Semi-empirical correlation of solid solute solubility in supercritical carbon dioxide: Comparative study and proposition of a novel density-based model

A comprehensive data set on experimental solubility of 210 solid solutes in supercritical CO₂ counting 5550 data points has been used for comparison of the correlation performance of 21 empirical models. On the basis of the comparison results a new eight-parameter density-based model has been proposed. The comparison shows that the three-parameter models are the least accurate. The results also show that models that relate the logarithm of the solubility to the logarithm of solvent density and temperature are more accurate than models that include the pressure. When comparing the overall correlating performance in terms of average absolute relative deviation the proposed model is by far the best with an average absolute relative deviation lying in the range 0.17–81.99% and an average value of 8.88%.     

Mathematical representation of solubility of electrolytes in binary solvent mixtures using Jouyban-Acree model

Applicability of a solution model for calculating salt's solubility in binary solvent mixtures was shown. The accuracy of the proposed model was evaluated by computing mean percentage deviation (MPD) employing available solubility data of electrolytes in binary solvents at various temperatures from the literature. The overall MPD (+/-S.D.) for correlation of solubility data was 4.7+/-5.1% and for prediction using model trained by a minimum number of experimental data points was 10.5+/-12.5%.     

Solubility prediction of paracetamol in water-ethanol-propylene glycol mixtures at 25 and 30 degrees C using practical approaches

The solubility of paracetamol in water-ethanol-propylene glycol binary and ternary mixtures at 25 and 30 degrees C was determined using flask shake method. The generated data extended the solubility database for further computational investigations and also was used to assess the prediction capability of the Jouyban-Acree model. A new version of the model was proposed for modeling the solubility data in water-cosolvent mixtures with the cosolvent concentration of <50% which is required in pharmaceutical formulations. The accuracy of the predicted solubilities was evaluated by the mean percentage deviation (MPD) between the predicted and experimental solubilities. The overall MPD of the Jouyban-Acree model and the log-linear model of Yalkowsky for the entire composition range of the cosolvents were 11.0+/-8.7 and 55.4+/-17.8%, respectively; the corresponding values for the predicted solubilities in mixtures having a cosolvent concentration of <50% were 12.0+/-9.1 and 22.0+/-11.0%.     

Predicting solubility of anthracene in non-aqueous solvent mixtures using a combination of Jouyban-Acree and Abraham models

Quantitative structure property relationships were proposed to calculate the binary interaction terms of the Jouyban-Acree model using coefficients of Abraham solvational models. The applicability of the proposed methods for reproducing solubility data of anthracene in binary solvents has been evaluated using 56 solubility data sets collected from the literature. The mean percentage deviation (MPD) of experimental and calculated solubilities, using predicted mole fraction solubility of anthracene in solvents 1 and 2, has been computed as a measure of accuracy and the MPD of the proposed methods were 5.5 and 4.2%. The accuracy of the method was compared with that of a previously reported method where the MPD was 14.4% and the mean differences between proposed and previous methods was statistically significant. To provide a predictive model, solubility of anthracene was computed using Abraham solvational models and employed to predict the solubility in binary solvents using derived model constants of Jouyban-Acree model and the obtained MPDs were 37.9 and 22.2%, respectively.     

Novel density-based model for the correlation of solid drugs solubility in supercritical carbon dioxide

A novel density-based model derived by a simple modification of the Jouyban et al. model has been proposed to correlate the solubility of solid drugs in supercritical carbon dioxide. The six-parameter model expresses the solubility only as a function of the solvent density and the equilibrium temperature. This model is in contrast to the Jouyban et al. (J. Superiority. Fluids 24 (2002) 19) model, which gives the solubility as a function of the solvent density and the equilibrium temperature and pressure. The performance of the model has been tested on a database of 100 drugs that account for 2891 experimental data points collected from the literature. The comparison in terms of the mean absolute relative deviation for each solid drug and for the entire database between the proposed model and models that have been suggested to be mostly more accurate demonstrates that the proposed model has the best global correlation performance, exhibiting an overall average absolute relative deviation of 8.13%.     

Solubility prediction of drugs in water-polyethylene glycol 400 mixtures using Jouyban-acree model

A numerical method is proposed for predicting solubility of drugs in water-PEG 400 mixtures based on the Jouyban-Acree cosolvency model. The accuracy of the proposed method is evaluated by computing mean percentage deviation (MPD) and compared with that of log-linear model of Yalkowsky. The overall MPDs of the Jouyban-Acree model and the most accurate version of Yalkowsky's model are 39.8 (+/-46.7) % and 175.8 (+/-266.4) %, respectively, and the mean difference is statistically significant (p < 0.0005). The proposed method produces acceptable residual distribution and the probability of solubility prediction with residual log of solubility <0.5 unit is 0.86. The applicability of the proposed method could be extended for predicting the solubility of drugs in water-PEG 400 mixtures at various temperatures. The impact of various log P values computed using different software is also studied and the results of ANOVA revealed that there are no significant differences between the accuracy of the predicted solubilities employing various log P values.     

Modeling the entrainer effects on solubility of solutes in supercritical carbon dioxide

Applicability of a previously published equation for calculating the solubility of solutes in supercritical carbon dioxide was extended to calculate the solubility in entrained supercritical carbon dioxide employing 42 experimental data sets collected from the literature. The accuracy of the proposed model was evaluated by calculating both the average absolute relative deviation and the individual absolute relative deviation. The proposed model showed superiority to a previously published similar model, from both correlation and prediction points of view.     

Measurement and Correlation Solubility of Sodium Succinate in Binary Mixed Solvents of Water + (Methanol or Ethanol) Mixtures

The solubility of sodium succinate in binary solvent mixtures was measured by an analytical stirred-flask method in the temperature range 278.15–318.15 K at atmospheric pressure. It was found that the solubility of sodium succinate in the system increased with increasing temperature and decreased with the increasing mass fractions of methanol or ethanol. The modified Apelblat equation, the Buchwski–Ksiazaczak λh equation and the combined nearly ideal binary solvent/Redlich–Kister (CNIBS/R–K) equation were proposed for correlating the experimental data. The modified Apelblat equation was found to regress the solubility data much better than the Buchwski–Ksiazaczak equation and the CNIBS/R–K equation in a binary solvent system. The dissolution enthalpy and dissolution entropy of sodium succinate were calculated from the solubility data, using the Van’t Hoff equation. The experiment results and correlation models could be used as essential data in the purification of sodium succinate.     

Solubility prediction of deferiprone in N-methyl-2-pyrrolidone + ethanol mixtures at various temperatures using a minimum number of experimental data

Experimental solubility of deferiprone (DFP) in N-methyl-2-pyrrolidone (NMP) + ethanol (EtOH) mixtures at 293.2, 298.2, 303.2 and 308.2 K was determined and mathematically represented using various models. The trained versions of the van’t Hoff equation, its combined version with log-linear model, Jouyban–Acree model and a combination of van’t Hoff + Jouyban–Acree model were reported to simulate DFP solubility in the binary mixture compositions at various temperatures. The mean percentage deviation (MPD) was used as an accuracy criterion. The obtained overall MPDs for back-calculated and predicted solubility of DFP in NMP + EtOH mixtures varied from 1.1% to 3.2% and 2.6% to 6.6%, respectively. Some of apparent thermodynamic quantities for the dissolution processes of DFP are also reported.     

Models to predict solubility in ternary solvents based on sub-binary experimental data

The capability of the extended forms, of two well established cosolvency models, i.e. the combined nearly ideal binary solvent/Redlich-Kister equation and the modified Wilson model, used to predict the solute solubility in non-aqueous ternary solvent mixtures is presented. These predictions are based on the measured solubilities of anthracene in binary solvent mixtures. As a result the values of average percent deviations were less than 2% for the anthracene solubility in ternary mixtures. This work was also extended to other cosolvency models, ie. the extended Hildebrand solubility approach and the mixture response surface method, which are also commonly used for correlating solubility data in ternary solvents. The accuracy of the models is compared with each other and also with a published solubility model for ternary mixtures. The results illustrate that all models produced comparable accuracy.     

Solubility prediction of anthracene in mixed solvents using a minimum number of experimental data

Numerical methods to predict the solubility of anthracene in mixed solvents have been proposed. A minimum number of 3 solubility data points in sub-binary solvents has been employed to calculate the solvent-solute interaction terms of a well established colsolvency model, i.e. the combined nearly ideal binary solvent/Redlich-Kister model. The calculated interaction terms were used to predict the solubility in binary and ternary solvent systems. The predicted solubilities have been compared with experimental solubility data and the absolute percentage mean deviation (APMD) has been computed as a criterion of prediction capability. The overall APMD for 25 anthracene data sets in binary solvents is 0.40%. In order to provide a predictive method, which is based fully on theoretical calculations, the quantitative relationships between sub-binary interaction terms and physicochemical properties of the solvents have been presented. The overall APMD value for 41 binary data sets is 9.19%. The estimated binary interaction terms using a minimum number of data points and the quantitative relationships have then been used to predict anthracene solubility data in 30 ternary solvent systems. The produced APMD values are 3.72 and 15.79%, respectively. To provide an accurate correlation for solubility in ternary solvent systems, an extension to the combined nearly ideal multicomponenet solvent/Redlich-Kister (CNIMS/R-K) model was proposed and the corresponding overall AMPD is 0.38%.     

New LSER Model Based on Solvent Empirical Parameters for the Prediction and Description of the Solubility of Buckminsterfullerene in Various Solvents

Because of the importance of the solubility of buckminsterfullerene, C₆₀, as the most well-known carbon nanomaterial, a multiparameter linear model is proposed for C₆₀ solubility in different solvents using solvent empirical parameters. The obtained model covers more than 81 and 87 % of the variance in the training and test sets, respectively. On the other hand, because of the potential of solvent empirical parameters for probing different aspects of the solvent–solute interactions, some information about the solubility of C₆₀ in solution phase was obtained. The results showed that hydrogen bond donation ability, basicity scale and dispersion interactions were some of the effective parameters for correlating the solubility of C₆₀ in various solvents.     

Solubility of polycyclic aromatics in binary solvent mixtures using activity coefficient models

Polycyclic aromatic hydrocarbons (PAHs) precipitation is one of the major problems in the hydrocracking units. In this investigation, pyrene and phenanthrene were selected because they were found to be in higher concentrations in the feed to hydrocracking units. Their solubilities were investigated in toluene solvent mixture of iso-octane and heptane over a temperature range from 293 to 323 K. The experimental solubility data were used to predict the interaction parameters for seven different solid–liquid equilibrium models. The following activity coefficient models were used; Wilson, NIBS/Redlich–Kister, UNIQUAC, modified UNIFAC, modified UNIFAC (Dortmund), Flory–Huggins and Sheng. The interaction parameters were expressed as a second-order polynomial function in temperature. In order to test the models, the average absolute deviation percentage (AADP) was used. The overall AADP was found to range from approximately 7 to 14%. The models can be arranged according to their accuracy in a descending order based on AADP as follows: NIBS/Redlich–Kister, Wilson, UNIQUAC, Sheng, Flory–Huggins, modified UNIFAC (Dortmund) and finally modified UNIFAC. All models used in this work gave reasonable results; however, the group contribution models can also be used as a predictive tool for the solubility measurement of pyrene and phenanthrene in other solvents containing the same groups of the solvents used in this study.     

Prediction of interfacial tension between an organic solvent and aqueous solutions of mixed-electrolytes

The recently proposed approach for representing and predicting surface tension of aqueous electrolyte solutions [Chem. Eng. Sci. 56 (2001) 2879] is extended to the prediction of interfacial tension between an organic solvent and aqueous multi-electrolyte solutions. The method of Meissner was adopted in all the calculations of activity coefficient of electrolytes. Model parameters were determined by correlating interfacial tensions reported in the literature for 11 single electrolytes, including 10 inorganic salts and one inorganic acid at isothermal conditions. The correlation yielded an overall average absolute percentage deviation (AAPD) of 0.42. Using these model parameters, the proposed approach was successfully applied to the prediction of interfacial tensions available in the literature for aqueous FeCl₃–HCl, NiCl₂–FeCl₃–HCl and NiCl₂–CoCl₂–FeCl₃–HCl solutions with an AAPD of 5.73.     

Surface tension calculation of mixed solvents with respect to solvent composition and temperature by using Jouyban-Acree model

Applicability of a solution model, i.e. Jouyban-Acree model (JAM), for calculating surface tension of binary and ternary solvents at various temperatures has been shown employing experimental surface tension data collected from the literature. The accuracy of the model was evaluated by calculating average percentage deviation (APD) between calculated and observed values. The obtained overall APD (+/-S.D.) for JAM using binary solvent data were 4.06 (+/-4.27) and 8.07 (+/-9.78)%, respectively for correlative and predictive analyses. The corresponding values for the best similar model from the literature were 8.86 (+/-6.40) and 37.10 (+/-27.65)% and the mean APD differences between JAM and previously published model were significant (p<0.003). The capability of JAM for correlating surface tension of ternary solvents at various temperatures was also shown and the overall APD was 1.39 (+/-0.37)%.     

一种半经验的关联-预测活度系数的系统

提出一种半经验的关联-预测活度系数的系统。二元系的活度系数用一过量自由焓模型推算。该模型的模型参数从2个代数方程联立求解, 其一关联模型参数与γ^∞, 另一关联模型参数与(dγ-dx)x=0。γ^∞用MOSCED模型由纯组分性质关联。(dγ/dx)x=0用三维溶解度参数关联。用该系统对145组等温极性二元系作了预测, 对计算结果与实验值作了对比。F0T6R19     

Multiple solubility maxima of oxolinic acid in mixed solvents and a new extension of Hildebrand solubility approach

A new extension of the Hildebrand solubility approach which describes drug solubility in solvent mixtures showing multiple solubility peaks, the chameleonic effect, is proposed. The experimental solubilities of oxolinic acid were measured at 25 degrees C in solvent mixtures of ethanol-water and ethanol-ethyl acetate. A plot of the mole fraction of the drug against the solubility parameter (delta) of the solvent mixtures displays two peaks at delta = 30.78 MPa1/2 (80% v/v of ethanol in water) and at delta = 20.90 MPa1/2 (30% v/v of ethanol in ethyl acetate). The new extension proposed reproduces two solubility peaks. The thermograms of the solid phase before and after equilibration with the solvent mixtures did not show significant changes. The new extension was also tested with experimental data previously reported for drugs showing two solubility peaks of different height. The accuracy of other published models for describing two solubility maxima is also compared.     

Solution thermodynamics and preferential solvation of hesperidin in aqueous cosolvent mixtures of ethanol,isopropanol, propylene glycol,and n-propanol

The solubility of hesperidin in some {cosolvent (1) + water (2)} mixtures expressed in mole fraction at temperatures from 293.15 K to 333.15 K reported by Xu et al. has been used to calculate the apparent thermodynamic functions, Gibbs energy, enthalpy, and entropy, of the dissolution processes by means of the van’t Hoff and Gibbs equations. Non-linear enthalpy–entropy relationships were observed for this drug in the plots of enthalpy vs. Gibbs energy of dissolution with positive or negative slopes regarding mixtures composition and/or cosolvent. Moreover, the preferential solvation of hesperidin by the cosolvents was analysed by using the inverse Kirkwood–Buff integrals observing that this drug is preferentially solvated by water in water-rich but preferentially solvated by cosolvents in mixtures 0.20 (or 0.24) ≤ x₁° ≤ 1.00. Furthermore, a new mathematical model was proposed for correlating/predicting the solubility of hesperidin in binary solvent mixtures at various temperatures.     

Meloxicam Solubility in Ethanol+Water Mixtures According to the Extended Hildebrand Solubility Approach

In this work the extended Hildebrand solubility approach (EHSA) was applied to evaluate the solubility of the analgesic drug meloxicam in ethanol+water mixtures at 298.15 K. An acceptable correlative capacity of EHSA was found using a regular polynomial model in fifth order (overall deviation 0.52 %), where the W interaction parameter is related to the solubility parameter of the co-solvent mixtures. Nevertheless, the deviations obtained in the estimated solubility with respect to experimental solubility were similar to those obtained directly by means of an empirical regression of the logarithm of the experimental solubility as a function of the same polarity index (near to 0.51 %).     

Aqueous solubility calculation of aromatic acids within a wide temperature range using a modified regular solution model

Abstract  

The modified RSFH model, based on the regular solution theory coupled with the Flory-Huggins entropy term, was extended to calculate the solubility of aromatic acids in water within wide temperature ranges. The aqueous solubility data on aromatic acids from the published literature were assembled and validated. A total of 1,009 aqueous solubility data points for 25 aromatic acids within the temperature range of 273–463 K were selected for modeling. The calculation results showed that the solubility of aromatic acids in water could be well represented by the proposed four-parameter solution model within a wide temperature range. The overall absolute average deviation (δ _AAD) is 6.76%. The estimated cohesive energies of the aromatic acids were found to be about 20–30 kJ mol⁻¹. For the majority of the aromatic acids investigated, the cohesive energy could be considered as a constant. Strong temperature dependency, however, was also observed for a few aromatic acids, and misleading results may be obtained if this dependency is neglected. The model also has a certain prediction ability and could be extrapolated to a high temperature range where no experimental solubility data are available.