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 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 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 (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 d2Þ þ 1 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 ðd1 d2Þ 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 of solubility calculation using the generalized parameters was solid solubilities. Furthermore, accuracy for solid solubility finally presented. calculation can be enhanced by classifying the pharmaceutical We have compared the calculated solubilities of pharmaceuti- systems as various categories (Su and Chen, 2008). Solubility for two cal compounds from the newly correlated solution model with categories of solid solutes, phenolic compounds and steroids, in other semi-empirical equations. Each semi-empirical equation had supercritical CO2 were investigated in this study by applying the three adjustable parameters in dimensionless forms: solution model. The solution model equations are expressed in (a) The Me´ndez-Santiago and Teja (MST) model (Me´ndez- dimensionless forms in this study. The correlation results of this Santiago and Teja, 1999): study are compared with those from other semi-empirical models. The predictive ability of the solution model is also demonstrated. Trlnðy2PrÞ¼a þ b rr;1 þ c Tr (5) 610 C.-S. Su et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 608–615

where Tr and Pr were the reduced temperature and pressure, (c) The Bartle model (Bartle et al., 1991): respectively. y2 was the solid solute solubility in mole fraction. The reduced density of supercritical CO2 (rr,1) was defined by: y2P g ln ¼ f þ þ h ðrr;1 1Þ (10) Pre f Tr rr;1 ¼ r1=rc;1 (6)

where Pref was the reference pressure at 0.1 MPa. The 3 where rc,1 was the critical density of CO2. There were 3 adjustable dimensionless adjustable parameters of the Bartle model were and dimensionless parameters, a*, b* and c*. f*, g* and h*. (b) The Chrastil model (Chrastil, 1982):

d 3. Results and discussion lnS2 ¼ k ln rr;1 þ þ e (7) Tr 3.1. Data systems where S2 was the dimensionless solid solubility defined as: Solid solubilities in supercritical carbon dioxide for two S2 categories of phenolic compounds and steroids were correlated S2 ¼ (8) rc;1 in this study using the solution model. Compounds containing benzoic ring with at least one hydroxyl group were classified as the phenolic systems. This category comprised lots of phenolic r1M2y2 S2 ¼ (9) antioxidants such as ferulic acid and . The steroid M1ð1 y2Þ category included typical compounds like cholesterol and proges- terone with classical steroidal structure. The thermodynamic M1 and M2 were the molecular weight of CO2 and the solid properties of phenolic compounds and steroids in our calculation solute, respectively. The 3 dimensionless adjustable parameters of are presented in Table 1. the Chrastil model were k*, d* and e*.

Table 1 Data reference and physical properties of phenolic compounds and steroids in this study.

fus vap Compound CAS Formula M (kg/mol) Tm DH DU T range P range Data Ref. (K) (kJ/mol) (kJ/mol) (K) (MPa) points

Phenolic compounds

4-tert-Butylphenol 98-54-4 C10H14O 0.1502 371.15 17.79 77.30 308 10–28 7 Ravipaty et al. (2006)

Dodecyl gallate 1166-52-5 C19H30O5 0.3384 369.65 51.30 201.02 313–333 15–25 8 Cortesi et al. (1999)

Ethylvanillin 121-32-4 C9H10O3 0.1662 350.65 22.72 96.04 313–333 8–31 21 Sˇkerget et al. (2005)

o-Ethylvanillin 492-88-6 C9H10O3 0.1662 338.65 21.94 96.04 313–333 10–30 19 Sˇkerget et al. (2005)

Ferulic acid 537-98-4 C10H10O4 0.1942 443.15 28.72 106.00 303–333 12–30 18 Sovova´ (2001)

Methyl gallate 99-24-1 C8H8O5 0.1841 475.15 27.27 146.71 313–333 10–50 27 Murga et al. (2002)

Methylparaben 99-76-3 C8H8O3 0.1521 404.15 23.20 84.41 308–348 12–36 40 Asghari-Khiavi and Yamini (2003)

Phenol 108-95-2 C6H6O 0.0941 323.15 14.30 61.71 308 7–25 25 Van Leer and Paulaitis (1980)

4-Phenyl 92-69-3 C12H10O 0.1702 439.15 19.43 93.64 308 10–28 7 Ravipaty et al. (2006)

Propyl gallate 121-79-9 C10H12O5 0.2122 403.15 29.11 156.59 313–333 15–25 8 Cortesi et al. (1999)

Pyrocatechol 120-80-9 C6H6O2 0.1101 377.75 16.71 91.50 308–363 10–41 65 Garcı´a-Gonza´lez et al. (2001) Yamini et al. (1998)

Salicylic acid 69-72-7 C7H6O3 0.1381 432.15 21.61 89.33 308–328 8–28 104 Gurdial and Foster (1991) Ke et al. (1996) Lucien and Foster (1996) Ravipaty et al. (2008) Stassi et al. (2000)

Syringic acid 530-57-4 C9H10O5 0.1982 477.65 30.95 105.44 313–333 10–50 26 Murga et al. (2004)

2,3,5-Trimethyl phenol 697-82-5 C9H12O 0.1362 367.65 18.38 75.84 308 10–28 7 Ravipaty et al. (2006)

2,4,6-Trimethyl phenol 527-60-6 C9H12O 0.1362 346.15 17.31 75.84 308 10–24 6 Ravipaty et al. (2006)

Vanillic acid 121-34-6 C8H8O4 0.1681 484.65 27.82 97.38 313–333 8–50 28 Murga et al. (2004)

Vanillin 121-33-5 C8H8O3 0.1521 354.65 20.36 91.11 313–353 8–28 34 Sˇkerget et al. (2005)

2,3-Xylenol 526-75-0 C8H10O 0.1222 345.65 17.28 71.13 308 10–28 7 Ravipaty et al. (2006)

2,5-Xylenol 95-87-4 C8H10O 0.1222 347.95 17.40 71.13 308 7–28 15 Ravipaty et al. (2006) Iwai et al. (1990)

3,4-Xylenol 95-65-8 C8H10O 0.1222 338.15 16.91 71.13 308 8–27 7 Mori et al. (1992) Steroids

Beclomethasone 5534-09-8 C28H37ClO7 0.5210 391.15 36.92 219.93 338–358 21–39 21 Vatanara et al. (2005) dipropionate

Budesonide 51333-22-3 C25H34O6 0.4305 499.15 36.04 200.48 338–358 21–39 21 Vatanara et al. (2005)

Cholesterol 57-88-5 C27H46O 0.3867 421.65 35.12 149.06 313–333 10–25 24 Huang et al. (2004)

Cholesteryl acetate 604-35-3 C29H48O2 0.4287 388.65 36.69 144.68 308–328 9–24 24 Huang et al. (2004)

Cholesteryl benzoate 604-32-0 C34H50O2 0.4908 424.45 41.64 171.90 308–328 12–27 20 Huang et al. (2004)

Cholesteryl butyrate 521-13-1 C31H52O2 0.4568 372.15 40.64 154.56 308–328 10–24 20 Huang et al. (2004)

Cyproterone acetate 427-51-0 C24H29ClO4 0.4169 473.65 28.94 156.82 308–348 12–36 40 Asghari-Khiavi et al. (2004)

Medroxyprogesterone 71-58-9 C24H34O4 0.3865 480.65 29.37 146.13 308–348 11–36 48 Asghari-Khiavi et al. (2004) acetate Alessi et al. (1996)

Progesterone 57-83-0 C21H30O2 0.3145 402.15 20.11 119.47 313–333 9–24 11 Alessi et al. (1996)

Stigmasterol 83-48-7 C29H48O 0.4127 443.15 36.91 155.94 308–333 9–31 19 Wong and Johnston (1986) [()TD$FIG] C.-S. Su et al. / Journal of the Taiwan Institute of[()TD$FIG] Chemical Engineers 42 (2011) 608–615 611

2.0 2.1

Opimally fitted valuevalve Opimally fitted valuevalve 1.8 Correlation result 2.0 Correlation result

1.6 1.9

1.4 1.8 1.2 * * 1.7 2 2 V V 1.0 ln ln 1.6 0.8 OH 1.5 0.6

0.4 1.4 O O O O 0.2 1.3 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 lnρ lnρ r,1 r,1

Fig. 1. Plot of optimally fitted dimensionless molar volume of (2) in Fig. 2. Plot of optimally fitted dimensionless molar volume of cholesteryl butyrate supercritical carbon dioxide (1) against the reduced density of pure carbon dioxide. (2) in supercritical carbon dioxide (1) against the reduced density of pure carbon dioxide.

relative deviation in solid solubility (AADY) over all data points: 3.2. Correlation results Xn exp cal 100 jy y2;kj The solid solubilities of phenolic compounds and steroids in AADY ¼ 2;k (13) n yexp k¼1 2;k supercritical CO2 were correlated using Eq. (4). The molar volume of the solid solute in supercritical CO (V ) was taken as an 2 2 where n, ycal and yexp are number of data points, calculated solid adjustable parameter. For each solid solubility data point at given 2;k 2;k solubility value and experimental solid solubility data for a specific temperature and pressure, one V value was determined from Eq. 2 solid solute, respectively. (4). A dimensionless molar volume of solute was defined in this Table 2 presents the optimally fitted value of a* and b* in Eq. study: (12) for phenolic compounds and steroids. By applying the two- parameter solution model, the grand AADY was 7.89% and 13.15% V ¼ V r (11) 2 2 c;1 for phenolic compounds and steroids, respectively. Table 2 also lists the correlation results from the MST, Chrastil and Bartle For each solid solute, the values of ln V 2 at all experimental models. It is observed that the two-parameter solution model conditions were observed as a linear function of the logarithmic yielded comparable grand deviations to those of semi-empirical reduced densities of supercritical CO2 (ln rr,1). This is the similar equations for all solid solutes. Most of the solid compounds had trend reported in previous literature (Cheng et al., 2002; Iwai et al., AADY less than 20% that was within possible experimental 1992; Su and Chen, 2007, 2008). Fig. 1 presents a typical example accuracy. Fig. 3 shows the comparison of the calculated results for the plot of ln V 2 values of methylparaben against ln rr,1. A well of a phenolic compound, methyl gallate, using the two-parameter correlated linear function is observed and all other phenolic solution model and the MST model. It is observed that either model compounds listed in Table 1 had the same behavior with almost provided satisfactory accuracy. Fig. 4 presents the similar the same slope but different intercepts. Fig. 2 depicts this linear comparison for a steroid, cholesteryl acetate. It is again confirmed correlation result for a typical steroid of cholesteryl butyrate. It is that the solution model with only 2 parameters resulted in again found that all the steroids listed in Table 1 showed the acceptable accuracy. similar linear behavior but with different slopes than that of the A further simplification for the solution model parameters was phenolic compounds. This linear behavior was mathematically attempted by setting either a*orb* in Eq. (12) as a constant. It was expressed in a dimensionless form as: observed that different categories of solid solutes had their best fitted a*orb* constant. For phenolic compounds and steroids in lnV 2 ¼ a lnrr;1 þ b (12) this study, it is found that the dimensionless solution model parameter a* was better taken as a constant. The best fitted a* where a* and b* were two dimensionless and temperature values are reported as 1.2383 for phenolic compounds and independent parameters for each solid solute. This linear behavior 1.1649 for steroids, respectively. Once the a* value was fixed, b* was an important progress in applying the solution model. Firstly, was left as the only adjustable parameter. This is defined as the it reduced the number of model parameters to 2 while most of one-parameter model. Data regression was again conducted with a other semi-empirical models had 3 or more parameters. Secondly, constant a*, and the optimally fitted b* values are presented also in the slope in the linear correlation for a specific category of solid Table 2 for the one-parameter model. It is noticed that with only solutes was almost a constant. The number of adjustable one adjustable parameter in the solution model, the phenolic parameters could further be reduced and prediction of solid compounds and steroids had AADY of 11.51% and 17.18%, solubility could be possible. respectively. More than 80% of these compounds had AADY less These two temperature-independent parameters were fitted than 20% with the simplification of model parameters. Fig. 5 from experimental data by minimizing the average absolute demonstrates the comparison of two- and one-parameter solution 612 C.-S. Su et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 608–615

Table 2 Correlation results of solid solubility using various models.

Compound Solution model Semi-empirical model

Two-parameter One-parameter MST Chrastil Bartle

a* b* AADY (%) b* AADY (%) AADY (%) AADY (%) AADY (%)

(a*=1.2383) Phenolic compounds 4-tert-Butylphenol 1.1954 1.3867 1.93 1.4124 3.72 0.59 1.82 0.59 Dodecyl gallate 1.3351 2.3569 9.52 2.3033 25.00 3.81 4.21 2.76 Ethylvanillin 1.2178 1.6657 20.34 1.6772 21.62 17.09 18.77 15.37 o-Ethylvanillin 1.1997 1.7352 12.47 1.7568 17.78 11.84 11.10 10.23 Ferulic acid 1.2105 1.3952 4.73 1.4096 7.10 6.49 4.94 7.25 Methyl gallate 1.2539 1.8304 12.97 1.8206 13.35 8.75 10.65 10.13 Methylparaben 1.2782 1.3094 12.12 1.2864 13.62 9.29 9.47 11.12 Phenol 1.2921 1.1625 2.29 1.1314 6.10 8.07 2.30 8.07 4-Phenyl phenol 1.2072 1.3783 3.10 1.3974 3.84 5.41 3.30 5.41 Propyl gallate 1.3251 2.0268 3.12 1.9779 14.39 4.80 3.43 5.60 Pyrocatechol 1.2811 1.5036 16.83 1.4864 18.16 15.21 13.39 11.43 1.2277 1.4403 13.20 1.4440 13.32 9.92 9.95 9.77 Syringic acid 1.1279 1.3495 8.15 1.4110 25.47 6.70 6.94 7.90 2,3,5-Trimethyl phenol 1.2645 1.3630 2.03 1.3482 2.28 0.70 1.87 0.70 2,4,6-Trimethyl phenol 1.2403 1.4771 0.91 1.4759 0.98 1.59 0.85 1.59 Vanillic acid 1.2134 1.3968 11.84 1.4146 12.31 11.45 10.29 11.86 Vanillin 1.2681 1.5640 15.52 1.5520 17.29 18.19 16.04 17.49 2,3-Xylenol 1.1319 1.2670 1.92 1.3256 7.78 4.24 2.00 4.24 2,5-Xylenol 1.2348 1.3198 3.42 1.3213 3.48 4.57 3.96 4.57 3,4-Xylenol 1.2604 1.2823 1.48 1.2685 2.53 8.63 1.70 8.63 Grand average deviation 7.89 11.51 7.87 6.85 7.74 (a*=1.1649) Steroids Beclomethasone-17,21-dipropionate 1.2338 2.3900 13.65 2.3544 16.96 10.66 10.77 10.58 Budesonide 1.2011 2.3445 11.62 2.3273 13.49 11.16 11.47 11.14 Cholesterol 1.2041 2.0519 7.48 2.0330 11.20 6.25 6.00 5.87 Cholesteryl acetate 1.1727 2.0605 12.61 2.0577 12.81 9.40 10.07 8.28 Cholesteryl benzoate 1.1804 2.1853 8.20 2.1774 8.46 6.85 6.74 6.65 Cholesteryl butyrate 1.1385 2.1109 10.03 2.1223 12.28 7.38 6.43 6.53 1.0365 2.0331 28.58 2.1011 34.69 17.18 17.51 18.06 acetate 1.1658 2.0434 17.02 2.0428 17.04 16.85 17.50 17.61 1.0825 1.7262 5.07 1.7589 24.31 8.61 3.90 6.24 Stigmasterol 1.2338 2.0820 17.23 2.0438 20.59 12.34 13.28 13.17 Grand average deviation 13.15 17.18 10.67 10.37 10.41 model for a phenolic compound, vanillic acid. It is observed that even one-parameter solution model yielded larger AADY values in with a single adjustable parameter, the solid solubility was comparison to the three-parameter semi-empirical models as satisfactorily correlated. Fig. 6 presents the other example for a shown in Table 2. The reduction of model parameters is still complex steroid compound, cholesterol. The calculated results using desirable for engineering application and for further generalization [()TD$FIG]the one-parameter solution model were again found acceptable. The [()TD$FIG]with the objective of prediction.

10-5 OH HO OH 10-3

O

O O O 10-6

10-4

y y 2 2

10-7 10-5 313.2 K 308.2 K 323.2 K 318.2 K 333.2 K 328.2 K This study, two-parameter model This study, two-parameter model MST model MST model 10-8 10-6 51525354555 8 12162024 P (MPa) P (MPa)

Fig. 3. Comparison of the experimental and calculated solubility for methyl gallate Fig. 4. Comparison of the experimental and calculated solubility for cholesteryl (2) in supercritical carbon dioxide (1) using the solution and MST models. acetate (2) in supercritical carbon dioxide (1) using the solution and MST models. [()TD$FIG] C.-S. Su et al. / Journal of the Taiwan Institute of[()TD$FIG] Chemical Engineers 42 (2011) 608–615 613

10-4 2.4 OH Opimally fitted valuevalve O 2.2 Correlation result

2.0 O OH

10-5 1.8

y β* 2 1.6

1.4 313.2 K 323.2 K 333.2 K -6 1.2 10 This study, two-parameter model This study, one-parameter model 1.0 51525354555 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 P (MPa) ln(ΔU vap/RT ) 2 m,2

Fig. 5. Comparison of the experimental and calculated solubility for vanillic acid (2) Fig. 7. Plot of the optimally fitted parameter b* against the physical property of solid in supercritical carbon dioxide (1) using the one- and two-parameter solution solute for various phenolic compounds. models.

3.3. Generalization results found the similar generalization of b* parameters: The single dimensionless solution model parameters b* were DUvap b ¼ 0:9408 ln 2 1:7982 (15) further generalized with dimensionless property of each solid RTc;1 solute listed in Table 1. We found that the dimensionless internal energy change on vaporization was the best parameter for It was observed that the constants in the generalization generalization. For the phenolic compound, the following general- equations were dependent on the nature of category. It is also ization equation was obtained: noticed that Tc,1 was more suitable for steroids, instead of Tm,2 for phenolic compounds, in expressing the dimensionless form of vap DU internal energy of vaporization. Fig. 8 shows the generalization of b ¼ 1:0309ln 2 1:9657 (14) RTm;2 b* for steroids in this study. This linear correlation was again acceptable for the complex structures of steroid pharmaceuticals.

Fig. 7 presents the graphical generalization results for phenolic The solid solubility in supercritical CO2 were predicted using compounds in this study. Generally, the b* values showed the constant value of a* and the generalized equation of b* for each acceptable correlation with the dimensionless properties of pure category of solid solutes. This is defined as the prediction model of solid solutes. For the other category of steroids in this study, we this study. The dash curves in Fig. 9 present the typical results from [()TD$FIG] [()TD$FIG]

2.5

Opimally fitted valuevalve 2.4 Correlation result 10-4

HO 2.3

2.2

2.1 y * 2 10-5 β

2.0

313.2 K 318.2 K 1.9 323.2 K This study, two-parameter model 1.8 10-6 This study, one-parameter model

81216202428 1.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 P (MPa) ln(ΔU vap/RT ) 2 c,1 Fig. 6. Comparison of the experimental and calculated solubility for cholesterol (2) in supercritical carbon dioxide (1) using the one- and two-parameter solution Fig. 8. Plot of the optimally fitted parameter b* against the physical property of solid models. solute for various steroids. 614[()TD$FIG] C.-S. Su et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 608–615

-2 10 one data point adjustment method. The solid curves in Fig. 9 OH present the results from one data point adjustment method with OH significant improvement in solid solubility calculation. The similar trend was observed for steroids in this study. Fig. 10 shows the calculation results using either the predictive model or one data point adjustment method for a steroid compound of cholesteryl benzoate. The dash curves had an AADY of 50%. With one experimental data for adjustment, the solubilities of this complex pharmaceutical compound at all three temperatures showed an 10-3 y AADY of 25%. 2 The solution model yielded comparable calculation results for

solid solubilities in supercritical CO2 to other semi-empirical models. The solution model needs less adjustable parameters, and 308.2 K provides acceptable results for the generalization of model 318.2 K 328.2 K parameters in dimensionless forms. The generalization of param- One data point Predictive adjustment model method I eters was applicable for each category of solids with specific Predictive model Predictive model II chemical structures or pharmaceutical functions. It provides 10-4 advantages for engineering process design and evaluation. 10 15 20 25 30 35 40 45

P (MPa) 4. Conclusion

Fig. 9. Comparison of the experimental and calculated solubility for pyrocatechol (2) in supercritical carbon dioxide (1) using the predictive models and the one data The solid solubilities in supercritical CO2 for two categories of point adjustment method. phenolic compounds and steroids were correlated using the solution model. Satisfactory correlation results for solid solubilities were obtained from the solution model with comparable accuracy the prediction model for a phenolic compound, pyrocatechol. The to commonly used semi-empirical equations. The solution model AADY of this prediction was 31.87%. For all phenolic compounds has only 2 dimensionless adjustable parameters * and *. investigated in this study, one thirds of the solid solutes had a b Parameter * was further fixed for a given category of solid predicted AADY less than 50%. The other one thirds had AADY from a solutes. The one-parameter solution model still yielded acceptable 60 to 100%. The similar results were observed for steroids in this accuracy. The generalization of the other solution model parame- study. ter b* was investigated in this study. Linear type generalization equations for two categories of solid solutes are reported. With the 3.4. Calculation of solid solubility using a single experimental generalization of solution model parameters, acceptable predic- data point tion for solubilities of complex pharmaceutical compounds in supercritical CO was presented. As we have suggested in our previous study (Su and Chen, 2 2008), the prediction can be improved by using one experimental data point to determine a temperature-independent b* value for a Acknowledgement specific solid solute. Taking pyrocatechol as an example, one experimental solubility data at the lowest temperature and The authors are grateful to the support of National Science pressure[()TD$FIG] was used to evaluate its b* value. This was defined as Council, Taiwan, ROC for this study.

10-4 References

Alessi, P., A. Cortesi, I. Kikic, N. R. Foster, S. J. Macnaughton, and I. Colombo, ‘‘Particle

O Production of Steroid Drugs Using Supercritical Fluid Processing,’’ Ind. Eng. Chem. Res., 35, 4718 (1996). O Asghari-Khiavi, M. and Y. Yamini, ‘‘Solubility of the Drugs Bisacodyl, Methimazole, Methylparaben, and Iodoquinol in Supercritical Carbon Dioxide,’’ J. Chem. Eng. Data, 48, 61 (2003). Asghari-Khiavi, M., Y. Yamini, and M. A. Farajzadeh, ‘‘Solubilities of Two Steroid Drugs and Their Mixtures in Supercritical Carbon Dioxide,’’ J. Supercrit. Fluids, 30, 111 10-5 (2004). y Bartle, K. D., A. A. Clifford, S. A. Jafar, and G. F. Shilstone, ‘‘Solubilities of Solids and 2 Liquids of Low Volatility in Supercritical Carbon Dioxide,’’ J. Phys. Chem. Ref. Data, 20, 713 (1991).

Beckman, E. J., ‘‘Supercritical and Near-critical CO2 in Green Chemical Synthesis and Processing,’’ J. Supercrit. Fluids, 28, 121 (2004). 308.2 K Bush, D. and C. A. Eckert, ‘‘Prediction of Solid–fluid Equilibria in Supercritical Carbon 318.2 K Dioxide Using Linear Solvation Energy Relationships,’’ Fluid Phase Equilib., 150– 328.2 K 151, 479 (1998). One data point Predictive adjustment model method I Cheng, J. S., M. Tang, and Y. P. Chen, ‘‘Correlation of Solid Solubility for Biological Predictive model Predictive model II Compounds in Supercritical Carbon Dioxide: Comparative Study Using Solution Model and Other Approaches,’’ Fluid Phase Equilib., 194–197, 483 (2002). 10-6 Chrastil, J., ‘‘Solubility of Solids and Liquids in Supercritical Gases,’’ J. Phys. Chem., 86, 10 15 20 25 30 3016 (1982). ´ P (MPa) Cocero, M. J., A. Martı´n, F. Mattea, and S. Varona, ‘‘Encapsulation and Co-precipita- tion Processes with Supercritical Fluids: Fundamentals and Applications,’’ J. Supercrit. Fluids, 47,546(2009). Fig. 10. Comparison of the experimental and calculated solubility for cholesteryl Cortesi, A., I. Kikic, P. Alessi, G. Turtoi, and S. Garnier, ‘‘Effect of Chemical Structure on benzoate (2) in supercritical carbon dioxide (1) using the predictive models and the the Solubility of Antioxidants in Supercritical Carbon Dioxide: Experimental Data one data point adjustment method. and Correlation,’’ J. Supercrit. Fluids, 14, 139 (1999). C.-S. Su et al. / Journal of the Taiwan Institute of Chemical Engineers 42 (2011) 608–615 615

Ely, J. F., W. M. Haynes, and B. C. Bain, ‘‘Isochoric (P, Vm, T) Measurements on CO2 and Ravipaty, S., K. J. Koebke, and D. J. Chesney, ‘‘Polar Mixed-solid Solute Systems in on (0. 982 CO2 + 0. 018 N2) from 250 to 330 K at Pressures to 35 MPa,’’ J. Chem. Supercritical Carbon Dioxide: Entrainer Effect and Its Influence on Solubility and Thermodyn., 21, 879 (1989). Selectivity,’’ J. Chem. Eng. Data, 53, 415 (2008). Fedors, R. F., ‘‘A Method for Estimating both the Solubility Parameters and Molar Ravipaty, S., A. G. Sclafani, B. R. Fonslow, and D. J. Chesney, ‘‘Solubilities of Substituted Volumes of Liquids,’’ Poly. Eng. Sci., 14, 147 (1974). in Supercritical Carbon Dioxide,’’ J. Chem. Eng. Data, 51, 1310 (2006). Garcı´a-Gonza´lez, J., M. J. Molina, F. Rodrı´guez, and F. Mirada, ‘‘Solubilities of Phenol and Reverchon, E. and G. Della Porta, ‘‘Particle Design Using Supercritical Fluids,’’ Chem. Pyrocatechol in Supercritical Carbon Dioxide,’’ J. Chem. Eng. Data, 46, 918 (2001). Eng. Technol., 26, 840 (2003). Gurdial, G. S. and N. R. Foster, ‘‘Solubility of o-Hydroxybenzoic Acid in Supercritical Sˇkerget, M., L. Cˇretnik, Zˇ. Knez, and M. Sˇkrinjar, ‘‘Influence of the Aromatic Ring

Carbon Dioxide,’’ Ind. Eng. Chem. Res., 30, 575 (1991). Substituents on Phase Equilibria of Vanillins in Binary Systems with CO2,’’ Fluid Huang, Z., S. Kawi, and Y. C. Chiew, ‘‘Solubility of Cholesterol and Its Esters in Phase Equilib., 231, 11 (2005). Supercritical Carbon Dioxide with and without Cosolvents,’’ J. Supercrit. Fluids, Sovova´, H., ‘‘Solubility of Ferulic Acid in Supercritical Carbon Dioxide with Ethanol as 30, 25 (2004). Cosolvent,’’ J. Chem. Eng. Data, 46, 1255 (2001). Iwai, Y., Y. Koga, T. Fukuda, and Y. Arai, ‘‘Correlation of Solubilities of High-boiling Sparks, D. L., R. Hernandez, and L. A. Este´vez, ‘‘Evaluation of Density-based Models for Components in Supercritical Carbon Dioxide Using a Solution Model,’’ J. Chem. Eng. the Solubility of Solids in Supercritical Carbon Dioxide and Formulation of a New Jpn., 25, 757 (1992). Model,’’ Chem. Eng. Sci., 63, 4292 (2008). Iwai, Y., H. Yamamoto, Y. Tanaka, and Y. Arai, ‘‘Solubilities of 2,5- and 2,6-Xylenols in Stassi, A., R. Bettini, A. Gazzaniga, F. Giordano, and A. Schiraldi, ‘‘Assessment of

Supercritical Carbon Dioxide,’’ J. Chem. Eng. Data, 35, 174 (1990). Solubility of Ketoprofen and Vanillic Acid in Supercritical CO2 under Dynamic Ke, J., C. Mao, M. Zhong, B. Han, and H. Yan, ‘‘Solubilities of Salicylic Acid in Supercritical Conditions,’’ J. Chem. Eng. Data, 45, 161 (2000). Carbon Dioxide with Ethanol Cosolvent,’’ J. Supercrit. Fluids, 9, 82 (1996). Su, C. S. and Y. P. Chen, ‘‘Correlation for the Solubilities of Pharmaceutical Compounds Lucien, F. P. and N. R. Foster, ‘‘Influence of Matrix Composition on the Solubility of in Supercritical Carbon Dioxide,’’ Fluid Phase Equilib., 254, 167 (2007). Hydroxybenzoic Acid Isomers in Supercritical Carbon Dioxide,’’ Ind. Eng. Chem. Su, C. S. and Y. P. Chen, ‘‘Measurement and Correlation for the Solid Solubility of Non- Res., 35, 4686 (1996). steroidal Anti-inflammatory Drugs (NSAIDs) in Supercritical Carbon Dioxide,’’ J. Martı´n, A. and M. J. Cocero, ‘‘Micronization Processes with Supercritical Fluids: Supercrit. Fluids, 43, 438 (2008). Fundamentals and Mechanism,’’ Adv. Drug Deliv. Rev., 60, 339 (2008). Teja, A. S. and C. A. Eckert, ‘‘Commentary on Supercritical Fluids: Research and Me´ndez-Santiago, J. and A. S. Teja, ‘‘The Solubility of Solids in Supercritical Fluids,’’ Applications,’’ Ind. Eng. Chem. Res., 39, 4442 (2000). Fluid Phase Equilib., 158–160, 501 (1999). Van Leer, R. A. and M. E. Paulaitis, ‘‘Solubilities of Phenol and Chlorinated Phenols in Mori, Y., T. Shimizu, Y. Iwai, and Y. Arai, ‘‘Solubilities of 3,4-Xylenol and Naphtha- Supercritical Carbon Dioxide,’’ J. Chem. Eng. Data, 25, 257 (1980). lene + 2,5-Xylenol in Supercritical Carbon Dioxide at 35 8C,’’ J. Chem. Eng. Data, 37, Vatanara, A., A. R. Najafabadi, M. Khajeh, and Y. Yamini, ‘‘Solubility of Some Inhaled 317 (1992). Glucocorticoids in Supercritical Carbon Dioxide,’’ J. Supercrit. Fluids, 33, 21 (2005). Murga, R., M. T. Sanz, S. Beltra´ n, and J. L. Cabezas, ‘‘Solubility of Some Phenolic Wong, J. M. and K. P. Johnston, ‘‘Solubilization of Biomolecules in Carbon Dioxide Based Compounds Contained in Grape Seeds, in Supercritical Carbon Dioxide,’’ J. Super- Supercritical Fluids,’’ Biotechnol. Prog., 2, 29 (1986). crit. Fluids, 23, 113 (2002). Yalkowsky, S. H., ‘‘Estimation of Entropies of Fusion of Organic Compounds,’’ Ind. Eng. Murga, R., M. T. Sanz, S. Beltra´ n, and J. L. Cabezas, ‘‘Solubility of Syringic and Vanillic Chem. Fundam., 18, 108 (1979). Acids in Supercritical Carbon Dioxide,’’ J. Chem. Eng. Data, 49, 779 (2004). Yamini, Y., M. R. Fat’hi, N. Alizadeh, and M. Shamsipur, ‘‘Solubility of Dihydroxyben- Pasquali, I., R. Bettini, and F. Giordano, ‘‘Solid-state Chemistry and Particle Engineering zene Isomers in Supercritical Carbon Dioxide,’’ Fluid Phase Equilib., 152, 299 (1998). with Supercritical Fluids in Pharmaceutics,’’ Eur. J. Pharm. Sci., 27, 299 (2006). Zhong, M., B. Han, J. Ke, H. Yan, and D. Y. Peng, ‘‘A Model for Correlating the Solubility of

Peng, D. Y. and D. B. Robinson, ‘‘A New Two-constant Equation of State,’’ Ind. Eng. Chem. Solids in Supercritical CO2,’’ Fluid Phase Equilib., 146, 93 (1998). Fundam., 15, 59 (1976).