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Solubility of cholesterol in selected organic solvents
Fluid Phase Equilibria,
97 (1994) 191-200
Solubility of cholesterol in selected organic solvents Urszula Domariska
*, Cveto Klofutar
‘, Spela Paljk
’
Department of Chemistry, Warsaw Technical University, 00664 Warsaw, Poland (Received August 26, 1993; accepted in final form January 19, 1994)
Abstract Domafiska, U., Klofutar, C. and Paljk, s., 1994. Solubility of cholesterol in selected organic solvents. Fluid Phase Equilibria, 97: 191-200. The solubilities of cholesterol have been determined experimentally in six solvents - benzene, toluene, cyclohexane, 1,2-dichloroethane, trichloromethane and tetrachloromethane - by a dynamic method in the temperature range 290-350 K. The large influence of the solute-solvent interaction on the temperature of the cholesterol solid-solid phase transition has been observed. The results have been correlated by the Wilson equation, UNIQUAC theory and the UNIQUAC association solution model. Keywords: Experiments;
Data; Solid-liquid;
Cholesterol
1. Introduction
The solubility of cholesterol has long attracted the attention of experimenters. The enhancement of its solubility was observed by Weichherz and Marschik (1932) in binary solvent mixtures of benzene + hexane, or benzene + 1,Cdioxane. The solubility of cholesterol in various fats and oils at 310 K was studied by Kritchevsky and Tepper ( 1964). Stauffer and Bischoff (1966) observed the influence of crystalline forms of cholesterol on solubility in oils, various organic solvents and water at 311 K. Solubilities of cholesterol in n-alkanols from methanol to undecanol and their binary mixtures was reported by Flynn et al. (1979). Authors indicated that cholesterol “solvates” of each alcohol were formed, which had an influence on the enthalpy of
* Corresponding author. I Permanent address: J. Stefan Institute,
“E. Kardelj” University of Ljubljana,
0378-3812/94/%07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZ 0378-3812(94)02485-J
61000 Ljubljana,
Slovenia.
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
192
melting and temperature of the solid phase transition. Their experiences with cholesterol indicated that the solid phase is remarkably sensitive to the solvents used. Such effects were observed previously by Ostrenga and Steinmetz (1970) for corticosteroids. The effects of various macromolecules, dextrans, on increasing the aqueous solubility of cholesterol were examined by Cadwallader and Madan (1981). Solubilities of cholesterol at various temperatures ranging from 284 to 322 K in methanol, ethanol, 2-propanone, acetonitrile and propan-l-01, and in some aqueous mixtures of these solvents, were presented by Bar et al. (1984) without any information about solid-phase transitions in this temperature region. In spite of this literature on cholesterol, there is comparatively little precise information regarding the interconversion of the crystalline forms of cholesterol connected with solubility. The solubilities of cholesterol in six solvents - benzene, toluene, cyclohexane, l,Zdichloroethane, trichloromethane and tetrachloromethane - have recently been determined in our laboratory by a dynamic method in the temperature range from 290 to 350 K. 2. Experimental Solubilities were determined by a dynamic (synthetic) method, described in full by Domanska (1986). Mixtures of solute and solvent, prepared by weighing, were heated very slowly (heating rate did not exceed 2 K h-l near the equilibrium temperature) with stirring. The temperature at which the last crystals disappeared (the solution was no longer cloudy) was taken as the temperature of the solution-crystal equilibrium. Measurements were performed for a wide range of solute concentrations from x1 = 0 to x1 = 0.2 for benzene, and from x1 = 0.0008 to x1 = 0.35 for other solvents, and over the phase transition temperature region. The accuracy of temperature measurements was +0.05 K. Reproducibility of measurements was to within 0.1 K, which corresponded to a root error in composition 6x1 = 0.001. Table 1 Characteristics
of solvents
Substance
pe98.15
(m3mop)
a
Source
298.15 nD
Literature Benzene
89.40
Toluene
106.80
Cyclohexane
108.70
1,2-Dichloroethane
79.40 b
Trichloromethane
80.68 b
Tetrachloromethane
97.10
B Barton (1975). b Riddick and Bunger (1970).
Merck-Schuchard Mtinchen Merck-Alkaloid Skopje, Yugoslavia Merck-Alkaloid Skopje, Yugoslavia Merck-Schuchard Miinchen Kemika Zagreb, Yugoslavia Zorka Sabac Yugoslavia
T,,,
b
W)
Observed
1.49792
1.49785
314.9
1.49413
1.44304
321.3
1.42354
1.42352
316.1
1.4421
1.44241
313.6
1.44293
1.44291
323.6
1.45739
1.45732
301.7
193
U. Domariska et al. / Fluid Phase Equilibria 97 (1994) 191-200
All solvents were purified by fractional distillation and then dried over 4 8, molecular sieves (SERVA Chemical). The data concerning solvents are given in Table 1. Cholesterol (SIGMA, USA), standard for chromatography (99 +%), was used without further purification. The observed melting temperature of solute was 421.15 K and the following values of enthalpy of fusion and phase transition, taken from the work of Garti et al. (1980) for benzene solutions, were used in the calculations: AH,,,, = 28.034 kJ mol-’ and AH,,, = 2.845 kJ mol-‘. There was no information about heat of transition and melting after crystallization of cholesterol from other solvents, except from tetrachloromethane, where two different values of the enthalpy of fusion were observed. The temperatures of phase transition, observed in different solvents, were taken from the solubility curves and are shown in Table 1. The value of the molar volume of cholesterol at 298.15 K is V, = 338.32 cm3 mol-’ and the values of the solvent molar volumes shown in Table 1. All the direct experimental data are collected in Table 2, where T” and Tp are high and low polymorphic experimental equilibrium temperatures, respectively, Tkenet is the metastable phase equilibrium temperature, and T2 is the solute 2 liquidus equilibrium temperature.
Table 2 Solubility measurements of cholesterol in organic solvents Xl
T” (K)
Benzene 0.2019 0.1760 0.1664 0.1564 0.1471 0.1405 0.1310 0.1240 0.1186 0.1119 0.1074 0.1007
349.7 341.6 338.2 334.6 329.6 326.5 322.3 319.6 317.5 314.5 312.8
CL W
309.5
a
TaW)
314.6 314.6
XI
Ts(K)
0.0919 0.0852 0.0768 0.0638 0.0511 0.0430 0.0252 0.0175 0.0115 0.0048 0.0
313.5 312.4 310.8 307.7 304.6 302.2 295.6 291.7 278.9
0.1156 0.1019 0.0861 0.0770 0.0653 0.0588 0.0510 0.0425 0.0331
312.9 310.1 306.7 304.2 301.0 299.8 296.2 291.9 286.3
0.0477 0.0419
314.5 313.1
278.2 278.6
Toluene 0.3438 0.3230 0.2941 0.2570 0.2239 6.1978 0.1794 0.1710 0.1519 0.1294 Cyclohexane 0.1821 0.1758
372.3 366.4 358.6 348.7 338.1 329.1 323.1 321.3 319.4 315.3 352.4 349.4
Tz W
b
194
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
Table 2 (continued)
TsWI
0.0354 0.0306 0.0201 0.0132 0.0094 0.0064 0.0008
311.4 309.1 305.7 301.6 298.7 281.1 280.0
353.1 346.7 342.9 337.8 332.5 327.4 323.0 320.0 316.3 313.6
0.0175 0.0082 0.0045 0.0020
312.4 309.3 304.6 295.6
334.1 331.9 330.3 326.8 324.4
0.0561 0.0493 0.0428 0.0365 0.0323 0.0290 0.0241 0.0204 0.0162 0.0133
317.6 315.6 312.9 309.6 307.0 304.7 300.6 296.3 290.6 286.4
0.0819
297.9 295.6 293.4 290.6
T” W)
0.1640 0.1447 0.1338 0.1185 0.1029 0.0880 0.0783 0.0706 0.0626 0.0549
346.0 339.9 338.4 331.9 326.6 321.6 318.4 315.6
1,2_Dichlorethane 0.1711 0.1428 0.1237 0.1006 0.0795 0.0609 0.0479 0.0409 0.0325 0.0262 Trichloromethane 0.1254 0.1183 0.1138 0.1065 0.1003 0.0939 0.0867 0.0816 0.0753 0.0659 Tetrachloromethane 0.1934 0.1812 0.1751 0.1604 0.1455 0.1356 0.1252 0.1160 0.1113 0.0947
a
Xl
Xl
T&e,W
312.6 309.8
TsWI
315.6 315.1
323.1 322.9 321.8 320.8 319.5
350.6 344.1 341.1 334.6 327.7 322.6 316.9 312.6 307.0
a tl metastable phase equilibrium
0.0713 0.0615 0.0506 0.0418
290.6
temperature.
287.4
300.4 b Solute 2 liquidus equilibrium
temperature.
T, (K) b
U. Domahska et al. / Fluid Phase Equilibria 97 (1994) 191-200
195
3. Results and discussion The solubility of cholesterol in hydrocarbons is similar to that in halohydrocarbons, and decreases in the order toluene > benzene > cyclohexane and tetrachloromethane > trichloromethane > 1,2-dichloroethane. Toluene proved to be the best solvent. The cholesterol molecule has a hydroxyl group and a double bond, thus having the potential for interaction with both polar and aromatic solvents. Solutes apparently reduce the self-association in tetrachloromethane and trichloromethane, but show a greater interaction with aromatic solvents than with trichloromethane, where the possibility of hydrogen bonding with the trichloromethane may be expected. The solubility in tetrachloromethane, toluene and benzene is higher than in trichloromethane. In benzene, toluene and tetrachloromethane the solubility is higher than ideal, and the experimental activity coefficient of the solute (7,) is in the range 0.43- 1.O; in cyclohexane, trichloromethane and 1,Zdichloroethane the solubility it is lower than ideal, and the activity coefficient of the solute (yl) is in the range 1.3-16.8. The shapes of the liquidus curves are shown in Fig. 1 for the cholesterol + benzene system as an example. The temperature and mole fraction of solute 1 were Ttrl = 314.9 K, x1 = 0.113 and
350
330
290
270 0
0.05
0.15
0.1
0.2
0.25
Xl
Fig. 1. Solid-liquid equilbrium diagram for cholesterol( 1) + benzene(2) binary system. Solid lines: calculated by the Wilson equation. Dotted line: ideal solubility.
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
196
TE = 277.3 K, x = 0.001 at the phase transition and eutectic point, respectively. The thermal transition of cholesterol has been studied by differential thermal analysis (DTA) in many different laboratories. Spier and Senden ( 1965) observed one point at 313 K and no further transitions up to the melting point. Pietropawlow et al. (1988) measured the enthalpy of the phase transition AH,,, = 2.5 kJ mol-’ at 304.8 K. The effect of various organic solvents on the structure of crystals, enthalpy, and temperature of phase transition and fusion have been studied by Garti et al. (1980, 1981). The authors suggested that the polymorphic transition of cholesterol may be divided into several sub-transitions, each one corresponding to a slight configurational change, that can be attributed to a possible flip-over of the aliphatic chain of the cholesterol. Authors find differences in crystal habit, indicating dependence on the solvent-solute interaction even under the same crystallization conditions. Plates and needle-like crystals of different sizes were observed, depending mainly on the kind of solvent. Owing to the hydroxyl group and the double bond in a cholesterol molecule, it is reasonable to assume that the crystal habit of cholesterol is dictated by the solvent-solute interaction as well as by the crystallization conditions. The temperature of phase transition, observed during our solubility measurements, differs from 301.7 K in tetrachloromethane to 323.6 K in trichloromethane (see Table 1). The solubility of a solid non-electrolyte, 1, in a liquid solvent, can be expressed as -lnx,
=+
(+-$--)-+[In(&)++-l]+lny,
(1)
yl, AH,,, ACpml,T,, and T are the mole fraction, activity coefficient, enthalpy of fusion, solute heat capacity during the melting process, melting temperature of the solute, and equilibrium temperature, respectively. If the solid-solid transition occurs before fusion, an additional term must be added to the right-hand-side of Eq. (1) (Weimer and Prausnitz, 1965; Choi and McLaughlin, 1983):
where x1,
-lnX,=+($-+--)-*[,n($-)++-l]++(+-$--)+lny,
(2)
where AH,,, and Tt,, are the enthalpy and temperature of the solid-solid transitions of the solute. In this work, Eq. ( 1) was used for temperatures above the transition temperature and Eq. (2) at lower temperatures. It was assumed that the solute heat capacity during the melting process is A&, = 8.8 J K-i, as was found for the phase transition process (Labowitz, 1972). In this study, three methods were used to represent the solute activity coefficient (yi) from the so-called correlation equations that describe the Gibbs excess free energy of mixing (GE): the Wilson equation (Wilson, 1964), the UNIQUAC equation (Abrams and Prausuitz, 1975) and the UNIQUAC associated-solution model (Nagata, 1985). The exact mathematical forms of the equations have been presented in a previous paper (Domanska et al., 1989). The parameters were fitted by the optimization technique. The objective function was as follows: F(A,, AZ) = i wY2[ln x,iYii(T, xii, Ai, i-l
A2)
-
In
adTi)12
(3)
where In aii denotes an “experimental” value of the logarithm of solute activity, taken as the right-hand-side of Eq. (l), wi is the weight of an experimental point, Ai and A2 are the two
V. Domariska et al. 1Fluid Phase Equilibria 97 (1994) 191-200
197
adjustable parameters of the correlation equations, i denotes the ith experimental point, and n is the number of experimental data. The weights were calculated by means of the error propagation formula: a In xlyl - a In aj 2 dT ( > T=
+
2
(ATi>’ + Ti
a ‘;;I” (
1
thli)
>Xi’Xli
(4)
where AT and Ax, are the estimated errors of T and x1, respectively. According to the above formulation, the objective function is consistent with the maximum likelihood principle, provided that the first-order approximation (Eq. 4) is valid. Neau and Peneloux (1981) called such a procedure the observed deviation method. The experimental errors of temperature and solute mole fraction were fixed for all cases and set to AT = 0.1 K, Ax, = 0.001. The root-mean-square deviation of temperature defined by Eq. (5) was used as a measure of the goodness of fit of the solubility curves: d = T
i [ i=l
(Ty'
1
- TJ’ 1’2
(n-1)
(5)
where Ty8’ and Ti are, respectively, the calculated and experimental temperatures of the ith point, and n is the number of experimental points. The calculated values of the equation parameters and corresponding root-mean-square deviations are presented in Table 3. It can be noted that a description is not very good (CT > 2 K) and in the same range for both two-parameter equations. Average deviations are 4.6 and 5.4 K for the Wilson and UNIQUAC equations, respectively. The calculations with the Wilson equation utilizing simple temperature dependent parameters, i.e. (gg - gji) = auT-‘, have given comparable results. The calculations with the UNIQUAC associated-solution model carried out by using different literature data sets of self-association of cholesterol in trichloromethane (Foster et al., 1981) and in tetrachloromethane (Kunst et al,, 1979; Foster et al., 1981; Costas and Patterson, 1985; Caceres-Alonso et al., 1988), have been compared with the simple UNIQUAC and the rootmean-square deviations of correlations varied from 4.5 K (for benzene and cyclohexane with the self-association constant K2 = 5077 at 298.15 K, through hydrogen bonding h, = -24.0 kJ mol-’ from Costas and Patterson, 1985) to 13.7 K for tetrachloromethane. So, in addition, calculation with K2 as the third adjustable parameter at the temperature 298.15 K were made using values of the hydrogen-bond formation enthalpy h2 = - 24.0 kJ mol-*, taken from Costas and Patterson (1985). The temperature dependence of the association constants was calculated from the van’t Hoff relation, assuming the enthalpy of hydrogen-bond formation to be temperature independent. The results are presented in Table 3. Overly large values of the root-mean-square deviations have been observed in the system of cholesterol in tetrachloromethane, (flT = 7.1 K), where the more complicated model of association (monomer < dimer < trimer < tetramer) may be expected.
4. Conclusion The phenomenon of solid-solid phase transition of cholesterol in every tested solvent has been noted at different temperatures as a result of solute-solvent interactions.
No. of dam points
22
20
22
15
21
16
Solvent
Benzene
Toluene
Cyclohexane
1,2-Dichloroethane
Trichloromethane
Tetrachloromethane
5037.67 171.75 60129.80 - 728.39 9766.10 - 53.93 7904.21 1265.20 2036.46 1236.49 - 1467.87 916.74
giz -g11 g12 - g22 (J mol- ‘)
Wilson
Parameters
-1191.05 2231.67 - 2034.45 3939.86 - 1778.93 3598.53 - 1024.84 2567.33 160.78 546.06 2368.32 - 1498.65
$iOP,
UNIQUAC AU,,
-1181.00 2200.53 512.34 - 540.87 3309.19 - 1934.43 2492.89 - 1230.83 283.66 418.87 49.56 48.49
(J mol-‘)
Au21
UNIQUAC A%?
ASM
2.32
0.0
0.0
0.0
224.8
446.7
K,
6.8
2.0
4.3
6.0
4.5
4.0
%
Wilson
5.7
2.0
7.5
9.0
4.3
4.0
Y-6
UNIQUAC
and UNIQUAC
Deviations
Table 3 Correlation of the solubility data for cholesterol in organic solvents by means of the Wilson, UNIQUAC of parameters and measures of deviations
7.1
2.3
1.3
4.3
4.7
3.7
&
UNIQUAC
ASM
ASM equations: values
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
199
The best results of the correlation of experimental points in binary systems of cholesterol have been obtained by the use of the Wilson equation.
5. List of symbols a1
au AI,
~42
gij AC,,, AH,, AH,,, h2 K2 n I
R T AT TCBI
T ml T tr1 vi X1 AXI W
activity of the solute proportionality constant of the Wilson equation defined by (gV - g& = avT- ’ binary interaction parameters of the Wilson and UNIQUAC equations molar energy of interaction between i and j difference between heat capacities of the solute in the solid and liquid states at T,, molar enthalpy of fusion of the solute molar enthalpy of first-order solid-solid transition enthalpy of hydrogen-bond formation association constant, (@2i+#D2$DzM)[i/(i+ l)] number of experimental points number of adjustable parameters universal gas constant experimental equilibrium temperature estimated error of temperature calculated equilibrium temperature melting point temperature of the pure solute temperature of transition point molar volume of the solute or solvent mole fraction of the solute estimated error of the solute mole fraction weight of experimental point
5.1. Greek letters a, P Yl CT
high- and low-temperature polymorphic structure of the solute activity coefficient of the solute root-mean-square deviation in temperature
6. References Abrams, D.S. and Prausnitz, J.M., 1975. Statistical thermodynamics of liquid mixtures; a new expression for. the excess Gibbs energy of partly or completely miscible systems. AIChE J., 21: 116-128. Bar, L.K., Gartl, N., Sarlg, S. and Bar, R., 1984. Solubilities of cholesterol, sitosterol and cholesteryl acetate in polar organic solvents. J. Chem. Eng. Data, 29: 440-443. Barton, A.F.M., 1975. Solubility parameters. Chem. Rev., 76: 731-753.
200
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
Caceres-Alonso, M., Costas, M., Andreolli-Ball, L. and Patterson, D., 1988. Steric effects on the self-association of branched and cyclic alcohols in inert solvents. Apparent heat capacities of secondary and tertiary alcohols in hydrocarbons. Can. J. Chem., 66: 989-998. Cadwallader, D.E. and Madan, D.K., 1981. Effect of macromolecules on aqueous solubility of cholesterol and hormone drugs. J. Pharm. Sci., 70: 442-445. Choi, P.B. and McLaughlin, E., 1983. Effect of phase transition on the solubility of solid. AIChE J., 29: 150-153. Costas, M. and Patterson, D., 1985. Thermodynamics of cholesterol self-association and its interaction with tripalmitin and l-a-lecithin. J. Chem. Sot., Faraday Trans. 1, 81: 655-671. Domanska, U., 1986. Vapour-liquid-solid equilibrium of eicosanoic acid in one- and two-component solvents. Fluid Phase Equilibria, 26: 201-220. Domanska, U., Domanski, K., Klofutar, C. and Paljk, S., 1989. Solubility of tetracosane in aliphatic alcohols. Fluid Phase Equilibria, 46: 25-39. Flynn, G.L., Shah, Y., Prakongpan, S., Kwan, K.H., Higuchi, W.J. and Hofmann, A.F., 1979. Cholesterol solubility in organic solvents. J. Pharm. Sci., 68: 1090-1097. Foster, B.W., Robeson, J., Tagata, N., Beckerdite, M., Huggins, R.L. and Adams, Jr., E.T., 1981. Self-association of cholesterol in nonaqueous solutions. J. Phys. Chem., 85: 3715-3720. Garti, N., Karpuj, L. and Sarig, S., 1980. Phase transitions in cholesterol crystallized from various solvents. Thermochim. Acta, 35: 343-348. Garti, N., Karpuj, L. and Sarig, S., 1981. The effect of solvents and crystallization conditions on crystal habit of cholesterol. Cryst. Res. Technol., 16: 1 11 l- 1115. Kritchevsky, D. and Tepper, S.A., 1964. Solubility of cholesterol in various fats and oils. Proc. Sot. Biol. Med., 116: 104-107. Kunst, M., van Duijn, D. and Bordewijk, P., 1979. Self-association of cholesterol in carbon tetrachloride. Z. Naturforsch, Teil A, 34: 369-374. Labowitz, L.C., 1972. Change of phase and change of state in biological systems. Thermochim. Acta, 3: 419-420. Nagata, I., 1985. On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilibria, 19: 153-174. Neau, E. and Peneloux, A., 1981. Estimation of model parameters. Comparison of methods based on the maximum likelihood principle. Fluid Phase Equilibria, 6: 1 - 19. Ostrenga, J.A. and Steinmetz, C. 1970. Estimation of steroids solubility: use of fractional molar attraction constants. J. Pharm. Sci. 59: 414-416. Pietropawlow, I.I., Cygajkowa, I.G. and Tislenko, L.A., 1988. Microcalorimetriczeskie issledowanija polimernych perehodow w organiczeskih krystallah. Crystallogr., 33: 1433- 1436. Riddick, J.A. and Bunger, W.B., 1970. Techniques of Chemistry, Vol. II. Organic Solvents, Physical Properties and Methods of Purification, Wiley-Interscience, New York. Spier, H.L. and Senden, K.G., 1965. Phase transition of cholesterol. Steroids, 6: 871-873. Stauffer, R. and Bischoff, F., 1966. Solubility determination of cholesterol polymorphs in organic solvents. Clin. Chem., 12: 206-210. Weichherz, J. and Marschik, H., 1932. Die lijslichkeit des cholesterol in ldsungsmittelgemischen. B&hem. Z., 249: 312-322. Weimer, R.F. and Prausnitz, J.M. 1965. Complex formation between carbon tetrachloride and aromatic hydrocarbons. J. Chem. Phys., 42: 3643-3644. Wilson, G.M., 1964. Vapor-liquid equilibrium. XI. A new expression for the excess free energy of mixing. J. Am. Chem. Sot., 86: 127-130.
97 (1994) 191-200
Solubility of cholesterol in selected organic solvents Urszula Domariska
*, Cveto Klofutar
‘, Spela Paljk
’
Department of Chemistry, Warsaw Technical University, 00664 Warsaw, Poland (Received August 26, 1993; accepted in final form January 19, 1994)
Abstract Domafiska, U., Klofutar, C. and Paljk, s., 1994. Solubility of cholesterol in selected organic solvents. Fluid Phase Equilibria, 97: 191-200. The solubilities of cholesterol have been determined experimentally in six solvents - benzene, toluene, cyclohexane, 1,2-dichloroethane, trichloromethane and tetrachloromethane - by a dynamic method in the temperature range 290-350 K. The large influence of the solute-solvent interaction on the temperature of the cholesterol solid-solid phase transition has been observed. The results have been correlated by the Wilson equation, UNIQUAC theory and the UNIQUAC association solution model. Keywords: Experiments;
Data; Solid-liquid;
Cholesterol
1. Introduction
The solubility of cholesterol has long attracted the attention of experimenters. The enhancement of its solubility was observed by Weichherz and Marschik (1932) in binary solvent mixtures of benzene + hexane, or benzene + 1,Cdioxane. The solubility of cholesterol in various fats and oils at 310 K was studied by Kritchevsky and Tepper ( 1964). Stauffer and Bischoff (1966) observed the influence of crystalline forms of cholesterol on solubility in oils, various organic solvents and water at 311 K. Solubilities of cholesterol in n-alkanols from methanol to undecanol and their binary mixtures was reported by Flynn et al. (1979). Authors indicated that cholesterol “solvates” of each alcohol were formed, which had an influence on the enthalpy of
* Corresponding author. I Permanent address: J. Stefan Institute,
“E. Kardelj” University of Ljubljana,
0378-3812/94/%07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZ 0378-3812(94)02485-J
61000 Ljubljana,
Slovenia.
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
192
melting and temperature of the solid phase transition. Their experiences with cholesterol indicated that the solid phase is remarkably sensitive to the solvents used. Such effects were observed previously by Ostrenga and Steinmetz (1970) for corticosteroids. The effects of various macromolecules, dextrans, on increasing the aqueous solubility of cholesterol were examined by Cadwallader and Madan (1981). Solubilities of cholesterol at various temperatures ranging from 284 to 322 K in methanol, ethanol, 2-propanone, acetonitrile and propan-l-01, and in some aqueous mixtures of these solvents, were presented by Bar et al. (1984) without any information about solid-phase transitions in this temperature region. In spite of this literature on cholesterol, there is comparatively little precise information regarding the interconversion of the crystalline forms of cholesterol connected with solubility. The solubilities of cholesterol in six solvents - benzene, toluene, cyclohexane, l,Zdichloroethane, trichloromethane and tetrachloromethane - have recently been determined in our laboratory by a dynamic method in the temperature range from 290 to 350 K. 2. Experimental Solubilities were determined by a dynamic (synthetic) method, described in full by Domanska (1986). Mixtures of solute and solvent, prepared by weighing, were heated very slowly (heating rate did not exceed 2 K h-l near the equilibrium temperature) with stirring. The temperature at which the last crystals disappeared (the solution was no longer cloudy) was taken as the temperature of the solution-crystal equilibrium. Measurements were performed for a wide range of solute concentrations from x1 = 0 to x1 = 0.2 for benzene, and from x1 = 0.0008 to x1 = 0.35 for other solvents, and over the phase transition temperature region. The accuracy of temperature measurements was +0.05 K. Reproducibility of measurements was to within 0.1 K, which corresponded to a root error in composition 6x1 = 0.001. Table 1 Characteristics
of solvents
Substance
pe98.15
(m3mop)
a
Source
298.15 nD
Literature Benzene
89.40
Toluene
106.80
Cyclohexane
108.70
1,2-Dichloroethane
79.40 b
Trichloromethane
80.68 b
Tetrachloromethane
97.10
B Barton (1975). b Riddick and Bunger (1970).
Merck-Schuchard Mtinchen Merck-Alkaloid Skopje, Yugoslavia Merck-Alkaloid Skopje, Yugoslavia Merck-Schuchard Miinchen Kemika Zagreb, Yugoslavia Zorka Sabac Yugoslavia
T,,,
b
W)
Observed
1.49792
1.49785
314.9
1.49413
1.44304
321.3
1.42354
1.42352
316.1
1.4421
1.44241
313.6
1.44293
1.44291
323.6
1.45739
1.45732
301.7
193
U. Domariska et al. / Fluid Phase Equilibria 97 (1994) 191-200
All solvents were purified by fractional distillation and then dried over 4 8, molecular sieves (SERVA Chemical). The data concerning solvents are given in Table 1. Cholesterol (SIGMA, USA), standard for chromatography (99 +%), was used without further purification. The observed melting temperature of solute was 421.15 K and the following values of enthalpy of fusion and phase transition, taken from the work of Garti et al. (1980) for benzene solutions, were used in the calculations: AH,,,, = 28.034 kJ mol-’ and AH,,, = 2.845 kJ mol-‘. There was no information about heat of transition and melting after crystallization of cholesterol from other solvents, except from tetrachloromethane, where two different values of the enthalpy of fusion were observed. The temperatures of phase transition, observed in different solvents, were taken from the solubility curves and are shown in Table 1. The value of the molar volume of cholesterol at 298.15 K is V, = 338.32 cm3 mol-’ and the values of the solvent molar volumes shown in Table 1. All the direct experimental data are collected in Table 2, where T” and Tp are high and low polymorphic experimental equilibrium temperatures, respectively, Tkenet is the metastable phase equilibrium temperature, and T2 is the solute 2 liquidus equilibrium temperature.
Table 2 Solubility measurements of cholesterol in organic solvents Xl
T” (K)
Benzene 0.2019 0.1760 0.1664 0.1564 0.1471 0.1405 0.1310 0.1240 0.1186 0.1119 0.1074 0.1007
349.7 341.6 338.2 334.6 329.6 326.5 322.3 319.6 317.5 314.5 312.8
CL W
309.5
a
TaW)
314.6 314.6
XI
Ts(K)
0.0919 0.0852 0.0768 0.0638 0.0511 0.0430 0.0252 0.0175 0.0115 0.0048 0.0
313.5 312.4 310.8 307.7 304.6 302.2 295.6 291.7 278.9
0.1156 0.1019 0.0861 0.0770 0.0653 0.0588 0.0510 0.0425 0.0331
312.9 310.1 306.7 304.2 301.0 299.8 296.2 291.9 286.3
0.0477 0.0419
314.5 313.1
278.2 278.6
Toluene 0.3438 0.3230 0.2941 0.2570 0.2239 6.1978 0.1794 0.1710 0.1519 0.1294 Cyclohexane 0.1821 0.1758
372.3 366.4 358.6 348.7 338.1 329.1 323.1 321.3 319.4 315.3 352.4 349.4
Tz W
b
194
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
Table 2 (continued)
TsWI
0.0354 0.0306 0.0201 0.0132 0.0094 0.0064 0.0008
311.4 309.1 305.7 301.6 298.7 281.1 280.0
353.1 346.7 342.9 337.8 332.5 327.4 323.0 320.0 316.3 313.6
0.0175 0.0082 0.0045 0.0020
312.4 309.3 304.6 295.6
334.1 331.9 330.3 326.8 324.4
0.0561 0.0493 0.0428 0.0365 0.0323 0.0290 0.0241 0.0204 0.0162 0.0133
317.6 315.6 312.9 309.6 307.0 304.7 300.6 296.3 290.6 286.4
0.0819
297.9 295.6 293.4 290.6
T” W)
0.1640 0.1447 0.1338 0.1185 0.1029 0.0880 0.0783 0.0706 0.0626 0.0549
346.0 339.9 338.4 331.9 326.6 321.6 318.4 315.6
1,2_Dichlorethane 0.1711 0.1428 0.1237 0.1006 0.0795 0.0609 0.0479 0.0409 0.0325 0.0262 Trichloromethane 0.1254 0.1183 0.1138 0.1065 0.1003 0.0939 0.0867 0.0816 0.0753 0.0659 Tetrachloromethane 0.1934 0.1812 0.1751 0.1604 0.1455 0.1356 0.1252 0.1160 0.1113 0.0947
a
Xl
Xl
T&e,W
312.6 309.8
TsWI
315.6 315.1
323.1 322.9 321.8 320.8 319.5
350.6 344.1 341.1 334.6 327.7 322.6 316.9 312.6 307.0
a tl metastable phase equilibrium
0.0713 0.0615 0.0506 0.0418
290.6
temperature.
287.4
300.4 b Solute 2 liquidus equilibrium
temperature.
T, (K) b
U. Domahska et al. / Fluid Phase Equilibria 97 (1994) 191-200
195
3. Results and discussion The solubility of cholesterol in hydrocarbons is similar to that in halohydrocarbons, and decreases in the order toluene > benzene > cyclohexane and tetrachloromethane > trichloromethane > 1,2-dichloroethane. Toluene proved to be the best solvent. The cholesterol molecule has a hydroxyl group and a double bond, thus having the potential for interaction with both polar and aromatic solvents. Solutes apparently reduce the self-association in tetrachloromethane and trichloromethane, but show a greater interaction with aromatic solvents than with trichloromethane, where the possibility of hydrogen bonding with the trichloromethane may be expected. The solubility in tetrachloromethane, toluene and benzene is higher than in trichloromethane. In benzene, toluene and tetrachloromethane the solubility is higher than ideal, and the experimental activity coefficient of the solute (7,) is in the range 0.43- 1.O; in cyclohexane, trichloromethane and 1,Zdichloroethane the solubility it is lower than ideal, and the activity coefficient of the solute (yl) is in the range 1.3-16.8. The shapes of the liquidus curves are shown in Fig. 1 for the cholesterol + benzene system as an example. The temperature and mole fraction of solute 1 were Ttrl = 314.9 K, x1 = 0.113 and
350
330
290
270 0
0.05
0.15
0.1
0.2
0.25
Xl
Fig. 1. Solid-liquid equilbrium diagram for cholesterol( 1) + benzene(2) binary system. Solid lines: calculated by the Wilson equation. Dotted line: ideal solubility.
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
196
TE = 277.3 K, x = 0.001 at the phase transition and eutectic point, respectively. The thermal transition of cholesterol has been studied by differential thermal analysis (DTA) in many different laboratories. Spier and Senden ( 1965) observed one point at 313 K and no further transitions up to the melting point. Pietropawlow et al. (1988) measured the enthalpy of the phase transition AH,,, = 2.5 kJ mol-’ at 304.8 K. The effect of various organic solvents on the structure of crystals, enthalpy, and temperature of phase transition and fusion have been studied by Garti et al. (1980, 1981). The authors suggested that the polymorphic transition of cholesterol may be divided into several sub-transitions, each one corresponding to a slight configurational change, that can be attributed to a possible flip-over of the aliphatic chain of the cholesterol. Authors find differences in crystal habit, indicating dependence on the solvent-solute interaction even under the same crystallization conditions. Plates and needle-like crystals of different sizes were observed, depending mainly on the kind of solvent. Owing to the hydroxyl group and the double bond in a cholesterol molecule, it is reasonable to assume that the crystal habit of cholesterol is dictated by the solvent-solute interaction as well as by the crystallization conditions. The temperature of phase transition, observed during our solubility measurements, differs from 301.7 K in tetrachloromethane to 323.6 K in trichloromethane (see Table 1). The solubility of a solid non-electrolyte, 1, in a liquid solvent, can be expressed as -lnx,
=+
(+-$--)-+[In(&)++-l]+lny,
(1)
yl, AH,,, ACpml,T,, and T are the mole fraction, activity coefficient, enthalpy of fusion, solute heat capacity during the melting process, melting temperature of the solute, and equilibrium temperature, respectively. If the solid-solid transition occurs before fusion, an additional term must be added to the right-hand-side of Eq. (1) (Weimer and Prausnitz, 1965; Choi and McLaughlin, 1983):
where x1,
-lnX,=+($-+--)-*[,n($-)++-l]++(+-$--)+lny,
(2)
where AH,,, and Tt,, are the enthalpy and temperature of the solid-solid transitions of the solute. In this work, Eq. ( 1) was used for temperatures above the transition temperature and Eq. (2) at lower temperatures. It was assumed that the solute heat capacity during the melting process is A&, = 8.8 J K-i, as was found for the phase transition process (Labowitz, 1972). In this study, three methods were used to represent the solute activity coefficient (yi) from the so-called correlation equations that describe the Gibbs excess free energy of mixing (GE): the Wilson equation (Wilson, 1964), the UNIQUAC equation (Abrams and Prausuitz, 1975) and the UNIQUAC associated-solution model (Nagata, 1985). The exact mathematical forms of the equations have been presented in a previous paper (Domanska et al., 1989). The parameters were fitted by the optimization technique. The objective function was as follows: F(A,, AZ) = i wY2[ln x,iYii(T, xii, Ai, i-l
A2)
-
In
adTi)12
(3)
where In aii denotes an “experimental” value of the logarithm of solute activity, taken as the right-hand-side of Eq. (l), wi is the weight of an experimental point, Ai and A2 are the two
V. Domariska et al. 1Fluid Phase Equilibria 97 (1994) 191-200
197
adjustable parameters of the correlation equations, i denotes the ith experimental point, and n is the number of experimental data. The weights were calculated by means of the error propagation formula: a In xlyl - a In aj 2 dT ( > T=
+
2
(ATi>’ + Ti
a ‘;;I” (
1
thli)
>Xi’Xli
(4)
where AT and Ax, are the estimated errors of T and x1, respectively. According to the above formulation, the objective function is consistent with the maximum likelihood principle, provided that the first-order approximation (Eq. 4) is valid. Neau and Peneloux (1981) called such a procedure the observed deviation method. The experimental errors of temperature and solute mole fraction were fixed for all cases and set to AT = 0.1 K, Ax, = 0.001. The root-mean-square deviation of temperature defined by Eq. (5) was used as a measure of the goodness of fit of the solubility curves: d = T
i [ i=l
(Ty'
1
- TJ’ 1’2
(n-1)
(5)
where Ty8’ and Ti are, respectively, the calculated and experimental temperatures of the ith point, and n is the number of experimental points. The calculated values of the equation parameters and corresponding root-mean-square deviations are presented in Table 3. It can be noted that a description is not very good (CT > 2 K) and in the same range for both two-parameter equations. Average deviations are 4.6 and 5.4 K for the Wilson and UNIQUAC equations, respectively. The calculations with the Wilson equation utilizing simple temperature dependent parameters, i.e. (gg - gji) = auT-‘, have given comparable results. The calculations with the UNIQUAC associated-solution model carried out by using different literature data sets of self-association of cholesterol in trichloromethane (Foster et al., 1981) and in tetrachloromethane (Kunst et al,, 1979; Foster et al., 1981; Costas and Patterson, 1985; Caceres-Alonso et al., 1988), have been compared with the simple UNIQUAC and the rootmean-square deviations of correlations varied from 4.5 K (for benzene and cyclohexane with the self-association constant K2 = 5077 at 298.15 K, through hydrogen bonding h, = -24.0 kJ mol-’ from Costas and Patterson, 1985) to 13.7 K for tetrachloromethane. So, in addition, calculation with K2 as the third adjustable parameter at the temperature 298.15 K were made using values of the hydrogen-bond formation enthalpy h2 = - 24.0 kJ mol-*, taken from Costas and Patterson (1985). The temperature dependence of the association constants was calculated from the van’t Hoff relation, assuming the enthalpy of hydrogen-bond formation to be temperature independent. The results are presented in Table 3. Overly large values of the root-mean-square deviations have been observed in the system of cholesterol in tetrachloromethane, (flT = 7.1 K), where the more complicated model of association (monomer < dimer < trimer < tetramer) may be expected.
4. Conclusion The phenomenon of solid-solid phase transition of cholesterol in every tested solvent has been noted at different temperatures as a result of solute-solvent interactions.
No. of dam points
22
20
22
15
21
16
Solvent
Benzene
Toluene
Cyclohexane
1,2-Dichloroethane
Trichloromethane
Tetrachloromethane
5037.67 171.75 60129.80 - 728.39 9766.10 - 53.93 7904.21 1265.20 2036.46 1236.49 - 1467.87 916.74
giz -g11 g12 - g22 (J mol- ‘)
Wilson
Parameters
-1191.05 2231.67 - 2034.45 3939.86 - 1778.93 3598.53 - 1024.84 2567.33 160.78 546.06 2368.32 - 1498.65
$iOP,
UNIQUAC AU,,
-1181.00 2200.53 512.34 - 540.87 3309.19 - 1934.43 2492.89 - 1230.83 283.66 418.87 49.56 48.49
(J mol-‘)
Au21
UNIQUAC A%?
ASM
2.32
0.0
0.0
0.0
224.8
446.7
K,
6.8
2.0
4.3
6.0
4.5
4.0
%
Wilson
5.7
2.0
7.5
9.0
4.3
4.0
Y-6
UNIQUAC
and UNIQUAC
Deviations
Table 3 Correlation of the solubility data for cholesterol in organic solvents by means of the Wilson, UNIQUAC of parameters and measures of deviations
7.1
2.3
1.3
4.3
4.7
3.7
&
UNIQUAC
ASM
ASM equations: values
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
199
The best results of the correlation of experimental points in binary systems of cholesterol have been obtained by the use of the Wilson equation.
5. List of symbols a1
au AI,
~42
gij AC,,, AH,, AH,,, h2 K2 n I
R T AT TCBI
T ml T tr1 vi X1 AXI W
activity of the solute proportionality constant of the Wilson equation defined by (gV - g& = avT- ’ binary interaction parameters of the Wilson and UNIQUAC equations molar energy of interaction between i and j difference between heat capacities of the solute in the solid and liquid states at T,, molar enthalpy of fusion of the solute molar enthalpy of first-order solid-solid transition enthalpy of hydrogen-bond formation association constant, (@2i+#D2$DzM)[i/(i+ l)] number of experimental points number of adjustable parameters universal gas constant experimental equilibrium temperature estimated error of temperature calculated equilibrium temperature melting point temperature of the pure solute temperature of transition point molar volume of the solute or solvent mole fraction of the solute estimated error of the solute mole fraction weight of experimental point
5.1. Greek letters a, P Yl CT
high- and low-temperature polymorphic structure of the solute activity coefficient of the solute root-mean-square deviation in temperature
6. References Abrams, D.S. and Prausnitz, J.M., 1975. Statistical thermodynamics of liquid mixtures; a new expression for. the excess Gibbs energy of partly or completely miscible systems. AIChE J., 21: 116-128. Bar, L.K., Gartl, N., Sarlg, S. and Bar, R., 1984. Solubilities of cholesterol, sitosterol and cholesteryl acetate in polar organic solvents. J. Chem. Eng. Data, 29: 440-443. Barton, A.F.M., 1975. Solubility parameters. Chem. Rev., 76: 731-753.
200
U. Domariska et al. 1 Fluid Phase Equilibria 97 (1994) 191-200
Caceres-Alonso, M., Costas, M., Andreolli-Ball, L. and Patterson, D., 1988. Steric effects on the self-association of branched and cyclic alcohols in inert solvents. Apparent heat capacities of secondary and tertiary alcohols in hydrocarbons. Can. J. Chem., 66: 989-998. Cadwallader, D.E. and Madan, D.K., 1981. Effect of macromolecules on aqueous solubility of cholesterol and hormone drugs. J. Pharm. Sci., 70: 442-445. Choi, P.B. and McLaughlin, E., 1983. Effect of phase transition on the solubility of solid. AIChE J., 29: 150-153. Costas, M. and Patterson, D., 1985. Thermodynamics of cholesterol self-association and its interaction with tripalmitin and l-a-lecithin. J. Chem. Sot., Faraday Trans. 1, 81: 655-671. Domanska, U., 1986. Vapour-liquid-solid equilibrium of eicosanoic acid in one- and two-component solvents. Fluid Phase Equilibria, 26: 201-220. Domanska, U., Domanski, K., Klofutar, C. and Paljk, S., 1989. Solubility of tetracosane in aliphatic alcohols. Fluid Phase Equilibria, 46: 25-39. Flynn, G.L., Shah, Y., Prakongpan, S., Kwan, K.H., Higuchi, W.J. and Hofmann, A.F., 1979. Cholesterol solubility in organic solvents. J. Pharm. Sci., 68: 1090-1097. Foster, B.W., Robeson, J., Tagata, N., Beckerdite, M., Huggins, R.L. and Adams, Jr., E.T., 1981. Self-association of cholesterol in nonaqueous solutions. J. Phys. Chem., 85: 3715-3720. Garti, N., Karpuj, L. and Sarig, S., 1980. Phase transitions in cholesterol crystallized from various solvents. Thermochim. Acta, 35: 343-348. Garti, N., Karpuj, L. and Sarig, S., 1981. The effect of solvents and crystallization conditions on crystal habit of cholesterol. Cryst. Res. Technol., 16: 1 11 l- 1115. Kritchevsky, D. and Tepper, S.A., 1964. Solubility of cholesterol in various fats and oils. Proc. Sot. Biol. Med., 116: 104-107. Kunst, M., van Duijn, D. and Bordewijk, P., 1979. Self-association of cholesterol in carbon tetrachloride. Z. Naturforsch, Teil A, 34: 369-374. Labowitz, L.C., 1972. Change of phase and change of state in biological systems. Thermochim. Acta, 3: 419-420. Nagata, I., 1985. On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilibria, 19: 153-174. Neau, E. and Peneloux, A., 1981. Estimation of model parameters. Comparison of methods based on the maximum likelihood principle. Fluid Phase Equilibria, 6: 1 - 19. Ostrenga, J.A. and Steinmetz, C. 1970. Estimation of steroids solubility: use of fractional molar attraction constants. J. Pharm. Sci. 59: 414-416. Pietropawlow, I.I., Cygajkowa, I.G. and Tislenko, L.A., 1988. Microcalorimetriczeskie issledowanija polimernych perehodow w organiczeskih krystallah. Crystallogr., 33: 1433- 1436. Riddick, J.A. and Bunger, W.B., 1970. Techniques of Chemistry, Vol. II. Organic Solvents, Physical Properties and Methods of Purification, Wiley-Interscience, New York. Spier, H.L. and Senden, K.G., 1965. Phase transition of cholesterol. Steroids, 6: 871-873. Stauffer, R. and Bischoff, F., 1966. Solubility determination of cholesterol polymorphs in organic solvents. Clin. Chem., 12: 206-210. Weichherz, J. and Marschik, H., 1932. Die lijslichkeit des cholesterol in ldsungsmittelgemischen. B&hem. Z., 249: 312-322. Weimer, R.F. and Prausnitz, J.M. 1965. Complex formation between carbon tetrachloride and aromatic hydrocarbons. J. Chem. Phys., 42: 3643-3644. Wilson, G.M., 1964. Vapor-liquid equilibrium. XI. A new expression for the excess free energy of mixing. J. Am. Chem. Sot., 86: 127-130.