Simultaneous measurement of the concentration of a supercritical gas absorbed in a polymer and of the concomitant change in volume of the polymer. The coupled VW-pVT technique revisited

The purpose of this article is to re-examine the simultaneous measurements of the concentration of a supercritical gas in a polymer and of the concomitant change in volume of the polymer with the coupled VW-pVT technique [Hilic S, Pádua AAH, Grolier J-PE. Rev Sci Instrum 71 (11) (2000) 4236-41; Hilic S, Boyer SAE, Pádua AAH, Grolier J-PE. J Polym Sci B: Polym Phys 39 (2001) 2063-2070]. The experimental set-up consists of an original coupling of two techniques, a vibrating-wire sensor VW to weigh the polymer sample during the sorption and a pressure decay pVT-method to measure the quantity of gas, transferred from a high-pressure calibrated volume, which is absorbed by the polymer sample. The present study is related to the sorption and desorption of light gases (like CH₄, CO₂, H₂S, N₂) usually found in petroleum products circulating in pipelines made of semicrystalline polymers (like polyolefins and fluorinated polymers).Results for CO₂ in medium-density polyethylene, MDPE, and in poly(vinylidene fluoride), PVDF (or PVF₂), in the range of temperatures up to 391 K and pressures up to 43 MPa, are reported and discussed. Experiments allow the apparent concentration of gas dissolved in the polymer to be established; the associated swelling of the polymer is estimated using the Sanchez-Lacombe equation of state. Then, the data of the corrected concentration of the gas in the polymer are correlated with the semi-empirical ‘dual-mode’ model. Whenever possible to compare our results are in good agreement with existing literature data.     

Prediction of solute solubility in supercritical carbon dioxide: A novel semi-empirical model

Solubility data of solutes in supercritical fluids (SCF) are crucial for designing extraction processes, such as extraction using SCF or micronization of drug powders. A new empirical equation is proposed to correlate solute solubility in supercritical carbon dioxide (SC CO₂) with temperature, pressure and density of pure SC CO₂. The proposed equation is ln y₂ = J₀ + J₁P² + J₂T² + J₃ ln ρ where y₂ is the mole fraction solubility of the solute in the supercritical phase, J₀ − J₃ are the model constants calculated by least squares method, P (bar) is the applied pressure, T is temperature (K) and ρ is the density of pure SC CO₂. The accuracy of the proposed model and three other empirical equations employing P, T and ρ variables was evaluated using 16 published solubility data sets by calculating the average of absolute relative deviation (AARD). The mean AARD for the proposed model is 7.46 (±4.54) %, which is an acceptable error when compared with the experimental uncertainty. The AARD values for other equations were 11.70 (±23.10), 6.895 (± 3.81) and 6.39 (±6.41). The mean AARD of the new equation is significantly lower than that obtained from Chrastil et al. model and has the same accuracy as compared with Bartle et al. and Mèndez-Santiago–Teja model. The proposed model presents more accurate correlation for solubility data in SC CO₂. It can be employed to speed up the process of SCF applications in industry.     

Supercritical CO2 and highly selective aromatase inhibitors: Experimental solubility and empirical data correlation

The solubility of highly selective and potent third-generation aromatase inhibitors includes the non-steroidal agents letrozole and anastrozole and the steroid exemestane in supercritical carbon dioxide (SC-CO₂) has been investigated. The experiments were carried out using the simple and static method at pressures in the range of 12.1–35.5 MPa and temperatures ranging from 308 to 348 K. The mole fraction solubilities ranged from 0.22 × 10⁻⁵ to 1.88 × 10⁻⁴. Solubility data were correlated using six empirical models (Chrastil model, dV–A model, K–J model, Bartle model, Yu model and Gordillo model). The results showed that these models can be applied to satisfactory solubility predictions at different pressures and temperatures. A comparison among the six models revealed that the K–J, and Gordillo models gave much better correlations of the solubility data with an average absolute relative deviation (AARD%) ranging from 0.2 to 2.3 and from 1.6 to 2.5%, respectively. Using the correlation results, the heat of drug–CO₂ solvation and that of drug vaporization was separately approximated in the range of −17.3 to −17.5 and 93.0–112.1 kJ mol⁻¹.     

Solubility analysis of clozapine and lamotrigine in supercritical carbon dioxide using static system

The experimental techniques used to obtain the solubilities of clozapine and lamotrigine in supercritical carbon dioxide include a simple static technique. The solubility measurements were performed at temperatures between 318 and 348 K and pressures between 121.6 and 354.0 bar. These chemicals have solubilities with values ranging from 3.6 × 10⁻⁶ to 4.2 × 10⁻⁵ (clozapine) and 1 × 10⁻⁶ to 6 × 10⁻⁵ (lamotrigine) mole fraction. The solubility data were correlated using four semi-empirical density-based models (Chrastil, Bartle, K-J and M-T models). Correlation of the results shows good self-consistency of the data obtained with the Bartle model for clozapine with an overall average absolute relative deviation (AARD%) of 11.21. The calculated results with each four models show satisfactory agreement with the experimental data for lamotrigine with an overall AARD% 11.72, 8.99, 2.75, 3.86 for Chrastil, K-J, Bartle, M-T models, respectively. Using the correlation results, the heat of drug-CO₂ solvation and that of drug vaporization were approximated.     

Determination and calculation of solubility of bisphenol A in supercritical carbon dioxide

Supercritical fluid technology (SFT) as a new technique is very important for clean environment and removal of chemical pollutants. The lack of solubility data of solid solute in certain supercritical fluid is a great obstacle to the successful implementation of SFT. In this work, the solubility of bisphenol A in supercritical carbon dioxide was determined by the dynamic method at the temperatures ranging from 308 to 328 K and pressure range of 11.0–21.0 MPa. The effects of temperature and pressure on solubility were analyzed according to molecular motion theory. The solubility data were correlated using eight different semi-empirical models (Chrastil, Adachi–Lu, Kumar–Johnston, Tang, Sung–Shim, Bartle, Méndez Santiago–Teja and Yu). The comparison between different models was discussed. The thermodynamic properties (total enthalpy ΔH, enthalpy of sublimation Δ_subH and enthalpy of solvation Δ_solvH) of the solid solute were obtained.     

Development of activity coefficient model based on COSMO method for prediction of solubilities of solid solutes in supercritical carbon dioxide

A COSMO base activity coefficient model was newly developed to predict the solubilities of solid solutes in supercritical carbon dioxide. This activity coefficient model describes that the system is composed of the surface segments on the solvent molecule and vacancy unlike the conventional model based on COSMO method. The density change of supercritical fluid can be represented by the change of the surface area of the vacancy. This prediction model is referred to “COSMO-vac (vacancy)” model. The solubilities of 16 pharmaceuticals in supercritical carbon dioxide were predicted by COSMO-vac model. The averaged deviations between the logarithmic experimental and predicted results are smaller than unity. Furthermore, the predicted results for the solutes composed of only C, H and O atoms are better than those for the solutes including the other atoms. The percentage of the predicted results within the order of the experimental data at the pressure over 15 MPa is higher than that at the pressures below 15 MPa.     

A study of solvation of o-/m-hydroxybenzoic acid in supercritical CO2-methanol co-solvent system based on intermolecular interaction by molecular dynamics simulation

Solvation behavior of o-hydroxybenzoic acid (o-HBA) and m-hydroxybenzoic acid (m-HBA) in CO₂ and methanol mixtures was investigated by molecular dynamics simulation. The results indicated that the distribution of methanol around o-, m-HBA molecules was different, and it was ascribed to the different hydrogen bonding numbers formed between methanol and HBA molecules. Moreover, the interaction or hydrogen bonds between m-HBA and methanol was much stronger than that between o-HBA and methanol, and with the increasing of CO₂ pressure, it did not change for the former, but decreased for the latter. In addition, the local mole fraction enhancement was also studied. It was demonstrated that the methanol molecules become less aggregate with increasing CO₂ pressure.     

A study on the predictive capability of the SAFT-VR equation of state for solubility of solids in supercritical CO2

In this study, a version of the SAFT-VR equation of state based on the Yukawa potential is used for modeling the solubility of diverse organic compounds, mostly drugs, in supercritical carbon dioxide. Prior to any calculations, the SAFT parameters of pure CO₂ were obtained by correlating the vapor–liquid equilibrium data within the range of 220–300 K. The validity of these parameters was examined by applying them in prediction of the compressibility factor and density in wide temperature and pressure ranges. Due to dependence of the rest of the calculations on the sublimation pressure and lack of its experimental values for most of the solids, it was estimated through two main approaches: application of a group contribution method prior to correlating the solubility data, and calculating it in relation with temperature while correlating the solubility data. For each compound, the first isothermal set of the available experimental data was used for correlation and the rest were predicted. Adopting the same procedure for three empirical models and comparing the resulting deviation percents validated the superiority and high capability of this equation of state in correlating and particularly predicting the solubility in supercritical region. The predicted densities were also in very good agreement with the available experimental values.     

Solubility and partial molar volume of N,N-dimethylformamide diethyl acetal in supercritical carbon dioxide: Measurement and correlations

The solubilities of N,N-dimethylformamide diethyl acetal were measured at temperatures ranging from 313 to 353 K and pressures from 7.8 to 13.3 MPa in supercritical carbon dioxide. The measured solubility data were correlated using the Chrastil, Sung and Shim (SS), and Jouyban–Chan–Foster (JCF) semiempirical models. Consequently, the calculated results showed satisfactory agreement with experimental data and differed from the measured values by between 4.56 and 6.10%. The correlated results indicated that the JCF model provided the best fitness. Solubility data were also utilized to estimate the partial molar volume for the compound in the supercritical phase using the theory developed by Kumar and Johnston.     

Correlation of solute solubility in supercritical carbon dioxide using a new empirical equation

A new empirical equation is proposed to correlate solute solubility in supercritical carbon dioxide (SCCO₂). The new empirical model has four parameters per each solute that can be obtained by correlation of the experimental solubility data. The input variables of the equation are pressure, temperature and density of pure SCCO₂. The new equation is applied for correlation of solubility of 24 compounds in SCCO₂ at wide range of temperatures and pressures. The overall percent of absolute average relative deviation (%AARD) of the new equation for correlation of the experimental data is 6.54%. Comparison of the results of the present model with a three-parameter and a four-parameter empirical model demonstrates good accuracy of the new empirical model.     

Equilibrium solubilities of a p-toluenesulfonamide and sulfanilamide mixture in supercritical carbon dioxide with and without ethanol

Supercritical separation processes for a multi-component mixture of solutes are of practical interest. In this study, the experimental equilibrium solubilities of two solute mixtures, p-toluenesulfonamide (p-TSA) and sulfanilamide (SNA), in supercritical carbon dioxide (SC CO₂) were measured at temperatures of 308, 318 and 328 K and pressures in the range of 11.0-21.0 MPa using a dynamic flow method. The effect of cosolvent on the multi-component system was investigated by the addition of a 3.5 mol% ethanol. In the ternary system (p-TSA + SNA + CO₂), the solubility of SNA increased as compared to its binary system (SNA + CO₂), while the solubility of p-TSA decreased. In the quaternary system (p-TSA + SNA + ethanol + CO₂), a significant solubility enhancement was observed for both p-TSA and SNA. The selectivity, which is thought to imply the intermolecular interactions between p-TSA and SNA, was also enhanced by the presence of ethanol so that the two solutes could be separated by a max. purity of 99.4%. The influence of the hydrogen bond interaction on solubility was discussed. The equations of Chrastil, Méndez-Santiago and Teja, and their modified forms were used to correlate the experimental data.