Prediction of the infinite-dilution partial molar volumes of organic solutes in supercritical carbon dioxide using the Kirkwood-Buff fluctuation integral with the hard sphere expansion (HSE) theory

Two thermodynamic models were used to predict the infinite dilution partial molar volumes (PMVs) of organic solutes in supercritical carbon dioxide: (1) the Kirkwood Buff fluctuation integral with the hard sphere expansion (HSE) theory incorporated (KB-HSE fluctuation integral method) and (2) the Peng-Robinson equation of state with the classical mixing rule. While an equation of state only for pure supercritical carbon dioxide is needed in the KB-HSE fluctuation integral model, and thus, there is no need to know the critical properties of solutes, two molecular parameters (one size parameter σ₁₂ and one dimensionless parameter α₁₂) in the KB-HSE fluctuation integral model are determined to fit the experimental data published on the infinite dilution PMVs of solutes. The KB-HSE fluctuation integral method produced better results on the infinite dilution PMVs of eight organic solutes tested in this work than the Peng-Robinson equation of state with the classical mixing rule.     

Measurements and correlation of effect of cosolvents on the solubilities of complex molecules in supercritical carbon dioxide

A new transparent microscale circulation-type high pressure equilibrium cell with on-line sampling was devised. With this apparatus, experimental solubility of molecularly complex species such as steroids (cholesterol, stigmasterol and ergosterol) and fatty acids (palmitic acid and stearic acid) in supercritical carbon dioxide(sc-C0₂) were measured. Also, to find an appropriate substance for enhancing both the polarity and the solubility power of the SC-CO₂ solvent, we arbitrarily selected three polar substances such as acetone, methanol and water and the effect of these cosolvents on the solubility of solutes in SC-CO₂ are examined. The supercritical phase equilibrium data of solute-cosolvent-sc-CO₂ systems were quantitatively correlated using a new equation of state based on the lattice fluid theory incorporated with the concept of multibody interaction. We found that the addition of tracer amount of acetone or methanol to SC-CO₂ enhances the solubility of all solutes about thirty to sixty times when compared with the case of pure sc-CO₂ However, for the case of cosolvent water, no further enhancement of the solubility of solutes was realized. Also, the versatile fittability of the equation of state proposed in this work was demonstrated with the newly measured ternary supercritical equilibrium data.     

Theoretical Models of Thermodynamic Properties of Supercritical Solutions

Abstract

Several separation processes, including supercritical extraction and supercritical fluid chroma-tography, take advantage of the striking solubility behavior of supercritical fluids. A general theoretical framework is presented for modeling thermodynamic properties of supercritical solutions based on the theory of Kirkwood and Buff. The theory is expressed in terms of the Kirkwood fluctuation integral from statistical mechanics and permits introduction of appropriate molecular solution approximations. Thus, the solute-solvent interaction may be expressed using a local composition approximation, for example, with an accurate equation of state for the pure solvent. This approach is illustrated for two molecular solution approximations and is compared with solubility and partial molecular volume data.     

Development of artificial neural network models for supercritical fluid solvency in presence of co-solvents

This paper presents the application of artificial neural networks (ANN) to develop new models of liquid solvent dissolution of supercritical fluids with solutes in the presence of cosolvents. The neural network model of the liquid solvent dissolution of CO₂ was built as a function of pressure, temperature, and concentrations of the solutes and cosolvents. Different experimental measurements of liquid solvent dissolution of supercritical fluids (CO₂) with solutes in the presence of cosolvents were collected. The collected data are divided into two parts. The first part was used in building the models, and the second part was used to test and validate the developed models against the Peng-Robinson equation of state. The developed ANN models showed high accuracy, within the studied variables range, in predicting the solubility of the 2-naphthol, anthracene, and aspirin in the supercritical fluid in the presence and absence of co-solvents compared to (EoS). Therefore, the developed ANN models could be considered as a good tool in predicting the solubility of tested solutes in supercritical fluid.     

Reverse Micelle Supercritical Fluid Separations

Abstract

Initial results are presented showing the potential applications of reverse micelle supercritical fluid solvents in separation processes. The formation of reverse micelles in supercritical nalkane continuous phases is described. Phase diagrams obtained from view-cell studies of micellar and microemulsion phases formed in supercritical fluids are reported and shown to be strongly dependent on pressure. The solubility of AOT in ethane and propane over a range of pressures shows behavior typical of solids in supercritical fluids. The maximum water-to-surfactant ratio (W_O) increased dramatically in both ethane and propane systems as pressure was increased. At 300 bar W_O = 4 for ethane at 37 'C and W_O = 12 for propane at 103 _*C. The initial use of supercritical fluids containing reverse micelles for the extraction of solutes from an aqueous phase, and as mobile phases in chromatography, is described.     

Prediction of solubilities of solid solutes in carbon dioxide-expanded organic solvents using the predictive Soave–Redlich–Kwong (PSRK) equation of state

In this study, the solubilities of solid solutes in carbon dioxide (CO₂)-expanded organic solvents are predicted using the predictive Soave–Redlich–Kwong (PSRK) equation of state (EOS). The liquid-phase compositions and volume expansion ratios of CO₂-expanded organic solvents are predicted prior to the solubility predictions. With predicted liquid-phase compositions and volumetric properties, the solubilities of cholesterol in CO₂-expanded acetone, naphthalene in CO₂-expanded toluene, stearic acid in CO₂ expanded ethyl acetate and tetradecanoic acid in CO₂-expanded ethyl acetate are predicted according to their reference solubilities in pure organic solvents. In addition to satisfactory predictions of liquid-phase composition and volume expansion ratios, the PSRK EOS also provides qualitative prediction ability for solubilities of solid solutes in CO₂-expanded organic solvent. This study demonstrated that the PSRK EOS was a simple model with predictive ability for solubility evaluation in preliminary process design and development for supercritical fluid technology using CO₂-expanded organic solvents.     

Distribution of solutes between polymer and supercritical fluid by inverse supercritical fluid chromatography

Two methods of inverse supercritical fluid chromatography (ISFC), frontal analysis supercritical fluid chromatography (SFC) and elution SFC, have been compared for the determination of distribution coefficients of solutes between a polymer and a supercritical CO₂. The logarithm of the distribution coefficient showed monotonic decrease with the density of the supercritical fluid (SF). The abnormal-maximum behavior of solute sorption in the polymer phase was explained by the fluid and solute properties, ϕ₂P/P ₂ ^sat . Interesting open-elliptic shapes of sorption and volume-fraction curves were obtained and explained with the fugacity coefficient. Correction to the capacity factor was employed to eliminate the retention due to the adsorption on the surface of the silica support. A model based on the Flory equation and the Peng-Robinson equation of state (EOS) successfully predicted the phase behavior of the ternary solutesupercritical fluid-polymer systems using only interaction parameters obtained from the binary systems. The solute distribution coefficient at infinite dilution was used to calculate the phase equilibrium at finite concentration using a ternary-phase diagram.     

Mass transfer and hydrodynamic study of supercritical carbon dioxide extraction of 1,8-cineole from small cardamom seeds

This study investigates mass transfer and hydrodynamic parameters of supercritical carbon dioxide (sc-CO₂) extraction of 1,8-cineole from small cardamom seeds (SCs). Solubility of 1,8-cineole in sc-CO₂, its diffusivity, and release kinetics from SCs have been explored. A correlated Chrastil equation has been developed for predicting solubility under varying extraction conditions. Empirical correlations among Reynolds, Schmidt, and Sherwood numbers considering Wilke–Chang equation for diffusivity showed a better fit as compared with those obtained using Stokes–Einstein equation. The extraction kinetics was in agreement with the Sovová model showing plug flow behavior. Release kinetics of 1,8-cineole from SCs was best explained by the Higuchi model. A high R² value (0.93) of the empirical equation involving dimensionless numbers suggested that the extraction process has been satisfactorily modeled. This model would help in scaling up the production of this significant biotherapeutic molecule from cardamom and similar seed matrices.     

A comparison between semiempirical equations to predict the solubility of pharmaceutical compounds in supercritical carbon dioxide

The aim of this work is to determine, depending on the operation conditions, which semiempirical equation provides the best fit to solubility data of pharmaceutical compounds in supercritical CO₂. Solubility data from 27 different pharmaceutical solutes were collected from literature and the different density-based models (Chrastil, Adachi-Lu, del Valle-Aguilera, Sparks, Kumar-Johnston, Bartle, Méndez Santiago-Teja) together with the Yu's model and Gordillo's model were employed. The results showed that, in general, Sparks’ equation provides the best fit to the solubility data for this kind of solids in supercritical CO₂. However, at certain specific conditions, the best correlation is obtained using Gordillo's equation. By means of a brief comparison with Peng-Robinson equation of state, semiempirical equations present a more accuracy prediction compared to cubic equations of state, and present no drawbacks such as properties estimation and computational difficulties.     

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.     

A comparative study between LS-SVM method and semi empirical equations for modeling the solubility of different solutes in supercritical carbon dioxide

A genetic algorithm based least square support vector machine has been used to predict the solubility of 25 different solutes in supercritical carbon dioxide. This model consists of three inputs including temperature, pressure and density of supercritical carbon dioxide and a single output which is the solubility of different solutes in supercritical carbon dioxide. The model predictions were compared with the outputs of seven well-known semi empirical correlations. Results showed that the present method has an average relative deviation of about 4.92% for 25 solutes while the best semi empirical equation resulted an average relative deviation of about 13.60% for same solutes.     

THE SOLUBILITY OF PARAFFINIC HYDROCARBONS AND THEIR DERIVATIVES IN SUPERCRITICAL CARBON DIOXIDE

The solubilities of twenty-five paraffinic model compounds, octadecane (C₁₈H₃₈) through tetracosane (C₂₄H₅₀) and related monofunctional derivatives, were measured in supercritical carbon dioxide at 310 and 320 K. The derivatives included sulfides, amines, phosphines, ketones and other functional groups. Several of the solutes were liquids at the extraction temperatures and pressures, and both liquid and fluid phase binary composition data are reported in some cases. A systematic attempt was made to explore how the presence of a particular functional group on the solute molecule affected the solubility of the compound relative to the parent hydrocarbon of equivalent chain length.     

A comparison between models based on equations of state and density-based models for describing the solubility of solutes in CO2

The poor dissolution behaviour of solid drugs in biological environment leads to a low bioavailability. However, the dissolution rate of such drugs can be enhanced dramatically by reduction of the particle size. At present, supercritical fluid based particle size reduction processes are gaining in importance in pharmaceutical technology. For the design of such particle formation processes and the determination of their best operating conditions the knowledge of phase equilibrium and solute solubility in a supercritical fluid is essential. Today, models based on equations of state, together with different mixing rules, are most widely used to correlate and predict the solubility in supercritical fluids. Therefore the accurate knowledge of the required solute data, such as critical parameters, acentric factor, solid molar volume, and sublimation pressure of the solutes is essential. However, the common, non-equation of state based group-contribution methods are mostly empirical and often lead to inconsistent and unreliable results. Thus, due to the lack of information on these data, density-based models are often used for the correlation of experimental solubility data. In this investigation, the solubility of Salicylic acid, of S-Naproxen, of RS-Ibuprofen and of Phytosterol in CO₂ is correlated by different methods: two methods for the pressure-solubility correlation and two methods for the density-solubility correlation. In addition, the influence of solute data predicted by different group-contribution methods is investigated. With the exception of S-Naproxen all systems investigated can be modelled sufficient well with a non-cubic equation of state while a cubic equation of state gives less accurate results. In addition, it is shown that for the solutes investigated, the equation of state based method is very sensitive to the values of the sublimation pressure.     

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.     

Coupled Supercritical Fluid Extraction/Chromatography of Polycyclic Aromatic Hydrocarbons: Correlation with Solubility Calculations

The solubility of: naphthalene, fluorene, phenanthrene, pyrene, and chrysene in supercritical CO₂ at two temperatures and pressures up to 200 atm were calculated from fugacities derived via the Peng-Robinson equation of state. The calculated solubilities were correlated with the results of experiments in which polycyclic aromatic hydrocarbons (PAH) in fuel mixtures were extracted with supercritical CO₂ and analysed by supercritical fluid chromatography and by gas chromatography.     

Predicting the effect of dissolved carbon dioxide on the glass transition temperature of poly(acrylic acid)

The morphology and size of poly(acrylic acid) (PAA) particles produced by precipitation polymerization in supercritical CO₂ (scCO₂) depends on the glass transition temperature (T_g) of the polymer at reaction conditions. In this study, the use of the Sanchez–Lacombe equation of state (SL‐EOS), in conjunction with Chow's equation, to predict the effect of CO₂ pressure on the T_g of PAA was evaluated. Characteristic parameters for PAA were determined by fitting density data. Characteristic parameters for CO₂ were determined by fitting density data in the supercritical region. When the SL‐EOS was used in a purely predictive mode, with a binary interaction parameter (ψ) of 1, the solubility of CO₂ in PAA was underestimated and T_g was overestimated, although the trend of T_g with CO₂ pressure was captured. When was determined by fitting the SL‐EOS to the measured sorption of scCO₂ in PAA, the calculated T_g's agreed very well with measured values. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Dimensionless Empirical Model to Correlate Pharmaceutical Compound Solubility in Supercritical Carbon Dioxide

The accurate experimental determination of pharmaceutical compound solubilities at various temperature and pressure ranges in supercritical carbon dioxide (ScCO₂) is a challenging and time‐consuming task. Therefore, prediction or correlations of solute solubilities are essential for implementation of ScCO₂ technologies to pharmaceutical industries. Solubilities of 41 pharmaceutical compounds in ScCO₂ are correlated by an empirical model, which is developed based on the degree of freedom analysis. Its correlating ability is compared with existing solubility models elaborated by other authors and evaluated in terms of global mean absolute relative deviation, sum of squares due to error, root mean square deviation, R², and Adj. R². The proposed model is found to correlate better than existing models.     

Estimation of solubility parameter components of solutes and polymers using heat of vaporization and heat of sorption of solutes

In a recent study, a two‐dimensional solubility parameter model was used to correlate the heat of solution for solutes ranging from n‐alkanes to alcohols, dissolved in isotatic polypropylene (PP), poly(ethyl ethylene) (PEE), and poly(dimethylsiloxane) (PDMS). When literature data of solubility parameter components of solutes were used, the correlation had some scattering for solutes with low values of cohesive energy density. In this study, the components of solubility parameters of solutes and polymers were estimated from cohesive energy and heat of sorption of solutes. Good correlation was obtained for the specific heat of sorption (ΔU_sorp/V) for solutes ranging from n‐alkanes to alcohols, and PDMS had a polar component as previously estimated. Free volume effect in solution process may be the source of a small systematic deviation from the model. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Solution properties of homogeneous polyglycerol dodecyl ether nonionic surfactants

The synthesis and solution properties of a homologous series of polyglycerol dodecyl ethers (R₁₂G_n) are described. The phase behavior, surface tension, cloud point and HLB value (hydrophile lipophile balance) of these surfactants in aqueous solutions and in mixed solutions of water/oil have been investigated and compared with values for polyoxyethylene dodecyl ether (R₁₂EO_n). The surface tension measurements showed that R₁₂G_n have sufficiently low values of surface tension and critical micellization concentration (cmc) to serve as useful nonionic surfactants. The mesophases appearing in the R₁₂G_n systems were more stable in a high temperature range than the mesophases of the R₁₂EO_n systems. The cloud point and HLB data indicated that addition of one glycerol group was equivalent to the addition of three oxyethylene units, as far as the hydrophilic property was concerned. The phase diagrams of the R₁₂G_n/dodecane/water systems showed that the solubilizing and emulsifying powers of R₁₂G_n were greater than those of R₁₂EO_n. It is concluded that the polyglycerol chain can be even more useful as the hydrophilic part of nonionic surfactants than the conventional oxyethylene chain.     

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.