Solvent Activity Coefficients Research Articles

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 solutionsPart 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.

Correlation of infinite dilution activity coefficients of solvents in polymer solutions using connectivity indices

In this work, correlations for the estimation of the infinite dilution activity coefficients of non-polar solvents in polystyrene (PS), poly(vinyl acetate) (PVAc), poly( n-butyl methacrylate) (PBMA), poly(dimethyl siloxane), poly(methyl methacrylate) (PMMA), poly(ethylene oxide) (PEO), poly(vinyl chloride) (PVC), polyisobutylene and polyethylene (PE), and that of polar solvents in PS, PVAc, PBMA, PMMA, PEO, PVC and PE are proposed. A total of 205 polymer/non-polar solvent systems with 1708 data points, and 118 polymer/polar solvent systems with 695 data points were used to develop the correlations. The overall average errors were 9.6% and 11.3%, respectively, significantly lower than other predictive models. Since the new correlations require only the connectivity indices of the solvents in the calculations, and the connectivity indices can be calculated easily once the molecular structure of the substance in question is known, they are easy to apply, and are useful for process design and development.

Studies of Osmotic and Activity Coefficients in Aqueous and CCl4 Solutions of 18-Crown-6 at 25 °C

The osmotic coefficients and densities of aqueous and CCl4 solutions involving 18-crown-6 (18C6) as solute in the concentration range 0.1 to 2.0 m at 25 °C were measured. The data obtained is used to calculate activities of solvent and activity coefficient of solute and solvent at 25 °C as a function of concentration. It has been observed that activity coefficient of 18C6 increases with increase in concentration of 18C6 while the reverse is true for CCl4 solutions. Using the partial molar volume of the solute at infinite dilution, the solute−solvent cluster integral values were evaluated which yielded information on solute−solvent interaction. Application of McMillan-Mayer theory enabled us to obtain second and third virial coefficients for solute, which have been decomposed into attractive and repulsive contributions to solute−solute interactions. These are compared with other solutes such as sucrose, glucose, urea, etc. On the basis of attractive and repulsive contributions to solute−solvent and solute−...

A Flory–Huggins model based on the Hansen solubility parameters

The Hansen solubility parameters are typically used, especially in the paint and coatings industry, for selecting suitable solvents for polymer binders. In such applications, the radius of solubility needs to be determined by experiments. Moreover, other calculations, e.g. related to drying of paints, require thermodynamic description over extended concentration ranges. On the other hand, the well-known Flory–Huggins model captures satisfactorily several of the characteristics of polymer solutions, but the interaction parameter of the model usually also has to be determined by experiments. In this work, we present a methodology, based on which the Hansen solubility parameters can be incorporated in the Flory–Huggins model. The resulting model is predictive and yields good predictions of solvent activity coefficients at infinite dilution in several acrylate and acetate polymers. The results are as accurate as other predictive polymer models based on the group-contribution (GC) principle, but in contrast to these models, knowledge of molecular structures is not required in the Hansen/Flory–Huggins model. The new model makes thus use of the extensive literature of Hansen solubility parameters, which are tabulated for very many solvents, pigments and polymers.

UNIFAC-FV Applied to Dendritic Macromolecules in Solution: Comment on “Vapor−Liquid Equilibria for Dendritic-Polymer Solutions” (Lieu, J. G.; Liu, M.; Fréchet, J. M. J.; Prausnitz, J. M. J. Chem. Eng. Data 1999, 44, 613−620)

Dendrimers have been proposed as rheology modifiers for use as processing aids,1 as well as for other more specialized applications where predicting solubility in both small molecule solvents and polymer melts will be essential for tailoring the dendritic molecules for specific uses. The large number of end groups, core-shell structure, and constrained molecular conformations due to the high degree of branching make thermodynamic modeling of these macromolecules challenging. In a recent article, Lieu et al.2 report solvent activity coefficients measured in vapor-liquid equilibria experiments on dendritic polymer solutions. They further demonstrate that some but not all of their data can be correlated by a modified version of the Flory-Huggins lattice theory. The use of a model derived for linear polymer chains in semidilute solution to describe the more globular structure of dendrimers in solution is questionable, however, given the wealth of recent X-ray and small angle neutron scattering measurements as well as simulations3 of dendrimer structures in solution.4-10 Similarly, solution rheological properties strongly suggest a globular, unentangled structure for most dendrimers in solution and in the melt.9-13 Given this recent wealth of structural data, we propose that the solvent activity of dendrimer solutions may be predicted by group-contribution methods that have been modified to account for the free volume contributions of the molecular architecture. The free-volume modification14 of the UNIFAC15 model (UNIFAC-FV) is a predictive group-contribution method that accounts for the free volume of mixing of a structured macromolecule with a small molecule solvent. Flory’s polymer equation of state16 provides a correction for the effects of polymer architecture (as characterized by the molecular free volume) on raising the free energy of the solution. This correction involves a “reduced volume” (ratio of specific volume to the hard-core specific volume) for the solvent and the mixture (which is presumed to be additive). In calculating this reduced volume, an empirical dimensionless parameter (b) is introduced as an adjustable fit parameter. Oishi and Prausnitz14 successfully correlated VLE data for solutions of linear chains with the UNIFACFV theory with a single parameter value of b ) 1.28. As this parameter reflects the determination of the hard-core specific volume of the molecules, we might anticipate that it will be affected by a high degree of branching in the macromolecule, as this would be expected to affect the ability of the solvent to penetrate into the dendrimers. Further, this would be expected to manifest itself as an increasing value of the excluded hard-core volume as the solvent’s molecular size is increased for a fixed macro* Corresponding author. Figure 1. (a) Acetone activity in solution with the A4 dendrimer at 50 °C.2 (b) Chloroform activity in solution with the B4 dendrimer at 70 °C.2 376 J. Chem. Eng. Data 2002, 47, 376-377

Osmotic Pressures for Binary Solutions of Non-electrolytes

A comprehensive new theory of osmotic pressure is mechanistically derived to be applicable to incompressible binary solutions of non-electrolytes independent of solute concentrations, membrane selectivity, solution ideality, and without recourse to adjustable parameters. The approach employed relies on Fick’s diffusion laws, and introduces the concept of uncoupled aggregate diffusion. The theory is verified using direct and indirect experimental data of sucrose solutions and then compared to conventional osmotic pressure laws. Direct consequences of the new theory entail novel a priori expressions for the activity, activity coefficient, and chemical potential of solvent. Applications to drug delivery and biomolecular separation nanotechnology are discussed.

Phase equilibria for complex polymer solutions

Many commercially important mixtures contain complex polymers, e.g. paints and coatings. If a good thermodynamic description can be given of these systems it is possible to develop paints, which possess a certain set of properties and at the same time meet some basic requirement as, e.g. regarding the content of organic solvents. This work presents an investigation of the three polymer models Entropic-FV (EFV), UNIFAC-FV (UFV) and GC-Flory (GCF) for their capability of predicting solvent activity coefficients in binary systems containing complex polymers. It is possible to obtain good predictions at finite concentrations and satisfactory predictions at infinite dilution, particularly with the EFV model. The investigation shows that EFV is the most robust and stable of the models, which indicates that it is the most well suited model for further development of methods for predicting the miscibility behavior of paints and related systems.

Prediction of Activity Coefficients in Polymer and Copolymer Solutions Using Simple Activity Coefficient Models

Using an extensive database that covers activity coefficients in systems of polymers and copolymers with nonpolar and polar solvents, we test the predictive capabilities of two simple activity coefficient models: the Entropic-FV (free volume) and a recent modification of UNIFAC by Zhong et al. (Fluid Phase Equilib. 1996, 123, 97). The only information required for their application is the structure of the components and in the case of Entropic-FV also their molar volumes. The results, which include solvent and polymer activity coefficient predictions (the latter based on data from molecular simulation), indicate that both models provide satisfactory predictionsexcept where association is presentconsidering their simplicity, with the Entropic-FV one being superior to the modified UNIFAC proposed by Zhong et al. The latter, however, is a very good alternative when no accurate molar volumes are available.

Infinite-Dilution Activity Coefficients of Polar and Nonpolar Solvents in Solutions of Hyperbranched Polymers

Infinite-dilution activity coefficients are measured for several polar and nonpolar solvents in hyperbranched polymers using inverse gas chromatography in the temperature range 40−160 °C. Two kinds of polymers are studied: comb polymers and dendritic polymers. The combs are poly(styrene-co-maleic anhydride) with alkyl side chains of different lengths (C12, C22). The solvents are: acetone, toluene, tetrahydrofuran (THF), and chloroform. Solvent solubility in the combs depends on the ratio between the polar backbone and the nonpolar side chain of the polymer. The dendrimers are amine-terminated poly(propylenimine) of generation 2 to 5. The solvents are: methanol, ethanol, ethyl acetate, toluene, and THF. Solvent activity coefficients change with respect to the dendrimer generation number, reaching a minimum at generation 4. Because the dendrimers are basic, the solvent quality is higher for slightly acidic solvents, such as methanol and ethanol. Flory's interaction parameters are calculated for the solve...

Activity coefficients of solvents in elastomers measured with a quartz crystal microbalance

A piezoelectric quartz crystal microbalance (QCM) has been used to measure the sorption of solvents into elastomers. The equipment can operate from ambient temperature and pressure up to 180°C and 60 bar. The polymers are deposited on the quartz crystal from solution to form films on the order of 0.1 to 1 μm. Because the time to reach equilibrium scales with the square of the film thickness, this technique can generate data much more rapidly than alternative gravimetric techniques, such as electronic or quartz spring microbalances. However, at high mass loading the frequency–mass response of the QCM becomes non-linear. For the systems studied this typically occurred at solvent vapor sorption levels of 20 to 30 wt.%. From the sorption data, we have generated the activity coefficient on a weight fraction basis for solvents in these polymers from about 0.01 to 0.3 weight fraction. To test this method on coatings of polymers with heterogeneous morphology, we measured the sorption of solvents into a series of triblock copolymers comprising styrene endblocks and midblocks of butadiene, isoprene, or hydrogenated butadiene. The microphase domain sizes in these polymers are about an order-of-magnitude smaller than the typical film thickness used in these experiments. The results have been correlated with elastomer structure. Where comparisons are possible, these activity coefficients agree reasonably with those measured by conventional methods at finite concentration using bulk polymer samples, but sometimes appear low relative to activity coefficients at infinite-dilution measured by inverse gas chromatography (IGC). Advantages and limitations of the QCM are summarized.

Predicting liquid–liquid transitions in polymer solutions using the GCLF equation of state

Group contribution lattice fluid equation of state (GCLF-EOS) have been extended and used to calculate phase equilibria in polymer solutions. Group parameters for three group contributions and nine new group contributions have been calculated. Saturation vapor pressure for pure solvent and weight fraction activity coefficients in polymer solutions have been calculated and the agreement obtained with experimental data indicated the accuracy of the parameters. A combining rule consisting a pair interaction parameter with temperature dependency was proposed. The area method was used with GCLF-EOS to obtain phase diagram for liquid equilibrium (LLE) of polymer solutions. The method was able to predict both lower critical solution temperature (LCST) and upper critical solution temperature (UCST).

Empirical Method To Correlate and To Predict the Vapor−Liquid Equilibrium and Liquid−Liquid Equilibrium of Binary Amorpous Polymer Solutions

A previous method of the author is modified in order to ensure (i) a better evaluation of the solvent activity coefficients at infinite dilution and (ii) the calculation of liquid−liquid equilibriu...

Partial molar heat of mixing at infinite dilution in solvent/polymer (PEG, PMMA, P(ET-VA)) solutions

Inverse gas chromatography (IGC) was used to measure various thermodynamic properties (activity coefficients, Flory–Huggins interaction parameters, partial molar heats of mixing, heats of solution, and heats of vaporization) at infinite dilution for polymer solution systems. The experimental temperature ranges were from 353.15 K to 463.15 K and they were carried out over melting point or glass transition temperature of each polymer. The solvent(1)/polymer(2) systems were made up of polyethyleneglycol, polymethylemthacrylate, and poly(ethylene(80)–vinylacetate(20)) as the polymers, polar solvents (methylethylketone, n-butylacetate, butanol, ethylacetate, chloroform, methanol, toluene, ethanol, 1,4-dioxane, ethylbenzene, methylisobutylketone) and nonpolar solvents (acetone, benzene, carbontetrachloride, cyclohexane, p-xylene, n-decane) as the solvents. The UNIFAC-FV model was modified to predict the partial molar heat of mixing the solvents at infinite dilution for polymer solution systems. The modified UNIFAC-FV model included the external degree of freedom, which is a function of temperature, and had the new parameters, which were estimated by the infinite dilution activity coefficients of solvents in polymer solutions. The calculated activity coefficients of solvents agreed with the experimental data within an error average range of 1.09 (2.12%). The new estimated parameters were extended to predict the partial molar heats of mixing the solvents at infinite dilution in polymer solutions. The predicted values were compared with the experimental data.

Simplified criteria for the development of new absorption working pairs

A thermodynamic analysis, also based on a simplified mathematical model, allows one to evaluate the effect of the working pair on both dimensions and performance of absorption heat pumps and heat transformers. In particular, the solvent activity coefficient, which determines the decrease of the solvent vapor pressure over the solution, and the solvent heat of vaporization mainly affect the dimensions of the apparatus. A smaller effect is observed for the coefficient of performance, which can be attributed to the excess enthalpy of solution. From those results, few easy-to-use criteria are derived, which are deemed useful in order to optimize the development of new absorption working pairs.

Estimation of vapor-liquid equilibria for polymer solutions by a group-contribution method

A new group-contribution method is presented for prediction of vapor-liquid equilibria of polymer solutions. It is based on a close-packed lattice model developed previously; this model contains a revised Flory-Huggins entropy and a series expression for excess internal energy, as well as a double-lattice model to account for specific, oriented interactions. The group-contribution method includes three contributions: the combinatorial and free-volume contribution which is primarily responsible for entropy, the van der Waals energy contribution responsible for dispersion and polar forces, and the specific energy contribution from hydrogen bonding. Most of the model parameters can be estimated using pure-component properties, either from experimental data or from group-contribution methods in the literature. The group-contribution method described in this work gives parameters for the cross specific interaction energy from hydrogen bonding between segments of polymers and segments of solvents. Parameters for pairs of groups are obtained by correlating experimental data for vapor pressures and infinite-dilution activity coefficients of solvents in polymer solutions. The method shown here gives improved results for prediction when compared with those of other group-contribution models.

Simplified Hole Theory Equation of State for Liquid Polymers and Solvents and Their Solutions

In the simplified hole theory equation of state proposed by our group (Zhong, C.; Wang, W.; Lu, H. Fluid Phase Equilib. 1993, 86, 137), the occupied site fraction for the Simha−Somcynsky equation of state (Simha, R.; Somcynsky, T. Macromolecules 1969, 2, 342) was derived as a simple exponential function of temperature alone, in terms of the theory for an imperfect crystal with thermal defects. In this work, the simplified hole theory equation of state has been applied to an accurate description of the pressure−volume−temperature relationship for 67 liquid polymers and 61 solvents and compared with four commonly used equations of state. An approximate expression for the activity coefficient of a solvent in polymer−solvent solutions has been derived, which enables one to calculate the activity coefficient for the solvent analytically. The grand absolute average deviation between the calculated and experimental solvent activity coefficients for 95 data sets is 2.4%, which indicates that this equation of stat...

Prediction of infinite dilution solvent activity coefficients in polymer solutions: comparison of prediction models

The modified group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting accurately vapor-liquid equilibria in polymer-solvent solutions, was developed by calculating group contributions for the adjustable parameters from the equilibrium properties of low molecular weight compounds only. The modified GCLF-EOS has been used to predict the solvent activity coefficients at infinite dilution of solvents, and its prediction results have been compared with those of the original GCLF-EOS, the UNIFAC-free volume (FV), the entropic-FV, and the revised GC-Flory EOS. Extensive statistical analyses were performed using all the currently available experimental data. The modified GCLF-EOS provided the best performance in the prediction of infinite dilution activity coefficients. The modified GCLF-EOS requires only the structures of the solvent and polymer in terms of their functional groups as input information.

A molecular simulation-based method for the estimation of activity coefficients for alkane solutions

In a recent study Sheng et al. (1995, A.I.Ch.E. J. 41 (10) 2306–2313) presented activity coefficients calculated by molecular simulation (MS) for athermal model polymer-solvent systems. Both activity coefficients of the monomeric solvent in the polymer ( γ 1 ∞) and of the polymer in the solvent ( γ 2 ∞) were calculated at infinite dilution conditions. The MS data cover a broad range of system asymmetry with respect to size in the area of oligomer-solvent mixtures (up to segment ratio 60 1 which corresponds to e.g. a system of n-heptane with nC 460). The MS results were compared with classical and recently proposed free-volume (FV) activity coefficient models in order to conclude on the suitability of the models for phase equilibrium calculations for asymmetric systems. On the basis of the work by Sheng et al., extrapolation methods for estimating the activity coefficient of a solvent and that of a polymer in real solvent-polymer systems are developed here. The so-obtained MS-based activity coefficients are compared with experimental data (in the case of solvent activities) and with the predictions of various activity coefficients models (in the case of polymer activities).

Solvent activity coefficients at infinite dilution in polystyrene-hydrocarbon systems from inverse gas chromatography

Inverse gas chromatography was used to measure activity coefficients of solvents at infinite dilution over a temperature range from 373.15K to 423.15 K for monodisperse polystyrene-hydrocarbon systems. Polystyrene has average molecular weight 2.89 ×105. Solvents include six aliphatic hydrocarbons such as cyclohexane, methylethylketone,n-hexane, carbon tetrachloride, acetonitrile and acetone and three aromatic ones as benzene, toluene andp-xylene. The measured data of activity coefficients of solvents were predicted by UNIFAC-FV model. We, also, presented a modified UNIFAC-FV model by empirically assigning to it a temperature-dependent C parameter in the free volume contribution of the model. Fitted results demonstrated that the modification of the model fitted the experiments better than the original one.