On the use of semiempirical models of (solid + supercritical fluid) systems to determine solid sublimation properties

Experimental solubility data of solid–supercritical fluids have significantly increased in the last few years, and semiempirical models are emerging as one of the best choices to fit this type of data. This work establishes a methodology to calculate sublimation pressures using this type of equations. It requires the use of Bartle’s equation to model equilibria data solid–supercritical fluids with the aim of determining the vaporization enthalpy of the compound. Using this method, low deviations were obtained by calculating sublimation pressures and sublimation enthalpies. The values of the sublimation pressures were subsequently used to successfully model different multiphasic equilibria, as solid–supercritical fluids and solid–solvent–supercritical fluids with the Peng–Robinson equation of state (without considering the sublimation pressure as an adjustable parameter). On the other hand, the sublimation pressures were also used to calculate solid sublimation properties and acetaminophen solvation properties in some solvents. Also, solubility data solid–supercritical fluids from 62 pharmaceuticals were fitted with different semiempirical equations (Chrastil, Kumar-Johnston and Bartle models) in order to present the values of solvation enthalpies in sc-CO₂ and vaporization enthalpies for these compounds. All of these results highlight that semiempirical models can be used for any other purpose as well as modeling (solid + supercritical fluids) equilibria.     

Solubility measurement of α-asarone in supercritical carbon dioxide

The solubility of α-asarone in supercritical CO₂ (sc-CO₂) has been measured using the dynamic method. The measurement was conducted in the pressure range from 9.0 to 18.0 MPa at temperature 35–49 °C. The experimental data were correlated using the Chrastil model. The results show that the solubility increases as the pressure rises and decreases as the temperature rises, which is well correlated with the Chrastil model.     

Solubility of amphenicol bacteriostats in CO2

The solubilities of three veterinary amphenicol bacteriostats, chloramphenicol, florfenicol and thiamphenicol, were measured in supercritical carbon dioxide (SC-CO₂) by a re-circulating method at temperatures of 313.15 and 333.15 K and pressures ranging from 11.0 to 49.0 MPa. These compounds displayed very limited solubility in SC-CO₂ (10⁻⁵ to 10⁻⁷ mole fraction) over the range of experimental conditions. Chloramphenicol had the highest observed solubility of the three amphenicols, while the solubilities of florfenicol and thiamphenicol were almost an order of magnitude lower. The experimental solubility data were correlated with seven known density-based models. The density models (ln y versus ln ρ or ln ρ_r) gave better correlation than the semi-log scale of ln y versus ρ_r. Four models for ln E versus density correlations also gave better correlation than the semi-log scale of ln y versus ρ_r by introducing the enhancement factor E. The correlation accuracy of all the seven models mainly depends on the system investigated, measured density and temperature range.     

Solubility of a spiroindolinonaphthoxazine photochromic dye in supercritical carbon dioxide: Experimental determination and correlation

The measurement and correlation of the experimental solubility of a spiroindolinonaphthoxazine photochromic dye (1,3-dihydro-3,3-dimethyl-1-isopropyl-6′-(2,3)-(dihydroindole-1-yl)spiro[2H-indole-2,3′-3H-naphtho[2,1-b] [1,4] oxazine]) in supercritical carbon dioxide (scCO₂) is reported. Results were obtained using a static analytical method, at 308.0, 318.0 and 328.0 K, and in a pressure range from 10.0 to 26.0 MPa. Solubility experimental data were correlated with three density-based models (Chrastil, Bartle and Méndez-Santiago–Teja models), with the Ziger–Eckert semi-empirical correlation and with two cubic equation-of-state (EOS) models, namely the Peng–Robinson EOS (PR-EOS) and the Soave–Redlich–Kwong EOS (SRK-EOS), together with the conventional van der Waals mixing and combining rules. Good correlation results were obtained between the calculated and experimental solubility, to all fitted models. Solubility results clearly indicate the feasibility of processing this dye, and possibly this class of photochromic dyes, using supercritical fluid technologies and processes, for example, supercritical fluid dye impregnation of polymer host materials.     

Measurement and correlation of solubility of anthraquinone dyestuffs in supercritical carbon dioxide

Solubility data of 1,4-diaminoanthraquinone (C.I. Disperse Violet 1) and 1,4-bis(ethylamino)anthraquinone (C.I. Solvent Blue 59) in supercritical carbon dioxide (sc-CO₂) have been measured at the temperatures of (323.15, 353.15, and 383.15) K and over the pressure range from (12.5 to 25.0) MPa by a flow-type apparatus. The solubility of two anthraquinone dyestuffs was obtained over the mole fraction ranges of (1.3 to 26.1) · 10⁻⁷ for 1,4-diaminoanthraquinone (C.I. Disperse Violet 1) and (1.1 to 148.5) · 10⁻⁷ for 1,4-bis(ethylamino)anthraquinone (C.I. Solvent Blue 59). The experimental results have been correlated with the empirical equations of Mendez-Santiago–Teja and Kumar–Johnston expressed in terms of the density of sc-CO₂, and also analyzed thermodynamically by the regular solution model with the Flory–Huggins theory and the Peng–Robinson equation of state modified by Stryjek and Vera (PRSV-EOS) with the conventional mixing rules. Good agreement between the experimental and calculated solubilities of the dyestuffs was obtained.     

Measurement and modeling of metoclopramide hydrochloride (anti-emetic drug) solubility in supercritical carbon dioxide

Knowledge of drug solubility data in supercritical carbon dioxide (SC-CO₂) is a fundamental step in producing nano and microparticles through supercritical fluid technology. In this work, for the first time, the solubility of metoclopramide hydrochloride (MCP) in SC-CO₂ was measured in pressure and temperature range of 12 to 27 MPa and 308 to 338 K, respectively. The results represented a range mole fractions of 0.15 × 10^-5 to 5.56 × 10^-5. To expand the application of the obtained data, six semi-empirical models and three models based on the Peng-Robinson equation of state (PR + VDW, PR + WS + Wilson and PR + MHV1 + COSMOSAC) with different mixing rules and various ways to describe intermolecular interactions were investigated. Furthermore, total enthalpy, sublimation enthalpy and solvation enthalpy relevant to MCP solvating in SC-CO₂ were estimated.     

Novel numerical simulation of drug solubility in supercritical CO2 using machine learning technique: Lenalidomide case study

In pharmaceutical industry, finding promising ways to enhance the solubility of disparate types of drugs is an important challenge for the orally administered drug delivery system. Disparate techniques based on drug characteristics, nature of dosage form and properties of excipients have recently been under extensive evaluation all over the world to improve the solubility of poorly water-soluble drugs. Among them, supercritical fluid carbon dioxide (SC-CO₂) has received paramount attentions due to having considerable advantages like cost-effectiveness and low flammability. Lenalidomide belongs is an orally administered anti-cancer agent, which has recently received indication for the treatment of adult patients with different bone marrow-related malignancies such as multiple myeloma, mantle cell lymphoma and follicular lymphoma. Predicting the optimized value of Lenalidomide inside the SC-CO₂ in a wide range of pressure and temperature via developing mathematical models based on artificial intelligence (AI) is the main objective of this paper. In this study, three different machine learning based models are selected to predict and optimized the drug solubility. The available data includes 28 rows of data with two inputs including temperature and pressure and two outputs including density and solubility. Selected models are Kernel Ridge Regression (KRR), least angle regression (LAR), and Multilayer Perceptron (MLP). After optimizing models and comparing the results, the MLP was selected as the primary model of this research. The models illustrated R-squared scores of 0.999 and 0.994 for density and solubility. The maximum errors are also 2.92 and 6.44 × 10^-2 for these outputs, which shows the accuracy and significant generality of the model.     

Biological Xenogenic Vessel Prostheses: Effect of H<Subscript>2</Subscript>O/CO<Subscript>2</Subscript> and EtOH Media on the Structure and Mechanical Properties of the Bovine Jugular Veins

The effect of the H₂O/CO₂ and EtOH/CO₂ media at pressures and temperatures corresponding to the formation of supercritical (sc) carbon dioxide on the structure and mechanical properties of bovine jugular veins was studied for the first time. Treatment of bovine jugular veins in an sc-CO₂ + ethanol or sc-CO₂ + water medium considerably devitalized the tissue and increased the tissue elasticity, which allows considering the treated veins as promising vascular grafts with expected high capacity to suppress calcification and good hemodynamic properties.     

Solubility enhancement of decitabine as anticancer drug via green chemistry solvent: Novel computational prediction and optimization

Nowadays, supercritical fluid technology (SFT) has been an interesting scientific subject in disparate industrial-based activities such as drug delivery, chromatography, and purification. In this technology, solubility plays an incontrovertible role. Therefore, achieving more knowledge about the development of promising numerical/computational methods of solubility prediction to validate the experimental data may be advantageous for increasing the quality of research and therefore, the efficacy of novel drugs. Decitabine with the chemical formula C₈H₁₂N₄O₄ is a chemotherapeutic agent applied for the treatment of disparate bone-marrow-related malignancies such as acute myeloid leukemia (AML) by preventing DNA methyltransferase and activation of silent genes. This study aims to predict the optimum value of decitabine solubility in CO₂SCF by employing different machine learning-based mathematical models. In this investigation, we used AdaBoost (Adaptive Boosting) to boost three base models such as Linear Regression (LR), Decision Tree (DT), and GRNN. We used a dataset that has 32 sample points to make solubility models. One of the two input features is P (bar) and the other is T (k). ADA-DT (Adaboost Algorithm-Decision Tree), ADA-LR (Adaboost Algorithm-Linear Regresion), and ADA-GRNN (Generative Regression Neural Network) models showed MAE of 6.54 × 10^?5, 4.66 × 10^?5, and 8.35 × 10^?5, respectively. Also, in terms of R-squared score, these models have 0.986, 0.983, and 0.911 scores, respectively. ADA-LR was selected as the primary model according to numerical and visual analysis. Finally, the optimal values are (P = 400 bar, T = 3.38 K × 102, Y = 1.064 × 10^?3 mol fraction) using this model.     

Solubilities and partial molar volumes of three bis(2-ethoxyethyl) ethanedioate derivatives in supercritical carbon dioxide

Three new CO₂-philic bis(2-ethoxyethyl) ethanedioate derivatives, bis(2-(2-methoxyethoxy)ethyl) ethanedioate (compound 1), bis(2-(2-ethoxyethoxy)ethyl) ethanedioate (compound 2), and bis(2-(2-butoxyethoxy)ethyl) ethanedioate (compound 3), were designed and synthesized and their solubilities in supercritical carbon dioxide (scCO₂) were then measured at different temperatures (313, 323, 333) K over the pressure range (8.9 to 13.9) MPa. The measured solubility data were correlated with five different theoretical semi-empirical models (Chrastil, kJ, SS, MST, JCF) and satisfactory agreements were obtained. The JCF model provided the best fit and the lowest average absolute relative deviation (AARD) varied from (3.58 to 6.80)%. Furthermore, the partial molar volumes of three compounds in the supercritical phase were also calculated according to the Kumar and Johnston theory, and the values were between −(19105 and 3510) cm³ · mol⁻¹.     

Extraction of brominated flame retardants from polymeric waste material using different solvents and supercritical carbon dioxide

Different procedures were examined to extract pure and high concentrations of a series of brominated flame retardants from various polymer materials. These procedures include supercritical carbon dioxide (sc-CO₂), modified sc-CO₂, solvent and soxhlet extraction. Extraction with sc-CO₂ gave low extraction efficiencies (between 6 and 20%) probably due to the low pressure of sc-CO₂ used. The use of toluene, acetonitrile and THF as modifier in sc-CO₂ raised the extraction efficiencies for many flame retardants. High extraction efficiencies were achieved for tetrabromobisphenol A (TBBPA), TBBPA-bis-(2,3-dibromopropylether) (TBBPA-dbp), TBBPA-carbonatoligomer (TBBPA-co) and decabromodiphenylether (DECA) (between 93 and 100%) by using 1-propanol as solvent during soxhlet extraction. Toluene instead of 1-propanol was used where insufficient extraction of the flame retardant occurred. The materials (before and after extraction) were analysed with energy dispersive X-ray fluorescence analysis (EDXRF), high performance liquid chromatography with ultraviolet detection (HPLC/UV), gas chromatography/mass spectrometry (GC/MS) and infrared spectroscopy (IR) techniques. The properties of the extracted flame retardants such as TBBPA, TBBPA-dbp and 1,2-bis(tribromophenoxy)-ethane (TBPE) are in good agreement with those of standard reference materials.     

Study of bromide salts solubility in the (m1NaBr + m2MgBr2)(aq) system at T = 323.15 K. Thermodynamic model of solution behavior and (solid + liquid) equilibria in the (Na + K + Mg + Br + H2O) system to high concentration and temperature

The bromide minerals solubility in the mixed system (m₁NaBr + m₂MgBr₂)(aq) have been investigated at T = 323.15 K by the physico-chemical analysis method. The equilibrium crystallization of NaBr·2H₂O(cr), NaBr(cr), and MgBr₂·6H₂O(cr) has been established. The solubility-measurements results obtained have been combined with all other experimental equilibrium solubility data available in literature at T = (273.15 and 298.15) K to construct a chemical model that calculates (solid + liquid) equilibria in the mixed system (m₁NaBr + m₂MgBr₂)(aq). The solubility modeling approach based on fundamental Pitzer specific interaction equations is employed. The model gives a very good agreement with bromide salts equilibrium solubility data. Temperature extrapolation of the mixed system model provides reasonable mineral solubility at high temperature (up to 100 °C). This model expands the previously published temperature variable sodium–potassium–bromide and potassium–magnesium–bromide models by evaluating sodium–magnesium mixing parameters. The resulting model for quaternary system (Na + K + Mg + Br + H₂O) is validated by comparing solubility predictions with those given in literature, and not used in the parameterization process. Limitations of the mixed solution models due to data insufficiencies at high temperature are discussed.     

Efficient preparative separation of 6‐(4‐aminophenyl)‐5‐methyl‐4, 5‐dihydro‐3(2H)‐pyridazinone enantiomers on polysaccharide‐based stationary phases in polar organic solvent chromatography and supercritical fluid chromatography

6‐(4‐Aminophenyl)‐5‐methyl‐4,5‐dihydro‐3(2H)‐pyridazinone is a key synthetic intermediate for cardiotonic agent levosimendan. Very few studies address the use of chiral stationary phases in chromatography for the enantioseparation of this intermediate. This study presents two efficient preparative methods for the isolation of (R)(?)‐6‐(4‐aminophenyl)‐5‐methyl‐4,5‐dihydro‐3(2H)‐pyridazinone in polar organic solvent chromatography and supercritical fluid chromatography using polysaccharide‐based chiral stationary phases and volatile organic mobile phases without additives in isocratic mode. Under optimum conditions, Chiralcel OJ column showed the best performance (α = 1.71, Rs = 5.47) in polar organic solvent chromatography, while Chiralpak AS column exhibited remarkable separations (α = 1.81 and Rs = 6.51) in supercritical fluid chromatography with an opposite enantiomer elution order. Considering the sample solubility, runtime and solvent cost, the preparations were carried out on Chiralcel OJ column and Chiralpak AS column (250 × 20 mm i.d.; 10 µm) in polar organic mode and supercritical fluid chromatography mode with methanol and CO₂/methanol as mobile phases, respectively. By utilizing the advantages of chromatographic techniques and polysaccharide‐based chiral stationary phases, this work provides two methods for the fast and economic preparation of (R)(?)‐6‐(4‐aminophenyl)‐5‐methyl‐4,5‐dihydro‐3(2H)‐pyridazinone, which are suitable for the pharmaceutical industry.     

Characteristics of an oxa-diamide–HNO3 extractant in the supercritical fluid extraction of uranium

An extractant is required in the recovery process to drive the uranium to a stage that enables it to be extracted using the extraction solvent. This paper proposes the composition of a composite extractant, N,N,N′,N′-tetrabutyl-3-oxapentane-diamide–HNO₃ (TBODA–HNO₃) as an extractant, to successfully achieve the objective using supercritical carbon dioxide (sc-CO₂). The composite TBODA–HNO₃ extractant has a chemical composition of TBODA(HNO₃)_1.0(H₂O)_1.5. The U(IV) in the UO₂ containing solid phase is directly oxidized to U(VI) in the form of $ {\rm UO}_{2}^{2 + } $ in sc-CO₂, which contains a CO₂-soluble TBODA–HNO₃ extractant at 200 atm and 50 °C. The resulting $ {\rm UO}_{2}^{2 + } $ /TBODA complex can be consequently extracted using acetone-modified sc-CO₂. The chemical composition of the $ {\rm UO}_{2}^{2 + } $ /TBODA complex, which can be extracted by nonpolar sc-CO₂, is proposed in the form of an ion pair: [UO₂(TBODA)₂]²⁺–2( $ {\rm NO}_{3}^{ - } $ ).     

Solubility of climbazole and triclocarban in supercritical carbon dioxide: Measurement and correlation

The supercritical technology has been considered as an appropriate alternative for separation of biomaterials from cosmetic, food, and pharmaceutical products. The solid solubility of biological compounds is the most important thermodynamic parameter in the supercritical extraction and purification. The equilibrium solubility of two biocides, climbazole, and triclocarban was measured in supercritical carbon dioxide with static method in the pressure range from (10 to 40) MPa and at temperatures equal to (313.2, 323.2, and 333.2) K. The experimental data were correlated by Peng–Robinson equation of state and quasi-chemical nonrandom lattice fluid model.     

Measurement and correlation of antifungal drugs solubility in pure supercritical CO2 using semiempirical models

In the present study the solubilities of two antifungal drugs of ketoconazole and clotrimazole in supercritical carbon dioxide were measured using a simple static method. The experimental data were measured at (308 to 348) K, over the pressure range of (12.2 to 35.5) MPa. The mole fraction solubilities ranged from 0.2 · 10^?6 to 17.45 · 10^?5. In this study five density based models were used to calculate the solubility of drugs in supercritical carbon dioxide. The density based models are Chrastil, modified Chrastil, Bartle, modified Bartle and Mendez-Santiago and Teja (M–T). Interaction parameters for the studied models were obtained and the percentage of average absolute relative deviation (AARD%) in each calculation was displayed. The correlation results showed good agreement with the experimental data. A comparison among the five models revealed that the Bartle and its modified models gave much better correlations of the solubility data with an average absolute relative deviation (AARD%) ranging from 4.8% to 6.2% and from 4.5% to 6.3% for ketoconazole and clotrimazole, respectively. Using the correlation results, the heat of drug–CO₂ solvation and that of drug vaporization was separately approximated in the range of (?22.1 to ?26.4 and 88.3 to 125.9) kJ · mol^?1.     

Influence of the aromatic ring substituents on phase equilibria of vanillins in binary systems with CO2

Solid–liquid phase transitions of vanillin, ethylvanillin, o-vanillin and o-ethylvanillin in presence of compressed CO₂ were determined with the modified capillary method. Furthermore, the solubilities of the above mentioned vanillins in supercritical CO₂ were measured at 313.2, 333.2 and 353.2 K and in the pressure range 8–30 MPa using a static–analytic method. The experimental equilibrium solubility data have been fitted to the Peng–Robinson equation in combination with two parameter van der Waals mixing rules and binary parameters were determined from the best fit. Results showed that the phase equilibria of vanillins in dense CO₂ are influenced by the position of the hydroxyl group bound to the aromatic ring. Under the pressure of CO₂ the melting point depression and also the solubility of both o-vanillins was higher than those of p-vanillins. Oppositely, the alchoxy group (methoxy or ethoxy) showed no significant influence on the solubility of vanillins.     

Effect of supercritical carbon dioxide on nanoporous polyhexafluoropropylene

The effect of supercritical CO₂ (sc-CO₂) on the size distribution of free volume holes (nanopores) in a polyhexafluoropropylene (PHFP) polymer matrix has been studied. Residual (after CO₂ release) swelling improves gas transport properties of the material. Relaxation of these properties over time has been compared with changes in permeability and nanoporosity. For PHFP samples with different histories, the data on nanoporosity have been obtained using positron annihilation lifetime spectroscopy (micropores) and the lowtemperature gas sorption technique (mesopores and part of micropores). Matching of the data is intended to reveal the role of pores of different sizes in permeability of membrane materials to different gases and determine the specifics of application of the positron annihilation technique to studying sc-CO₂-modified objects.     

Solubility of novel open-chain crown ether bridged diphosphates in supercritical carbon dioxide

The solubility of newly synthesized chelating agents, i.e., tetraethylene glycol bis (2-ethylhexyl) dimethyl diphosphate (EG4EH), tetraethylene glycol bis (n-octyl) dimethyl diphosphate (EG4Oct), and tetraethylene glycol bis (2-butoxyethyl) dimethyl diphosphate (EG4BOE) in supercritical carbon dioxide (scCO₂) were determined at temperatures ranging from (318.15 to 333.15) K and pressures ranging from (12 to 21) MPa. Solubility increases in the order of EG4Oct (MW = 606.33) < EG4BOE (MW = 582.26) < EG4EH (MW = 606.33), indicating that branched side chains of the ligands play an important part in increasing solubility in scCO₂. Semi empirical density-based models proposed by Bartle and Chrastil were used to correlate the experimental data, and AARD values were calculated to be (1.2 to 2.9)% and (0.40 to 0.93)% for Bartle and Chrastil model, respectively. Additionally, the partial molar volumes of those compounds were estimated following the theory developed by Kumar and Johnston.