Measurement and correlation of the solubility of two steroid drugs in supercritical carbon dioxide using semi empirical models

J. of Supercritical Fluids 78 (2013) 28–33

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Measurement and correlation of the solubility of two steroid drugs in supercritical carbon dioxide using semi empirical models Hamid Asiabi a , Yadollah Yamini a,∗ , Moslem Tayyebi a , Morteza Moradi b , Alireza Vatanara c , Kiarash Keshmiri d a

Department of Chemistry, Faculty of Sciences, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran Department of Semiconductors, Materials and Energy Research Center, Karaj, Iran c Department of Pharmaceutical, School of Pharmacy, Tehran University of Medical Sciences, Tehran, Iran d Department of Chemical Engineering, Faculty of Engineering, Tehran University, Tehran, Iran b

a r t i c l e

i n f o

Article history: Received 27 November 2012 Received in revised form 15 March 2013 Accepted 16 March 2013 Keywords: Desoxycorticosterone acetate Clobetasol propionate Density based model Solubility Supercritical carbon dioxide

a b s t r a c t The solubilities of desoxycorticosterone acetate (DA) and clobetasole propionate (CP) in supercritical carbon dioxide (SC-CO2 ) were measured at temperature ranging from (308 to 348) K and pressures from (12.2 to 35.5) MPa using a static method. The mole fraction solubilities ranged from 10−7 to 13.93 × 10−5 . The crossover region was observed for DA and CP at 24.3 and 25.3 MPa, respectively. Solubility data were correlated using four semi-empirical density-based models (Chrastil, Bartle, Kumar, Johnston (K–J) and Mendez-Santiago and Teja (M–T) models). The average absolute relative deviations (AARD%) ranged from 9.3 to 13.6; 8.9 to 11.9; 6.5 to 10.3 and from 10.4 to 13.4 for Chrastil, Bartle, K–J and M–T models, respectively. A comparison among the four models revealed that the K–J model gave much better correlation of the solubilities in comparison with other models. Using the correlation results, the heat of drug–CO2 solvation and that of drug vaporization was separately approximated in the range of −24.2 to −24.5 and 63.8 to 64.8 kJ mol−1 . The correlation results showed good agreement with the experimental data. © 2013 Elsevier B.V. All rights reserved.

1. Introduction DA and CP are two examples of mineralocorticoid and glucocorticosteroid respectively. Mineralocorticoid and glucocorticosteroid are natural hormones with a steroidal structure [1–5]. Glucocorticoids control carbohydrate, fat and protein metabolism and are anti-inflammatory by preventing phospholipid release, decreasing eosinophil action and a number of other mechanisms and mineralocorticoids control electrolyte and water levels, mainly by promoting sodium retention in the kidney. CP is used only topically on the skin and its effects are limited to the local anti-inflammatory activity. It is indicated for the treatment of psoriasis, dry hyperkeratotic dermatoses, initial control of all forms of hyperacute eczema, chronic hyperkeratotic eczema, contact dermatitis, atopic dermatitis, lichen planus associated with severe pruritis, discoid lumps erythema and granulomatous disorders. It is available in dosage forms such as cream, gel, ointment, etc. [1–4]. DA prolongs the lives and restores many of the functions of patients suffering from Addison’s disease and of adrenalectomized animals. The effect of DA, with or without an extra supply of sodium chloride, on blood

∗ Corresponding author. Tel.: +98 21 82883417; fax: +98 21 82883455. E-mail address: [email protected] (Y. Yamini). 0896-8446/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.supflu.2013.03.018

pressure and renal function has been studied by a number of authors in man and in animal experiments [5,6]. Application of supercritical fluids (SCFs) in chemical processes has attracted much attention in recent years and has been widely applied in, pharmaceutical industries, chemical reaction and a variety of extractions [7–10]. Compared to conventional organic solvents, supercritical fluids (SCFs) have several interesting properties like high diffusivity, low viscosity and low surface tension [11–14]. Carbon dioxide is the most used SCF, which is widely used in supercritical fluid applications as a “green solvent”. Because it is nontoxic, inflammable, abundance, non-explosive, and inexpensive and low critical temperature and pressure (Tc = 304.15 K, Pc = 7.38 MPa) [15–17]. The solubility is probably the most important property that is needed to be known for the production and purification of pharmaceuticals. Based on our knowledge, there is no any information about the solubility of DA and CP in supercritical carbon dioxide available in the literature. The determination of equilibrium solubilities of solids in SCFs at different temperatures and pressures is expensive; hence, the modeling of the solubilities is essential. Models used for correlating the solubility data can be broadly classified as equation of state (EoS) based models and semi-empirical models [12–20]. EoS models require many physical properties (macroscopic critical properties and sublimation pressure are needed for cubic equations

H. Asiabi et al. / J. of Supercritical Fluids 78 (2013) 28–33

of state and molecular parameters for perturbed equations), which are estimated by group contribution methods leading to erroneous correlations [18–21]. On the other hand, semi-empirical equations, like density based models, only need available independent variables like pressure, temperature and density of pure SCF instead of solid properties. They are based on simple error minimization. The density-based models are widely used for the correlation of solid–SC-CO2 equilibrium mainly due to their accurate semi-empirical description and easy application. Recently, many semi-empirical models such as Chrastil model [22], Bartle model [23], Gordillo model [24], Sparks model [25], MendezSantiago and Teja (M–T) model [26], Adachi and Lu model [27], and Kumar and Johnston (K–J) model [28] were used for correlating the solubility data of solid compounds in SC-CO2 . In this study, the equilibrium solubility of DA and CP was measured in supercritical carbon dioxide with static method in the pressure range from (12.2 to 35.5) MPa and at temperatures equal to (308, 318, 328, 338 and 348 K). Then five semi-empirical models (Chrastil model, Bartle model, K–J model and M–T model) were applied for the correlation and prediction of the solubilities of DA and CP in supercritical carbon dioxide at different conditions.

2. Experimental 2.1. Materials Carbon dioxide with 99.99% minimum purity was purchased from Sabalan Co. (Tehran, Iran) and used for all extractions. HPLCgrade methanol from Merck (Darmstadt, Germany) was used as received. The drugs, DA and CP (with purity > 99.5%), were obtained from the Department of Pharmaceutics of Tehran University (Tehran, Iran) and used without further purification. The chemical structures and physical properties of the drugs are summarized in Table 1.

2.2. Apparatus and analysis A Suprex (Pittsburgh, PA) MPS/225 system equipped with a modified static mode for solubility determination was used [29]. Solubility measurements were accomplished with a 1-mL extraction vessel in the pressure range from 12.2 to 35.5 MPa at the temperatures of 308–348 K for duration of 30 min. The solid solutes (200 mg) were mixed with some 1 g of glass beads and packed into the extraction vessel. The equilibrium temperature and pressure were measured with accuracies of ±1 K and ±0.1 MPa, respectively. A schematic diagram of the modified static system used in this study is shown in Fig. 1 [29,30]. This procedure prevents channeling, increases the contact surface between the sample and the supercritical fluid, and, consequently, reduces the equilibration time. Sintered stainless steel filters (5 ␮m) were used to prevent any carry-over of the solutes. Supercritical CO2 was pressurized and passed into the vessel D through the 5-port, 4-position valve C. After equilibrium at the desired temperature and pressure (for about 30 min), a 83.5 ␮L portion of the saturated supercritical CO2 was loaded into injection loop F by means of a 10port, 2-position valve E. Then the loop was depressurized into the collection vial J containing a known volume of methanol by switching the injection valve E. It is noteworthy that, by monitoring the solubility data versus time, 30 min was found adequate to ensure the attainment of equilibrium. In order to prevent solvent dispersal, the depressurizing rate of sample loop was adjusted using the valve I. Finally, the G and I valves were opened completely and the sample loop was washed with methanol (5 mL) and transferred into the collection vial J. The loop was dried by passing N2 gas through it.

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Fig. 1. Schematic diagram of experimental apparatus for measuring solubilities: (A) CO2 gas tank; (B) supercritical fluid pump; (C) 5-port, 4-position valve; (D) 1-mL equilibrium cell; (E) 10-port, 2-postition valve; (F) injection loop; (G) on:off valve; (H) syringe; (I) microadjusting valve; and (J) collection vial.

The concentration of DA and CP in the solutions was calculated by absorbance measurements at suitable wavelength for each compound (Table 1) using a model Cecil Aquarius CE 7200 Double Beam UV-Vis spectrophotometer (London, UK) with 1-cm pass length quarts cells. The stock solution of the drug compounds (1000 mg L−1 ) was prepared by dissolving 10 mg of compounds in 10 mL of methanol. A set of six standard solutions was then prepared by appropriate dilution of the stock solutions. The calibration curves obtained (with regression coefficient about 0.999) were used to establish the concentration of the drugs in the collection vial. The densities of CO2 , calculated by the computer system of the Suprex MPS/225 at various pressures and temperatures, were used to determine the solubility of drugs. It is noteworthy that the Suprex MPS/225 uses the modified equation of state extended to include high-pressure fluids as proposed by Pitzer et al. [31]. 3. Result and discussion 3.1. Experimental results The solubilities of the two drugs along with the temperature, pressure, and density of CO2 that corresponded to each measurement were listed in Table 2. Fig. 2 compares the calculated results using the Bartle equation for DA with the experimental solubility

Fig. 2. Comparison of experimental (points) and calculated (line) solubility of DA based on the Bartle model at various temperatures.

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H. Asiabi et al. / J. of Supercritical Fluids 78 (2013) 28–33

Table 1 Structure of the drugs used and their physicochemical properties. MW/g mol−1 a

Tm /Kb

/nmc

C23 H32 O4

372.497

430 ± 2

240

C25 H32 ClFO5

466.97

469 ± 2

240

Compound

Formula

DA

CP

a b c

Structure

Molecular weight. Melting temperature. Maximum wavelength.

values. It showed good agreement with the experimental and calculated results. The mole fraction of solutes was generally reproducible within ±4.5% (based on three replicates). The solubility of CP is considerably small compared to DA. This is expected since CP is a polar compound and it is not more soluble in non-polar solvents. Carbon dioxide has no dipole moment and has only a small quadrupole moment, a small polarizability volume, and a low relative permittivity. Examination of the solubility data in Table 2 and Fig. 2 reveals that the solubilities of drugs increase with an increase in pressure at all temperatures. This is due to the increase density of CO2 by increasing pressure, which happens since dissolving power of CO2 is directly related to the density. Temperature has two opposite effects on the solute solubilities. At pressure beyond the crossover point (25.3 MPa for CP and 24.3 MPa for DA), solubility increases with increasing temperature, while below this point, solubility decreases by increasing temperature; because at lower pressures, the effect of the density on the solubility is more important. At higher pressures, the SC-CO2 density is less dependent on temperature, so increasing of vapor pressure at higher temperatures is responsible for increasing solubility of the drugs. Similar observations have already been reported in the literature [32–34]. The existence of a crossover pressure in solid–SCF equilibrium is an indication of the reliability and consistency of the obtained solubility data.

The model proposed by Chrastil [22], which simply represents the relationship between the solubility of the solute in SC-CO2 and its density, is based on the solvation of solvent molecules surrounding solute molecules, as follows: ln y2 = a0 + a1 ln  + a2 =

Hvap + Hsolv R

(1) (2)

where y2 is the solubility of the solid substance in the SCF;  (kg m−3 ) is the density of supercritical fluids, a0 is a function of the association number and molecular weights of the solute and SCF, a1 is an association constant describes the number of SCF molecules in the solvated complex. Hvap and Hsolv denote the enthalpies of vaporization of solute and solvation, respectively. Parameter a2 is a constant which is related to heat of solvation and heat of vaporization in Eq. (2). The parameters a0 , a1 and a2 are determined by fitting the correlation to experimental data. For the Chrastil correlation, all the mole fraction solubility at different temperatures will coincide to a single straight line when plotting ln(y2 ) − a2 /T as a function of ln  (kg m−3 ) for DA and CP (Fig. 3). Kumar and Johnston [28] pointed out that the linear relationships are observed between ln(y) and ln(). Similar to Eq. (1), linear relation between ln(y2 ) and  could be written as:

3.2. Correlation of solubility data ln y2 = b0 + b1  + Semi-empirical and empirical correlations, based on the density of the pure SC-CO2 , were widely used for the correlation of solid–supercritical fluid equilibrium mainly due to their simplicity and easy application. In the present study the experimental solubility data were correlated using four semi-empirical models: Chrastil, Bartle, K–J and M–T models.

a2 T

b2 T

(3)

where y2 is the mole fraction solubility of solute in SCF,  (kg m−3 ) is the solvent density, T (K) is temperature, and b0 , b1 and b2 are the adjustable parameters which can obtain by regression analysis of the solubility data. The value of b2 is related to the total heat Htotal (heat of solvation Hsolv , plus heat of vaporization of the solute

H. Asiabi et al. / J. of Supercritical Fluids 78 (2013) 28–33

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Table 2 Solubilities of desoxycorticosterone acetate and clobetasol propionate in SC-CO2 (y2 : mole fraction of solid). T/K

308

318

328

338

348

a

P/MPa

12.2 15.2 18.2 21.3 24.3 27.4 30.4 33.4 35.5 12.2 15.2 18.2 21.3 24.3 27.4 30.4 33.4 35.5 12.2 15.2 18.2 21.3 24.3 27.4 30.4 33.4 35.5 12.2 15.2 18.2 21.3 24.3 27.4 30.4 33.4 35.5 12.2 15.2 18.2 21.3 24.3 27.4 30.4 33.4 35.5

/kg m−3

771 818 850 876 897 916 931 946 955 661 745 792 826 852 875 893 910 919 516 657 726 771 804 831 853 872 884 396 561 654 712 754 786 812 834 848 327 477 585 652 702 740 772 796 811

DA

CP

10 S/g L−1

105 y2 a

RSD%

10 S/g L−1

105 y2 a

RSD%

1.26 1.78 2.24 2.80 3.54 3.92 4.36 4.83 5.21 0.55 1.22 1.85 2.42 3.32 4.20 5.09 5.75 6.24 0.13 0.56 1.33 2.11 3.22 4.38 5.41 6.29 7.27 0.78 0.36 0.97 1.85 3.02 4.55 5.90 7.09 8.12 0.03 0.20 0.79 1.61 2.91 4.76 6.72 8.35 9.58

1.93 2.58 3.12 3.77 4.66 5.05 5.53 6.03 6.44 0.98 1.93 2.76 3.46 4.6 5.67 6.73 7.45 8.02 0.31 1.01 2.16 3.23 4.73 6.22 7.49 8.51 9.7 0.23 0.76 1.76 3.08 4.72 6.83 8.58 10.04 11.30 0.09 0.5 1.59 2.91 4.90 7.6 10.27 12.37 13.93

3.7 3.3 3.1 2.5 1.9 1.85 2.6 2.1 1.9 4.1 3.6 4.0 3.9 3.5 3.3 3.1 2.8 2.8 4.4 4.1 3.9 3.8 3.5 3.0 2.7 2.3 2.0 4.1 4.1 3.9 3.3 2.5 2.9 2.4 1.9 1.6 4.3 3.8 3.3 2.7 2.3 2.3 1.6 1.3 1.2

0.03 0.06 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.02 0.04 0.06 0.08 0.09 0.13 0.15 0.17 0.18 0.01 0.02 0.04 0.07 0.08 0.13 0.17 0.22 0.24 0.01 0.02 0.03 0.06 0.08 0.15 0.19 0.23 0.25 0.0003 0.003 0.02 0.05 0.07 0.16 0.21 0.25 0.30

0.04 0.07 0.07 0.1 0.11 0.12 0.14 0.15 0.17 0.03 0.05 0.07 0.09 0.1 0.14 0.16 0.17 0.19 0.02 0.04 0.06 0.08 0.1 0.15 0.19 0.24 0.25 0.02 0.03 0.05 0.08 0.1 0.18 0.23 0.27 0.27 0.01 0.03 0.08 0.1 0.21 0.25 0.29 0.35

4.5 4.4 4.5 4.1 3.9 4.0 3.6 3.6 3.6 3.9 3.5 4.1 4.3 3.8 3.3 3.5 3.1 2.5 4.3 4.3 4.1 4.2 3.9 3.2 2.9 2.6 2.7 3.8 3.9 4.0 3.5 3.2 2.0 2.5 2.4 2.4 4.5 4.1 4.1 3.9 2.5 2.3 2.2 1.8

The precision of the measurements, expressed as relative standard deviation (RSD%) varied between 1.2 and 4.5%.

Hvap ), and defined as b2 = Htotal /R, parameter b0 is a constant only acquired from the experimental data. Bartle et al. [23] developed a straightforward semi-empirical correlation which relates the solubility of the solid in the SCF (expressed in terms of solid solute mole fraction, y2 ) with experimental pressure and pure SCF density. It is possible to describe Bartle’s equation as follows:

 ln

Fig. 3. Plot of ln y2 − (a2 /T) as a function of ln  (kg m−3 ) based on Chrastil model for DA and CP (, CO2 density; y2 , solid substance solubility in the SCF; T, temperature; and a2 , constant).

y2 p Pref

 = c0 + c1 ( − ref ) +

c2 T

(4)

In this expression, y2 is the mole fraction solubility Pref , is a standard reference pressure (set equal to 0.1 MPa); ref is a reference density (considered as 700 kg m−3 ) and T is the experimental temperature (K). The coefficients c0 , c1 and c2 can be obtained by fitting the correlation to experimental data. The parameter c2 can be directly used to estimate the heat of vaporization of the solute, Hvap using Hvap = −c2 R. Based on the values of Htotal and Hvap , the heat of solvation, Hsolv can be approximated for each solute–CO2 system.

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H. Asiabi et al. / J. of Supercritical Fluids 78 (2013) 28–33 Table 3 Different parameters of the drug–CO2 binary systems obtained by using the Chrastil, K–J, Bartle and M–T models. Chrastil model

a0

a1

a2 /K

AARD%

Compound DA CP

−55.74 −62.68

6.46318 6.88648

−4991.1 −5264.3

9.3 13.6 11.4

Average K–J model

b0

b1

b2 /K

AARD%

Compound DA CP

−0.37 −4.01

3.97E−04 4.10E−04

−4763.5 −4842.3

6.5 10.3

Average

8.4

Bartle model

c0

c1 /L g−1

c2 /K

AARD%

Compound DA CP

20.13 16.83

0.01258 0.01288

−7675.5 −7799.9

8.9 11.9 10.4

Average M–T model

d0 /K

d1 /K L g−1

d2

AARD%

Compound DA CP

−11,466 −11,580

0.1424 0.14426

17.256 17.506

13.4 10.4

Average

11.9

Table 4 Approximated total reaction (Htotal ), salvation (Hvap ) and vaporization (Hsol ) enthalpies for the drugs. Fig. 4. Plot of ln(y2 P) − d2 T as a function of  (kg m−3 ) based on M–T model for DA and CP (, CO2 density; y2 (mol mol−1 ), mole fraction of solute in SCF; T, temperature; P (MPa), pressure and d2 , pressure and temperature independent constant).

Another density-based model was proposed by MendezSantiago and Teja (M–T) [26]. This model comes from the linear relationship between T ln(y2 P) and , which was derived from the theory of dilute solutions. T ln(y2 P) = d0 + d1  + d2 T

100 N

 |ycal − yObs | i

i

yiObs

Htotal a (kJ mol−1 )

Htotal b (kJ mol−1 )

Hvap c (kJ mol−1 )

Hsol d (kJ mol−1 )

DA CP

41.5 43.8

39.6 40.3

63.8 64.8

−24.2 −24.5

a b c d

Obtained from the Chrastil model. Obtained from the K–J model. Obtained from the Bartle model. Obtained from the difference between the Htotal and Hvap .

(5)

Here d0 , d1 and d2 are pressure and temperature independent constants that should be obtained by the multiple linear regression of the solubility experimental data.  (mol cm−3 ) is the density of supercritical fluids, y2 (mol mol−1 ) is the mole fraction of solute in supercritical fluids, P (MPa) is the pressure of the system, and T is the temperature. The consistency of the solubility experimental data can be checked by the convergence of all the solubility isotherms into a single straight line. The plots of T ln y2 P − d2 T versus  (kg m−3 ) resulted in a nice straight line (Fig. 4). The experimental solubility data are correlated by using semiempirical models, Chrastil, K–J, Bartle and M–T, which are described as Eqs. (1)–(5). The average absolute relative deviations (AARDs%) is calculated by Eq. (6). AARD% =

Compound

(6)

where N is the number of experimental data points, yical is the cal-

culated value of the mole fraction solubility of solute, yiObs is the experimental value of the mole fraction solubility of solute, and N is the number of experimental points. The correlated results and optimal parameters of the experimental solubility data using Chrastil, K–J, Bartle and M–T models (Eqs. (1)–(5)) are listed in Table 3. As shown in this table, the AARD% values ranging from 9.3 to 13.6, from 6.5 to 10.3, from 8.9 to 11.9 and from 10.4 to 13.4% for Chrastil, K–J, Bartle and M–T models; respectively. The obtained results from

Eqs. (1) and (5) are shown in Figs. 3 and 4. As can be seen in Table 3 and with obtained AARD% values, all the four density-based models were able to successfully correlate the experimental solid drugs SC-CO2 solubility data. The Chrastil, K–J and Bartle models explicitly include an energy term, i.e., the coefficient of temperature term. From the regressed energy parameters, the total reaction heat, vaporization heat and solvation heat (Htotal , Hvap , and Hsolv ) for examined drug–CO2 systems can be conveniently estimated. The obtained thermodynamic properties of the drugs are listed in Table 4. Since the vaporization is endothermic whereas the solvation is exothermic, the vaporization heat is very higher than the total reaction heat for each drug. As shown in these tables, the total reaction heat values are ranging from 41.5 to 43.8 and 39.6 to 40.3 kJ mol−1 for Chrastil and K–J models, respectively. The enthalpy of drugs vaporization that was computed using the Bartle model, ranged from 63.8 to 64.8 kJ mol−1 . From difference between vaporization and total reaction heats the obtained solute–solvent solvation heats were −24.2 kJ mol−1 and −24.5 kJ mol−1 for DA and CP, respectively. 4. Conclusion In this work, the solubility of DA and CP in SC-CO2 was determined at T = (308, 318, 328, 338 and 348) K, over a pressure range from (12.2 to 35.5) MPa. The solubility data for drugs have been correlated by four density-based models (Chrastil, K–J, Bartle and

H. Asiabi et al. / J. of Supercritical Fluids 78 (2013) 28–33

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