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.     

Analyzing the solubility of fluoxetine hydrochloride in supercritical carbon dioxide

In the pharmaceutical industry where the supercritical fluid-based technologies are utilized it is very important and vital to know the accurate value of the equilibrium solubility of solids required for the engineers to determine the size of the equipments. According to this requirement, the purpose of this study was measuring the solubility of fluoxetine hydrochloride with IUPAC name of 3-phenyl-3-[4-(trifluoromethyl)phenoxy]propan-1-amine hydrochloride using a static method coupled with gravimetric method. The measured solubility data at the temperature and pressure range of 308.15–338.15 K and 16–40 MPa was ranged between 2.65 × 10⁻⁵ and 8.12 × 10⁻⁴ based on the mole fraction. The results revealed that the solubility was increased when the pressure was increased while the effect of the temperature was more complex. Finally, the measured solubility data were correlated using three different correlations namely Bartle et al., Mendez-Santiago–Teja and Kumar and Johnston. The results of modeling revealed that the Bartle et al. model leads to the lowest average absolute relative deviation (AARD %) of 9.48.     

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.     

Measurement and modeling solubility of bioactive coumarin and its derivatives in supercritical carbon dioxide

To design a supercritical fluid extraction process for the separation of bioactive substances from natural products, a quantitative knowledge of phase equilibria between target biosolutes and solvent is necessary. How-ever, mostly no such information is available in literature to date. Thus in the present study, illustratively the solubility of bioactive coumarin and its various derivatives (i.e., hydroxy-, methyl-, and methoxy-derivatives) in supercritical CO₂ were measured at 308.15–328.15 K and 10–30 MPa. Also, the pure physical properties such as normal boiling point, critical constants, acentric factor, molar volume and standard vapor pressure for coumarin and its derivatives were estimated. By these estimated information, the measured solubilities were quantitatively correlated by an approximate lattice equation of state proposed recently by the present authors.     

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%.     

Estimation of solubility of solids in supercritical carbon dioxide

Peng-Robinson equation of state(PR EOS)was chosen for modeling the thermodynamic be-havior of supercritical(SC)-CO_2/Solid systems.The necessary critical constants and acentric factorof the solute were obtained by the Sigmund and Trebble(1992)method based on the molecular weightand boiling temperature,and the vapor pressure of the solute was calculated by its meltingtemperature and heat of fusion.This approach compared very favorably with the conventional corres-ponding state theory,but without using critical constants and vapor pressure of solutes.Four mixingrules were tested for the calculation of solid solubility in SC-CO_2.van der Waals(vdW)mixing rulewith one parameter was considered to be most suitable for the estimation of solubility.A simplecorrelation was developed for the SC-CO_2/solid binary interaction coefficient k_(ij) with the meltingtemperature of pure solutes.The solubilities of solids in SC-CO_2 were estimated for eleven binarysystems at various temperatures,the total absolute average     

胆甾醇在超临界CO2中的溶解度测定与关联

利用动态法测定了胆甾醇在超临界CO2中的溶解度。在10—30 MPa,313—343 K下,胆甾醇的溶解度摩尔分率为10-6—10-4。引入与密度有关的混合规则,将二元交互参数表示为密度的函数,采用PR状态方程,关联胆甾醇在超临界CO2中的溶解度。改进后的溶解度模型克服了采用经典混合规则的PR方程不能很好地关联胆甾醇大分子物质的缺陷,大大提高了关联精度。     

Measurement and calculation of solubility of quinine in supercritical carbon dioxide

Solubility of quinine in supercritical carbon dioxide(SCCO_2) was experimentally measured in the pressure range of 8 to 24 MPa, at three constant temperatures: 308.15 K, 318.15 K and 328.15 K. Measurement was carried out in a semi-dynamic system. Experimental data were correlated by iso-fugacity model(based on cubic equations of state, CEOS), Modified Mendez–Santiago–Teja(MST) and Modified Bartle semi-empirical models. Two cubic equations of state: Peng–Robinson(PR) and Dashtizadeh–Pazuki–Ghotbi–Taghikhani(DPTG) were adopted for calculation of equilibrium parameters in CEOS modeling. Interaction coefficients(k_(ij) l_(ij)) of van der Waals(vdW) mixing rules were considered as the correlation parameters in CEOS-based modeling and their contribution to the accuracy of model was investigated. Average Absolute Relative Deviation(AARD) between correlated and experimental data was calculated and compared as the index of validity and accuracy for different modeling systems. In this basis it was realized that the semi-empirical equations especially Modified MST can accurately support the theoretical studies on phase equilibrium behavior of quinine–SCCO_2 media. Among the cubic equations of state DPGT within two-parametric vd W mixing rules provided the best data fitting and PR within one-parametric vd W mixing rules demonstrated the highest deviation respecting to the experimental data. Overall, in each individual modeling system the best fitting was observed on the data points attained at 318 K, which could be perhaps due to the moderate thermodynamic state of supercritical phase.     

Artificial Neural Network modeling of solubility of supercritical carbon dioxide in 24 commonly used ionic liquids

Application of supercritical CO₂ for separation of ionic liquids from their organic solvents or extraction of various solutes from ionic liquid solvents have found great interest during recent years. Knowledge of phase behaviors of the mixtures of supercritical CO₂+ionic liquids is therefore drastic in order to efficiently design such separation processes. In this communication, Artificial Neural Network procedure has been applied to represent the solubility of supercritical CO₂ in 24 mostly used ionic liquids. An optimized Three-Layer Feed Forward Neural Network using critical properties of ionic liquids and operational temperature and pressure has been developed. Application of this model for 1128 data points of 24 ionic liquids show squared correlation coefficients of 0.993 and average absolute deviation of 3.6% from experimental values for calculated/estimated solubilities. The aforementioned deviations show the prediction capability of the presented model.     

Experimental studies of solubility of elemental sulphur in supercritical carbon dioxide

In recent years, more and more problems of elemental sulphur deposits in natural gas transmission line systems have been reported. Available experimental data on the solubility of sulphur in gases are in too high ranges of temperature, pressure and hydrogen sulphide amount compared to the transport conditions of natural gas. An original experimental apparatus, designed from the study of available works on this subject, is presented and allows the measurement of sulphur solubility. An equilibrium cell establishes the solid–gas equilibrium in conditions of natural gas transportation. To measure the amount of sulphur contained in a known volume of gas, a sample of saturated gas is withdrawn from the equilibrium cell by the way of a flash and pass through a trapping solution. Gaseous elemental sulphur is reactively absorbed into a trapping mixture. Gas chromatography (GC) allows an indirect quantification of sulphur. Experimental isotherm data of sulphur solubility in supercritical carbon dioxide are presented and compared to available studies.     

超临界CO2一步法制备载盐酸阿霉素和紫杉醇壳聚糖纳米粒

双载药纳米给药系统能有效增强抗癌药物协同治疗效果、降低毒副作用.本研究以水-乙醇为共溶剂、利用强化混合超临界流体辅助雾化(SAA-HCM)技术一步法制备了同时负载盐酸阿霉素和紫杉醇的壳聚糖纳米粒,详细考察了水与乙醇的体积比、待处理液浓度、CO2与溶液质量流量比、壳聚糖相对分子质量和沉淀器温度对纳米粒形貌及粒径分布的影响...     

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.     

Formulation of a new generic density-based model for modeling solubility of polyphenols in supercritical carbon dioxide and ethanol

The aim of this work is to present a first approach in formulating a generic model for polyphenols solubility in ternary mixtures (polyphenol + ethanol + sc-CO₂). Solubility data of six polyphenols were collected from the literature, and six different groups of parameters were proposed for the new generic model in order to evaluate their effects and find the best set for each polyphenol. Likewise, four dimensional groups of factors were proposed to evaluate the effect of dimensions on solubility data calculation. The results show that the originally formulated model and its modifications are particularly useful in calculating polyphenols solubility data; for instance, when resveratrol solubility data was fitted, the AARD decreased from a value of 38.52 to 14.03, upon changing from a simple to a complex model. Additionally, this generic model with a specific modification can estimate solubility maxima occurring in the ternary resveratrol + ethanol + sc-CO₂ system.     

Extraction and solubility evaluation of functional seed oil in supercritical carbon dioxide

Hemp (Cannabis sativa L.) seed oil is valued for its nutritional properties and for the health benefits associated with it. Its greatest feature is that the ratio of linoleic acid and linolenic acid is the desirable value of 3:1. In this research, supercritical carbon dioxide was applied to extraction of functional oil from hemp seed. In order to determine the effect of temperature and pressure on the yield of extracted components, the oil was extracted from hemp seed at temperatures between 40 and 80 °C, pressures of 20–40 MPa and a CO₂ flow rate of 3 mL/min. The solubility of hemp seed oil in SCCO₂ determined experimentally was fitted to the Chrastil equation to determine the model parameters. The solubility calculated by Chrastil equation was compared with the experimental data. Finally, the fatty acid profile of the oil was evaluated by gas chromatography-flame ionization detection (GC-FID). There are no significant differences in the compositions of five abundant fatty acid components of the oil obtained at different sampling times with SCCO₂ extraction and other extraction methods.     

超临界CO2流体中染料溶解度研究进展

综述了超临界CO2流体中染料溶解度的测试装置与方法。分析了超临界CO2流体工艺参数与染料化学结构对分散染料溶解度的影响规律；总结了国内外近二十年的分散染料在超临界CO2流体中溶解度数据，并介绍了分散染料在超临界CO2中的溶解度增溶技术。指出加强染料结构对其溶解性能作用原理及影响规律剖析，超临界CO2中染料溶解行为数据库构建，染料拼色与配色研究三方面为未来的研究重点。     

Polymer plasticization using supercritical carbon dioxide

The plasticizing effect of supercritical CO₂ (scCO₂) during the extrusion of polymers was investigated. A modified extrusion system was used to demonstrate the viscosity‐reducing effect of scCO₂ together with a capability to produce foam‐free extrudate with selected polymers, including poly(vinyl chloride). Samples of extrudate and materials prepared off‐line by using a pressure vessel were characterized by thermal, mechanical, and X‐ray techniques. After gas diffusion from the polymer, there was no long‐term effect on polymer structure and properties. J. VINYL ADDIT. TECHNOL., 2008. © 2008 Society of Plastics Engineers.     

Molecular modeling and experimental verification of lipase-catalyzed enantioselective esterification of racemic naproxen in supercritical carbon dioxide

Experimental and simulation analyses were performed on the lipase-catalyzed esterification reaction of racemic naproxen by CALB (candida antarctica lipase B) enzyme in supercritical carbon dioxide. The reaction pathways were investigated by quantum mechanical analysis, and the enantioselectivity of the products was predicted by molecular dynamics simulation analysis. Calculated results from molecular modeling in supercritical carbon dioxide were qualitatively compared with experimental data by using racemic naproxen as a substrate. All molecular modeling results and experimental data were acquired and compared with those in ambient and supercritical condition. Moreover, to verify the stability of enzymatic reaction in each solvent condition, reaction pathways were investigated in several solvent conditions (vacuum, water, hexane and supercritical carbon dioxide), and the stability of enzymatic reaction in supercritical carbon dioxide was compared with other solvent conditions. This paper is dedicated to Professor Chul Soo Lee on the occasion of his retirement from Korea University.     

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.     

Ternary solubility of mono- and di-tert-butyl ethers of glycerol in supercritical carbon dioxide

Using a continuous flow apparatus, the ternary solubility of mono- and di-tert-butyl ethers of glycerol (MTBG and DTBG, respectively) in supercritical carbon dioxide was measured at the temperatures of 313.15, 333.15, and 348.15 K; a pressure range of 80-200 bar; and an expanded gas flow rate of 180 ± 10 mL min⁻¹ at average laboratory temperature of 300.15 K and pressure of 0.89 bar. The ternary solubility of the ethers at the constant temperatures of 333.15 and 348.15 K increased with increasing pressure up to the crossover point (i.e., 152 bar for MTBG and 170 bar for DTBG). MTBG exhibited a higher solubility than DTBG in scCO₂. The experimental data for the ternary solubility of MTBG and DTBG were correlated using the Bartle equation.