Solubility Measurement of Diclofenac Acid in the Supercritical CO2

Article pubs.acs.org/jced

Solubility Measurement of Diclofenac Acid in the Supercritical CO2 Ali Zeinolabedini Hezave and Feridun Esmaeilzadeh*,† School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345-1719, Iran ABSTRACT: The equilibrium solubility of the diclofenac acid in supercritical carbon dioxide was determined with a static method. The measurements were performed at pressures ranging from (120 to 400) bar and temperatures from (308.15 to 338.15) K. The results show that diclofenac acid solubility was increased by increasing pressure. The experimental solubility data were well correlated with enhanced density-based models including the Chrastil model, Méndez-Santiago and Teja model, Kumar and Johnston model, and the Bartle and co-workers model with an average absolute relative deviation (AARD) of 8.7 %, 6.6 %, 7.2 %, and 9.7 %, respectively. In addition, the solubility data satisfied the self-consistency test, proposed by Méndez-Santiago and Teja.

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INTRODUCTION In the past three decades, there has been considerable interest in the use of supercritical fluid extraction (SFE) as an alternative to conventional procedures for the preparation of samples for analysis. Supercritical carbon dioxide has received ever-increasing attention since it can be potentially used to replace conventional toxic liquid solvents in both analytical applications and engineering processes. In fact, supercritical fluid technology has been successfully commissioned for caffeine, tea, spices, hops, and flavor extraction processes on a large commercial scale in USA and Europe.1 Among the factors that affect the development of the SCF extraction processes and other SCF technologies, knowledge of supercritical solubility data has been frequently highlighted.1−3 The design of chemical and pharmaceutical processes based on SCFs and the determination of their best operating conditions require knowledge of phase equilibria and drug solubility in a supercritical fluid. In the last two decades, the solubility of a large number of different low-volatility compounds in SCFs has been measured, reported, and reviewed.4−15 However, the development of new supercritical processes and new applications for existing substances has maintained the need for new experimental solubility determinations. SCFs have been used in synthesis of drugs,16 and several methods of drug synthesis in supercritical carbon dioxide (SC− CO2) have been reported.17 The knowledge of the equilibrium solubility of the drugs in SC−CO2 is a critical parameter in the design of both extraction and synthetic processes. The solubilities of various pharmaceutical compounds in SC−CO2 have been determined.3−6,8−10,12,15 However, the solubilities of diclofenac acid have not been reported. Diclofenac acid is from a family of nonsteroidal anti-inflammatory drugs. Diclofenac acid is taken to reduce inflammation and as an analgesic reducing pain in conditions such as arthritis or acute injury. © 2012 American Chemical Society

Both equation of state (EOS) based models and semiempirical models are commonly used for the correlation of solids in SC−CO2. In the EOS approach, the sublimation pressure, molar volume in solid form, and the critical properties of the solute are required. For complex solids, the EOS method is usually limited due to these uncertain data. Therefore semiempirical models are often utilized in correlating solubilities of solids in SC−CO2.18−21 Although there are several semiempirical equations in the literature, the best equation to correlate the solubilities of pharmaceutical compounds in SCFs varies from study to study. Recently, in an extensive work, Tabernero et al.22 have compared the solubilities of 27 pharmaceutical compounds with the 9 most used semiempirical equations. These nine models are the Chrastil model,18 Mendez-Santiago and Teja model,19 Bartle model,20 Gordillo model,21 del Valle and Aguilera (VA) model,23 Adachi and Lu (AL) model,24 Sparks model,25 Kumar and Johnston (KJ) model,26 and the YU model.27 The best correlation was obtained by the Gordillo and Sparks’s model, while the Sparks and other equations are density based models, the equation proposed by Gordillo includes pressure and temperature as parameters. This is because the solubility shows a curvilinear behavior with pressure at constant temperature and with temperature at constant pressure.26 In this work, the solubilities of diclofenac acid in supercritical carbon dioxide were determined by using a static method combined with gravimetric analysis over a wide range of pressures (120 to 400) bar and temperatures at (308.15, 318.15, 328.15, and 338.15) K. The measured solubility data are modeled with different empirical and semiempirical correlations including the Mendez-Santiago-Teja,19 Chrastil,18 Received: October 11, 2011 Accepted: March 2, 2012 Published: May 7, 2012 1659

dx.doi.org/10.1021/je200012x | J. Chem. Eng. Data 2012, 57, 1659−1664

Journal of Chemical & Engineering Data

Article

Table 1. Physio-Chemical Properties of the Diclofenac Acid

Figure 1. Solubility measurement apparatus.

Bartle et al.,20 and Kumar and Johnston26 models to describe the diclofenac acid−CO2 binary systems.

free high pressure manual pump (Haskel Pump, USA) to the desired pressure. The pressure in the displacer was monitored by a bourdon gauge pressure with a range of (0 to 450) bar (DEWIT) with the division of 1 bar. The homemade variable volume equilibrium cell was wrapped by a circulating oil jacket making it possible to control the system temperature at the desired level. The temperature of the cell was controlled by a feedback controller connected to the PT-100 controller with precision of ± 1 K. Also, the pressure of the equilibrium cell was monitored by a digital pressure gauge (WIKA, 3769867) ranged up to 400 bar with the division of 0.1 bar. The system pressure of each experiment was maintained to within ± 0.5 % of the desired pressure. The equilibrium cell was rated for pressures of 600 bar at 673.15 K. It was made of stainless steel 316 with an internal volume of 30 cm3 equipped with a sapphire window. All of the process tubing used in this apparatus was 1/8 inch O.D. tubing made of stainless steel 316. One gram of diclofenac acid powder was compacted in a compactor instrument (Compactor, T555228, MELLAT MASHIN SAZI Company, Iran) under a pressure of 20 bar to change the powder to a tablet with a diameter of 5 mm. This tablet wrapped with tissue was then exposed to the SC−CO2 in the equilibrium cell. In this study, the compacted drug powder in the equilibrium cell was held at constant desired pressure and temperature for about 2.5 to 3 h to ensure equilibrium was reached. The

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EXPERIMENTAL SECTION Materials. The drugs, diclofenac acid, and piroxicam (see Table 1) were supplied by Alma Concept Company (France) and were used without any further purification. The purity of the diclofenac acid and piroxicam were 96.4 % and 97.1 %, respectively, which were obtained using a HPLC instrument (KNAUER). In brief, the separation was performed using a mixture containing 30 volumes, of equal volumes of a 0.1 % w/ v solution of orthophosphoric acid and a 0.16 % w/v solution of sodium dihydrogen orthophosphate (adjusted to pH 2.5), was prepared with 70 volumes of methanol at a flow rate of 0.2 mL/ min additionally; the main chromatographic temperature was kept constant at 45 °C. Also, carbon dioxide (99.8 % < purity) was purchased from Abughadareh Industrial Gas Company (Iran) and used as the solvent for all extractions. The molecular structures and properties of drugs used are shown in Table 1. Experimental Apparatus and Procedure for the Solid Solubility. A static solubility measurement apparatus (see Figure 1) was used to measure the solubility of diclofenac acid. The set up consisted of two main parts: (1) supplying supercritical CO2 and (2) keeping equilibrium between solid and supercritical CO2. CO2 first entered the displacer, and it was then pressurized by means of a reciprocating oil-free water1660



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equilibrated solution was then rapidly depressurized through two valves simultaneously. After that, the sample was reweighted, and the difference between the initial and final mass of the drug was considered as the solubilized drug per cell volume of gas at standard conditions. The mass of solute was determined to 0.1 mg using a Sartorius BA110S Basic series balance. The typical mass of solute for each experiment was greater than 50 mg, giving a potential error due to weighing of 0.2 wt %. Melting Point Measurement. The melting point of the diclofenac particles was evaluated by using an Electrothermal Melting point apparatus (IA9200/MK4). The glass capillary tubes were fulfilled with 10 mg of samples. The samples were heated from 45 to 250 °C. The used heating rate was 0.2 °C/ min, in 0.1 °C increments, and the temperature range was (35 to 200) °C.

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Figure 2. Plotted solubility data of diclofenac acid at different pressures and temperatures.

RESULTS AND DISCUSSION The reliability of the apparatus was preliminarily checked by measuring the solubility (mole fraction, y) of piroxicam in supercritical carbon dioxide at 312.15 K, and the results are listed in Table 2. The values given in Table 2 are obtained from

Table 3. Solubility Data of the Diclofenac Acid at Different Pressures and Temperatures (mol solute/mol CO2) temp (K)

Table 2. Comparison of the Obtained Solubilities of Piroxicam with Solubilities Reported with Other Literature temp (K)

pressure (bar)

Macnaughton et al. data (ref 28) solubility (mol solute/mol CO2)

this work solubility (mol solute/mol CO2)

312.15 312.15 312.15 312.15

100 130 160 190

1.30·10−5 2.08·10−5 3.12·10−5 4.41·10−5

1.21·10−5 1.92·10−5 2.92·10−5 4.23·10−5

pressure (bar)

308.15

318.15

328.15

338.15

120 160 200 240 280 320 360 400

4.01·10−5 7.45·10−5 1.01·10−4 1.23·10−4 1.63·10−4 1.68·10−4 1.98·10−4 2.23·10−4

5.23·10−5 1.34·10−4 1.92·10−4 2.38·10−4 3.23·10−4 3.78·10−4 4.36·10−4 5.21·10−4

2.34·10−5 1.53·10−4 2.87·10−4 4.64·10−4 5.87·10−4 7.21·10−4 8.98·10−4 1.01·10−3

2.35·10−5 1.56·10−4 3.87·10−4 6.54·10−4 9.34·10−4 1.31·10−3 1.62·10−3 1.98·10−3

temperature. However, the solute sublimation effect becomes dominant at higher pressure than the crossover pressure, and the density of the solvent turns less sensitive to the pressure, hence the solubility increases as temperature rises. The existence of a crossover pressure in solid-SF systems has been suggested as an indication of the reliability and consistency of experimental solubility data.31 Subsequent graphical representations of y versus P are most helpful to understand the exact meaning of the crossover region. Modeling Results. Modeling of solubility especially using EOS seems to be difficult because of the lack of knowledge of the physical properties. In other words, as aforementioned, critical properties, sublimation pressure, and molar volume of the solutes are necessary, while the experimental measurements of these values are scarce and difficult or impossible in some cases. Although, using some predictive tools such as group contribution methods showed great feasibility of these methods for the physiochemical properties estimation, but their predicted values have deviations in comparison to the experimental ones, consequently make errors in the modeling. Because of the lack of information on the thermo-physical data of the substances, the correlation of solubility data is, quite often, done using simple empirical correlations such as densitybased correlations. These empirical models are based on simple error minimization using least-squares methods, and for the majority of them, there is no need to use the estimated thermophysical properties. The most commonly used model is the Chrastil’s model,18 which correlates the solubility of a solute in a supercritical solvent to the density and temperature. This model is based on the hypothesis that each molecule of a solute associates with k molecules of a supercritical solvent to form a

an arithmetic average of three replicate measurements with relative standard deviations less than 5.8 %. This deviation is indicative of the reliability of the method used and the expected accuracy of experimental results obtained. This deviation occurs because the individual equipment errors contribute to the overall error (i.e., pressure, temperature, mass, and volume). In other words, this deviation is due to random experimental errors associated with the difficulties of working with high-pressure supercritical fluids. The solubility of diclofenac acid in supercritical CO2 at (308.15, 318.15, 328.15, and 338.15) K were measured at pressures ranging from (120 to 400) bar (see Figure 2). The solubility results obtained are presented in Table 3 and shown graphically in Figure 2. From the data given in Table 3, it is readily observed that the diclofenac acid solubility increases with increasing pressure at constant temperature, following expected trends. This trend was observed for all four temperatures. The reason for this is that the solvent density increased and that the mean intermolecular distance of the carbon dioxide molecules decreased, thereby increasing the specific interaction between the solute and solvent molecules. At higher temperature, the solubility increases much more rapidly with increasing pressure, but temperature affects the solubility through two competing factors: solute sublimation (i.e., vapor pressure) and SCF solvent density.1,29,30 These two temperature dependent factors lead to the crossover pressure between solubility isotherms. It means that at pressures lower than the crossover pressure, the density effect, sensitive to the pressure, is dominant; the solute is more soluble at low 1661



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Table 4. Obtained Fitting Constants and Sublimation Enthalpy for Four Density-Based Correlations constant model

a

correlation

b

c

ΔHsub (kJ·mol−1) 98.29

Bartle

⎛ y p⎞ ln⎜⎜ 2ref ⎟⎟ = a + (b/T(K)) + c(ρ − ρref ) ⎝p ⎠

32.3

−11805.4

0.013

Mendez-Santiago−Teja

⎛ y p⎞ T ln⎜⎜ 2ref ⎟⎟ = a + bT(K) + cρ(kg·m−3) ⎝p ⎠

−15818

35.816

4.1364

Kumar and Johnston

ln y = a + (b/T(K)) + cρ(kmol ·m−3)

15.834

−10081

0.3876

83.94

−21.109

−9448.3

7.5802

78.67

Chrastil

−3

−3

ln s(kg·m ) = a + (b/T(K)) + c ln ρ(kg·m )

equation that follows a simple relationship for the solubility of solids in supercritical fluids was deduced.

solvate complex, which is in equilibrium with the system. The Chrastil relationship between solubility and density can be expressed as ln s(kg· m−3) = a + (b /T (K)) + C ln ρ(kg· m−3)

T ln(y2 p /p2 sub ) = A + cρ

(1)

(2)

where T is the temperature, y2 is the solubility of the compound in terms of mole fraction, p is the pressure, p2sub is the sublimation pressure of the solid at temperature T, ρ is the density of the fluid, and A and c are constants independent of temperature. Because the sublimation pressures are not often available, a Clausius−Clapeyron type expression for the sublimation pressure was incorporated, and a semiempirical relationship, with three adjustable parameters, for the solid solubility was derived.33

where the parameters a, b, and c are determined by fitting the correlation to experimental data. In this model, it is assumed that the molecule of a solute could associate with c molecules of supercritical solvent to form a solvate complex that is in equilibrium with the supercritical solvent. The solvate complex assumption is close to the cluster conception that the local composition around the solute molecules is to be enriched with solvent molecules and likely very different from the bulk solution.32 The parameter a, used to describe the solvation interaction, may not be an integral through the data regression. The total reaction heat ΔH (heat of solvation plus heat of vaporization of the solute) may be approximated by ΔH = −bR. The correlated results of solubilities of diclofenac acid with the Chrastil model are tabulated in Table 4. This density-based model performs very well for diclofenac acid with an AARD of 8.74 %. The correlations obtained by using the Chrastil model for diclofenac acid are plotted as ln y2 versus ln ρ, based on eq 1. As shown in Figure 3, a specific straight line is obtained for

T ln(y p /pstd ) = a + cρ + bT

(3)

The parameters of the Mendez-Santiago and Teja’s correlation are expressed as below: Values for a, b, and c were obtained by performing a multiple linear regression to T ln(y2p/pstd) as a function of ρ and T. The results of the multiple linear regression leads to find the parameters of a(−15818), b(35.816), and c(4.1364). The AADR % of the predicted solubilities with the MST model was about 6.55 %, which was the lowest AADR % between the four tested correlations in this study. The self-consistency tests were also examined for the experimental data using either the MST or Chrastil model. For the self-consistency test from the MST model, the experimental results of T ln(y2p/pstd) − cT was plotted against the density of supercritical CO2, and a linear curve should be observed. The self-consistency test result using the MST model is illustrated in Figure 4. The linear behavior shown in Figure 4 confirms that the measured solid solubility data are consistent at all experimental conditions. The correlated model parameters shown in Table 4 are thus feasible for data extrapolation. Another empirical density based model that was used is a model proposed by Bartle et al.20,34 ⎛ y p⎞ ln⎜⎜ 2ref ⎟⎟ = A + c(ρ − ρref ) ⎝p ⎠

Figure 3. Plotted experimental data and those obtained with the Chrastil model.

each isotherm. From the figure, the solubility is observed to increase monotonically and almost linearly with pure solvent density, i.e., SC−CO2 density.31 By performing a multiple linear regression on ln s as a function of ln ρ and 1/T, one obtains a (−21.109), b (−9448.3), and c (7.5802). Mendez-Santiago and Teja have presented another empirical model based on the theory of infinitely dilute solutions.19 An

(4)

where

A = a + b/T (K)

(5)

and ⎛ y p⎞ ln⎜⎜ 2ref ⎟⎟ = a + b/T (K) + c(ρ − ρref ) ⎝p ⎠ 1662

(6)



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Figure 5. Plotted experimental data and those obtained with the Bartle model.

Figure 4. Test of self-consistency for solubility of diclofenac acid in supercritical CO2 using the MST model.

ln y = a + (b/T (K)) + cρ(kmol ·m−3) ref

Again the parameters a, b, and c (see Table 4) are obtained by fitting the correlation to experimental data. Diclofenac acid solubilities ln y2 are plotted as a function of ln ρ in Figure 6.

where y2 is the mole fraction solubility, p is the pressure, p is a reference pressure of 1 bar, ρ is the density (taken as the density of pure CO2), ρref is a reference density for which a value of 700 kg·m−3 is used,20 and A and c are constant values for a given temperature. The reason for using ρref is to make the constant A much less sensitive to experimental errors in the solubility data. Also, to avoid the large variations caused by extrapolation to zero density, the value of c, which results physically from solvation of the solute by supercritical fluid, is assumed to remain constant over the entire temperature range studied. This point has already been reported by Bartle and coworkers.20,33 In the first step, the ln(y2p/pref) values were plotted against density, and the resulting plots were fitted to a straight line by least-squares regression to estimate A and c values. According to eq 4, the plots are expected to be reasonably straight lines with similar slopes. The values of c, obtained from the slopes of the corresponding plots, were then averaged for each compound (Table 4). By holding c at its average value, the experimental solubility data were then used to evaluate the A values at various temperatures for diclofenac acid. The plots of A versus 1/T for each compound resulted in a nice straight line from the intercept and slope of which the a and b values were obtained, respectively. The results of the a and b values are also reported in Table 4. Finally, having the values of a, b, and c parameters and considering the fact that the ρ values are known at any specific temperature and pressure, eq 6 can be used to evaluate the solubility, y, at any given temperature and pressure. Figure 5 compares the calculated isotherms with the experimental data for the drug. One can see that the Bartel method provides a rather good fit, with absolute average relative deviation (AARD) in the range of 9.69 % for drugs in different temperatures. The parameter b is approximately related to the enthalpy of sublimation of the solid solutes, ΔHsub, (Miller et al.35) by

ΔHsub = −Rb

(8)

Figure 6. Plotted experimental data and those obtained with the Kumar and Johnston model.

The figure indicates that the solubilities are almost linear functions of pure solvent density, i.e., SC−CO2 density.32 Also, the solubility is observed to increase monotonically with temperature as a result of vapor pressure effect. The % AARD obtained for diclofenac acid is about 7.18 %. At last, the sublimation enthalpies obtained from different used correlations were given in Table 4.

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CONCLUSIONS The equilibrium solubility of a pharmaceutical compound, diclofenac acid, in supercritical carbon dioxide (SC−CO2) was experimentally determined by a static method at (308.15, 318.15, 328.15, and 338.15) K, over the pressure range of (120 to 400) bar. The experimental standard deviation was less than 5.8 % on the basis of the average of three separate measurements for each experimental data. The solubility of the diclofenac acid under the different temperatures and pressures were in the range of 2.34·10−5 to 1.98·10−3. Because the solubilities depend on the solvent density and therefore the experimental binary solid−fluid equilibrium data were correlated as a function of solvent density. So, not only these

(7)

where R is the gas constant. The validity of eq 7 relies on the assumption that the enhancement factor ln(y2p/psub), where psub is the vapor pressure of the solute, is independent of temperature. Finally, the Kumar and Johnston model was used to correlate the experimental solubility data. The proposed correlation by Kumar and Johnston is another density based model as follows: 1663



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(14) Esmaeilzadeh, F.; Goodarznia, I. Supercritical extraction of phenanthrene in the crossover region. J. Chem. Eng. Data 2005, 50, 49−51. (15) Goodarznia, I.; Esmaeilzadeh, F. Solubility of an anthracene, phenanthrene, and carbazole mixture in supercritical carbon dioxide. J. Chem. Eng. Data 2002, 47, 333−338. (16) Subramaniam, B.; Rajewski, R. A.; Snavely, K. Pharmaceutical processing with supercritical carbon dioxide. J. Pharm. Sci. 1997, 86, 885−890. (17) Elvassore, N.; Kikic, I. Pharmaceutical Processing with Supercritical Fluids. In High Pressure Process Technology: Fundamentals and Applications; Bertucco, A., Vetter, G., Eds.; Elsevier Science: Amsterdam, The Netherlands, 2001; p 612. (18) Chrastil, J. Solubility of solids and liquids in supercritical gases. J. Phys. Chem. 1982, 86, 3016−3021. (19) Méndez-Santiago, J.; Teja, A. S. The solubility of solids in supercritical fluids. Fluid Phase Equilib. 1999, 158, 501−510. (20) Bartle, K. D.; Clifford, A. A.; Jafar, S. A.; Shilstone, G. F. Solubilities of solids and liquids of low volatility in supercritical carbon dioxide. J. Phys. Chem. Ref. Data. 1991, 20, 713−756. (21) Gordillo, M. D.; Blanco, M. A.; Molero, A.; Martinez de la Ossa, E. Solubility of solids and liquids in supercritical gases. J. Supercrit. Fluids. 1999, 15, 183−190. (22) Tabernero, A.; del Valle, E. M. M.; Galán, M. A. A comparison between semiempirical equations to predict the solubility of pharmaceutical compounds in supercritical carbon dioxide. J. Supercrit. Fluids. 2010, 52, 161−174. (23) del Valle, J. M.; Aguilera, J. M. An improved equation for predicting the solubility of vegetable oils in supercritical CO2. Ind. Eng. Chem. Res. 1988, 27, 1551−1553. (24) Adachi, Y.; Lu, B. C. Y. Supercritical fluid extraction with carbon dioxide and ethylene. Fluid Phase Equilib. 1983, 14, 147−156. (25) Sparks, D. L.; Hernandez, R.; Estévez, L. A. Evaluation of density-based models for the solubility of solids in supercritical carbon dioxide and formulation of a new model. Chem. Eng. Sci. 2008, 63, 4292−4301. (26) Kumar, S.; Johnston, K. P. Modelling the solubility of solids in supercritical fluids with density as the independent variable. J. Supercrit. Fluids 1988, 27, 1551−1553. (27) Yu, Z.; Singh, B.; Rizvi, S. S. H.; Zollewg, J. A. Solubilities of fatty acids, fatty acid esters, triglycerides, and fats and oils in supercritical carbon dioxide. J. Supercrit. Fluids 1994, 7, 51−59. (28) Macnaughton, S. J.; Kikic, I.; Foster, N. R.; Alessi, P.; Cortesi, A.; Colombo, I. Solubility of anti-inflammatory drugs in supercritical carbon dioxide. J. Chem. Eng. Data 1996, 41, 1083−1086. (29) Huang, Z.; Kawi, S.; Chiew, Y. C. Solubility of cholesterol and its esters in supercritical carbon dioxide with and without cosolvents. J. Supercrit. Fluids 2004, 30, 25−39. (30) Huang, Z.; Lu, W.-D.; Kawi, S.; Chiew, Y. C. Solubility of aspirin in supercritical carbon dioxide with and without acetone. J. Chem. Eng. Data 2004, 49, 1323−1327. (31) Foster, N. R.; Gurdial, G. S.; Yun, J. S. L.; Liang, K. K.; Tially, K. D.; Ting, S. S. T.; Singh, H.; Lee, J. H. Ind. Eng. Chem. Res. 1991, 30, 1955−1964. (32) Brennecke, J. F.; Eckert, C. A. Phase equilibria for supercritical fluid process design. AIChE J. 1989, 35, 1409−1427. (33) Sauceau, M.; Letourneau, J.-J.; Richon, D.; Fages, J. Enhanced denity-based models for solid compound solubilities in supercritical carbon dioxide with cosolvents. Fluid Phase Equilib. 2003, 208, 99− 113. (34) Safa-Ozcan, A.; Clifford, A. A.; Bartle, K. D. Solubility of disperse dyes in supercritical carbon dioxide. J. Chem. Eng. Data 1997, 42, 590−592. (35) Miller, D. J.; Hawthorne, S. B.; Clifford, A. A.; Zhu, S. Solubility of polycyclic aromatic hydrocarbons in supercritical carbon dioxide from 313 to 523 K and pressures from 100 to 450 bar. J. Chem. Eng. Data 1996, 41, 779−786.

measured solid solubilities were correlated by the semiempirical models of Mendez-Santiago−Teja and Chrastil but also two other density based models including the Kumar and Johnston model and the Bartle model were applied. The absolute average deviation (AARD %) in solid solubility from the semiempirical models, the MST model and the Chrastil model, were 6.55 % and 8.74 %, respectively, and from the density based models, the Kumar and Johnston model and the Bartle model, were 9.69 % and 7.18 %, respectively. In addition, the measured data satisfied the self-consistency test, proposed by Méndez-Santiago and Teja, and the optimally fitted parameters were reported.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +98 711 2303071. Fax: +98 711 6287294. E-mail: [email protected] or [email protected]. Present Address †

School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Shiraz University for supporting this research. REFERENCES

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Solubility Measurement of Diclofenac Acid in the Supercritical CO2

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