Langmuir 1994,10,2100-2105
2100
Effects of Kryptofix 222 on Volumetric and Transport Properties of Diluted Aqueous Solutions of Sodium Glycodeoxycholate Alessandro D'Aprano,* Bianca Sesta, Margherita Iammarino, Catia Filippi, Antonio Princi, and Noemi Proietti Department of Chemistry, University "La Sapienza", PuleA. Mor0 5, 00185 Roma, Italy Received July 14,1993. I n Final Form: March 16, 1994@
+
The viscosity and the density of sodium glycodeoxycholate (NaGDO) in pure water and in water 4,7,13,16,21,24-hexaoxa-l,l0-diazabicyclo[8.8.81hexacosane (C222) mixtures have been measured at 5 and 25 "C in order to investigate the specificrole of ionic solvation on the modification of the micellar properties of the bile salt caused by the complexation of sodium counterion with C222. The hydrodynamic volumes (V,) of NaGDO in water-macrobicyclic solutions, lower than those in pure water, have been justified in terms of the electrical shielding of sodium ion by the hosting macrocycle. Significant differences between V,, and the apparent molal volume (av) were also found. These discrepancies have been attributed to the solvent molecules interacting with solute and involved in the flow process. The feature of the apparent molal volumes of NaGDO in aqueous solutions containing Kryptofw 222 is very peculiar; namely, QV progressively increases up to a maximum occurring at the equivalent ratio between cryptate and bile salt concentrations. This phenomenon has been related to the collapse of the cation hydration shell occurring in the complexation process.
Introduction
the molecular aggregation of NaGDO begins, has been also noted. The thermodynamic analysis of the surface Cryptates are macrobicyclic molecules with three oxytension results has shown, in addition, that the entropic ethylene chains linked to two ammonium groups and contribution to the NaGDO's micellar stability is less surrounding a n internal cavity of about spherical shape pronounced in a water C222 mixture than in pure water. well suited to contain alkali and alkaline-earth cations. Since the entropic contribution of the micellar process is The properties of cryptates as complexing agents are well generally related to the loss of the water molecules known and have been largely investigated in the past surrounding the hydrophobic situ of the surfactant molecules, it was of interest to investigate further the Encapsulation of small cations by macrocyclic comspecific role of water on the NaGDO-C222 interactions. pounds alters many physical properties of electrolytic For this purpose the hydrodynamic and volumetric solutions (i.e., solubility, transport properties, etc.). As properties of sodium glycodeoxycholate aqueous solutions, far as ionic surfactants are concerned it has been shown with and without added C222, have been studied and the that the micellar properties of these substances could be results presented and discussed in this paper. changed by modulation of counterion binding through These two parallel studies, carried out a t different complexation with macrocyclic cryptates or with crown temperatures and focused in a narrow bile salt concenethers.6-10 tration range, where small molecular aggregates (i.e., In a previous paper1' we have extended such studies to dimers, tetramers, or primary micelles) have been biological amphiphiles by investigating the perturbation p o s t ~ l a t e d , ' ~provide - ~ ~ the opportunity to compare the of sodium glycodeoxycholate (NaGDO) self-association, apparent and the hydrodynamic volumes of NaGDO in induced by 4,7,13,16,21,24-hexaoxa-l,l0-diazabicyclo- pure water and in a water C222 mixture and to estimate [8.8.8lhexacosane(C222). The conductometric and surface the extent of ionic solvation in both systems. From such tension results have shown that the addition of C222 to information the effect of a macrocyclic ligand on the ionthe NaGDO aqueous solutions resulted in larger interfacial micelle binding and on the ion-water interactions should areas per molecule a t the air-water interface and in a be clarified. significant decrease of the ionic mobility. A favorable effect on the stability of sodium glycodeoxycholate micelles, as Experimental Section indicated by the decrease of the concentration a t which (A) Chemicals. Sodium glycodeoxycholate(Sigma product)
+
+
* To whom correspondence should be addressed. Abstract published in Advance A C S Abstracts, June 15,1994. (1)Lehn, J. M. ACC.Chem. Res. 1978,11, 49. (2)Lehn, J. M. Pure Appl. Chem. 1980,52,2303. (3)Graf, E.; Lehn, J. M. Helv. Chim. Acta 1981,64, 1040. (4)Frere, Y.;Gramain, P. Makromol. Chem. 1983,182,2163. (5)DAprano, A.;Sesta, B. J. Solution Chem. 1988,17, 117. (6) Evans, D. F.; Evans, J. B.; Sen, R.; Warr, G. G. J . Phys. Chem. 1988,92,784. (7)Miller, D. D.;Evans, D. F.; Warr, G. G.; Bellare, J. R.; Ninham, B.W. J . Colloid Interface Sci. 1987,116,598. (8)Evans, D. F.; Sen, R.; Warr, G. G. J . Phys. Chem. 1986,90,5500. (9)Miller, D. D.; Evans, D. F.; Talmon, Y.; Ninham, B. W. J. Phys. Chem. 1987,91,674. (10)Brady, J. E.; Evans, E. F.; Warr, G. G.; Grieser, F.; Ninham, B. W. J . Phys. Chem. 1986,90,1853. (11)Sesta, B.; D'Aprano, A.; Princi, A.; Filippi, C.; Iammarino, M. J. Phys. Chem. 1992,96,9545. @
was purified and dried as previously described.11 4,7,13,16,-
21,24-Hexaoxa-1,10-diazabicyclo[8.8.8lhexacosane from MerckSchuchard was used as received. Sodium chloride (Suprapur Merck) was dried under vacuum at 150 "C. Bidistilled and degassed water was used to prepare the solutions. Its conductivity was lower than 3 x lo-' (SZ-1 cm-1). (B)Apparatus and Methods. Dynamic viscositiesofNaGDO solutions were measured with Ubbelhode viscometers with a long flow time in order to minimize the kinetic energy correction. The viscometers were carefully cleaned, rinsed several times with water and ethyl alcohol, dried before using, and positioned (12)Small, D. M. In TheBile Acids;Padmanabhan, P.N., Kritchevsky, D., Eds.; Plenum Press, New York, 1971;Vol. I, Chapter 8. (13)Carey, M. C.; Small, D. M. Arch. Intern. Med. 1972,130, 511. (14)Kratohvil, J. P. Hepatology 1984,4 , 858.
0743-746319412410-2100$04.50/0 0 1994 American Chemical Society
Langmuir, Vol.10,No.7,1994 2101
Effects of Kryptofix 222 Table 1. Molarity (MI and Relative Viscosity (ar)of NaGDO in Pure Water and in Water C222 (0.04 M) Mixtures at 5 and 25 "C
+
'
o
5 "C 103M
Dr
0.0 0.5120 0.9969 1.4873 2.4910 4.1996 6.2092 7.8732 9.8224 11.975 13.924 15.921 17.831 19.855
1.0 1.0015 1.0025 1.0028 1.0061 1.0116 1.0172 1.0220 1.0283 1.0359 1.0429 1.0488 1.0565 1.0626
0.0 1.0350 1.9799 3.0323 4.0438 5.9999 8.1025 9.9851 11.874 13.955 15.957 17.943 19.857
1.0 1.0022 1.0049 1.0086 1.0113 1.0160 1.0224 1.0282 1.0337 1.0391 1.0446 1.0515 1.0581
run I, 25 "C 103M Dr Water 0.0 1.0 0.8434 1.0026 2.1400 1.0046 3.4152 1.0080 3.9551 1.0099 9.0340 1.0239 11.920 1.0337 14.101 1.0394 16.073 1.0451 18.268 1.0505
+
Water C222 (0.04 M) 0.0 1.0 0.5391 1.0007 1.5100 1.0019 2.4079 1.0044 3.7251 1.0066 5.4440 1.0109 9.8710 1.0225 11.480 1.0282 13.479 1.0322 15.958 1.0401 18.401 1.0466 20.507 1.0527
l 11, 25 "C run
10s M
Dr
0.0 0.5155 0.9940 1.4829 2.3940 4.1874 7.8502 9.0794 11.940 13.882
1.0 1.0000 1.0019 1.0027 1.0058 1.0108 1.0197 1.0251 1.0331 1.0377
0.0 1.0104 1.9737 3.0228 4.0312 5.9812 8.0772 9.9542 11.836 13.911 15.907 17.886 19.794
1.0 1.0023 1.0024 1.0058 1.0080 1.0123 1.0183 1.0233 1.0290 1.0343 1.0404 1.0457 1.0503
in a thermostatic bath (temperature constant within f O . O 1 "C). Solutions filling the viscometer were accurately filtered with a fine fritted glass funnel. The flow times were measured with a digital stop watch with an accuracy of 0.01 s. The reproducibility of the viscosity values was within f0.01%. Viscometers were calibrated at each temperature with purified water and ethyl alcohol. Measurements were repeated four times for each sample. The dynamic viscosity ( q ) was calculated from the average measured flow times ( t ) and densities (d) by the Poiseuille equation in the form
The constants a and b were determined from plots of q/td us l/t2 using literature datal6for the viscosity and the density of selected liquids and the measured flow times ofthese liquids. The kinetic energy term of eq 1,for our viscometers, amounted to less than 0.01%,over the temperature range 5-25 "C, and therefore it was neglected in computing the viscosities of NaGDO aqueous solutions with and without added C222. Densities were measured by an A. Paar 602 vibrating tube densimeter with a cell of 1.5 mL. During the measurements the thermal stability, maintained by a suitable temperature controller (CBII-DBTfrom HETO), was within f0.002 "C as checked with an F 25 precision digital thermometer from Automatic System Laboratories. The densimeter was calibrated,16at each temperature, with water, methanol, and ethanol. The precision and the accuracy ofthe densities measurements were better than f l x 10-6gmL-l.
"
1 "1""
5
0
10 1000
15
20
w
Figure 1. Relative viscosity (11,) as a function of molar concentration (M) of NaGDO, in pure water at 5 (0)and 25 "C (D, +). The curve a t 5 "C is shifted by 0.27, units along the Y axis.
The graphical representation of qr us M, for NaGDO in pure water, is shown in Figure 1. The intersection of the two straight lines, representing the data a t low and high concentrations of surfactant, occurs in the region where the micellization process begins, which is around 7.2 x mol L-l at 5 and 25 "C,respectively. and 4.5 x For NaGDO in water C222 solutions (Figure 2), the narrow concentration region, where the bile salt exists in monomeric fully dissociated form, prevents us from defining, univocally, the discontinuity in the viscometric curves. Thus, cmc values can be only approximately and 3.1 x mol L-I a t 5 and estimated to be 2.5 x 25 "C,respectively. It must be pointed out that, although the cmc values obtained from viscosity measurements are not very reliable, the values obtained at 25 "C are in fair agreement with the previous values'l obtained by surface mol L-I for tension measurements (i.e., cmc = 4.7 x NaGDO in water and cmc = 3.8 x mol L-I for NaGDO in a water C222 mixture). Table 2 summarizes the densities ( d )of NaGDO in pure water and in water C222 mixtures at 5 and 25 "C.The apparent molal volumes CP, (cm3mol-I), also reported in Table 2, were calculated as
+
+
+
CP, = [(do- d ) x 103/mdd01+ (PWd)
(2)
Results Viscosity data of NaGDO in pure water and in water C222 mixtures at 5 and 25 "C, expressed as relative viscosity qr = q/qo(q = viscosity of solution, qo= viscosity of solvent), are reported in Table 1 as a function of NaGDO molar concentration M (mol L-I). Data a t 25 "C have been confirmed by duplicate runs.
where d and do are the density of solution and solvent, respectively, PM is the molecular weight of NaGDO,and m is the bile salt concentration on the molality scale. The CP, value obtained in pure water a t 25 "C(see Table 2) for the lowest bile salt concentration (i.e., 351.7 mL mol-l) is yery close to the partial molal volume at infinite dilution (Vz)estimated on the basis of the additivity rule of the volumes of the molecular groups reported in literature.16--'*
(15)CRCHandbook of Chemistry and Physics, 61st ed. Weast, R. C., Ed.; CRC Press: Boca Raton, 1980.
(16) Traube, J. Samml. Chem. Chem.-Tech. Vortrage 1899,4,255.
+
2102 Langmuir, Vol. 10,No. 7,1994
DAprano et al. Table 2. Molality (m), Density (d), and Apparent Molal Volume (9,)of NaGDO in Pure Water and in Water C222 (0.04 M) Mixtures at 5 and 25 "C
+
1.08
water
water 1 0 3 ~
mv
d
+ C222 (0.04 M)
103m
d
0.0 12.211 13.937 25.172 36.280 43.801 59.438
1.002 615 1.003 920 1.004 043 1.005 109 1.006 149 1.006 877 1.008 507
363.5 367.9 370.8 372.1 371.9 369.6
0.999 497 1.000 032 1.000 217 1.000 383 1.000 514 1.001 416 1.002 350 1.002 464 1.003 192 1.003 543 1.004 881
360.6 367.9 371.1 372.7 376.9 378.6 378.7 379.6 379.2 377.3
@V
5 "C 1.06
1.04
0.0 0.5121 3.0150 3.9481 7.8312 8.9870 13.691 27.349 44.110 60.338
0.999 992 1.000 065 1.000 345 1.000 447 1.000 876 1.001 003 1.001 518 1.003 015 1.004 840 1.006 560
350.0 354.4 355.9 358.2 358.6 359.4 359.9 359.9 360.3
0.0 0.5390 0.7930 3.1413 3.3990 6.0728 12.351 18.472 23.380 31.834 40.993
0.997 078 0.997 130 0.997 168 0.997 430 0.997 456 0.997 747 0.998 420 0.999 069 0.999 575 1.000 468 1.001 422
25 "C 0.0 351.7 4.8300 353.7 6.9561 358.9 8.8343 359.8 10.308 361.3 20.471 363.0 31.053 363.6 32.301 364.5 40.802 364.5 44.528 364.7 58.341
1 ',
1.02
1 .oo
1
c.m.c
n QAJ -."0
5
15
10
Table 3. Molality (m[NaCI]), Density (d[NaCl]), and Apparent Molal Volume (8v[NaC1]) of NaCl in Pure Water and in Water C222 (0.04 M) Mixtures at 25 "C
20
+
1000 M
Figure 2. Relative viscosity (7,) as a function of molar concentration(M)ofNaGDO, in water + C222 (0.04M) m i x t u r e s at 5 ( 0 )and 25 "C (El, 4). The curve at 5 "C is shifted by 0.211, unit along Y axis. Partial molal volumes (Vz) were derived from Qv by the relationship
Vz = Q" + J m ( d ~ 4 2 d J m )
(3)
valid for uni-univalent-electrolytes. For the micellar solutions, the function Vz(J m ) is approximately linear, both a t 5 and 25 "C. The difference between the molecular volume of NaGDO i_nthe monodisperse state (close to that a t infinite dilution V"z = Qov) and the molecular volume of the surfactant in micellar state is AV 13 f 2 mL mol-l a t 25 "C and AV 10 f 2 mL mol-I a t 5 "C. Listed in Table 3 are the densities (d[NaCl]) and the derived apparent molal volumes (@v[NaCl])in pure water and in water C222 mixtures a t 25 "C as a function of the NaCl molal concentrations (m[NaCl]). Such measurements were carried out in order to compare the influence of Na+ - C222 complexation on the apparent volumes of amphiphilic and nonamphiphilic substances (see Discussion).
+
Discussion According to Jones and Dole,lg the dependence of viscosity on concentration of the electrolytic solutions, up to 0.01 M, can be described by the polynomial function ~$7,= 1
+A
+
~ MBM
(4)
water + C222 (0.04 M)
water 1O3m[NaCll 0.0 4.9123 20.702 41.309 61.832
~ [ N ~ C I I @v[NaCl]
0.997 078 0.997 284 0.997 939 0.998 788 0.999 613
16.44 16.78 16.95 17.04
1O3m[NaC11 0.0 5.0621 10.233 14.892 25.064 40.109 50.033 59.754
d[~aC1] 0.999 544 0.999 737 0.999 837 0.999 950 1.000212 1.000 603 1.000 984 1.001 378
%[NaCIl
20.31 29.81 31.18 31.78 32.02 29.62 27.70
where A is a constant depending on ion-ion long range electrostatic interactions and B an experimental constant related to the size and shape of solute (Le., the Einstein volume effect20)and to the solvent-solute interactions. The constant A is always non-zero and positive and has been interpreted theoretically by Falkenhagen21 on the basis of the deformation of the Debye-Huckel spherical atmosphere under the shearing stress. Electrical conductance measurements,l' concerning NaGDO in pure water and in water C222 mixtures, have pointed out that the changes in size and shape of solute particles, occurring in the micellization process, influence both the solvent-solute interactions and the Debye-Hiickel cloud surrounding the ions. Under these circumstances the square root term of eq 4 cannot assume the classical meaning and does not give reliable indications on the electrostatic ion-ion interactions for amphiphilic solutions and, in parti ular, for NaGDO. Fortunately, the A coefficient plays the major role in very dilute solutions and gives only a negligible contribution to the relative viscosityfor the more concentrated systems. Thus, the viscometric trend of surfactant solutions can be a n a l y ~ e dby ~~ the , ~simplified ~ relationship
+
vr - 1 = BM (17)Cohn, E. J.;McMeekin, T.; Edsall, J. T.; Blanchar, M. H. J.Am. Chem. SOC.1934,56,784. (18)Djavanbakht, A,; Kale, K. M.; Zana, R. J. CoZZoidInterfuee Sei. 1977,59, 139. (19)Jones, G.; Dole, M. J. Am. Chem. Soc. 1929,51, 1950. (20) Einstein, A.Ann. Phys. 1906,19, 289.
(5)
Because of the above-mentioned limits, the following discussion will be focused on the micellar solutions. Table (21)Falkenhagen, H.; Vernon, E. L. Physik. 2. 1932,33, 140.
Effects of Kryptofix 222
Langmuir, Vol.10,No. 7,1994 2103
Table 4. B Coefficients and Hydrodynamic Volumes (V,,) of NaGDO in Pure Water and in Water + C222 (0.04 M) Mixtures at 5 and 26 "C water
T ("C) B (Lmol-') 5 25
3.40 2.89
water
V,(L mol-')
B (L mol-')
1.36 1.16
2.91 2.71
+ C222
37 1
V,,(L molb1) 1.16 1.08
4 summarizes the B coefficients of eq 5, obtained from the slope of (qr - 1) us M, for NaGDO in pure water and in water C222 mixtures above the cmc. The hydrodynamic volumes (V,) derived by the Einstein relation?O
+
V,, = Bl2.5
(6)
3501
1 0
5
10
15
20
30
25
are also included in Table 4. lOO-Jm As may be observed, B values are large and positive. It Figure 3 . Apparent molal volume (av)as a function of the is k n ~ w n that ~ - the ~ ~ contributions from the cospheres root of the molal concentration ( m )of NaGDO in pure square of the cation and the anion, indicated by B+ and B - , to the and 25 "C (e). water at 5 (8) total B coefficient are independent and therefore additive: B =B+ B-. The value assigned to sodium i 0 n s , 2 ~ - ~ ~ Other causes, like the loss of the 'water structure practically independent from the temperature, is B N ~=+ forming" p r ~ p e r t of y the ~ ~sodium ~ ~ ~ ion, when shielded by 0.086Lmol-l that corresponds, on the basis oftheEinstein Kryptofx 222, andlor the desolvation of cation occurring equation, to V,,(N~+) = 34 L mol-l. in the complexation process could concur to the decrease It is obvious (see Table 4) that the major contribution of B coefficients observed in water C222 mixtures. to the increase of viscositywith solute concentration must be assigned to GDO- because of its large size and of the In order to gain information on the extent of the NaGDO bulky molecular arrangement in the micellar structure. solvation in pure water and in water C222 mixtures we Further contributions are related with the solute-solvent consider next the apparent molal volumes. As shown in interactions due to the structure-making properties of Table 2, aVvalues of micellized NaGDO in pure water are GDO- anion containing a hydrophobic hydrophenantrenic around 360 mL mol-' and 364 mL mol-' at 5 and 25 "C, group. respectively. These values are comparatively lower than An inspection of Table 4 shows also that dBldT is the Einstein hydrodynamic volumes reported in Table 4. negative. This feature is in agreement with the behavior Similar discrepancies have been found for other bile salts of other solutes enforcing the water s t r u c t ~ r e . ~ ~ ~ ~ ~in aqueous m e d i ~ m . ~ l - ~ ~ The B coefficients and the related hydrodynamic The difference V,, - Qv may be assigned to the water volumes of NaGDO found in water C222 solutions are cages surrounding the moving electrolyte. It could be lower than those in pure water. Such a result seems to estimated that about 55 and 44 mol of solvent at 5 and be in apparent disagreement with our previous conduc25 "C,respectively, interact with 1 mol of solute. tometric data,ll showing a decrease of the ionic mobility In water C222 solutions, the difference between V,, (i.e., increase of the cationic hydrodynamic size) in water C222 mixtures. and Qv is approximately 800 mL mol-l at 5 "C and 700 The discrepancy between the conductometric and vismL mol-l at 25 "C. Such values, lower than those in pure cometric results can be understood considering that, in water, correspond to about 44 and 39 water mol involved the presence of the complexation process, the two techin the motion of the solute a t 5 and 25 "C,respectively. niques reflect two different aspects of ionic motion. Apart the above details, the general trends of Qv us the Conductance, as is well known, is the response of the ions bile salt concentration in pure water and in water C222 to the applied electric field. The drift velocity acquired mixtures are quite different. As may be observed in Figure by an ion in the direction of the electric field is inversely 3, just above the cmc, the Qv values increase with proportional to the mass of the ion; thus, the conductance increasing the square root of NaGDO molality. The of the bulky complexed ion must be lower than that of the phenomenon, already observed for the homologous bile free ion. Viscosity, on the contrary, is related to the friction salts as well as for most ionic surfactants, has been of the particles, solute and solvent, under the shearing related34s35to the removal of part of the water molecules, stress. Since the complexation process reduces the surrounding the hydrophobic surfactant, during the number of the particles in solution and the macrocycle micellization process. Since the primary micellization of has about the same size with and without sodium cation bile salts is a multistep e q ~ i l i b r i u m , the ~ ~ concomitant -~~ included in its cavity, the relative viscosity of NaGDO in increase of values, as observed for other cholic water C222 mixtures should be smaller than that in pure water.
+
+
+
+
+
+
+
+
(22)Mukejee, P. J . Colloid Interface Sci. 1984,19, 722. (23)Tamaki, K.;Ohara, Y.;Kurachi, H.; Ariyama, M.; Odaki, H. Bull. Chem. Soc. Jpn. 1974,47,384. (24)Gurney, R. M. In Ionic Processes in Solution; McGraw Hill Ed.: New York, 1953. (25)Kamisky, M. Disc.Faraday Soc. 1967,24,171. (26)Stokes, R.H.; Mills, R. In Viscosity OfElectrolytes and Related Properties; Pergamon: Oxford, 1965. (27)Blandamer, M.J. Quart. Rev. 1970,24,169. (28)Kay, R.L.;Vituccio, T.; Zawoyski, C.; Evans, D. F. J.Phys. Chem. 1966,70,2336.
(29)Tsangeris, J. M.; Martin, R. B. Arch. Biochem. Biophys. 1966,
112. 267. ---. -(30)Frank, H.S.;Evans, M. J. J . Chem. Phys. 1940,62,1044. --
(31)Fontell, K.Kolloid 2. u. 2. Pol. 1971,246,614. (32)Fontell, K. J . Colloid Sci. 1964,9 (Suppl. l),66. (33)Sesta, B.;La Mesa, C.; Bonincontro, Ar;Cametti, C.; Di Biasio, A. Ber. Bunsenges. Phys. Chem. 1981,85, 798. (34)Franks, F.; Quickenden, M. J.; Ravenhill, J.R.; Smith, H. T. J . Phys. Chem. 1968,72,2668. (35)Desnoyers, J.E.;De Lisi, R.; Perron, G. PureAppl. Chem. 1980, 52,433. (36)Ekwall, P.; Holmberg, P. Acta Chem. Scand. 1966,19, 573.
DAprano et al.
2104 Langmuir, Vol. 10, No. 7, 1994
4
380-
37s-
30-
3709"
9,.
365-
20I
360-
10
0
5
10
15
25
20
30
dm Figure 4. Apparent molal volume (@,) as a function of the
0
5
10
square root of the molal concentration( m )of NaGDO in a water C222(0.04m ) mixture at 5 (8) and 25 "C (+I.
+
is extended over a broad concentration range. Well above the cmc range, the @, us J m plots do not show significant variations. The trend of the CP, function a t 5 "C is quite similar to that at 25 "C, and as expected, the apparent molal expansibilities (dCPJdT) are positive. Dissimilar is the feature of NaGDO in water C222 mixture (Figure 4). In this case, the function @, (dm) increases even above the cmc up to a maximum, located around m = 0.04 molal (i.e., a t the concentration ofNaGDO equimolal with C222). At such a concentration the difference between CP, for the ternary and binary systems is about 16 mL mol-'. Since only bare ion can penetrate into the cavity of the host m a c r o ~ y c l e ,the ~ ~ collapse of the solvation shell surrounding the cation, occurring in the complexation process (i.e.,highly packed water molecules are transferred to the less dense and voluminous bulk), accounts for the increase of the apparent molal volume observed in water C222 mixtures. The above interpretation finds support on a theoretical basis. In water the intrinsic volume of sodium ion a t 25 "C is Vin(Na+j= 6.4 mL mol-' whereas the apparent molal = -7 mL mol-', volume a t infinite dilution is CP,"(N~+) largely affected from electrostriction effects.41 The difference Vin(Na+j- @.,"(Na+) = 13.4 mL mol-' is significant, and obviously it concerns the solvation shell of sodium cation. The correlation between the cation desolvation and the increase of the apparent molal volume observed in the system containing C222 is also supported by the influence of temperature on the phenomenon. In fact, as expected, the difference in @, between ternary and binary systems a t 5 "C is 12 mL mol-l relatively lower than that a t 25 "C. In a separate set of experiments the influence of the Na+ - C222 complexation on @,was further investigated in the case of NaC1, a nonsurfactant electrolyte. The results are shown in Figure 5. As can be seen, also in this case, the apparent molal volumes of NaCl in water + C222 mixtures are significantly higher than those in pure water. The shape of the curve CP, us J m in water C222 solutions closely resembles that of NaGDO. The maximum of the function @, ( J m )occurs, also in this case, at a molal ratio [electrolyte/C2221=1. At this point the differencebetween
+
+
+
(37) D'Arrigo, G.;Sesta, B.; La Mesa, C. J. Chem. Phys. 1980, 73, 4562. (38)Berchiesi, G.; Berchiesi, M. A.; La Mesa, C.; Sesta, B. J.Phys. Chem. 1984,88, 3665.
20
15
25
30
100 drn
100
Figure 5. Apparent molal volume (@,) as a function of the squareroot ofthe molal concentration ( m )ofNaCl in pure water (El) and in a water C222 (0.04 m ) mixture (e)at 25 "C.
+
ternary and binary systems is 16 mL mol-', practically equal to the value found for the NaGDO system a t 25 "C. In view ofthe above result we can assume that the different variation of the apparent molar volumes observed for the NaGDO in water C222 and in pure water is essentially due to the complexation of Na+ with C222. We can also assume that the contribution due to perturbation of the micellar properties, caused by C222, if it exists is, in any case, extremely small and completelymasked by the cation complexation process. I t has been shown by Evans6 that the increase of the repulsion between the surfactant head groups, induced by the formation of large sodium cryptate inclusion complex, decreases the micellar aggregation number of sodium dodecyl sulfate. Thus, the volume properties of the micellar aggregates are expected to change by the addition of C222 to the system. As is well known, bile salt micelles differ from that of classical surfactants in that the aggregation occurs over a relatively broad concentration range. The self-aggregation is, in addition, ~ t e p w i s e ; ~ initially, ~ - ~ ~ dimers and t e t r a m e r P l 4are formed whereas a t higher concentration such structures rearrange themselves in larger aggregates. Typical ionic detergents, on the contrary, aggregate over a narrow concentration range, and the resulting micelles usually contain 20- 100 monomers. The peculiarity of the bile salts self-association allows us to assume that the contribution due to the variation of the aggregation number of the volume properties of the NaGDO aggregates in water-C222 mixtures can be neglected. In order to test the above assumption we consider next the activation energy of viscous flow. According to Kauzman and Eyrine2 the viscosity of a newtonian liquid is expressed in terms of its activation parameters by the relationship
+
q = A e LW*IRT
e-ASs*IR
(7)
where A is proportional to the molar volume of liquid, AH*the activation energy, AS* the entropy of activation, R the gas constant, and T the Kelvin temperature. (39) Vadnere, M.; Natarajan, R.; Lindenbaum, S. J. Phys. Chem. 1980,84,1900. (40) Lehn, J. M.; Sauvage, J. P. Chem. Comm. 1971,440. (41) Desnoyers, J . E.; Jolicoeur, C. In Modern Aspects of Electrochemistry;Bockris, J. OM., Conway, B. E., Eds.; Plenum Press: London, 1969.
Effects of Kryptofix 222 In a moderate range of temperature A and AS* do not change significantly and eq 7 can be simplified as
Equation 8 requires a linear plot of In 7 us 1ITfrom which the slope AH* can be calculated. The analysis of viscosity data, from Table 1, by eq 8 shows that the AH* values for the NaGDO-water system [very close to that for pure water (AH*= 4.2cal mol-l)] remain unchanged for most of the concentration range investigated. Only at the highest concentrations,far from the primary cmc, an abrupt increase of AH* has been (42) Kauzman, W.; Eyring, H. J . Am. Chem. SOC.1940,62,3113.
Lungmuir, Vol. 10, No. 7, 1994 2105
+
observed. The results in water C222 mixtures, even if slightly higher than that in pure water, show a similar trend. The general behavior of AH* observed in both systems indicates that, according to the evolution ofbile salts’selfaggregati~n:~the size and shape of the primary sodium glycodeoxycholatemicelles remain practically unchanged in most of the concentration range examined and that, only at high concentrations,the self-associationofNaGDO progresses toward higher molecular aggregates.
Acknowledgment. Support by a MURST grant is gratefully acknowledged. (43) Lindenbaum, S.;Vadnere, M. In Reversed Micelles; Luisi, P., Straub, B. e., Eds.;Plenum: New York, 1984.
