Scatchard-Hildebrand Equation Research Articles

Imiquimod Solubility in Different Solvents: An Interpretative Approach.

Imiquimod (IMQ) has been successfully formulated to date mainly as semi-solid lipophilic formulations for topical application. In this study, we investigated the solubility of IMQ in solvents suitable for developing innovative formulations in the form of powder obtained, for instance, by spray drying; thus, water, ethanol, methanol, acetone, acetonitrile, and dimethyl sulfoxide were tested at different temperatures. Temperature variations, stirring intensity, and the contact time between IMQ and the solvent greatly affected the evaluation of IMQ equilibrium solubility. The attainment of the solid-liquid equilibrium requires 13 days starting from solid IMQ and 2 days from a cooled-down supersaturated IMQ solution. A correlation between IMQ solubility and the solubility parameters of solvents was not found. IMQ solutions in water, ethanol, methanol, acetonitrile, and dimethyl sulfoxide were neither ideal nor regular. The Scatchard-Hildebrand equation does not apply to IMQ solutions because of association phenomena due to intermolecular hydrogen bonds and/or π-stacking, as supported by the hyperchromic effect that was very pronounced in highly polar solvents, such as water, with the increase in temperature. Finally, IMQ solubility values measured in acetone cannot be considered reliable due to the reaction with the solvent, leading to the formation of new molecules.

Solubility of solid intermediate of pharmaceutical compounds in pure organic solvents using semi-empirical models

A new semi-theoretical equation is suggested for correlation of solid-liquid solubility data with temperature. The (solid + liquid) equilibrium for Terephthaldialdehyde, 4-Nitro-o-phennylenediamine, 2,4-dihydro- 5-methyl-2-(4-methylphenyl)-3H-pyrazol-3-one (also named 1-(p-tolyl)-3-methyl-5pyrazolone (PTMP)), 2-Amino-5-methylthiazole and 5-chloro-1-methyl-4-nitroimidazole in 18 solvents is correlated with semi-empirical models at temperatures T = 273.15−318.15 K under a pressure of 101.2 kPa. Moreover, a modified Apelblat model, λh model, Wilson model, NRTL model, new flexible equation as Akbari, Dideban and Farhang model (ADF) and for first time the modified Scatchard-Hildebrand equation were utilized to calculate the experiment values. The performance of both ADF and modified Scatchard-Hildebrand equation have been checked by calculating the solubility data with the AARD% of 1.3808% (for 775 data points) and 0.65% (for 100 data points), respectively. The Wilson model is applied to estimate the mixing Gibbs energy, mixing enthalpy, mixing entropy, activity coefficient (ln γ1∞) and reduced excess enthalpy (H1E, ∞) at infinitesimal concentration were calculated.

Interactions between molecular solutes and task-specific ionic liquid: Measurements of infinite dilution activity coefficients and modeling

Infinite dilution activity coefficients of 35 molecular compounds in novel ionic liquid (IL) 1-(2-hydroxyethyl)-1-methylpyrrolidinium dimethylphosphate are presented in a wide range of temperature. Basic thermal characteristics and liquid density of the IL at ambient pressure are also reported. The measured activity coefficients are discussed in terms of molecular interactions between the solutes and the IL's cation and anion. An impact of strongly basic anion and the cation functionalization is elucidated. Application of the studied IL in aromatic-aliphatic separations and extractive desulfurization is evaluated on the basis infinite dilution selectivity and capacity. The experimental data are treated in terms of three distinct approaches: linear solvation-energy relationship (LSER), regular solution theory and conductor-like screening model for real solvents (COSMO-RS). In particular: temperature-dependent LSER correlation able to accurately reproduce gas-liquid partition coefficients derived from activity coefficients is presented, the solubility parameters of pure IL are derived on the basis of treatment of measured data with the Scatchard-Hildebrand equation and the predictive capacity of the COSMO-RS approach in calculating limiting activity coefficients for the considered systems is tested.

Solubility Prediction of Pioglitazone Hydrochloride in Aqueous N, N-Dimethylsulfoxide Mixtures Using Extended Hildebrand Solubility Approach

Aims: Models for predicting solubility of drugs in solvent mixtures have an important practical application. Solubility behavior of pioglitazone hydrochloride in solvent blends ranging from non-polar to highly polar is essential. So the present investigation deals with study of pioglitazone hydrochloride in binary solvent systems. Methods: The solubility of pioglitazone hydrochloride in various dimethylsulfoxide-water mixtures was analyzed in terms of solute-solvent interactions using modified Hildebrand-Scatchard treatment. The solubility of pioglitazone hydrochloride in dimethylsulfoxide-water shows a curve with solubility maxima well above the ideal solubility of the drug. Results: The discrepancy between the results using the original Hildebrand-Scatchard equation and experimental points demonstrates that regular solution theory cannot be used to predict drug solubility in dimethylsulfoxide-water binary systems. This behavior has been dealt with the theoretical replacement of mean geometric solubility parameters (δ1δ2) term with the interaction energy term (W). This is attributed to solvation of drug with the dimethylsulfoxide-water mixture, and indicates that the solute-solvent interaction energy (W) is larger than the geometric mean (δ1δ2).The new approach 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 solvent mixture. Quadratic, cubic, and quartic expressions were utilized for predicting the solubility of pioglitazone hydrochloride in dimethylsulfoxide-water mixtures. But a quartic expression of ‘W’ in terms of solvent solubility parameter was found appropriate for predicting the mole fraction solubility and yields an error ~27.68%, a value approximating that of the experimentally determined solubility. Conclusions: Extended Hildebrand Solubility Approach was successfully applied to reproduce the solubility behavior of pioglitazone hydrochloride in dimethylsulfoxide-water binary mixtures within the accuracy. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.

Kinetics of the Synthesis of 1‐Alkyl‐3‐methylimidazolium Ionic Liquids in Dilute and Concentrated Solutions

ABSTRACTThe kinetics of the reactions of 1‐methylimidazole with iodoethane, 1‐iodobutane, 1‐bromobutane, 1‐bromohexane, 1‐bromooctane resulting in the formation of corresponding 1‐alkyl‐3‐methylimidazolium halide ionic liquids in acetonitrile and cyclopentanone solutions has been studied in a wide range of concentrations and degrees of conversion. The studied reactions were found to follow the SN2 rate law in the dilute solutions. The significant deviations from the simple SN2 rate law observed at higher concentrations of the reactants were assigned to the concentration dependence of activity coefficients for the reactants and the transition states. The experimental data were processed with the conductor‐like screening model–segment activity coefficient (COSMO‐SAC) model and the Scatchard–Hildebrand equation. The latter was found to provide somewhat better description of the experimental results; however, the former has a wider predictive ability. The Arrhenius activation energies and the activation enthalpies were calculated for the investigated systems. The rate constants at infinite dilution were obtained for a large number of 1‐haloalkane + 1‐methylimidazole + solvent systems with the use of the COSMO‐SAC model. It was demonstrated that the rate constants of the studied reactions in various non‐hydrogen‐bonding solvents can be estimated from a correlation with the Hildebrand solubility parameter.

Correlation of Vapor-Liquid Equilibria for Ethanol + Hydrocarbon Binary Systems Using Regular Solution Model with Exponent-Type Mixing Rule

The regular solution model (the Hildebrand–Scatchard equation) has been improved so that it can be applied to polar mixtures by introducing the exponent-type mixing rule and interaction parameters between unlike molecules. The applicability of the proposed regular solution model is examined by correlating vapor–liquid equilibria of several ethanol + hydrocarbon binary systems, and it is found that the proposed model can be adopted for polar mixtures. For calculations, solubility parameters and liquid molar volumes at given temperatures can be estimated from the molecular structures of constituent pure components by using additive methods.

Evaluation of the Hydrophilic Property of Sodium Ion-pair Complexes with 3m-Crown-m Ethers (m = 5, 6) and Their Benzo-derivatives by Solvent Extraction

The ion-pair formation constants {K(j)(0): j = MA (metal salt), MLA} of NaO(2)CCF(3) (Na(+)tfa(-)) and its ion-pair complexes (MLA) in water (w) were determined potentiometrically at 25 degrees C and an ionic strength (I) of zero. 15-Crown-5 (15C5), 18-crown-6 ethers (18C6), and their mono-benzo derivatives were used as crown ethers (L). The extraction of Natfa by these four L from w into 1,2-dichloroethane was done at 25 degrees C, and then the extraction constants (K(ex)) for NaLtfa were calculated by using the K(j) values, which were estimated from the corresponding K(j)(0) ones at I of the w-phases, and other equilibrium constants. Also, the distribution constants (K(D,MLA)) of NaLtfa between the two phases were obtained from a thermodynamic cycle expressing K(ex). An interaction of w-molecules with NaLA was considered using a relation of log K(D,MLA) with log K(D,L), derived from the Scatchard-Hildebrand equation, where K(D,L) denotes the distribution constant of L between the two phases. The interaction increased in the order of NaL (picrate) < free L </= NaLMO(4) (M = Mn, Re) < NaLtfa for L = 15C5 and 18C6.

Hydration Effect on the Ion-pair Extraction of Lithium Picrate by Hydrophobic Benzo-15-crown-5 Ether into Various Less-polar Diluents

The ion-pair formation constant (K(MLA)(0) in mol(-1) dm(3)) for Li(B15C5)(+) with a picrate ion (Pic(-)) in water was determined by potentiometry with a K(+)-selective electrode at 25 degrees C and an ionic strength of 0, where B15C5 denotes benzo-15-crown-5 ether. Using the concentration equilibrium constants, K(MLA), estimated from this value, the extraction constants (mol(-2) dm(6) unit) of about ten diluents were re-calculated from previously reported extraction data. Also, the distribution constants of an ion-pair complex, Li(B15C5)Pic, between water and the diluents were re-estimated. A disagreement in the determined K(MLA) value between a solvent-extraction method and potentiometry was explained in terms of the Scatchard-Hildebrand equation; it came from the fact that the hydration of Li(I) in Li(B15C5)Pic was larger than that of free B15C5 in water. Then, the previously determined value by the former method was re-estimated using the potentiometric K(MLA) value.

Tetraalkylammonium Picrates in the Dichloromethane–Water System: Ion-Pair Formation and Liquid–Liquid Distribution of Free Ions and Ion Pairs

Equilibria concerning picrates of tetraalkylammonium ions (Me4N+, Et4N+, Pr4N+, Bu4N+, Bu3MeN+) in a dichloromethane−water system have been investigated at 25 ∘C. The 1:1 ion-pair formation constants (K IP,o o) in dichloromethane at infinite dilution were conductometrically determined. The distribution constants (K D o) of the ion pairs and the free cations between the solvents were determined by a batch-extraction method. The K IP,o o value varies in the cation sequence, Bu4N+ ≈ Pr4N+ ≈ Et4N+ < Bu3MeN+ < < Me4N+; this trend is explained by the electrostatic cation−anion interaction taking into account the structures of the ion pairs determined by density functional theory calculations. For the ion pairs of the symmetric R4N+ cations, there is a linear positive relationship between log10 K D o and the number of methylene groups in the cation (N CH 2). The ion pair of asymmetric Bu3MeN+ has a higher distribution constant than that expected from the above log10 K D o versus N CH 2 relationship. These cation dependencies of log10 K D o for the ion pairs are explained theoretically by using the Hildebrand-Scatchard equation. For all the cations, the log10 K D o value of the free cation increases linearly with N CH 2; the variation of log10 K D o is discussed by decomposing the distribution constant into the Born-type electrostatic contribution and the non-Born one, and attributed to the latter that is governed by the differences in the molar volumes of the cations. The cation dependencies of the ion-pair extractability and ion pairing in water are also discussed.

On the difference between ion-pair formation constants of crown ether-complex ions with picrate ion in water determined by solvent extraction and by potentiometry

Ion-pair formation constants ( K MLA°) for crown ether-complex ions (ML +) with picrate ion (Pic −) in water (w) at the ionic strength ( I) = 0 mol dm − 3 and 25 °C were determined by potentiometry with ion-selective electrodes for MPic-15-crown-5 ether (15C5), -benzo-15C5 (B15C5) (M = Na, K) and LiPic-18-crown-6 ether (18C6) systems. Also, the same kind of constant for Li + with Pic − was determined potentiometrically. The K MLA values estimated at given I were compared with those given previously by solvent extraction with its data analysis by the regular solution theory. Consequently, a large difference between these K MLA values was observed for the 15C5 systems; similar differences had been obtained for NaPic- and KPic-18C6 ones. The cause for these differences was discussed based on the Scatchard-Hildebrand equation and then the differences were corrected by referring to the potentiometric K MLA. In the correction, extraction constants for the above systems into more than ten organic (o) solvents were recalculated together with distribution constants for the ion-pair complexes ML +Pic − between the w- and o-phases.

安定性および燃焼性からみた舶用重油の最近における評価例

Developing techniques to evaluate fuel stability and combustibility is essential to ensure the quality of marine fuel oil.Experimental research was performed to determine the combustion performance of marine fuel using the thermogravimetry-differential thermal Analysis (TG-DTA) and the fuel droplet combustion method and the fuel ignition Analyzer (FIA-100) .The results made it possible to distinguish between normal fuel and fuels which caused combustion problems.Compatibility of fuel oils follows solubility theory. The solubility of asphaltene can be predicted by the Scatchard-Hildebrand equation. This paper describes how to apply the solubility theory to evaluate fuel stability of marine fuel oil.

The application of the Deiters equation of state to the estimation of the solubility of solidified substances in liquid nitrogen by the Preston–Prausnitz method

The solubility of selected halogenhydrocarbons in liquid nitrogen has been measured at 77.4 K 1–5 and on the basis of this measurement the parameter I 12 in the Scatchard–Hildebrand equation has been calculated. The properties of the pure halogenhydrocarbons (necessary for the calculation of the solubility by the Preston–Prausnitz method) collected from various experimental sources were verified by the Deiters equation of state. It was shown that the values of the parameters in the Deiters equation of state decrease when the number of fluorine atoms in the molecule of the halogen derivatives of methane increase.

Investigation of the Structure of the Hildebrand-Scatchard Equation by Use of the Peng-Robinson Equation of State

Article Investigation of the Structure of the Hildebrand-Scatchard Equation by Use of the Peng-Robinson Equation of State was published on June 1, 1996 in the journal Journal of Polymer Engineering (volume 16, issue 3).

Solubility of C 60 in alcohols and alkanes

The solubility of C 60 was determined at room temperature in seven normal alcohols, four isoalcohols, four diols, one triol, and seven alkanes. It was discovered that C 60 forms supersaturated solutions with alcohols and alkanes. The enigmatically low solubility of C 60 in octane, observed in previous studies, was confirmed. Solubilities are less than about 35 ng/g in solvents with cohesion parameters larger than about 30 MPa 1 2 . When the data are examined with the Hildebrand-Scatchard equation corrected for the Flory-Huggins size effect term, the datapoints of the alkanes and the normal alcohols fall on a common second order polynomial curve. The solubilities in the diols are about three orders of magnitude above that curve; the solubilities of the iso-alcohols lie slightly below the curve. From the data we have deduced a free energy of melting of C 60 to the undercooled liquid at room temperature of 108 kJ/mol.

Prediction of Flavor Sorption Using the Flory-Huggins Equation

Prediction of flavor sorption by packaging polymers was compared between the equation based on the regular solution theory and the Flory-Huggins equation. The Flory-Huggins equation gave much better predictions of flavor sorption than the Scatchard-Hildebrand equation. This indicates the entropic contribution is a significant factor in the flavor sorption by packaging polymers. The difference between the experimental and calculated values from the Flory-Huggins equation was relatively large. It seems the Flory-Huggins equation can provide only a qualitative prediction of flavor sorption, but this is potentially very useful for selection and design of packaging polymers

Vapour-liquid equilibria in non-polar mixtures. III. Binary mixtures of alkylbenzenes and n-alkanes at 313.15 K

Total vapour pressure measurements made by a modified static method for the binary systems of benzene, toluene, ethylbenzene and p-xylenene with n-hexane, n-heptane, n-octane and n-decane at 313.15 K are reported. The results were correlated with four equations for excess Gibbs energy. Comparison of their correlating ability was made. Agreement with literature data was checked. Experimental results were compared with prediction by the UNIFAC method and with the Hildebrand-Scatchard equation.

Solubilities of tetracosane in hydrocarbon solvents

The solubilities of tetracosane (n-C[sub 24]H[sub 50]) in heptane (n-C[sub 7]H[sub 16]), dodecane (n-C[sub 12]H[sub 26]), a mixture of isomers of decahydronaphthalene (C[sub 10]H[sub 18]), and m and p-xylene (C[sub 8]H[sub 10]) have been determined over the temperature range 279.3--305.8 K. These solvents were chosen as being representative of the types of molecules present in fuel oils. The results are well described by the equation ln x[sub 2] = [minus]([Delta]H[sup d]/RT) + ([Delta]S[sup d]/R) for which the parameters [Delta]H[sup d] and [Delta]S[sup d] are given. The liquid-phase activity coefficients for the solid at 293.2 K have been derived from the measured solubilities and compared with values calculated from the Scatchard-Hildebrand equation and the UNIFAC group contribution method. Relatively good agreement is obtained using the Scatchard-Hildebrand equation, especially in the case of normal hydrocarbon solvents.

Vapour-liquid equilibria in nonpolar mixtures: II. Carbon tetrachloride with alkylbenzenes and n-alkanes at 313.15 K

Góral, M. and Zawadzki, S., 1993. Vapour-liquid equilibria in nonpolar mixtures. II. Carbon tetrachloride with alkylbenzenes and n-alkanes at 313.15 K. Fluid Phase Equilibria, 90: 355-364. Total vapour pressure measurements using a modified static method at 313.15 K are reported for binary mixtures of CCl 4 with benzene, toluene, o-xylene, p-xylene, hexane, heptane, octane, nonane and decane. The results were correlated with the generalized Redlich-Kister equation for excess Gibbs energy. A comparison with literature vapour-liquid equilibrium data and excess enthalpy was made. Consistency within homologous series was checked. Predictions made using the UNIFAC method and the Hildebrand-Scatchard equation were compared.

Vapour-liquid equilibria in nonpolar mixtures

Abstract Goral, M. and Asmanova, N., 1993. Vapour-liquid equilibria in nonpolar mixtures. Part I. 2,2,4-Trimethylpentane with benzene, toluene, o-xylene, p-xylene, ethylbenzene and pro-pylbenzene at 313.15 K. Fluid Phase Equilibria, 86: 201-209 Total vapour pressure measurements made by a modified static method at 313.15 K are reported for binary mixtures of 2,2,4-trimethylpentane with benzene, toluene, ethylbenzene, o-xylene, p-xylene and propylbenzene. A correlation with various equations for excess Gibbs energy is discussed. A comparison has been made with literature data. A comparison with predictions by the UNIFAC method and with the Hildebrand-Scatchard equation was also carried out.

Prediction of solubility of sulfonamides in water and organic solvents based on the extended regular solution theory

A method for prediction of the solubility of sulfonamides in water and in some organic solvents based on the modified Hildebrand-Scatchard equation for regular solutions is described. Introduction into the equation of the dielectric constant or solvatochromic polarity parameter of the solvent allows the applicability of regular solution theory to be extended to polar systems which are widely employed in pharmaceutical practice. The predicted solubilities of 14 sulfonamides in water at various temperatures and of eight sulfonamides in organic solvents of different polarity were compared with those determined experimentally.