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.     

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.     

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.     

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.     

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 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 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.     

Comparison of methods for predicting dissolution and the theoretical implications of particle-size-dependent solubility

Experimental dissolution data of cilostazol suspensions and hydrocortisone powders were simulated using either the Wang-Flanagan equation (1999. J Pharm Sci 88:731-738; 2002. J Pharm Sci 91:534-542) or the method of Johnson and coworkers (1989. Int J Pharm 51:9-17; 1993. Pharm Res 10:1308-1314; 1996. Pharm Res 13:1795-1798; 2003. Drug Dev Ind Pharm 29:833-842). Both methods were able to simulate experimental data with similar accuracy. For the method of Johnson and coworkers (1989. Int J Pharm 51:9-17; 1993. Pharm Res 10:1308-1314; 1996. Pharm Res 13:1795-1798; 2003. Drug Dev Ind Pharm 29:833-842), a single set of hydrodynamic assumptions was able to simulate both cilostazol and hydrocortisone with similar accuracy. For the Wang-Flanagan equation (1999. J Pharm Sci 88:731-738; 2002. J Pharm Sci 91:534-542), significantly different diffusion layer thicknesses gave the best simulations for cilostazol and hydrocortisone, but a single value of 38 μm provided good overall simulation of dissolution. The general computational method was enhanced to make solubility dependent on particle size, according to the Ostwald-Freundlich equation; it was also able to simulate Ostwald ripening. The enhanced computational method provided no way to explain the large increase in bioavailability of cilostazol in dogs when the drug was dosed as a nanoparticle versus micronized preparation. The method provides a computational tool for exploring theoretical implications and explaining the behavior of nanoparticles.     

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.     

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.     

Determination of thermodynamics of halogen groups in solutions of drug molecules

The contribution of the halogen groups (F, Cl, Br, I) to solute activity and partition coefficients has been investigated using literature data. The activity coefficient for an aromatic solute at infinite dilution is increased as the size of the halogen group increases. Partition coefficients are affected similarly but there is variation among group values for a given halogen. This is related to group position and the partition solvent. Preferred group values for partition have been selected and for different solvent systems mean preferred values can be calculated for two general solvent classifications; polar and non-polar. There is excellent correlation between group values and the size of the halogen function as given by surface area. The group values for non-polar solvents are related to those of the polar solvents through the Hammett electronic substituent constant. The use of the group values in structure-activity relations is discussed with reference to the thermodynamic model of Higuchi and Davis.     

The effect of dry mixing on the apparent solubility of hydrophobic, sparingly soluble drugs.

The effect of dry mixing on the apparent solubility of two hydrophobic sparingly soluble drugs was studied. The materials were mixed with NaCl or glass beads in a Turbula mixer and the changes in solubility were monitored. It was shown that dry mixing caused an increase in the apparent solubility of test materials. It is suggested that the surfaces of the particles become activated and disordered during the dry mixing process. This peripheral surface disorder appears to be responsible for the increase in solubility. It was also shown that apparent solubility of the drugs after dry mixing was strongly dependent on the amount of drug added to the solvent, increasing with increasing concentrations. A plateau was established gradually at higher proportions of drug to solvent. Finally the applicability of the solubility model described by Mosharraf et al. (1999) [Mosharraf, M., Sebhatu, T., Nystr?m, C., 1999. The effects of disordered structure on solubility and dissolution rates of hydrophilic, sparingly soluble drugs. Int. J. Pharm. 177, 29-51] to the solubility behaviour of the hydrophobic sparingly soluble drugs tested in this study was confirmed. The results suggested that the equilibrium solubility plateau levels of a disordered material are determined by the degree and the location of disorder on the individual particles.     

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.     

Modeling the Solubility of Pharmaceuticals in Pure Solvents and Solvent Mixtures for Drug Process Design

The knowledge of the solubility of pharmaceuticals in pure solvents and solvent mixtures is crucial for designing the crystallization process of drug substances. The first step in finding optimal crystallization conditions is usually a solvent screening. Since experiments are very time consuming, a model which allows for solubility predictions in pure solvents and solvent mixtures based only on a small amount of experimental data is required. In this work, we investigated the applicability of the thermodynamic model perturbed-chain statistical associating fluid theory (PC-SAFT) to correlate and to predict the solubility of exemplary five typical drug substances and intermediates (paracetamol, ibuprofen, sulfadiazine, p-hydroxyphenylacetic acid, and p-aminophenylacetic acid) in pure solvents and solvent mixtures. © 2009 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:4205–4215, 2009     

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.     

Solubility advantage of amorphous pharmaceuticals: I. A thermodynamic analysis

In recent years there has been growing interest in advancing amorphous pharmaceuticals as an approach for achieving adequate solubility. Due to difficulties in the experimental measurement of solubility, a reliable estimate of the solubility enhancement ratio of an amorphous form of a drug relative to its crystalline counterpart would be highly useful. We have developed a rigorous thermodynamic approach to estimate enhancement in solubility that can be achieved by conversion of a crystalline form to the amorphous form. We rigorously treat the three factors that contribute to differences in solubility between amorphous and crystalline forms. First, we calculate the free energy difference between amorphous and crystalline forms from thermal properties measured by modulated differential scanning calorimetry (MDSC). Secondly, since an amorphous solute can absorb significant amounts of water, which reduces its activity and solubility, a correction is made using water sorption isotherm data and the Gibbs–Duhem equation. Next, a correction is made for differences in the degree of ionization due to differences in solubilities of the two forms. Utilizing this approach the theoretically estimated solubility enhancement ratio of 7.0 for indomethacin (amorphous/γ‐crystal) was found to be in close agreement with the experimentally determined ratio of 4.9. © 2009 Wiley‐Liss, Inc. and the American Pharmacists Association J Pharm Sci 99: 1254–1264, 2010     

Enantiomeric 3-Chloromandelic Acid System: Binary Melting Point Phase Diagram,Ternary Solubility Phase Diagrams and Polymorphism

A systematic study of binary melting point and ternary solubility phase diagrams of the enantiomeric 3-chloromandelic acid (3-ClMA) system was performed under consideration of polymorphism. The melting point phase diagram was measured by means of thermal analysis, that is, using heat-flux differential scanning calorimetry (DSC). The results reveal that 3-ClMA belongs to the racemic compound-forming systems. Polymorphism was found for both the enantiomer and the racemate as confirmed by X-ray powder diffraction analysis. The ternary solubility phase diagram of 3-ClMA in water was determined between 5 and 50°C by the classical isothermal technique. The solubilities of the pure enantiomers are extremely temperature- dependent. The solid-liquid equilibria of racemic 3-ClMA are not trivial due to the existence of polymorphism. The eutectic composition in the chiral system changes as a function of temperature. Further, solubility data in the alternative solvent toluene are also presented. © 2010 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 99:4084–4095, 2010