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 lnX₂ 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 lnX₂ in association with the four-parameter model which includes the acidic and basic partial-solubility parameters δ_a and δ_b instead of the Hansen hydrogen bonding parameter δ_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 lnX₂ 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.     

Solubilities of testosterone propionate in non-polar solvents at 100°

THE solubilities of the formate to valerate esters of testosterone in non-polar solvents at 25° were determined by James & Roberts (1968) who also compared them with ideal mole fraction solubilities (X₂), calculated from the equation, (Hildebrand & Scott 1962). ΔH^F is the heat of fusion of the solute and T_M the melting point. Changes in solubility as the homologous series is ascended were predicted by equation (1), but the individual experimental results did not agree with the calculated values. ΔH^F was calculated from the heat of fusion at the melting point, ΔH^F_M, by correcting for the differences in heat capacity of the solid and the supercooled liquid between T_M and T. The correction was estimated with a differential scanning calorimeter by extrapolating the liquid enthalpy line back to 25° and measuring the area between the extrapolation and the enthalpy line of the solid. The method was considered questionable, however, because it assumed that the enthalpy line of the supercooled liquid decreased linearly over the whole range of temperature. This theory is tested below by comparing the measured and calculated solubilities of testosterone propionate at a temperature just below its melting point, where the heat capacity correction is small and ΔH^F_M can be used for ΔH^F. The solvents examined by James & Roberts (1968) had smaller molar volumes than the testosterone esters, and it was suggested that the difference in molar volume between solute and solvent could prevent the random distribution assumed by regular solution theory. Prediction of solubility would thus improve as the molar volume of the solvent approached that of the solute. The test is applied below by determining the solubility of testosterone propionate in a range of solvents.     

Probing the effect of vehicles on topical delivery: understanding the basic relationship between solvent and solute penetration using silicone membranes

Purpose. In the present study we examined the relationship between solvent uptake into a model membrane (silicone) with the physical properties of the solvents (e.g., solubility parameter, melting point, molecular weight) and its potential predictability. We then assessed the subsequent topical penetration and retention kinetics of hydrocortisone from various solvents to define whether modifications to either solute diffusivity or partitioning were dominant in increasing permeability through solvent-modified membranes. Methods. Membrane sorption of solvents was determined from weight differences following immersion in individual solvents, corrected for differences in density. Permeability and retention kinetics of ³H-hydrocortisone, applied as saturated solutions in the various solvents, were determined over 48 h in horizontal Franz-type glass diffusion cells. Results. Solvent sorption into the membrane could be related to differences in solubility parameters, MW and hydrogen bonding (r²=0.76). The actual and predicted volume of solvent sorbed into the membrane was also found to be linearly related to Log hydrocortisone flux, with changes in both diffusivity and partitioning of hydrocortisone observed for the different solvent vehicles. Conclusions. A simple structure-based predictive model can be applied to the sorption of solvents into silicone membranes. Changes in solute diffusivity and partitioning appeared to contribute to the increased hydrocortisone flux observed with the various solvent vehicles. The application of this predictive model to the more complex skin membrane remains to be determined.     

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.     

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.     

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.     

Enthalpy and Entropy Contributions to the Solubility of Sulphamethoxypyridazine in Solvent Mixtures Showing Two Solubility Maxima

The solubility of sulphamethoxypyridazine was measured at several temperatures in mixtures of water: ethanol and ethanol: ethyl acetate. Sulphamethoxypyridazine was chosen as a model drug to compare the solvation effects of proton donor-proton acceptor (water and ethanol) and proton acceptor (ethyl acetate) solvents and mixtures of these solvents because this drug contains functional groups capable of Lewis acid-base interaction. A plot of the mole fraction solubility against the solubility parameter (δ₁) of these solvent mixtures showed two solubility maxima, one at δ₁ = 30·87 MPa^1/2 (20:80 v/v water: ethanol) and another at δ₁ = 20·88 MPa^1/2 (30:70 v/v ethanol: ethyl acetate) at all the temperatures under study. The enthalpies and entropies of mixing as well as the enthalpies and entropies of transfer of sulphamethoxypyridazine from ethanol to water:ethanol and ethanol:ethyl acetate mixtures were calculated to compare solvation characteristics of the solvent mixtures toward the drug. As ethanol is added to water, the entropy increases and the structure of the solvent mixture became less ordered, favouring the interaction of the drug with the solvent mixture. On the other hand, in the case of the ethanol: ethyl acetate mixture, solubility is favoured by the more negative enthalpy values. This way, the same result, i.e. a solubility maximum, is obtained by different routes. In the ethanol: water mixtures, the dissolution process is entropy-controlled while enthalpy is the driving force in the case of ethanol: ethyl acetate mixtures. The two solvent systems show enthalpy-entropy compensation. Water deviates from the linear relationship due possibly to its hydrophobic effect.     

Solubility behaviour of griseofulvin in fatty acids

The solubility of griseofulvin in the straight-chain alkanoic acids from C₂ to C₂₂ and in the C₄ and C₅ alkanoic acids branched at C-2 was measured at various temperatures. The enthalpy of fusion of griseofulvin, measured by differential scanning calorimetry, was 39.39 kJ mol^?1 at the melting point (495.15 K) and 36.95 kJ mol^?1 at 373.15 K. The standard Gibbs free energy (ΔG°), standard enthalpy (ΔH°) and standard entropy (ΔS°) of solution were calculated at 373.15 K, from the van't Hoff plot of the temperature dependence of the mole fraction solubility in terms of the pure supercooled liquid solute as the standard state. With increasing chain length of the alkanoic acid solvents, ΔG° increased in parallel with the increase in pK_a of the acids in water, suggesting that the solubility behaviour involves specific solute-solvent proton interactions, while ΔH° and ΔS° fluctuated but tended to decrease in parallel with the corresponding decreases in their enthalpies and entropies of ionization, respectively. The fluctuations in ΔH° and ΔS° may be attributed to the different solid adducts containing griseofulvin and the solvent. An observed non-linear (logarithmic) decrease in solubility with decreasing molality of the carboxyl group in the liquid solvent on ascending the homologous series is attributed to the disturbing influence of the hydrocarbon chains on the specific solute-solvent hydrogen bonding. Chain-branching of the solvent at C-2 gave a reduced solubility of griseofulvin and higher ΔG°, ΔH° and ΔS° values compared with the corresponding straight chain acid.     

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.     

Dependence of solute solubility parameters on solvent polarity

In nonpolar solvents a solute may self-associate through polar interactions, exposing its nonpolar surface to a solvent with a low solubility parameter, delta 1. In polar solvents a solute is solvated, presumably, by the polar groups of the solvent. This "chameleonic" effect results in different solubility parameters for a solute, depending on the polarity of the solvent. This report presents data for solute solubility parameters in solvents of variable polarity and gives suggestions for dealing with the chameleonic effect associated with solute-solvent interaction.     

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 two phase series model for the transport of steroids across the fully hydrated stratum corneum

A two phase series model for the permeability behaviour of the fully hydrated stratum corneum has been examined using Scheuplein's data on steroids, since these strongly encouraged the investigation of possible heterogeneous diffusion models that showed the dependence of the effective diffusion coefficient, D_e, upon the effective partition coefficient, K_e. The model described can be characterized by V_e and V_w, the volume fractions for the “cytoplasm” and the “cell wall” phases, K_e and K_w, the solute partition coefficients for the “cytoplasm” and the “cell wall” phases and D_e and D_w, the respective diffusion coefficient for the two phases. Reasonable correlations were found between the experimental P_e, effective permeability coefficient, values and the partition coefficients obtained with amyl caproate and those obtained with hexadecane. Also the magnitude of D_w was estimated and found to be about 10^?13 and 10^?11 cm²/s when the lipoidal nature of the cell wall was equated to hexadecane or amyl caproate. In general, reasonable self-consistencies among the various experimental results and parameters of the model were found.     

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 Prediction of Satranidazole in Propylene Glycol-Water Mixtures Using Extended Hildebrand Solubility Approach

Extended Hildebrand solubility approach is used to estimate the solubility of satranidazole in binary solvent systems. The solubility of satranidazole in various propylene glycol-water mixtures was analyzed in terms of solute-solvent interactions using a modified version of Hildebrand-Scatchard treatment for regular solutions. The solubility equation employs term interaction energy (W) to replace the geometric mean (δ₁δ₂), where δ₁ and δ₂ are the cohesive energy densities for the solvent and solute, respectively. The new equation provides an accurate prediction of solubility once the interaction energy, W, is obtained. In this case, the energy term is regressed against a polynomial in δ₁ of the binary mixture. A quartic expression of W in terms of solvent solubility parameter was found for predicting the solubility of satranidazole in propylene glycol-water mixtures. The expression yields an error in mole fraction solubility of ~3.74%, a value approximating that of the experimentally determined solubility. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.     

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.     

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.     

Determination of the thermodynamics of hydroxyl and carboxyl groups in solutions of drug molecules

The contributions of hydroxyl and carboxyl groups to solute activity and partition coefficients have been investigated using literature data. Both polar functions give rise to a reduced activity coefficient for aromatic solutes in water and differences exist between ring and asubstitution. Partition coefficients are similarly affected but the magnitude of the group contribution to the free energy of transfer is dependent on the nature of the solute and the organic partition solvent. The contribution for the groups in the terminal position in aliphatic compounds can be obtained by an extrapolation procedure where the group value is a composite of the polar function and a term that takes into account the inequality of aliphatic CH₂ and CH₃ groupings (H. .OH, H. .COOH). For a range of solvents there is good correlation between hydroxyl and carboxyl group values. In addition an attempt has been made to correlate group values for CH₂, CH₃, H. .OH, H. .COOH, with physico-chemical parameters that are characteristic of the partition system. The best correlations are obtained between group values and the solubility of water in the organic partition solvent. The H. .OH and H. .COOH group values can also be correlated with infrared spectroscopy data and self-association constants respectively.     

Acidic pH-activated Cl- Current and Intracellular Ca2+ Response in Human Keratinocytes

The layers of keratinocytes form an acid mantle on the surface of the skin. Herein, we investigated the effects of acidic pH on the membrane current and [Ca²⁺]_c of human primary keratinocytes from foreskins and human keratinocyte cell line (HaCaT). Acidic extracellular pH (pH_e≤ 5.5) activated outwardly rectifying Cl^- current (I_Cl,pH) with slow kinetics of voltage-dependent activation. I_Cl,pH was potently inhibited by an anion channel blocker 4,4''-diisothiocyanostilbene-2,2''-disulphonic acid (DIDS, 73.5% inhibition at 1 µM). I_Cl,pH became more sensitive to pH_e by raising temperature from 24℃ to 37℃. HaCaT cells also expressed Ca²⁺-activated Cl^- current (I_Cl,Ca), and the amplitude of I_Cl,Ca was increased by relatively weak acidic pH_e (7.0 and 6.8). Interestingly, the acidic pH_e (5.0) also induced a sharp increase in the intracellular [Ca²⁺] (Δ[Ca²⁺]_acid) of HaCaT cells. The Δ[Ca²⁺]_acid was independent of extracellular Ca²⁺, and was abolished by the pretreatment with PLC inhibitor, {"type":"entrez-nucleotide","attrs":{"text":"U73122","term_id":"4098075","term_text":"U73122"}}U73122. In primary human keratinocytes, 5 out of 28 tested cells showed Δ[Ca²⁺]_acid. In summary, we found I_Cl,pH and Δ[Ca²⁺]_acid in human keratinocytes, and these ionic signals might have implication in pathophysiological responses and differentiation of epidermal keratinocytes.     

Solubility of molecular crystals: polymorphism in the light of solubility theory

The thermodynamic theory of solubility of molecular crystals in solvents is reviewed with an emphasis on solutes showing polymorphism as in case of many pharmaceuticals. The relation between solubility and binary phase diagrams of the solute solvent system is treated. The astonishing variety of possible solubility curves as a function of temperature is explained using simple models for the solution thermodynamics assuming no mixing between the solvent and solute in the solid phase, though including the case of solvates or pseudo polymorphs. In passing a new method is introduced that allows to estimate the transition temperature of enantiotropically related polymorphs from melting temperatures and enthalpies of the polymorphs.