Self-association of cholesterol in benzene and toluene solutions

Spectrochimica Acta Part A 54 (1998) 709 – 717

Self-association of cholesterol in benzene and toluene solutions Marjan Senegac' nik Jr. a, Cveto Klofutar b,* b

a Uni6ersity of Maribor, Faculty of Organizational Sciences, 4000 Kranj, Slo6enia Department of Food Technology, Biotechnical Faculty, Uni6ersity of Ljubljana and J. Stefan Institute, 1000 Ljubljana, Slo6enia

Received 8 August 1997; accepted 11 November 1997

Abstract The self-association of cholesterol in dilute benzene and toluene solutions was investigated by conventional infrared spectroscopy. The sample spectra, recorded in the fundamental OH stretching range, were resolved into the bands of functionally different OH groups of associated cholesterol and its predominant species identified by analysis of their absorbances. The formation constants of oligomers were derived from monomer absorbances measured as a function of cholesterol concentration. In addition to the monomers A1, open A0 2 (DH0 2 = − 119 1 kJ mol − 1) and cyclic dimers A. 2 (DH. 2 = −249 2 kJ mol − 1) in benzene and open dimers A0 2 (DH0 2 = − 129 1 kJ mol − 1) and tetramers A4 (DH4 = −4796 kJ mol − 1) in toluene were established as the prevailing species. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Cholesterol; Benzene; Toluene

1. Introduction The behaviour of cholesterol in inert solvents is still a topical subject of investigation, motivated by the expectation that any new information obtained might contribute to a better understanding of its role in life processes. A related recent paper [1] reported a pronounced solvent effect on its IR spectra and mode of association in 1,2dichloroethane, trichloromethane and tetrachloromethane. Thus, depending on the solvent, after deconvolution two or three absorption bands were observed in the fundamental OH stretching region, differing in their position and * Corresponding author. Tel.: + 386 61 1231161; fax: + 386 61 266296.

intensity. Similarly, a striking solvent effect on its self-association was also established. The association of cholesterol in 1,2-dichloroethane was so found to be restricted to the formation of a cholesterol–solvent complex only, to open dimers A0 2 in trichloromethane and to open trimers A0 3 and cyclic hexamers A. 6 in tetrachloromethane. In the present paper, investigation of the selfassociation of cholesterol was extended to the aromatic solvents benzene and toluene. In view of its previous success, the same IR approach was used as with chlorinated hydrocarbons [1]. The direct experimental identification of prevailing species was expected to provide new independent information on both systems and to reveal whether different solvent effect might arise with closely similar solvents.

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2. Experimental

2.1. Materials Cholesterol (Sigma, St. Louis, MO) was used without further purification and stored in a desiccator over P4O10. Benzene and toluene (both Merck) were purified as recommended in [2]. Both solvents were kept under molecular sieves (4 A). The purity of the solvents was checked by measurement of their refractive index and density at 298 K. The values obtained were in satisfactory agreement with literature data [2].

inner ···O–H··· groups, acting both as proton donors and acceptors. Typical shapes of the absorption spectra and Gaussian deconvoluted bands obtained in each of the two solvents used are shown in Fig. 1(a–b). In Tables 1 and 2 the absorbances (peak heights) of a-, g- and d–OH deconvoluted bands (ha, hg, hd ) in benzene and

2.2. Solutions All solutions were prepared at 293 K on a molar concentration scale (mol dm − 3). The concentration range of cholesterol solutions investigated was 0.06–0.20 mol dm − 3 for benzene and 0.01 –0.20 mol dm − 3 for toluene. Molar concentrations of solutions in the temperature range 298 – 328 K were derived from those at 293 K by applying an appropriate correction for the thermal expansion of the solution [3].

2.3. IR measurements Infrared spectra of cholesterol solutions in the range 3000–4000 cm − 1 were obtained with a Philips PU 9712 double beam dispersive spectrophotometer. Using an absorption cell (0.047 cm) with KBr windows, thermostatted to 90.2 K, the spectra were recorded at the temperatures of 298, 308, 318 and 328 K, against pure solvent as reference.

3. Results and discussion As before [1] each sample spectrum in the fundamental stretching range 3100 – 3700 cm − 1 was numerically resolved by the method of least squares [4] into three bands: the a – OH band due to free –OH groups of monomers, the g– OH band of proton donating terminal – O – H··· groups, and the d – OH band corresponding to

Fig. 1. Experimental IR spectra (——), deconvoluted Gaussian OH bands (- - -) and fitted spectra ( · · · ) of associated cholesterol solutions in benzene (a) and toluene (b) at 298 K. Path length l =0.0047 dm; As =0.16 mol dm − 3. Frequencies (ni /cm − 1) of maximum intensities of bands in the order na, ng, nd : a — 3573, 3469, 3341; b — 3571, 3468, 3342. The band at n 3200 cm − 1 is probably due to C – H stretching modes.

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Table 1 Absorbances of a-, g- and d–OH deconvoluted bands of cholesterol solutions in benzene As (mol dm−3)

ha

hg

hd

As (mol dm−3)

ha

hg

hd

0.0597 0.0589 0.0582 0.0573

0.164 0.160 0.155 0.141

0.020 0.018 0.020 0.015

0.008 0.008 0.009 0.006

0.1392 0.1376 0.1358 0.1340

0.313 0.313 0.302 0.291

0.072 0.072 0.062 0.057

0.026 0.026 0.017 0.018

0.0795 0.0786 0.0776 0.0765

0.209 0.202 0.194 0.188

0.033 0.029 0.028 0.021

0.014 0.012 0.012 0.004

0.1591 0.1572 0.1552 0.1532

0.352 0.350 0.342 0.337

0.096 0.085 0.079 0.068

0.056 0.037 0.028 0.022

0.0994 0.0982 0.0970 0.0956

0.246 0.238 0.224 0.219

0.050 0.043 0.039 0.034

0.012 0.008 0.008 0.007

0.1790 0.1769 0.1747 0.1724

0.377 0.371 0.365 0.356

0.126 0.108 0.092 0.086

0.069 0.049 0.036 0.028

0.1193 0.1179 0.1164 0.1148

0.274 0.273 0.268 0.260

0.067 0.058 0.051 0.044

0.025 0.022 0.017 0.014

0.1989 0.1966 0.1941 0.1916

0.387* 0.410 0.385* 0.365

0.133 0.132 0.112 0.099

0.059 0.064 0.035 0.028

toluene solutions are represented as a function of stoichiometric cholesterol concentration (As) and temperature, respectively. The data for hj, As ( j = a, g, d), derived from the same sample initially prepared at 293 K, are listed in columns with the temperature increasing downwards in the order 298, 308, 318 and 328 K. The oligomer Ai preponderantly contributing to either g- or d–OH deconvoluted bands, was again identified from the slope ij of the diagnostic plot [1,5]. ln hj =ln bi



e ia +ij ln ha ; ej

j= g, d

(1)

where bi is the formation constant of Ai, ea =(oal) − 1 and ej =(oj l) − 1 with oa denoting the molar absorptivity of the monomer at na, oj that of Ai at nj, and l the optical path length, respectively. The respective plots of the maximum intensities of the g- and d – OH bands for benzene and toluene solutions at 298 K are shown in Fig. 2(a,b). The association parameters oa, bi were again derived [1] by optimization of the objective function S =% [(As/ha )exp − (As/ha )mod]2 i

where

(2)

As = eaha + % ibi (eaha )i,

(3)

i

refers to cholesterol mass balance expressed in terms of its established predominant species only. The output parameters were further improved by iterative minimization, using for oa and bi the regression values derived from the linear dependence of oa on temperature and ln bi ; on 1/T, respectively. The success of the models and association parameters derived in reproducing the measured As/ha ratios is expressed in terms of the standard deviation s = [S/(N −1)]1/2 of N experimental ha, As data points from the model values (Tables 3 and 4). The absorbances (peak heights) h *j in Tables 1 and 2, apparently deviating in the diagnostic plots (1) from the remaining ones, were not used in subsequent minimizations (2). With the exception of the enthalpies of dimerization in benzene (Eq. (5)), all other thermodynamic functions of association processes were calculated as previously from standard expressions relating these properties with the association constant. According to the position of their absorption maxima, the three bands in the resolved spectra of cholesterol solutions in benzene (Fig. 1(a)) can be classified as the a–OH (na = 35769 2 cm − 1), g– OH (ng = 34789 10 cm − 1) and d–OH (nd =

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Table 2 Absorbances of a-, g- and d–OH deconvoluted bands of cholesterol solutions in toluene As (mol dm−3)

ha

hg

hd

As (mol dm−3)

ha

hg

hd

0.0099 0.0098 0.0097 0.0096

0.028* 0.026* 0.028 0.026

— — — —

— — — —

0.1193 0.1180 0.1167 0.1154

0.281 0.282 0.274 0.257

0.059 0.054 0.045 0.037

0.025 0.020 0.007 0.006

0.0199 0.0197 0.0194 0.0192

0.060 0.051* 0.056 0.050

0.004 — — —

— — — —

0.1392 0.1377 0.1362 0.1347

0.307 0.304 0.295 0.295

0.079 0.071 0.061 0.049

0.040 0.024 0.015 0.008

0.0398 0.0393 0.0389 0.0384

0.111 0.108 0.106 0.097

0.010 0.009 0.008 0.007

— — — —

0.1591 0.1574 0.1557 0.1540

0.343 0.337 0.327 0.322

0.102 0.087 0.076 0.067

0.054 0.034 0.024 0.011

0.0597 0.0590 0.0583 0.0579

0.161 0.157 0.152 0.144

0.022 0.017 0.018 0.015

— — — —

0.1790 0.1771 0.1752 0.1733

0.374 0.378 0.365 0.351

0.121 0.108 0.092 0.081

0.082 0.051 0.035 0.019

0.0796 0.0787 0.0778 0.0769

0.207 0.197 0.189 0.186

0.035 0.031 0.027 0.023

0.0097 0.0055 0.0038 0.0025

0.1989 0.1968 0.1947 0.1925

0.368* 0.391 0.388 0.376

0.148 0.129 0.114 0.098

0.106 0.072 0.045 0.031

0.0995 0.0984 0.0973 0.0962

0.237 0.229 0.220 0.217

0.043 0.040 0.033 0.029

0.0133 0.0083 0.0022 —

3322913 cm − 1) bands, respectively. In order to establish the species causing the g- and d – OH band, their peak heights were analyzed as previously by plotting ln hj vs. ln ha ( j =g, d) (Eq. (1)). The slopes observed ig $id :2 (Fig. 2(a) and Table 3) showed that dimers were the species predominately absorbing both at ng and nd. Following the conventional classification of hydrogen bonded OH groups [6], the dimers causing the g– OH band are easily identified with open dimers A0 2. The recognition of the origin of the d – OH band, however, seems less straightforward. It might be either (i) a differential band of the g– OH band, or (ii) a band caused by a predominant cyclic dimer A. 2 absorbing at nd. A conclusive answer to this dilemma was provided from the enthalpies of formation DH2,g and DH2,d of A0 2 and a nonidentified dimer A2 contributing to the d – OH band. Namely, in case (i) the relation

DH2,d : DH2,g is to be expected, and DH2,d : 2DH2,g when cyclic dimers A0 2 are present. The procedure followed for the evaluation of DH2,g and DH2,d was analogous to that for the estimation of the enthalpy of formation of the cholesterol-1,2-dichloroethane complex [1]. After substituting the standard expression b2, j = e − DH2, j /RT · eDS2, j /R;

j= g, d

(4)

for the dimerization constant in Eq. (1), and assuming the ratio of ea /eg [7]1 and the entropy term DS2,j to be temperature independent, it can be rearranged to ( ln hj ( ln oa DH2, j = − R + ((1/T) ha ((1/T)





= − R[sk 2, j + so ];

n

j= g, d

1 The respective values for cholesterol solutions trichloromethane [1] and toluene (Table 4) support this.

(5) in

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The required values of the first term in brackets, sk 2, j, are experimentally available from the coefficients of the regression expression j=g, d

hj = k2, j h 2a ;

(6)

determined at all four temperatures considered (Table 3). Since



( ln hj ((1/T)

  =

ha



( ln k2, j ((1/T)

ha

=sk 2, j ;

j= g, d

(7)

sk 2, j is given by the slopes of the respective least square regression lines ln k2,g = − (2.6490.02) + (730 9100) ·

1 T

ln k2,d = − (8.4990.06) +(2260 9 250) ·

1 T

(8) (9)

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The values of the second term in parenthesis of Eq. (5), so, can similarly be obtained from the slope of the regression line ln oa = (4.5390.01)+(6309 40) ·

1 T

(10)

derived from oa values in Table 3. With the values of sk 2, j and so so calculated, the enthalpies of the corresponding dimerization processes were found to amount to DH2,g = DH0 2 = − 1191 kJ mol − 1 and DH2,d = DH. 2 = − 249 2 kJ mol − 1, respectively. Since DH2,d : 2DH2,g this proves that the d –OH band results from absorption of a cyclic dimer A. 2, i.e. from its inner d–OH group. Such an assignment seems to be further supported by its slightly lower frequency location (3322913 cm − 1) than in the spectra of toluene and tetrachloromethane solutions (33579 15 cm − 1), expected because of stronger hydrogen bonding in the cyclic dimer A. 2. On the basis of the evidence derived, a three species A1 + A0 2 + A. 2 model was thus felt to yield the best description of the association of cholesterol in benzene solutions. In the light of previous assignations the finding that the d–OH band results from cyclic dimers A. 2 is quite surprising, as this band was expected to be due to higher oligomers Ai (i] 3). The relevant form of Eq. (2) for this system does not enable a direct determination of the individual values of b0 2 and b. 2 but only their sum (Table 3). Hence, they were derived indirectly. With this in view their sum was expressed as 0 0 : . b0 2 + b. 2 = e − DH2/RT · eDS2/R + e − DH2/RT · eDS2/R (11)

Fig. 2. Diagnostic ln hj vs. ln ha ( j = g, d) least squares plots of peak heights of cholesterol deconvoluted bands in benzene (a) and toluene (b) solutions at 298 K. : − ln hg, : −ln hd ; slopes: ig =2.1 90.1 (a); 1.99 0.1 (b); id = 2.69 0.3 (a); 4.29 0.2 (b).

After inserting the values of DH0 2 and DH. 2 obtained, Eq. (11) was minimized with respect to DS0 2 and DS0 2, using b0 2 + b. 2 values achieved by previous optimization of the corresponding Eq. (2) at each of the four temperatures considered (Table 3). With the values of DS0 2 and DS. 2 so obtained, and with the corresponding enthalpies DH0 2 and DH. 2, the individual values of b0 2 and b. 2 were then calculated from Eq. (4). Their values, together with molar absorptivities oa, og and od are summarized in Table 3. The frequency shifts Dng =  1009 10 cm − 1 and Dnd = 2559 15 cm − 1 observed for the g- and

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Table 3 Association parameters of the cholesterol–benzene system T/K

ig

298 308 318 328

2.14 90.10 2.08 90.06 1.89 90.09 1.96 90.11

T/K

k2,g

298 308 318 328

0.84 90.02 0.76 90.01 0.70 90.01 0.68 90.02

oa (mol−1 dm2)

b0 2+b. 2 (mol−1 dm3)

751 9 4 712 9 3 666 9 5 620 97

3.19 90.06 2.60 9 0.05 2.17 9 0.07 1.83 9 0.09

k2,d

b0 2 (mol−1 dm3)

b. 2 (mol−1 dm3)

0.399 0.03 0.34 9 0.02 0.249 0.02 0.209 0.01

2.0 9 0.5 1.8 9 0.4 1.5 9 0.4 1.3 9 0.3

id 2.69 0.3 2.3 9 0.4 2.09 0.4 2.09 0.2

1.2 9 0.3 0.9 90.2 0.7 90.2 0.5 9 0.1

s

N 0.0004 0.0003 0.0006 0.0021

7 8 7 8

og (mol−1 dm2)

od (mol−1 dm2)

1120 9 30 1040 920 990 920 940 940

900 9 60 850 960 800 9 40 780 9 30

DH0 2 = −119 1 kJ mol−1 DS0 2,298 = −319 6 J mol−1 K−1 DG0 2,298 = −1.7 kJ 9 0.7 mol−1 DH. 2 = −249 2 kJ mol−1 DS. 2,298 = −799 8 J mol−1 K−1 DG. 2,298 = −0.59 0.7 kJ mol−1

d – OH band relative to the a – OH band (Fig. 1(a)) clearly show the diversity of bonding of OH groups in A0 2 and A. 2 as predicted by the classification of hydrogen bonded OH groups adopted [6]. In addition, owing to their different mode of electrostatic interaction with the oxygen atom of the second cholesterol molecule, a pronounced effect on their molar absorptivities is also expected [8,9]. Two types of such an interaction can be foreseen. In the hydrogen bond of an open dimer A0 2 (Fig. 3(a)) the O – H bond and the axis of the oxygen lone pair sp3 hybrid orbital are collinear and thus in the most favourable relative positions for maximum interaction. The bond moment of the polar O – H group induces an atomic dipole moment in the highly polarizable lone pair. During the stretching of the O – H bond the induced moment oscillates in phase with the inducing bond dipole. The component it contributes to the overall change of the dipole moment of the vibrating OH group leads to an increase in the molar absorptivity of its stretching mode relative to that of the a –OH group [9]. Because of the presence of the two hydrogen bonds in a cyclic dimer the effect of their OH group interaction is expected to be distinctly different from that in an

open dimer. Two models were proposed for cyclic dimers of primary alcohols in the past: a structure with planar hydrogen bonds and a configuration with nonplanar ones [10]. In both models the hydrogen bonds are assumed to be nonlinear, the deviation from linearity being the least in the planar model. In a more explicit representation of the planar model (Fig. 3(b)) the bond moments of the stretching OH bonds as the induced dipoles in oxygen lone pair sp3 orbitals are pairwise parallel but pointing in opposite directions. In a more realistic moderately nonplanar model the orientations of these dipoles are divergent but still such that their mutual compensation might result in a significant decrease in the overall bond moment of both OH groups. In view of this the molar absortivity of the d–OH group is expected to be lower than that of the monomer free OH group. The observed experimental values of og : 1.5 oa and od /2:0.6oa (cf. Table 3) are in good agreement with these predictions and provide additional support for the occurrence of cyclic dimers A. 2. The effect on the strength of the hydrogen bond in A. 2 is, however, less pronounced. Namely, the energy released in stronger O···H bonding is used for the stretching of its two O–H bonds and

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Table 4 Association parameters of the cholesterol–toluene system T/K

ig

id

oa (mol−1 dm2)

og (mol−1 dm2)

b0 2 (mol−1 dm3)

b4 (mol−3 dm9)

s

N

298 308 318 328

1.93 90.07 2.04 90.06 1.93 90.06 1.89 90.07

4.29 0.2 3.89 0.2 4.29 0.2 4.29 0.7

6969 6 6599 11 6259 6 5939 4

8679 14 866 9 20 822926 816921

2.2 9 0.2 1.9 9 0.2 1.6 9 0.2 1.4 9 0.1

11 92 8 93 4 93 291

0.0071 0.0120 0.0111 0.0069

9 9 11 11

DH0 2 = −12.090.8 kJ mol−1 DS0 2,298 = −349 3 J mol−1 K−1 DG0 2,298 = −1.99 0.2 kJ mol−1 K−1 DH4 = −479 6 kJ mol−1 DS4,298 = −1409 20 J mol−1 K−1 DG4,298 = −5.99 0.5 kJ mol−1 K−1

arrangement of both hydrogen bonds formed into the conformation required for the ‘double’ bond. The participation of the latter is also reflected in the entropy of formation DS. 2 – DS0 2 of the second hydrogen bond, the magnitude of which is  1.5 times than that of the first one. The expression % hj =% % bi (e ia /ej )h ia ; j

i

j= g, d;

i] 2

(12)

j

relating the absorbances of the deconvoluted bands to the formation constants bi and ej ’s of the associated species Ai provides an independent compatibility test for the association model applied. The respective absorbance plots (hg +hd )/ha vs. ha for cholesterol – benzene solutions correlated at all four temperatures satisfactorily, with the required straight lines going close to the origin and with slopes agreeing with their model values of sh = b0 2/eg +b. 2/ed, (Fig. 4(a)). Similarly, the model fraction of cholesterol, present in both dimers, increasing monotonically with the monomer concentration a from 25% (a =0.05 mol dm − 3) to 40% (a=0.10 mol dm − 3) at 298 K was found to be in good agreement with the observed one. The self-association of cholesterol in benzene was recently investigated by Klofutar et al. by IR spectroscopy and electric permittivity measurements [11], and by vapour pressure osmometry [12]. In both studies the experimental data were

interpreted by an association model including an extended series of oligomers. Their formation constant bi was described in terms of two independent parameters, i.e. the dimerization constant b2 and a constant K, given by bi = b2(i− 1)K (i − 2) (i] 2) ([13], Eq. (22)). The relevance of this model and of the corresponding association parameters was supported by its success in reproducing the cholesterol mass balance, its osmometric concentrations and electric permittivity over the whole concentration (0.025–0.250 mol kg − 1) and temperature range (298–328 K) studied. In the deconvoluted spectra of cholesterol in toluene solutions the centres of the a-, g- and d–OH bands are located within the ranges na = 35729 1 cm − 1, ng = 34779 5 cm − 1 and 3357 9 15 cm − 1, respectively (Fig. 1(b)). Attempts to characterize the multimers contributing predominantly to either the g- or d–OH band via diagnostic ln hj vs. ln ha ( j= g, d) plots at all four temperatures yielded slopes of ig : 2 and id : 4, respectively (Fig. 2(b) and Table 4). From these results open dimers A0 2 and tetramers of undetermined type A4 were identified as the main associated species of cholesterol in toluene solutions. Provided that the tetramers are of a sufficient concentration, their type can be recognized from their absorption at ng. Namely, when open (Fig. 3(c)), their g–OH group contributes to the absorbance hg, while the d–OH groups of cyclic tetramers A. 4 (Fig. 3(d)) do not. As may be con-

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Fig. 3. Schematic drawings of plausible structures of the major associated species of cholesterol established and their OH group classification (R = C27H45): (a) open dimer (A0 2): the O–H bond and the axis of the lone pair sp3 orbital on the oxygen atom are collinear, the angles R – O···H and H–O···H are tetrahedral, (b) planar model of cyclic dimer A. 2: the two O – H bonds and the axes of the bonding sp3 hybrid orbitals of both oxygen atoms are in the plane of the paper, the plane ROOR is perpendicular to it, the angle ROO is tetrahedral; (curvy arrow) vibrating O–H bond moment, (dotted curvey arrow) induced dipole; (c) open tetramer; (d) cyclic tetramer.

cluded from the values of b0 2 and b4 (Table 4), the concentration of tetramers is, however, too low (3 – 8% of that of the open dimers A0 2 only) to be clearly detected with the accuracy of hg determination. The results of the relevant hg /ha vs. ha plots [14], suggesting the absence of such absorption, thus merely indicate that open dimers are the dominant species contributing to the g– OH band. Some experimental evidence in favour of the predominance of cyclic tetramers A. 4 seems to come, however, from the established average value of the enthalpy of their hydrogen bond DH4/4 = − 1292 kJ mol − 1 (Table 4), which is the same as for the cyclic dimer A. 2 in benzene and the cyclic hexamer A. 6 in tetrachloromethane [1]. The likely analogy of the self-association of primary alcohols in inert solvents suggested, on the other hand, the occurrence of both types of tetramer with a moderately predominating concentration of either cyclic (A. 4) [5,15,16] or open (A0 4) ones [16]. The reasonable constancy of the absorbance ratio hd /h 4a observed over the ha range investigated proved that tetramers are the main contributor to the d– OH band. In the absence of

conclusive evidence on the type of tetramer, a model of major associated species A1 + A0 2 + A4 was adopted for these solutions, with A4 representing either both or a predominant tetramer only. The association parameters derived with this model from Eq. (3) are given in Table 4. It must be noted, however, that the values of the monomer and dimer parameters so obtained do not depend upon the kind of tetramers actually present. The compatibility of the model used with the solutions investigated was independently checked by respective (hg + hd )/h 2a vs. h 2a test plots (Eq. (12)). A satisfactory correlation with the required straight lines and the ordinate intercepts agreeing with their model values b0 2e 2a /eg were found at all four temperatures (Fig. 4(b)). Also consistent with the experimental data was the model fraction of cholesterol associated, increasing in the monomer concentration range studied from 20% (a=0.05 mol dm − 3) to 35% (a= O.10 mol dm − 3) at 298 K. The only IR information on cholesterol association in toluene seems to be that of Burstein et al.

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[17] who studied its dipole moment in these solutions. The three bands observed by them in the fundamental OH stretching range at 3600, 3500 and 3400 cm − 1, and ascribed to monomers, dimers and higher multimers, respectively, were used only as qualitative evidence for the self-association of cholesterol in toluene solutions. A survey of the behaviour of cholesterol in both aromatic solvents used shows that the effect of solvent on IR spectra is only small relative to that on its mode of self-association. The positions of the a- and g–OH band are, within experimental error, the same. The slightly lower location of the d – OH band in benzene is an expected result of the specific bonding of OH groups in cyclic dimers A. 2. The fact that cyclic dimers A. 2 are established in benzene only and tetramers A4 only in toluene, represents a pronounced solvent effect. The question why cyclic dimers A. 2 do not occur in toluene and tetramers in benzene can be answered in terms of their Gibbs

717

energy of formation. The reason is that the common contribution of the processes of monomer desolvation and solvation of these species is too positive to make the overall Gibbs energy of their formation sufficiently favourable for them to be formed in detectable concentrations. A comparison of the fraction of cholesterol associated at the same monomer concentration shows that the tendency to associate in benzene solutions is nearly 1.5 times larger than in toluene. Acknowledgements We are deeply grateful to Professor D. Hadzi for valuable discussion. We also thank Mrs J. Burger for her skilful technical assistance and the Ministry of Science, Research and Technology for financial support. References

Fig. 4. Compatibility test of association models at 308 K: (a) Cholesterol-benzene system, model A1 + A0 2 + A. 2, (hg + hd )/ ha = − (0.05 9 0.2) +(1.2 90.1) ha ; r = 0.98, (b) Cholesteroltoluene system, model A1 + A0 2 + A4, (hg +hd )/h 2a = (0.82 90.03) +(2.09 0.4) · h 2a; r= 0.94.

[1] M. Senegacnik Jr., C. Klolutar, Spectrochim. Acta Part A 53 (1997) 1495. [2] J.A. Riddick, W.B. Bunger, T. Sakano, A. Weisberger (Eds.), Techniques of Chemistry, vol. II, Wiley, New York, 1986. [3] C. KloIutar, S& . Paljk, S. Golc-Teger, Thermochim. Acta 196 (1992) 401. [4] H. Stone, J. Opt. Soc. Am. 52 (1962) 998. [5] A.N. Fletcher, C.A. Heller, J. Phys. Chem. 71 (1967) 3742. [6] A. Hall, J.L. Wood, Spectrochim. Acta, Part A 23A (1967) 2657. [7] A.W. Baker, H.O. Kerlinger, A.T. Shulgin, Spectrochim. Acta, Part A 20 (1964) 1467. [8] G.C. Pimentel, A.L. McClellan, The Hydrogen Bond, W.H. Freeman, San Francisco, CA, 1960, p. 248. [9] G.J. Boobyer, W.J. Orville-Thomas, Spectrochim. Acta, Part A 22 (1966) 147. [10] M. van Thiel, E.D. Becker, G.C. Pimentel, J. Chem. Phys. 27 (1957) 95. [11] C. Klofutar, S& . Paljk, V. Abram, Vestn. Slov. Kem. Drus. 39 (1992) 153. [12] C. Klofutar, S& . Paljk, V. Abram, J. Chem. Soc. Faraday Trans. 89 (1993) 3065. [13] F.J.C. Rossotti, H. Rossotti, J. Phys. Chem. 65 (1961) 926 and 930. [14] M. Kunst, D. van Duijn, P. Bordewijk, Z. Naturforsch. 34a (1979) 369. [15] A.N. Fletcher, J. Phys. Chem. 76 (1972) 2562. [16] W.M. Bartczak, Ber. Bunsenges. Phys. Chem. 83 (1979) 987. [17] L.L. Burstein, T.P. Stepanova, V. Purkina, Zh. Fiz. Kim. 54 (1980) 1493.