2704
J. Phys. Chem. $902, 86, 2784-2788
Effects of pH, pNa, and Temperature on Micelle Formation and Solubilization of Cholesterol in Aqueous Solutions of Bile Salts Gohruke Suglhara, Kazuko Yamakawa, Yoshlo Murala, and Mltsuru Tanaka DepaHmnt of Chemistry, Faculty of Science, Fukwka University, Jonan-ku, Fukuoka Clty 8 14-0 1, Japan (Received: September 9, 198 I; I n Final Form: December 14, 198 1)
The cholesterol solubilization by sodium cholate (NaC) and sodium deoxycholate (NaDC) in buffer solutions was investigated especially in connection with the effects of pH, the concentration of counterion ([Na’] or pNa), and temperature. The solubilization of cholesterol takes place abruptly above a certain Concentration of bile salts. This indicates that micelles are formed, so that the critical micellization concentration (cmc) is determinable from the plot of the amount of solubilized cholesterol (w)vs. the concentration of bile salt (C). The solubilizing power (S)was defined as the tangential slope of the w-C curve, S = dw/dC. The S of NaDC is greater than S of NaC. The effects of pH, pNa, and temperature on cholesterol solubilizationare larger and more complicated in the system of NaDC than that in NaC. The pH and pNa dependency of cmc of NaDC was clearly seen while that of NaC was not so appreciable. A thermodynamic consideration on the pH and pNa dependency of cmc led to an evaluation of counterion composition of H+ and Na+ on the micellar surface. The enthalpy and entropy on micelle formation were obtained from the temperature dependency of cmc.
Introduction The bile salts are well known as a family of surfactants acting as a solubilizer for lecithin and cholesterol in bile and as a solubilizer or emulsifier for hydrophobic dietary lipids in the intestine thus promoting absorption.’ Since the cholelithiasis and hypertension are attributed to cholesterol, it is desirable to know the behavior of cholesterol together with bile salts in detail. Cholesterol is the major component of most gallstones, and cholesterol (and lecithin) are sparingly soluble in water, so that the nature of physicochemical interaction between cholesterol and other biliary lipids has been extensively investigated.’-16 Elworthy et al. reviewed studies up to 1968 on the biological aspects of so1ubi1ization.” The newest and the most detailed study on the physical chemistry of cholesterol solubility in bile was published by Smallla and by Carey and Small.l9 In order to discuss the relationship of cho(1) M. C. Carey and D. M. S m d , Arch. Intern. Med., 130,506 (1972). (2)B. Isaksson, Acta Soc. Med. Ups., 59,296 (1953). (3)F. Nakayama, Clin. Chim. Acta, 14, 171 (1966). (4)W. H. Admirand and D. M. Small, J. Clin. Inuest., 47,1043(1968). (5)D. H. Neiderhier and H. P. Roth,R o c . SOC.Exp. Biol. Med., 128, 221 (1968). (6)D. R. Saunders and M. A. Wells, Biochim. Biophys. Acta, 176,828 (1969). (7)W. C. Hardison, J. Lab. Clin. Med., 77, 811 (1971). (8)F.G.Hegardt and H. Dam, Z.Ernuehrungswiss.,10,228 (1971). (9)J. C. Montet and D. G. Dervichian,Biochim. (Paris),53,751 (1971). (IO) R. T. Holzbach, M. Marsh, M. Olszewski, and K. Holan, J . Clin. Invest., 52, 1467 (1973). (11)R. T. Holzbach and M. Marsh, Mol. Cryst. Liq. Cryst., 28,217 (1975). (12)N. Tamesue, T. Inoue, and K. Juniper, Am. J. Dig. Dis., 18,670 (1973). (13)L.Swell, C. C. Bell, D. H. Gregory, and Z. R. Vlahcevic, Am. J. Dig. Dis., 19,261 (1974). (14)D. Mufson, K. Trivanond, J. E. Zarembo, and L. J. Ravin, J . Pharm. Sci., 63,327 (1974j. (15)H. Itoh, Fukuoka Acta Med., 66,351 (1975). (16)T. Nakama, Fukuoka Acta Med., 67, 413 (1976). (17)P. H. Elworthy, A. T. Florence, and C. B. Macfarlane, in “Solubilization by Surface-Active Agents”, Chapman and Hall, London, 1968,p 248. (18)D. M. Small, in “The Bile Acids”, Vol. 1, P. P. Nair and D. Kritchevski, Ed., Plenum Press, New York, 1971,p 294. 0022-3654/82/2086-2784$01.25/0
lesterol solubility with gallstone formation and its dissolution in the human body, they have performed experiments for aqueous bile salt-lecithin-cholesterol model systems and systematically investigated the effects of variations in total lipid concentration, type of bile salt, temperature, and ionic strength, etc., on cholesterol solubility. It may be desirable to carry out studies on systems which resemble human bile as much as possible. Such an approach, of course, will offer a lot of practical information, but the experimental results obtained from such complicated systems often make our essential understanding difficult or obscure. This paper, therefore, describes the experimental results on cholesterol solubility in two simple micellar systems, NaC and NaDC. The object of this work is to make clear the effects of pH, pNa, temperature, the concentration of bile salts, and the molecular structure of salt on the cholesterol solubilization, and furthermore to discuss thermodynamically the structure of the micelle and the mechanism of micelle formation from the data of cmc a t various conditions.
Experimental Section Sodium deoxycholate, sodium cholate, and cholesterol purchased from E. Merck Co. were recrystallized several times from an ethanol solution (for NaDC), a mixed solution of methanol and ethanol (for NaC), and a chloroform solution (for cholesterol). Then they were dried in vacuo at 110 “C for 24 h or longer. The cholesterol was dissolved in chloroform just after purification and the solution was stored in a refrigerator to avoid oxidation. The elemental analysis verified the purity of these materials. Sodium chloride, borax, and boric acid purchased from Nakarai Chemicals Co. were of guaranteed grade and were used without further purification. The thrice distilled water was used for the preparation of solutions. All bile salt solutions were prepared by dissolving in Palitzsch buffer solutions which were different mixtures of 0.55 M borax solution (A) and 0.2 M H3B03solution with the addition of 0.05 M NaCl (B). The pH and pNa (19)M.C. Carey and D. M. Small, J . Clin. Invest., 61,998 (1978).
0 1982 American Chemical Society
Solubilization of Cholesterol by Bile Salts
The Journal of Physical Chemistry, Vol. 86,No. 14, 1982 2785
h
,
-/,e,
I
2
1
3
CONCN. OF NaDC ( r n ~ l d m - ~ x l O ~ ) CONCN OF N a C (moldm-3)
Figure 1. Plots of the amount of solublllzed cholesterol vs. molar concentration of NaC at pH 8.3: (0)at 50 OC with 0.1 M NaCl added; (0)at 40 OC without NaCl added; cmc's are represented by arrows.
values of solutions were measured by the use of a Hitachi-Horiba pH-meter F-5 and a pNa meter N-5, respectively. A fixed amount of the stock solution of cholesterol-chloroform was injected into each ampoule and then chloroform was removed by aspiration. 5 mL of bile salt-buffer solution of each concentration were injected into the ampoule with dried cholesterol, and then sealed. The ampules were incubated a t each temperature with continuous shaking (180 cycle/min) for 24 h. After incubation the content was filtered through a membrane filter (Toyo Kagaku Sangyo Co., Tm-5 (0.1 p ) ) in order to remove the nonsolubilized cholesterol. The separation of solubilized cholesterol from the filtrate was made by four extractions into the mixed solvent of ethanol and hexane. A blank test was made to check whether nonsolubilized cholesterol exists in the filtrate or not. The extracted cholesterol solution was evaporated to dryness. The amount of solubilized cholesterol was measured by means of a Hitachi 124 spectrophotometer (wavelength 430 nm) according to the Liebermann-Burchard reaction.20
Results and Discussion 1. The Effect of pH and pNa on Cholesterol-Solubik i n g Power. As previous studies on cholesterol solubilization by bile salts had shown disagreements with each other, Furusawa et a1.21 made some experiments on the system of cholesterol-bile salt-150 mM NaCl solution to obtain basic information, and revealed that (1) not only the rate but also the degree of solubilization depend on the amount of excess cholesterol added and the concentration of bile salt; (2) an appropriate proportion of added cholesterol to bile salt was 15-10 (w/w); and (3) from a linear relation between solubilized cholesterol and bile salt concentration the solubilizing power can be defiied as the value of slope of the straight line in the plot. According to Furusawa et al., 5 mg of cholesterol was added per milliliter of bile salt solution, and the shaking (incubation) t i h e for ampuled samples was 24 h. The solubilized amount of cholesterol in NaC-buffer solution and that in NaDC-buffer solution are plotted against the concentration of bile salt, as shown in Figures 1 and 2, respectively. While a good straight line is obtained for the NaDC system, no linear relation is seen in the NaC system. In the case of the NaDC system the cmc can be determined easily by the intercept of the straight line on the abscissa. The cholesterol-solubilizing micelle of NaDC seems not to change its size with increase in the NaDC (20) W. M. Sperry and M. Webb, J . B i d . Chem., 187,97 (1950). (21) T. Furusawa, T. Nakama, T. Hisadome, and H. Itoh, Gastroentrol. Jpn., 11, 356 (1976).
Figure 2. Plots of solubilized cholesterol amount vs. NaDC concentration at pH 9.1 and 30 "C: (0)with 0.2 M NaCI; (0)without NaCI; cmc's are represented by arrows. 101
I
NaDC
4 '15 X
1
I
m
NaC
i
(ALx&x+x-VG
0
01
02
d 03
[Na'] (moldm3) Figure 3. Solubilizing power of bile salts as a function of [Na'] at 30 "C and various pH's: (A)pH 7.8; (0)pH 8.3; (0) pH 8.7; (X) pH 9.1. (A) S evaluated in 0.05 M NaC; (B) S evaluated in 0.15 M NaC (maximum S).
concentration at least in the concentration range studied, as will be described later. However, the line for NaC is significantly curved, especially near the cmc. This is attributed to the stepwise association with increasing NaC concentration, as pointed out by Chang and Cardinal.22 Fontella reported a study on the solubilization of p-xylene and 1-decanol by bile salts in which marked discontinuities in the solubilization curve were found over a wide range of bile salt concentration. However, our experimental result did not show such a discontinuity, although the concentration sufficiently covered the range up to "Limit 3" of Fontell. Solubilizing power (S)is defined as S = dw/d(C - cmc) = dw/dC; w, here, is the molar concentration of solubilized cholesterol and C is the total concentration of bile salt. Figure 3 shows the solubilizing power for NaDC and NaC as a function of [Na+] at different pH's and at 30 "C. S for the NaC system increases up to a constant value with increasing the concentration of NaC, so S was evaluated at concentration of 0.05 M (curve A). In the concentration range from 0.1 to 0.2 M NaC, the solubilization curve (Figure 1) is almost linear and its slope is at a maximum. Curve B in Figure 3 represents the maximum solubilizing power of NaC. The amount of solubilized cholesterol is little affected by the change in pH, and slightly increases with increase in [Na+]. A comparison of curves for NaDC with those for NaC tells us that NaDC exhibits more complex behavior in the pH and [Na+] dependency of S than NaC. The temperature effect on S was examined along with [Na+]effect for NaC and NaDC at pH 8.3. Any significant temperature dependency is hardly seen for NaC, (22) Y. Chang and J. R. Cardinal, J . Pharm. Sci., 67, 174 (1978). (23) K. Fontell, Kolloid 2.2.Polym., 250, 333 (1972).
2786
Sugihara et al.
The Journal of phvsical ChemktIy, Vol. 86, No. 14, 1982
TABLE I: Cholesterol-Solubilizing Powers (S X
l o z )of NaDC and NaC concn of NaCl added,a M
salt NaDC
NaC
a
pH
temp, "C
7.8 8.3 8.7 9.1 8.3 8.3
30
7.8 8.3 8.7 9.1 8.3 8.3
40 50 30
40 50
0
0.02
5.70 7.03 5.61 6.22 9.75 9.14
7.33
0.05
0.10
6.45 5.46
5.0 ( 1 . 7 ) 5.0 ( 1 . 8 ) 5.4 (1.8) 5.3 ( 2 . 0 ) 5.0 ( 1 . 7 ) 6 . 0 (1.8)
0.15
7.93 8.12 6.62 6.18 10.10 9.20
6.98
5.2 (2.2) 5.0 (1.9) 5.4 (2.0)
5.7 ( 2 . 1 ) 5.5 (2.1) 5.5 (2.5) 5.6 (2.1) 5.8 (1.5) 6.4 (2.0)
0.20
5.34 5.44 8.14 6.13
5.62 8.14 5.99 6.60 8.98 7.74
5.7 (2.5) 5.8 ( 2 . 0 ) 5.8 (2.7) 5.6 (2.3)
6.3 ( 2 . 3 ) 6.1 (2.0) 6 . 5 (2.4) 5.6 (2.5) 6.0 (2.7) 5.0 (2.6)
Values in parentheses were evaluated at 0.05 M NaC.
while a notable dependenncy can be seen for NaDC. The results suggest that the mixed micelle of NaC has, contrary to that of NaDC, little sensitivity to the change in the surroundings at least with respect to the cholesterol solubilization. The shape and size of the NaDC micelle do change sensitively with the change in surroundings, and thus its capacity for cholesterol must be affected by it. A complex and drastic change in the aggregation state with changing counterion concentration has been observed by us through various experiments (light scattering, viscosity, density, C.D., et^.).^^ Solubilizing powers at different conditions are listed in Table I. In general, the solubilizing power of NaDC is larger than that of NaC, especially at a lower concentration range. The reduction of one hydroxyl group from the steroid skeleton relatively enhances the hydrophobicity of the bile salt molecule and therefore leads to a smaller cmc, a larger aggregation number, and a larger hydrophobic core (larger capacity for the solubilizate). In the case of NaC, which has three hydroxyl groups, the micelle must have smaller size and looser structure than that of NaDC. 2. Thermodynamics of Micelle Formation. The cmc values obtained for NaDC-cholesterol and NaC-cholesterol systems are tabulated in Table 11. Here it should be noted that the cmc values for the cholesterol-solubilizing systems are different from cmc of pure single component bile salt, and that the phase separation model is applicable to the NaDC-cholesterol system because of a suficiently large aggregation number. From the light scattering measurement the aggregation number was determined as 43 for the NaDC micelle saturated with cholesterol at pH 7.8 and 30 0C.24 In our previous paper it was suggested that the proton H+ should be taken into account as a counterion as well as sodium ion Na+.25 Thus the composition of cholesterol-solubilizing micelle is assumed as BA-.P3Ch.@4H+$5Na+ where BA- denotes the surface-active anion of bile salt (NaBA), Ch is cholesterol, and p3, P4, and p5 are the number of solubilized cholesterol molecules, counterions H+, and Na+ per molecule of micelle-forming NaBA, respectively. At equilibrium of micelle formation BA-
+ P3Ch + P4H++ P5Na++ mi~elle(BA-$3&h.P~H+./3~Na+] (1)
TABLE 11: Cmc Values of NaDC and NaC, Determined by means of Cholesterol Solubilization at Various Conditions (M X lo3) concn of NaCl added, M temp, salt pH "C 0 0.02 0.05 0.10 0.15 0.20 NaDC 7.8 30 4.8 3.6 3.0 2.6 2.4 8.3 8.7 9.1 8.3 8.3
NaC
7.8 8.3 8.7 9.1 8.3 8.3
40 50 30
40 50
3.9 4.7
19 19 18 16 18 20
3.8
14 15 14
3.2 3.2 3.1 2.8 2.6
2.7 2.7 2.7
10 10 10 9
11 12 11 11 13 13
2.4 2.4 2.3 2.1 1.9 8 9 9 8 11 10
When the excess amount of cholesterol solid coexists in the system, the following equilibrium expression holds. Ch(so1id) == Ch(bu1k) == Ch(micel1e) (2) The chemical potential of the ith component in the solution is pi = pio + RT In ai (3) ai is the activity of i in the bulk solution and i = 2 , 3 , 4 , and 5 denote BA-, Ch, H+, and Na+, respectively.
where
If we regard the cholesterol-solubilizingmicelle as a pseudo phase, the chemical potential of micelle-forming species, BA-q33Ch$?4H+q35Na+ in the micelle can be expressed by the equation pm = lm'(T,P) (4) Here, it is considered that the respective contents of the mixed micelle are fixed as is shown by eq 1,so the mixed micelle has its own standard potential pmo. This value is, of course, different from that of the single component micelle. From eq 3 and 4 we obtain the Gibbs energy change on mkelle formation per mole of the micelle-forming species, A Gm AGm = p m - 112 - P = AG,'
- Rqln
a2
3 ~ 3 P 4 ~4 05~15
+ P3 In a3 + P4 In a4 + P5 In a5) (5)
Here AGmo = pmo - ~
(24) Y. Murata, G. Sugihara, N. Nishikido, and M. Tanaka, in 'Solution Behavior of Surfactante-Theoretical and Applied Aspects", K. L. Mittal and E. J. Fendler, Ed., Plenum Press, New York, 1982. (25) G. Sugihara and M. Tanaka, Bull. Chem. SOC.Jpn., 49, 3457 (1976).
5.3 5.4 5.0 4.9 4.6
- 83~3'- P4~4' - P5~5' =
2 '
constant (T,P)
Since AG, can be regarded as a function of temperature T, pressure P, a2,a3,of4, and a5,the following equation holds for the perfect differential of AG,
Solublllzatlon of Cholesterol by Blle Salts
The Journal of phvsical Chemistry, Vol. 86, No. 14, 1982 2787 I
I (6) When the solubilization experiment is made on such a system as the concentration of cholesterol in the bulk solution is kept constant under coexistence of cholesterol solid, the chemical potential in each phase has the following relation p3(micelle) = p3(bulk) = p3(solid) = k30(T,.F') =constant (7) and thus activity of it (a3)is regarded as unity, and then the term in cholesterol in eq 6 can be neglected. The differential coefficients of components 2,4, and 5 are obtained from eq 5 as -RT, -&RT, and -&RT, respectively. Hence, eq 8 is derived from eq 6 d(AOm) -ASm d T AVm dP RT(d In a2 p4 d In a4 + Os d In a5) (8)
+
1
I
91
I
I
-12
-10
-08
-06
l o g [Na'l
Flgure 4. Plots of log [Na'] vs. log cmc of NaDC at varlous pH's and 30 OC.
+
For the reversible micelle formation at a constant pressure, the changes in entropy and enthalpy upon micelle formation are expressed as a
m
ASm = -= -RT( T
T) t 3
In a2
P,etc
On the other hand, the following equation is derived from eq 4 and 5, since AGm = 0 at equilibrium In a2 = constant(TQ) - p3 In cy3 - p4 In a4 - p5 In a5 (10) In eq 10 too, the term in cholesterol can be regarded as a constant when eq 7 holds. As the cmc of cholesterolsolubilizing micelle is represented in terms of the concentration of bile salt itself, we suppose the activity of bile salt, a2,at the cmc is equal to cmc. Thus log (cmc) = constant(TQ) + P4pH + p5pNa (11) Equation 11 tells us that the slope of the curve in the plot of pH vs. log (cmc) at constant T,P, and pNa, (t3 log ( c m c ) / d ~ H ) ~gives ~ , ~p4, ~ and ~ , similarly (t3 log (cmc)/ t3 pNa)Tp,pHgives p5, respectively. The substitution of eq 11 into eq 9 leads to ASm = -2.303RT[(d log (cmc)/d7?p.etc where it is assumed that the temperature dependency of the activity coefficient of the cholesterol-solubilizingmicelle is negligible. Equation 12 enables us to estimate the entropy change upon micellization, if only we obtain the data relating to the slope of log (cmc) vs. T, that of pH at cmc vs. T, that of pNa at cmc vs. T, and p4and f15. Figure 4 shows the plot of log (cmc) of NaDC at various pH's against logarithmic concentration of sodium ions at 30 "C. As is well known, the slope gives p5. The values of p5 were obtained as 0.52 (pH 7.8), 0.62 (pH 8.3), 0.67 (pH 8.71, and 0.70 (pH 9.1), Le., the lower the pH value, the smaller the p5 value. "Iso-cmc curves" for NaDC system, as is shown in Figure 5, were obtained from Figure 4 as a function of pH and pNa at 30 O C . The pNa, here, was regarded as the logarithm of the reciprocal concentration of sodium ions instead of the value measured by the use of a pNa meter. It was found that the pNa value calculated from the analytical concentration of Na+ was, of course, a little
P Na Flgure 5. "Iso-cmc curves" of NaDC as a function of pH and pNa at 30 O C . Numerical values Indicate log cmc.
different from the one measured. However, the former may be considered to be enough to figure the general feature in the pH and pNa behavior. This figure indicates that at low pNa, e.g., pNa = 0.6, A log (cmc)/ApH = p4 0, but at high pNa (low concentration of Na+), e.g., pNa = 1.2, p4 = 0.15. This means that protons are adsorbed on the micellar surface as counterions even in the alkaline region, when the concentration of the sodium ion is low. For comparison, a figure similar to Figure 5 was made for NaC (but this is not given here because strictly speaking the thermodynamics based on a phase separation model cannot be applied to the NaC system due to the smallness in the aggregation number), and showed no pH dependency of cmc above pH 8.3 and thus p4 = 0. However, the cmc's at the lowest pH region studied (pH 7.8) are lower than those above pH 8.3. In the plot of log (cmc) of NaC vs. log [Na+], all measured points except those of pH 7.8 ride on a straight line, and thus it gives the same p5 value of 0.71, while the system at pH 7.8 is separated from them and has a different slope (p5 = 0.68). This may suggest that the systems at pH 7.8 have a small f14, Le., they also have protons as counterions. Generally speaking, the degree of the counterion binding, p4+ p5, is around 0.7 for both NaDC and NaC systems. The temperature change in cmc was examined for the system of NaDC at pH 8.3. Results are shown in Figure 6. The cmc's at different concentrations of added NaCl decrease monotonically with temperature. From Figure 6 we can evaluate the differentials, (a log (cmc)/dT)p,etc and B5(a~ N a l a T ) ~ ,at, ~the , cmc, and introducing them to eq 12, can-calculate the entropy change upon micelle formation, AS,. With respect to the system involving 0.1 M NaCl added at 40 "C, for instance, ASm = 11.8 cal K-' mol-' (eu) and ARm= 3.70 kcal mol-l are obtained. Also
J. Phys. Chem. 1982, 86, 2788-2793
2788
The enthalpy change AH,', thus, can be considered to be equal to M,, and by the use of AI?, and AG,' the entropy change AS," is estimated. As described before, is 2.30 kcal mol-', so that AS,' = 39.6 eu is obtained. Considering that the cmc value decreases with increased temperature, Le., > 0 and AS, > 0, it suggests that the disappearance of structured water around the hydrophobic part of bile salt molecule is predominant upon micelle formati~n.~'It is well known that there exists a minimum in the relation of cmc with temperature in the case of common ionic surfactants, e.g., sodium decyl sulfate (SDeS) and sodium dodecyl sulfate (SDS).28 The AI?, and dm of SDeS and SDS decrease with increased temperature. This corresponds to the melting of icebergs. AboveJhe temperature which gives a minimum cmc and AS, are negative, because the excited thermal motion of single-dispersed ions prevents the micelle formation and also the dissociation of micelle is promoted. On the other hand the cmc of a nonionic surfactant, CH3(CH2)9(OCH2CH&0H, decreases monotonically with increased temperature, at least in the temperature range studied (AI?, > 0, AS, > O).% This is considered to be due to not only the structural change of water but also the superiority of dehydration effect of polyoxyethylene chain to the micelle dissociation effect by heat. Although NaDC is a kind of ionic surfactant, its behavior relating to the temperature dependency of cmc resembles that of nonionic surfactants, considering the fact that the cmc of NaDC decreases with temperature. Also, comparing AS,''s of SDeS and SDS (18 and 16 eu at 25 "C, respectively) with those of dimethylalkyl amine oxides (DCldO: 25 eu and DC12AO: 29 eu at 25 0C).30 AS,'% of nonionic surfactants, in general, are larger than those of ionic surfactants. AS,' of NaDC is relatively larger than these values, but it is rather close to those of nonionic surfactants. This fact may be interpreted in terms of two hydroxyl groups and a partly hydrolyzed carboxyl group.
am
am
I -12
I
-10
-06
-C6
am
log IN d l
Fbwe 8. Plots of log [Na'] vs. log cmc of NaDC at various temperatures and pH 8.3: (A)30 "C; (0) 40 "C; (0) 50 'C.
a,
for the system without addition of NaCl at 30 'C and M, are evaluated as 7.61 eu and 2.30 kcal mol-', respectively. From eq 5 the Gikbs energy change, AG,', can be estimated, putting AG, = 0 above cmc. Here a2 (= cmc), a3 - a5 are the respective mole fractions at cmc. Concerning NaDC in the borate-buffer solution of pH 8.3 at 30 "C without NaCl added, (s, and (ss are given as 0.077 and 0.62, respectively, so its AG," is calculated as -9.7 kcal mol-' assuming the solubility of cholesterol2eto be 5 X lo4 M and (s3 N 0.056 (from the light scattering measurement"). Here y e have the following relations between AS,", AH,", AS,, and M,.
a In (cmc) -RP[
aT
5
a In ai
+ C3 P i F
1,
(13)
5
AS,'
= ASm - R(ln (cmc) + CPi In ai)
(14)
3
(26) M. E. Haberland and J. A. Reynolds, Proc. Natl. Acad. Sci. USA, 70, 2313 (1973).
(27) E. D. Goddard, C. A. Hoeve, and G. C. Benson, J. Phys. Chem., 61, 593 (1957). (28) P. Mukeriee and K. J. Mvsels. 'Critical Micelle Concentrations of Aoueous Sur%ctant Svstems'. NSRDS-NBS-36. US. Government Printing Office,Washingion, DC,' 1971. (29) E. D. Goddard and G. C. Benson, Can. J. Chem., 35,986 (1957). (30) L. Benjamin, J.Phys. Chem., 68, 3575 (1964).
Rayleigh and BriRouln Scattering in Aqueous Electrolyte Solutions David W. James and Roger Appleby' Department of Chemistry, Unlverslty of Oueensknd, Brlsbane, Aushalle 4067 (Received: October 7, 1981; I n Flnal Form: January 13, 1982)
The linearized hydrodynamic description of concentration fluctuations in ionic solutions can be used to predict the Rayleigh and Brillouin light scattering. Using new experimental results for solutions of potassium fluoride and potassium bromide, we critically examine and test the hydrodynamic description for a wide range of concentrations. Approximationswhich are used to calculate the piezooptic coefficient are shown to be inaccurate for all but low concentrations (less than 1 m). The previous practice of ignoring terms containing (dn/d!f')pc is found to be wrong, and these terms are shown to be important for these solutions. The information required to obtain mean activity coefficient data from light-scattering results is also outlined.
The dynamic processes in liquid systems have been studied by light scattering, and the subject is well re-
viewed.'-* Most results are interpreted in terms of a hydrodynamic theory first proposed by Landau and
0022-3654/82/2086-2788~0~ .25/0 0 1982 American Chemical Society
