Langmuir 1986, 2, 256-258
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Letters How Large Are the Micelles of Di-a-hydroxy Bile Salts at the Critical Micellization Concentrations in Aqueous Electrolyte Solutions? Results for Sodium Taurodeoxycholate and Sodium Deoxycholate Josip P. Kratohvil,* Wan P. Hsu, and Daw I. Kwok Department of Chemistry and Institute of Colloid and Surface Science, Clarkson University, Potsdam, New York 13676 Received September 17, 1985. I n Final Form: November 26, 1985 The mass-average aggregation numbers of the di-a-hydroxy bile salts sodium taurodeoxycholate and sodium deoxycholate were investigated by light scattering intensity measurements at concentrations close to the critical micellization concentrations (cmc) for different amounts of added NaCI (0-0.60 M) at 25 "C. The aggregation numbers at the cmc for sodium taurodeoxycholateincrease from 3.5 in water to 13.6 at 0.60 M NaCl, in accordance with a decrease of cmc with increasing NaCl concentration. The aggregation numbers for sodium deoxycholate are somewhat smaller than for the first surfactant, again paralleling the cmc variations. The results are discussed with reference to various models proposed for the formation and structure of bile salt micelles. The answers in the literature to the question posed in the title of this Letter are confusing and contradictory. The most comprehensive set of aggregation numbers of various bile salts was reported by Smal11v2from sedimentation equilibrium s t u d i e ~ . His ~ experiments provided the most valuable information on the dependence of the degree of aggregation on the chemical structure of bile salts, temperature, pH, and concentration of counterions (Na+) and urea. These results, combined with the consideration of the molecular space-filling models, led Small to formulate the concept of primary and secondary micelles of bile salts. Only the primary micelles of aggregation numbers from 2 to 10 are presumed to form through hydrophobic interactions in solutions of trihydroxy bile salts at any concentration of counterions and in solutions of dihydroxy compounds a t lower counterion concentrations. Larger, secondary micelles form at higher Na ion concentrations via the hydrogen bonding between the hydroxyl groups located on the surface of primary micelles. However, it is not generally recognized that, with a few exceptions, the experiments by Small were performed at a single surfactant concentration expressed in relative units of the area under the curve of a schlieren optical pattern in the sedimentation equilibrium run. By comparing the tabulated relative values with the concentration scale in Figure 1 of ref 1, one concludes that Small's experiments for most systems were conducted a t a bile salt concentration between 0.005 and 0.015 g ~ m - ~ Since . bile salts in general exhibit a pronounced concentration-dependent micellar growth at concentrations lower than those just Small's data do not provide information on (1)Small, D. M. Adu. Chem. Ser. 1968,84, 31. (2)Small, D. M. In "The Bile Acids"; Nair, P. P., Kritchevsky, D., Eds.; Plenum Press: New York, 1971;Vol. 1, p 249. (3)Solutions of sodium taurodeoxycholate were also investigated by light scattering intensity technique. (4) Kratohvil, J. P.; Hsu, W. P.; Jacobs, M. A.; Aminabhavi, T. M.; Mukunoki, Y. Colloid Polym. Sci. 1983,261, 781. (5)Kratohvil, J. P.;Aminabhavi, T. M.; Hsu, W. P.; Fujime, S.; Patkowski, A.; Chen, F. C.; Chu, B. Croat. Chem. Acta 1983,56,781.
micellar size a t the critical micellization concentration (cmc).' This conclusion applies also to a number of other studies, including the early work from this l a b o r a t ~ r y , ~ J ~ in which a particular experimental parameter related to the aggregation number, measured at bile salt concentrations much higher than the cmc, was linearly extrapolated to the cmc. The underlying assumption in this procedure is that the micellar size is invariant with the surfactant concentration, and the extrapolation to the cmc is needed to eliminate the effects of intermicellar interactions on the measured parameters. Mazer et al.ll investigated the dependence of Stokes radius, Rh, of the micelles, calculated from the diffusion coefficients measured by dynamic light scattering, on temperature (20-60 "C) and the bile salt and counterion concentrations. Little or no change of Rh with the surfactant concentration was observed for sodium taurodeoxycholate (NaTDC) or sodium taurocholate (NaTC) in solutions of 0.15 M NaC1. At 0.6 M NaCl there was a pronounced increase of Rh at increasing NaTDC concentrations, c,; in the range between 0.006 and 0.10 g ~ m - ~ . Mazer et al. suggested that the curves of Rh vs. :C at different temperatures could be extrapolated at the cmc to a common value of Rh = 1.5 nm, corresponding to an aggregation number of and that these values characterize the size of the primary micelles introduced by (6)Kratohvil, J. P.Hepatology (Baltimore) 1984,4,85S. This review article is being reprinted in: Adu. Colloid Interface Sci., in press. (7)Aggregation numbers obtained by Small were not corrected for the effect of the preferential interactions between micelles and solvent components on the buoyancy of the particles sedimenting in the ultracentrifuge.eb8 (8)Kratohvil, J. P.Colloid Polym. Sci. 1975,253,251. (9)Kratohvil, J. P.; DelliColli, H. T. Can. J.Biochem. 1968,46, 945. (10)Kratohvil, J. P.; DelliColli, H. T. Fed. Proc., Fed. Am. SOC.Exp. B i d . 1970,29, 1335. (11) Mazer, N. A.; Carey, M. C.; Kwasnick, R. F.; Benedek, G. B. Biochemistry 1979,18, 3064. (12)The aggregation numbers reported by Mazer et al." should not be taken as true values for reasons discussed elsewhere? Also, there are disagreements between the diffusion coefficients in their paper and those obtained by others.44
0743-7463/86/2402-0256$01.50/0 0 1986 American Chemical Society
Langmuir, Vol. 2, No. 2, 1986 257
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102c2(g~ m - ~ ) Figure 1. Lower panel: Total Rayleigh ratio, R9d, at the scattering angle of 90° and the wavelength in vacuum A,, = 436 nm, vs. the concentration, c2, of 12-tungstosilicicacid (12-TSA)in 0.30 M NaC1. Middle panel: Debye plot, i.e., Kcz/Rwvs. c2, for the data in the lower panel. R90 is excess Rayleigh ratio; c2 is con2/NAho4; n is centration of 12-TSA (g ~ m - ~K) =; 2a2n2(dn/dc2)c refractive index of solution, (dn/dc,),, = 0.1066 cmjg-' (from ref 23) is the refractive index increment at a constant concentration, c3, of added electrolyte,NA is Avogadro's number, and Xo is the wavelength in vacuum. The arrow at the ordinate indicates the reciprocal value of the formula molar mass of 12-TSA (2879 g mol-'). Upper panel: Debye plot for full range of concentrations. Note that the concentration range in this panel is an order of magnitude broader than in the two lower panels. Line a represents the extrapolation of the results from the high concentration re) , line b represents the results of gionZ3(c2 > 0.09, g ~ m - ~and Kronman and TimashefP2 (c20.005-0.10 g ~ m - ~ ) . Small.',2 In a later paper13 similar measurements were extended to the NaTDC solutions a t 0.8 M NaCl and 20 "C. Mazer e t al. concluded that the growth of secondary micelles was governed by primarily hydrophobic interactions. In the models proposed by Small and Mazer e t al. for the formation and the structure of bile salt micelles, as well as in most studies of their solution properties, the concept of a cmc for these surfactants is accepted. However, the existence of cmc's for bile salts has been questioned repeatedly.14-19 We have recently demonstrated4 that in aqueous electrolyte solutions of highly purified trihydroxy bile salt, NaTC, it is not possible to identify the cmc. The aggregation, as detected by light-scattering intensity and diffusion measurements, is occurring at concentrations ~
~~~~
(13)Schurtenberger, P.; Mazer, N.; Kanzig, W. J.Phys. Chem. 1983, 87,308. (14)Mukerjee, P. J. Pharm. Sci. 1974,63,972. (15)Mukerjee, P.;Cardinal, J. R. J.Pharm. Sci. 1976,65,882. (16)Djavanbakht, A.; Kale, K. M.; Zana, R. J. Colloid Interface Sci. 1977,59,139. (17)Chang, Y.;Cardinal, J. R. J.Pharm. Sci. 1978,67,174. (18)Chang, Y.; Cardinal, J. R. J.Pharm. Sci. 1978,67,994. (19)Roda, A.;Hofmann, A. F.; Mysels, K. J. J. Biol. Chem. 1983,258, 6362.
Figure 2. The variation of the mass-average apparent aggregation number, N*,, of sodium taurodeoxycholate (NaTDC) with the micellar concentration, c2, in the region close to the cmc, at different concentrations of NaCl. N*, = (Kc2/Rw)-'(M0)-',where Mo is the molar mass of NdTDC monomer (522 g mol-') and Rw is the Rayleigh ratio in excess of that at the cmc. K is defined as in the legend of Figure 1. The error bars indicate maximum deviations at each concentration (see the text). For NaTDC, c2 = 1.00 X g cm-3 = 1.92 X M. considerably lower than the concentration at which the slope of the plot of surface tension vs. log C; changes markedly. In contrast, our investigations of the di-ahydroxy compounds NaTDC (sodium salt of 3a,12a-dihydroxy-5~-cholanoyltaurine) and sodium deoxycholate (NaDC; sodium salt of 3a,l2a-dihydroxy-5~-cholanic a ~ i d )have ~ ~indicated ~ * ~the ~ absence ~ ~ ~ of aggregates below certain bile salt concentrations, dependent on NaCl concentration, but only for samples of adequate purity. These "critical" concentrations are identified as the cmc's. We emphasize that studies of the aggregation patterns of bile salts in solutions of unpurified or inadequately purified samples at low concentrations are meaningless. In our investigations the intensities of scattered light were measured in the region of very low bile salt concentrations which was not explored previously. We believe that these results are of such quality that it is possible to provide a precise answer to the question raised in the title. The data discussed in this paper are taken from comprehensive studies using several techniques over a broad concentration range.4-6p20,21The samples of purified bile salts, the experimental procedures, and the treatment of data were described in these references. Since low values of the excess Rayleigh ratio, Rw,just above the cmc were of interest, the experimental procedure was verified by measuring Rw on dilute solutions of 12-tungstosilicic acid (H4SiW12040; formula molar mass 2879 g mol-'), a nonassociating s o l ~ t e . ~ The *,~~ concentration range was chosen such that R, varied between 0.28 and 1.70 times the value (20)Hsu, W.P. Ph.D. Thesis, Clarkson University, Potsdam, NY, 1985. (21)Kwok, D. I. M. Sc. Thesis, Clarkson University, Potsdam, NY, 1984. (22)Kronman, M. J.; Timasheff, S. N. J.Phys. Chem. 1959,63,629. (23) Kratohvil, J. P.; Oppenheimer, L. E.; Kerker, M. J.Phys. Chem. 1966,70,2834.
Letters
258 Langmuir, Vol. 2, No. 2, 1986 Table I. Apparent ( N * )and Corrected ( N , ) Mass-Average Aggregation Numbers at Critical Micellization Concentrations and Auxiliary Quantities for Sodium Taurodeoxycholate (NaTDC) and Sodium Deoxycholate (NaDC) and at 25 "C and Various Concentrations of Added NaCl NaC1, M
cmc,n cmc: lo4 g cm-3 mM
(lowest c z ) / ( a n / d ~ ~ ) ~ . l bcmcc NaTDC
0 0.05 0.15 0.30 0.60
21 10 8.2 5.9 5.0
4.0 1.9 1.6 1.1 0.96
0.183 0.183 0.179 0.178 0.175
0.20 0.19 0.09 0.31 0.07
0.14gd 0.59'
10 6.0
2.4 1.45
NaDC 0.193 0.191
0.10 0.17
N*
N2
2.3 5.0 9.0 9.5 10.0
3.5 6.0 10.0 11.3 13.6
7.0 8.0 8.5 1l.d
From light scattering. bRefractive index increment (cm3 g-l). Lowest cz refers to Figure 2 (for NaTDC). Solutions also contained 0.001 M NaOH, pH >lo. e Solutions also contained 0.01 M NaOH, pH >11. fAssuming the ratio N,/N* = 1.36 as for NaTDC at 0.60 M NaC1.
for the solvent (0.30 M NaC1) (Figure 1). Even under these conditions, the resulting Debye plot (Kcz/Rwvs. c2) is linear and extrapolates very close to the reciprocal of the formula molar mass of the solute (the value at c2 = 0 is 2857 g mol-'). The error bars in Figure 1 represent the maximum deviations based mostly on the fluctuations in the intensity readings for a solution and the solvent which were subtracted from each other in calculating the excess Rayleigh ratios. The variation of the apparent aggregation number, N*,, of NaTDC with the micellar concentration, c2 = C: - cmc, where C: is the total surfactant concentration, at different concentrations of added NaCl and 25 "C is presented in Figure 2. These values of N*, are apparent and lower than the true values for two reasons. First, the effect of the second virial coefficient at finite concentrations is to reduce RgOand N*,. A t concentrations as low as in Figure 2 this effect is practically negligible. Second, the effects of the preferential interactions between charged micelles and solvent components, which do not vanish at the cmc, also lower Rw and N*a.6,10,20 The magnitude of the preferential interaction effects for NaTDC and NaDC micelles was evaluated by the procedure of Vrij and O ~ e r b e e kon~ the ~ basis of the variation of the co-ion of added electrolyte. The details are given elsewhere.6,20v21The values of the apparent aggregation numbers, N*,, are extrapolated to the cmc and the corresponding values corrected for the preferential interactions, N2,are listed in Table I, together with other pertinent information. The value of N* for NaTDC in water is indicated by an arrow. Because of a pronounced nonideality of solutions without added elec(24) Vrij, A.; Overbeek, J. Th. G. J. Colloid
Sci. 1962, 17,570.
trolyte, these results require special consideration20and will be the subject of a separate report. The variation of N*, with c2 for NaDC a t pH >10 was similar to that for NaTDC. In constructing the plots in Figure 2, the cmc's were subtracted from the total bile salt concentrations. This procedure assumes that the concentration of the surfactant monomer is constant at all C: and equal to the cmc. Recently, this assumption has been verified for NaTDC in water25and 0.15 M NaC1,26but not for NaTC.,O The range of c2 in Figure 2 extends, depending on NaCl concentration, from as low as 7% above the cmc to about 2.5 times the cmc. Even in this low-concentration region, except for the two lowest concentrations for which the excess Rayleigh ratios were extremely small, the data are sufficiently precise to allow reliable extrapolations to c2 = 0. The extrapolated apparent aggregation numbers, N*, at the three highest NaCl concentrations are very similar, 9-10. Although the highest concentrations of NaTDC in Figure 2 are about 4-5 times lower than the lowest concentration used by Mazer et al.,'l the above values of N* would seem to support their conclusions and the concept of the primary micelles of aggregation number equal to 10. However, after correcting N* values for the preferential interaction effects, the true mass-average aggregation numbers, N,, show some dependence on the counterion concentration. This trend is in accordance with the observed decrease of the cmc with increasing NaCl concentration (Table I). We conclude that the values of N2 at higher salt concentrations are too large to satisfy the criteria for the primary micelles. The effect of electrolyte on micellar size is more pronounced at higher c2. In fact, the rapid rise of N* with c2 at 0.30 and 0.60 M NaCl at such low concentrations is remarkable. We note that the values of N* and N 2 for NaDC are somewhat lower than for NaTDC, as expected from the higher cmc's (on molar basis) of NaDC. The results discussed in this paper bear also on the proposition of Oakenfull and F i ~ h e that r ~ at ~ the ~ ~ cmc ~ hydrogen-bonded dimers of bile salts are formed. Larger aggregates are supposed to form at increasing c2 from dimers through hydrophobic interactions. This concept has already been q u e s t i ~ n e d . ~Our ~ , ~results ~ provide no evidence for the sole existence of dimers at the cmc at any electrolyte concentration.
Acknowledgment. This work was supported in part by the National Science Foundation and the National Institutes of Health. (25) Ryu, K.; Lowery, J. M.; Evans, D. F.; Cussler, E. L. J . Phys. Chem. 1983,87, 5015. (26) Ammon, H. V.; Walter, L. G. Anal. Chem. 1982,54, 2079. (27) Oakenfull, D. G.; Fisher, L. R. J. Phys. Chem. 1977, 81, 1838. (28) Oakenfull, D. In "AggregationProcesses in Solution";Wyn-Jones, E., Gormally, J., Eds.; Elsevier: Amsterdam, 1983; p 118. (29) Zana, R. J.Phys. Chem. 1978,82, 2440. (30) Vadmere, M.; Natarajan, R.; Lindenbaum, S . J . Phys. Chem. 1980,84, 1900.
