Determination and calculation for solubility of m-nitroaniline and its mixture in supercritical carbon dioxide

Equilibrium solubility of m-nitroaniline and p-nitroaniline in supercritical carbon dioxide (SCCO₂) is essential to design the process of SCCO₂ extraction and to investigate the effect of each solute on the solubility in SCCO₂ ternary system. However, the solubility data is not reported so far. We performed the solubility measurements at the temperatures of 308–328 K and in the pressure range of 11.0–21.0 MPa. The experimental results showed the solubility of m-nitroaniline and p-nitroaniline was enhanced in m-nitroaniline + p-nitroaniline + SCCO₂ ternary system. The improvement factor (i), separation factor (μ) and separation efficiency (HE) in the ternary system were defined and calculated, and the best separation result could be obtained at 21.0 MPa and 328 K using SCCO₂ extraction, where the separation efficiency was up to 90.9%. Based on the chemical association theory, a new model was developed to calculate the solubility of mixed solutes in SCCO₂. The correlation result of the new model was tested by about 500 solubility data from 15 kinds of two solutes mixtures in SCCO₂. The correlated result showed that the new model could achieve much better AARD (%) than those of frequently used Sovova and Sovova-T models.     

Dye solubility in supercritical carbon dioxide. Effect of hydrogen bonding with cosolvents

The use of supercritical carbon dioxide is emerging as a potential method for achieving pollution-free dyeing. An important factor in supercritical fluid dyeing is the solubility of the dye in supercritical carbon dioxide. Our measurements show that the solubility of C. I. Disperse Red-60 dye in supercritical carbon dioxide is significantly enhanced upon addition of polar csolvents : ethanol and acetone. The solubility enhancement is attributed to the formation of hydrogen bonds between cosolvent and dye molecules. Observed solubility behavior is correlated using dilute-solution theory with lattice-fluid-hydrogen-bonding model. Needed physical and hydrogen-bonding molecular parameters are estimated using the experimental data.     

Cosolvent effects on the diffusions of 1,3-dichlorobenzene, l-carvone, geraniol and 3-fluorophenol in supercritical carbon dioxide

In order to get an insight into solute-cosolvent interactions and to predict the cosolvent effects on diffusions, several cosolvents and solutes with different size, hydrogen-bond donor (HBD) acidity, and hydrogen-bond acceptor (HBA) basicity were chosen, and the molecular diffusion coefficients of the solutes in pure and modified supercritical carbon dioxide were measured by the Taylor-Aris chromatographic peak broadening method. Cosolvent effect parameter, which is defined as the ratio of diffusion coefficient with and without cosolvent, respectively, is introduced to quantitatively compare the strength of different types of interaction between solute and cosolvent, especially hydrogen bonding. For cosolvent without hydrogen-bond ability, the cosolvent effect parameter decreases with the increase of molecular volume and weight of the solutes, in that the strength of dispersion force with cosolvent increases with their size. For cosolvent with only HBA basicity, the solute with higher HBD acidity has smaller cosolvent effect parameter, due to the fact that the strength of hydrogen-bond interaction between the solute and cosolvent only depends on and increases with the HBD acidity of the solute. For amphiprotic cosolvent, the solute with higher HBD acidity has smaller cosolvent effect parameter, it can be inferred from which that HBD acidity rather than HBA basicity of the solute makes a major contribution to the hydrogen-bond interaction between solute and cosolvent. These results are consistent with the interpretation by the Kamlet-Taft solvatochromic parameters (HBD acidity and HBA basicity). Moreover, a nonlinear decrease in diffusion coefficient with the increase of cosolvent concentration is observed, which is typical of the behavior of the system with strong interaction.     

Calculation of the solid solubilities in supercritical carbon dioxide using a new G mixing rule

The aim of this study is to develop a new EOS/G^ex-type mixing rule with special attention to calculating the solid solubilities of aromatic hydrocarbons, aliphatic carboxylic acids, aromatic acids, and heavy aliphatic and aromatic alcohols in supercritical carbon dioxide. A volume correction term is applied with a combination of second and third virial coefficients which the equation for the third virial coefficient is quadratic, according to the suggestion by Hall and Iglesias-Silva. In this study, the cubic Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state have been used to calculate the solid solubilities of 23 solutes in supercritical CO₂, by using six mixing rules, namely, the Wong-Sandler (WS) rule, the Orbey-Sandler (OS) rule, the van der Waals one fluid rule with one (VDW1) and two (VDW2) adjustable parameters, the covolume dependent (CVD) rule and the new mixing rule. In all cases, the NRTL model was chosen as the excess Gibbs free energy model. The coefficients of the NRTL model and the binary interaction parameters of six mixing rules with two EOSs (PR and SRK EOSs) have been determined for 100 data sets of 23 binary systems over a wide range of temperatures and pressures covering more than 970 experimental data points which are reported in the literature. The results show that the PR EOS with the new mixing rule model is more accurate than the PR and SRK EOSs with the other mixing rules for solid solubility calculations in supercritical carbon dioxide.The regressed interaction parameters of the binary system, without any further modification, were then extended to four ternary mixtures, giving satisfactory results of the solid solubilities in supercritical CO₂.     

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.     

Solubility of chlorpheniramine maleate in supercritical carbon dioxide

Solubility of chlorpheniramine maleate in supercritical carbon dioxide at different temperatures (308–338 K) and pressures (160–400 bar) is measured using static method coupled with gravimetric method. The measured solubility data demonstrated that the solubility of chlorpheniramine maleate was changed between 1.54 × 10⁻⁵ and 4.26 × 10⁻⁴ based on the mole fraction as the temperature and pressure are changed. The general trend of measured solubility data shows a direct effect of pressure and temperature on the solubility of chlorpheniramine maleate. Finally, the obtained solubilities correlated using four semi-empirical density-based correlations including Mendez Santiago–Teja (MST), Kumar and Johnston (KJ), Bartle et al., and Chrastil models. Although the results of modeling showed that the KJ model leads to the average absolute relative deviation percent (AARD %) of 8.1% which is the lowest AARD %, deviation of other utilized correlations are rather the same.     

Solubility of cyproheptadine in supercritical carbon dioxide; experimental and modeling approaches

Solubility of solute in supercritical fluids at different pressures and temperatures is one of the most important parameters necessary for design of any supercritical fluid-based processes. Among different supercritical fluids, carbon dioxide is one of the most widely used solvents due to its useful and green characteristics. In this work, with the assist of supercritical carbon dioxide as the solvent, solubility of cyproheptadine in different temperatures (308–338 K) and pressures (160–400 bar) are measured using static method. The obtained results demonstrated that solubility of cyproheptadine ranged between 3.35 × 10⁻⁵ and 3.09 × 10⁻³ based on mole fraction. A closer examination of measured solubility data show that not only solubility of cyproheptadine increases by increasing pressure but also experiences a cross over pressure about 200 bar. At last, the measured solubility data are correlated using four widely used density based correlations namely Mendez Santiago–Teja (MST), Kumar and Johnston (KJ), Bartle et al., and Chrastil models. The obtained results demonstrated that the best correlative capability was observed for KJ model leads to the average absolute relative deviation percent (AARD %) of 6.3%.     

Solubility prediction of disperse dyes in supercritical carbon dioxide and ethanol as co-solvent using neural network

Nowadays artificial neural networks(ANNs) with strong ability have been applied widely for prediction of nonlinear phenomenon. In this work an optimized ANN with 7 inputs that consist of temperature, pressure, critical temperature, critical pressure, density, molecular weight and acentric factor has been used for solubility prediction of three disperse dyes in supercritical carbon dioxide(SC-CO2) and ethanol as co-solvent. It was shown how a multi-layer perceptron network can be trained to represent the solubility of disperse dyes in SC-CO2. Numeric Sensitivity Analysis and Garson equation were utilized to find out the degree of effectiveness of different input variables on the efficiency of the proposed model. Results showed that our proposed ANN model has correlation coefficient, Nash–Sutcliffe model efficiency coefficient and discrepancy ratio about 0.998, 0.992, and 1.053 respectively.     

Thermodynamic modeling of solubilities of various solid compounds in supercritical carbon dioxide: Effects of equations of state and mixing rules

No one can ever deny the significance of calculations of solubilities of industrial solid compounds in supercritical CO₂ in separation processes. In this work, the Peng-Robinson (PR) and the Esmaeilzadeh-Roshanfekr (ER) equations of state (EoS) along with several mixing rules including the Wong-Sandler (WS), the covolume dependent (CVD) and the van der Waals one (VDW1) and two (VDW2) fluid mixing rules are applied to evaluate the solubilities of 52 mostly used solid compounds in supercritical carbon dioxide. Besides, the Van-Laar excess Gibbs energy (G^ex) model is applied in phase behavior calculations by the WS mixing rule. The optimal values of the proposed thermodynamic model parameters are evaluated using the DE (differential evolution) optimization strategy. The absolute average deviations of the model results from 1776 experimental data points and the optimal values of the adjustable parameters of the model are reported to investigate the capabilities of combinations of each equation of state with different mixing rules in calculations of the solubilities. The results indicate that the combination of the ER EoS with the WS mixing rule leads to more accurate results (AAD = 9.0%) compared with other ones.     

Experimental investigation and modeling of the solubility of carvedilol in supercritical carbon dioxide

This study was aimed to measure the solubility of carvedilol in the temperature and pressure ranges of 308⿿338 K and 160 bar to 400 bar, respectively. In this direction, a homemade high pressure visual equilibrium cell was used to measure the solubility of carvedilol using a static method coupled with gravimetric technique. The results revealed that the carvedilol solubility was ranged between 1.12 ÿ 10^⿿5 and 5.01 ÿ 10^⿿3 based on the mole fraction (mole of carvedilol/mole of carvedilol + mole of CO₂) in this study as the temperature and pressure was changed. Finally, the results were correlated using four density-based semi-empirical correlations including Chrastil, Mendez⿿Santiago⿿Teja (MST), Bartle et al., and Kumar and Johnston (K-J) models. Results revealed that although the K-J model leads to the lowest average absolute relative deviation percent (AARD %) of 6.27%, but it could not be considered as the most accurate correlation since all the used four correlations introduces AARD % of about 6⿿10% which may be in the same range as the experimental error.     

Solubilities of chlormezanone,metaxalone and methocarbamol in supercritical carbon dioxide

The solubilities of three active pharmaceutical ingredients (APIs) in supercritical carbon dioxide were measured in this study using a semi-flow apparatus. These APIs are chlormezanone (C₁₁H₁₂ClNO₃S), metaxalone (C₁₂H₁₅NO₃) and methocarbamol (C₁₁H₁₅NO₅) that are all used as skeletal muscle relaxants. The solubility data are reported for three isotherms at 308.2, 318.2 and 328.2 K, with the pressure range from 12 to 24 MPa. Most solubility data are within the range of 10⁻⁶ to 10⁻⁴ mole fraction for each API. The crossover phenomena were observed from the experimental results for all three systems. These solubility data satisfied the thermodynamic consistency tests. They were then correlated using three semi-empirical models. With the optimally fitted binary interaction parameters, satisfactory correlation agreement is presented for each binary mixture.     

Solubility of the silver nitrate in supercritical carbon dioxide with ethanol and ethylene glycol as double cosolvents: Experimental determination and correlation

Solubility of the silver nitrate in the supercritical carbon dioxide containing ethanol and ethylene glycol as double cosolvents was measured under certain pressure and temperature range(10–25 MPa, 323.15–333.15 K). The impact of the pressure and temperature on the solubility was also investigated. Based on the experiment data,a correlation model concerning solid's solubility in supercritical fluids was established by combining the solubility parameter with the thermodynamic equation when a binary interaction parameter and a mixed solvent solubility parameter were defined. Experiments show the solubility of AgNO_3 increases with the pressure at a certain temperature. However, the influence of temperature is related to a pressure defined as the turnover pressure(12.3 MPa). When the pressure is higher(or lower) than this turnover pressure, silver nitrate's solubility shows increasing(or decreasing) trend as the temperature rises. Satisfactory accuracy of our presented model was revealed by comparing experimental data with calculated results.     

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.     

Correlation and estimation of solubilities of fatty acids in supercritical carbon dioxide using solution model approach

In this study, solid solubility data of five fatty acids in supercritical carbon dioxide (CO₂) at different temperatures and pressures are correlated using a two-parameter solution model developed from the regular solution model coupled with the Flory⿿Huggins equation. The developed solution model with fewer parameters yields correlated results comparable to those from commonly used semi-empirical equations. In addition, both parameters in the solution model can be further generalized with the chain length of fatty acids and a new predictive solution model is proposed for solubility prediction. The predictive solution model proposed in this study provides better predicted results and yields average deviation in predicted solubilities of 22.1%. To further apply this solution model to other compounds, solid solubility data of three triglycerides in supercritical CO₂ at 313 K are also correlated. After model simplification and generalization, a new predictive solution model for triglycerides is also proposed, which yields average deviation in predicted solubilities of 29.8%. These results demonstrate that the solution model used in this study is applicable for correlation and prediction of solid solubilities of structure-related compounds in supercritical CO₂.     

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.     

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.     

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.     

Solubility of red palm oil in supercritical carbon dioxide: Measurement and modelling

The solubility of red palm oil(RPO) in supercritical carbon dioxide(scCO_2) was determined using a dynamic method at 8.5–25 MPa and, 313.15–333.15 K and at a fixed scCO_2 flow rate of 2.9 g·min~(-1) using a full factorial design. The solubility was determined under low pressures and temperatures as a preliminary study for RPO particle formation using scCO_2. The solubility of RPO was 0.5–11.3 mg·(g CO_2)~(-1) and was significantly affected by the pressure and temperature. RPO solubility increased with pressure and decreased with temperature. The Adachi–Lu model showed the best-fit for RPO solubility data with an average relative deviation of 14% with a high coefficient of determination, R~2 of 0.9667, whereas the Peng–Robinson equation of state thermodynamic model recorded deviations of 17%–30%.     

Polymerization of acrylonitrile in supercritical carbon dioxide

A series of fluorinated diblock copolymers, consisting of styrene (St)-acrylonitrile (AN) copolymer [poly(St-co-AN)] and poly-2-[(perfluorononenyl)oxy]ethyl methacrylate, with various compositions as well as with different molecular weights were synthesized by atom transfer radical polymerization and characterized. Dispersion polymerization of acrylonitrile in supercritical carbon dioxide (scCO₂) at 30 MPa and at 65 °C with this kind of amphiphilic block copolymer as a stabilizer and 2,2′-azobisisobutyronitrile as an initiator was investigated. The experimental results indicated that, in the presence of a small amount of poly(St-co-AN) (5 wt% to AN), spherical particles of polyacrylonitrile (PAN) were prepared with small diameter and narrow polydispersity (d_n = 153 nm, d_w/d_n = 1.12), resulting from the high stabilizing efficiency of this fluorinated block copolymer. Furthermore, the polymerization of AN in scCO₂ under different initial pressures especially under low pressure (<14 MPa) was studied. When the polymerization was carried out around the critical pressure of CO₂ (7.7-7.8 MPa), the PANs with high molecular weight (M_ν ≈ 130,000-194,000) were synthesized at high monomer conversion (>90%) no matter whether the stabilizer was added, compared to those synthesized by dispersion polymerization at 30 MPa. It was also found that the crystallinity of PAN synthesized at 7.7-7.8 MPa was somewhat higher than that synthesized at 30 MPa, while its crystallite size did not change.     

Solid solubility of antilipemic agents and micronization of gemfibrozil in supercritical carbon dioxide

The solid solubilities of three antilipemic agents of clofibric acid, fenofibrate and gemfibrozil in supercritical carbon dioxide were measured using a semi-flow apparatus. The experimental data were taken at three isotherms of 308.2, 318.2 and 328.2 K, with pressure range from 10 to 22 MPa. These measured solid solubilities were correlated by the semi-empirical models of Mendez-Santiago-Teja and Chrastil. A solution model was also employed to fit the measured data. The absolute average deviation in solid solubility from semi-empirical models was 3-7%, and that from the solution model was 4-8%. The measured data satisfied the self-consistency test, and the optimally fitted parameters were reported.Gemfibrozil of the above antilipemic agents had high ranking among the best-selling generic drugs. It was then micronized using the rapid expansion of supercritical solution (RESS) method in this study. The particle size of gemfibrozil was micronized from its original 14.3 to 5.8 μm. It was also demonstrated that the dissolution rate of micronized gemfibrozil in a simulated intestinal fluid was enhanced by 5.5 times compared to that of the original compound.