium solubilities of the first four homologous alkyl p-aminobenzoate esters were determined in methanol, ethanol, and 1-propanol at 25, 33, and 40 degrees; the esters and the alcohols comprise separate homologous series. The solution process of a solute may be considered to be the summation of two sequential steps, melting and mixing, and the magnitude of solubility depends upon temperature and the extent of interactions between solute and solvent molecules. Quantitative solute concentrations, obtained from spectrophotometric analysis, were converted to mole fractions. Statistical analysis of the logarithmic mole fraction solubilities of the aminobenzoates, which were linear with respect to both reciprocal absolute temperature and the logarithm of absolute temperature, generated enthalpies and entropies of solution, respectively. The heats of fusion and the melting points of these aminobenzoates were determined to calculate their ideal solubilities. Excess free energies and partial molal free energies of each solution were calculated from the activity coefficients of the solutes; the thermodynamic elements for these systems are discussed.     

The Estimation of Solubility in Binary Solvents: Application of the Reduced 3-Suffix Solubility Equation to Ethanol–Water Mixtures

The reduced 3-suffix solubility equation (R3SSE) is applied to the characterization of solubility in the ethanol–water system. The data needed are the solubility of the compound in each of the pure solvents and at one ethanol–water composition. This composition has been estimated from solubility data to be 0.56 volume fraction of ethanol. The solubility obtained at this volume fraction is used to estimate the ternary solute–solvent interaction constant, C ₂. The R3SSE, with the C ₂ thus obtained, predicts the mixed solvent solubilities of the compounds tested, as accurately as that obtained from several volume fractions. The superiority of the R3SSE over two related equations—a simple second-degree polynomial equation and a simplified form of the R3SSE which neglects contributions to solubility from the solvent mixture—is also demonstrated for a number of solutes.     

Solubility of (+/-)-ibuprofen and S (+)-ibuprofen in the presence of cosolvents and cyclodextrins

Aqueous solubility is an important parameter for the development of liquid formulations and in the determination of bioavailability of oral dosage forms. Ibuprofen (IB), a nonsteroidal anti-inflammatory drug, is a chiral molecule and is currently used clinically as a racemate (racIB). However, the S form of ibuprofen or S(+)-ibuprofen (SIB) is the biologically active isomer and is primarily responsible for the antiinflammatory activity. Phase solubility studies were carried out to compare the saturation solubilities of racIB and SIB in the presence of common pharmaceutical solvents such as glycerol, sorbitol solution, propylene glycol (PG), and polyethylene glycol (PEG 300) over the range of 20% to 80% v/v in aqueous based systems. The solubilities of the two compounds were also compared in the presence of cyclodextrins such as beta cyclodextrin (CD), hydroxypropyl beta cyclodextrin (HPCD), and beta cyclodextrin sulfobutyl ether sodium salt (CDSB) over the range of 5% to 25% w/v. Solubility determinations were carried at 25 degrees C and 37 degrees C. Cosolvents exponentially increased the solubility of both SIB and racIB, especially in the presence of PG and PEG 300. Glycerol was not very effective in increasing the aqueous solubilities of both compounds, whereas sorbitol solution had a minimal effect on their solubility. PG and PEG 300 increased the solubility of SIB by 400-fold and 1500-fold, respectively, whereas the rise in solubility for racIB was 193-fold and 700-fold, respectively, at 25 degrees C for the highest concentration of the cosolvents used (80% v/v). Of the two compounds studied, higher equilibrium solubilities were observed for SIB as compared with racIB. The derivatized cyclodextrins increased the aqueous solubility of racIB and SIB in a concentration-dependent manner giving AL type of phase diagrams. The phase solubility diagrams indicated the formation of soluble inclusion complexes between the drugs and HPCD and CDSB, which was of 1:1 stoichiometry. The addition of underivatized CD reduced the solubility of racIB and SIB via the formation of an insoluble complex. The S form formed more stable complexes with HPCD and CDSB as compared with raclB. The solubilization process is discussed in terms of solvent polarity and differential solid-state structure of raclB and SIB. The thermodynamic parameters for the solubilization process are presented.