Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 608–615
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Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 608–615 Contents lists available at ScienceDirect Journal of the Taiwan Institute of Chemical Engineers journal homepage: www.elsevier.com/locate/jtice Correlation of solid solubilities for phenolic compounds and steroids in supercritical carbon dioxide using the solution model Chie-Shaan Su, Yen-Ming Chen, Yan-Ping Chen * Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan ARTICLE INFO ABSTRACT Article history: The solid solubilities of phenolic compounds and steroids in supercritical carbon dioxide were correlated in Received 19 June 2010 this study using the solution model in its dimensionless form. The molar volume of solid solutes in Received in revised form 16 November 2010 supercritical carbon dioxide (V2) was taken as an adjustable parameter in this solution model. Their values Accepted 26 November 2010 for various solid solutes were determined from experimental solubility data at various temperatures and Available online 26 January 2011 pressures. The V2 parameters were well correlated with the densities of supercritical carbon dioxide. This correlation was further generalized to predict the solubility of complex solid in supercritical carbon Keywords: dioxide. The applicability of the solution model was presented in this study for two categories of phenolic Solubility and steroid compounds. The solution model with less parameters yielded comparably satisfactory results Supercritical carbon dioxide Solution model to those from commonly used semi-empirical models. The solution model with generalized parameters Phenolic compounds also yielded acceptable predicted results for these complex compounds. Steroids ß 2010 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. 1. Introduction pharmaceutical molecules. The semi-empirical equations contain- ing three or more parameters are widely used in literature. For Supercritical fluid (SCF) technology has been continuously example, Chrastil (1982) derived an equation that was based on the developed for the processing of food, pharmaceuticals, polymeric molecular association. Me´ndez-Santiago and Teja (1999) developed and specialty chemicals (Beckman, 2004; Teja and Eckert, 2000). a relationship for the solid solubility that incorporated the Clausius– Carbon dioxide is the most commonly used supercritical fluid due Clapeyron equation. Zhong et al.(1998)proposed a model based on to its environmentally benign properties. The SCF technology has the fact that the solute–solvent clusters were in chemical been employed in the value-added pharmaceutical processing equilibrium with the free solute and solvent molecules. Bartle et such as micronization, crystal properties modification and al.(1991)presented another equation by relating the enhancement particles design (Cocero et al., 2009; Martı´n and Cocero, 2008; factor of solid to the solvent density. Sparks et al.(2008)evaluated Pasquali et al., 2006; Reverchon and Della Porta, 2003). Supercritical various density-based semi-empirical models for 5 aromatic CO2 acts different roles as solvent in the rapid expansion of compounds and cholesterol. Although the semi-empirical, densi- supercritical solution (RESS) process, or as anti-solvent in the ty-based models yielded satisfactory correlation results, there is yet supercritical anti-solvent (SAS) process. The major criterion for any generalization of model parameters with the properties of choosing available process depends on the solubility of pharmaceu- complex solid solutes. tical compound in supercritical CO2. Experimental measurements of In order to improve these limitations, an alternative and the solid solubilities in supercritical CO2 provide essential informa- feasible approach for correlating the solubilities of complex tion for engineering process design. Increasing data are appearing in pharmaceutical compounds in supercritical CO2 was presented recent literature and it is the motivation of this study to develop a using the solution model. In this approach, the solid pharmaceu- simple, accurate enough correlation model with predictive ability. tical compound was assumed to be in phase equilibrium with the Three strategies for solubility calculation of solids in supercritical liquid supercritical CO2 solvent. An infinite dilution activity CO2 have been shown in literature by equation of state, solution coefficient was employed for the non-ideal behavior of solid– model, and semi-empirical equation. Among these approaches, the liquid equilibrium with low solubility. Iwai et al. (1992) first equation of state method is limited by the determination of correlated the solubility of high boiling point components in uncertain critical properties and sublimation pressures of complex supercritical CO2 using the regular solution model coupled with the Flory–Huggins equation. Bush and Eckert (1998) presented a predictive model based on the linear solvation energy relationship * Corresponding author. Fax: +886 2 2362 3040. (LSER), but large error was observed for polar compounds. In our E-mail address: [email protected] (Y.-P. Chen). previous studies (Cheng et al., 2002; Su and Chen, 2007), 1876-1070/$ – see front matter ß 2010 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2010.11.005 C.-S. Su et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 608–615 609 2. Mathematical model Nomenclature In the solution model, supercritical CO2 was assumed as an AADY absolute average deviation in solid solubility expanded liquid in equilibrium with the solid solute. The non-ideal a*, b*, c* parameters in the dimensionless Me´ndez-Santiago behavior between the solid solute and CO2 was represented by an and Teja model infinite dilution activity coefficient owing to the low solubility. The d*, e*, k* parameters in the dimensionless Chrastil model equilibrium solubility of solid solute (component 2) in supercriti- f*, g*, h* parameters in the dimensionless Bartle model cal CO2 (component 1) was thus expressed as: L f fugacity in supercritical phase S f2 S y ¼ (1) f fugacity in solid phase 2 1 L g2 f2 DHfus molar heat of fusion 1 M molecular weight where g2 was the infinite dilution activity coefficient of the solid solute. f S and f L were the fugacities of pure solute in the solid and n number of data points 2 2 supercritical phases, respectively. The ratio of these two fugacities P pressure was commonly approximated as: Pr reduced pressure ! fus Pref reference pressure in the Bartle model f S DH 1 1 ln 2 ¼ 2 À (2) R gas constant L f2 R Tm;2 T g1 infinite dilution activity coefficient fus S solid solubility in the dimensionless Chrastil model where DH2 was the molar heat of fusion of solute, and Tm,2 was S* dimensionless solid solubility in the dimensionless the melting temperature of solute. The infinite dilution activity coefficient 1 was expressed by the modified regular solution Chrastil model g2 model coupled with the Flory–Huggins equation. It was employed T temperature by Iwai et al. (1992) and our previous studies (Cheng et al., 2002; T critical temperature c Su and Chen, 2007, 2008). Tm melting temperature Tr reduced temperature 1 V 2 2 V 2 V 2 ln g ¼ ðd1 À d2Þ þ 1 À þ ln (3) vap 2 DU molar internal energy change of vaporization RT V 1 V 1 V molar volume where d was the solubility parameter and V was the molar V* dimensionless molar volume in the solution model volume. Incorporating this infinite dilution activity coefficient and y mole fraction the fugacities ratio, the solubility of solid solute in supercritical phase was: Greek symbols fus a*, b* parameters in the dimensionless solution model DH2 1 1 V 2 2 V 2 V 2 ln y2 ¼ À À ðd1 À d2Þ À 1 þ þ ln (4) d solubility parameter R Tm;2 T RT V 1 V 1 r density In Eq. (4), d1 was evaluated using the Peng–Robinson rc critical density equation of state (Peng and Robinson, 1976). The value of d2 was rr reduced density calculated using the molar volume of the solute (V 2)andthe va p molar internal energy change of vaporization of solute (DU2 ) Subscripts where the latter term was estimated by group contribution 1 component 1, CO2 method developed by Fedors (1974). The molar volume of 2 solid solute component 2 supercritical carbon dioxide (V 1) was estimated from the c critical point Jacobsen and Stewart equation of state with 32 constants regressed by Ely et al. (1989). The melting temperature of solute kkth experimental data point (Tm,2)inEq. (4) was taken from literature. The molar heat of fus fusion (DH2 ) was either taken from literature or estimated by Superscripts the method of Yalkowsky (1979). The molar volume of the cal calculated value solute in the supercritical phase (V 2) was the only adjustable exp experimental value parameter in Eq. (4). This parameter was determined using Eq. (4) and experimental solid solubility data for each solute molecule at various temperatures and pressures. The logarithm solid solubility of biological compounds including steroids, of the reduced V 2 wasobservedasalinearfunctionofthe antioxidants and xanthines in supercritical carbon dioxide were reduced density of CO2. The coefficients of this linear function correlated as an extension of the solution model of Iwai et al. were further generalized with the reduced internal energy of (1992). The major advantages of the solution model approach vaporization for pharmaceutical compounds. The predictive include the generalization of model parameters for the prediction