J. Phys. Chem. 1991, 95, 3837-3846
3837
Structural Studies of a Homologous Series of Alkyl Sucrose Ester Micelle by X-ray Scattering Takeshi Kawaguchi>t Toshiaki Hamanaka,*.*Yuji Kito,g Department of Biophysical Engineering, Faculty of Engineering Science, and Department of Biology, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan
and Hazime Machida Research Center, Mitsubishi Chemical Industries Ltd., Kamoshida, Midori- ku, Yokohama 227, Japan (Received: September 11, 1989)
The micelle structure of a homologous series of the fatty acid sucrose monoester, C S E (n = 10, 12, 14, 16), was systematically studied by X-ray scattering technique. The contrast variation method was used by changing the concentration of sucrose in solutions, and the obtained scattering data were converted into the absolute intensities. The data were corrected for the intermicellar interference effect. The morphological parameters such as micelle volume v I ,average electron density p l , radius of gyration of micelle shape R,,second moment of the electron density distribution a, and square average of the electron density distribution were determined from the data in the range of 0 Is I0.074 A-1, where s = 2 sin 8/A, 28 is the scattering angle, and A is the wavelength of X-ray. The v l , R,,and a increase but pl and (Apl)* decrease with increasing chain length of fatty acid. From relations among R, maximum dimension of micelle, and first isoscattering point, it is suggested that the micelles are not spherical in shape. The other parameters such as aggregation number, hydration ratio, etc. were also obtained in this study. Logarithms of the aggregation number and the micelle volume were found to show excellently linear dependence on the chain length. The models of micelle structure were constructed on the basis of the morphological parameters. Since the two-shell structure of ellipsoid of revolution was found to be an unsuitable model for the sucrose ester micelles, the micelle was modeled by three-shell structure of polar group layer, hydrocarbon core, and the terminal methyl group region which localizes at the center of core. The best fitted model was selected by R factors calculated for both the intensity curves and distribution functions. The micelle shape was oblate for Cl$E, C1+SE,and C , S E but prolate for C1$E. X-ray scattering curves show a possibility that both types of ellipsoid coexist in the solution of C1$E at 20 OC. Many structural parameters were found to change systematically with length of the hydrocarbon chain. However, the minor semiaxial length of hydrophobic core does not change consistently with the increase of chain length. This suggests the increase of gauchetrans-gauche (kink) sequence with increasing the chain length. It is also suggested that water molecules enter into near the boundary between hydrophobic core and hydrophilic layer but do not penetrate into the hydrophobic core. The polydispersity in micelle size was found to be small as a result of the model calculations assuming the Gaussian distribution of the micelle size. The structural change of CI6SEmicelle was found at 49%(w/v) sucrose concentration and interpreted as the change in the packing mode of the detergent molecule and/or the hydration.
1. Introduction The alkyl sucrose ester (abbreviated as sucrose ester below) is a nonionic detergent consisting of several hydrocarbon chains and a sucrose molecule. In synthetic process, the esterification occurs at some parts of eight hydroxyl groups in the sucrose molecule. Since the sucrose ester and its hydrolyzed products do not show any toxicity, it has been widely used in the food and medicine industries as an additive. Initially, the physical and chemical properties of sucrose ester were investigated by Osipow et al.'V2 Following the development of separation technique for mono-, di-, and polyester compounds, many systematic studies have been made on degree of esterification, hydrocarbon chain length of fatty acid, degree of unsaturation for the hydrocarbon chain, et^."^ When the degree of esterification is not particularly high, the sucrose esters exhibit detergency, and a wide range of hydrophiltlipophile balance values can be covered by changing the hydrocarbon chain length and the degree of esterification. The sucrose ester has been also used as solubilizing surfactant for membrane In the study of membrane protein, it is desirable to select a mild detergent which is not only able to quantitatively remove phospholipids from protein but is also able to simulate the natural environment of the protein. The extraction ability of membrane proteins with lauryl sucrose monoester (Cl#E) from bovine erythrocyte membrane ghosts is greater than lauryl ether of polyoxyethylene(9) alcohol (CI2&) and Triton X-100 at the concentrations below 1% (w/v).6 The thermal Present address: Department of Electrical and Computer Engineering, Na oya Institute of Technology, Showa-ku, Nagoya 466, Japan. !Department of Biophysical Engineering. 'Department of Biology.
0022-3654191 /2095-3831$02.50/0
stability of protein solubilized with CI2SEis also excellent compared with the other two detergentsa6In the study of cephalopod rhodop~in,~ it was reported that the sucrose ester behaves like phospholipids but other detergents (digitonin, CI2E9,Tween 80) change the protein conformation. The sucrose ester, therefore, has been frequently used in the study of membrane protein because of such advantageous properties."' However, little is known about the micelle structure. In the previous paper,12 we have reported on the micelle structures of BL-9ex. C,,SE, and stearyl sucrose monoester (C18SE). However, it is found out in the present study that the ( 1 ) Osipow, L.; Snell, F. D.; York,W. C.; Finchler, A. Ind. Eng. Chem. 1956, 48, 1459. (2) Osipow, L.; Snell, F. D.; Marra, D.; York, W. C. Ind. Eng. Chem. 1956,48, 1462. (3) Baba, T.; Takeshida, G. Kogyo-Kugaku Zasshi 1964, 67, 2077 (in Japanese). (4) Baba, T.; Namiki, K.; Maeda, S.Kogv~KugukuZasshi 1964,67,2081 (in Japanese). (5) Nashima, K.; Kawase, N.; Kito, Y. Biochim. Biophys. Acru 1980,626, 390. (6) Makino, S.; Ogimoto. S.;Koga, S. Agric. Bioi. Chem. 1983.47, 319. (7) Motoyama, H.; Hamanaka, T.; Kawase, N.; Boucher, F.; Kito, Y. Con. J . Biochem. Cell. Bioi. 1985, 63, 1152. (8) Baribeau, J.; Boucher, F. Cun. J. Biochem. Cell Bioi. 1985.63, 305. (9) Motoyama, H.; Hamanaka, T.; Kito, Y.; Morita, H.; Guerette, L.; Abran, D.; Boucher, F. Biochim. Biophys. Acru 1986, 861, 9. (IO) Baribeau, J.; Boucher, F. Biochim. Biophys. Act4 1987, 890, 275. (1 1 ) Abran, D.; Boucher, F.; Hamanaka, T.; Hiraki, K.; Kito, Y.; Koyama, K.; Leblanc, R. M.; Machida. H.; Munger, G.; Seidou, M.; Tessier, M. J. Colloid Interface Sci. 1989, 128, 230. (12) Kawaguchi, T.; Hamanaka, T.; Mitsui, T. J . Colloid InterJace Sci. 1983, 96, 437.
0 1991 American Chemical Society
3838 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 pure C,&E hardly dissolves in water at 20 OC and the sample used in the previous study seems to be a mixture of CI6SEand C18SE. Unfortunately, the structural parameters of C&E micelle listed in the previous paper cannot be used even as reference data of mixed micelle, since the ratio in the mixture is unknown. The information about micelle structure is indispensable to discuss the micelle formation or to analyze the structure of membrane proteindetergent complex. The structural studies of micelles by X-ray scattering was started by Reiss-Husson and L ~ z z a t i , ' and ~ J ~they confirmed that the micelle is composed of the hydrocarbon core and the polar group layer surrounding the core. Recently, the micelles of some 10 kind of detergents have been studied by X-ray or neutron scattering technique with the contrast variation m e t h ~ d . ' ~ - ~In ' spite of many studies, the detailed structure, especially the information concerning the packing mode of detergent molecule, is little known because of lack of systematic study, The purpose of the present study is to examine the dependence of micelle structure on the length of hydrocarbon chain. Therefore, this study was undertaken to clarify the micelle structures of a homologous series of sucrose monaester (C,,SE; n = 10, 12, 14, 16) by using X-ray scattering technique with the contrast variation method. In this study, we have performed the structure analysis by model calculation based on the morphological parameters such as average electron density p I , radius of gyration of micelle shape R,, second moment of electron density distribution a, micelle volume uI, and square average of the electron density distribution (ApI)*, which could be directly determined from X-ray scattering data. We have adopted the two-shell ellipsoid of revolution model which consisted simply of two different electron density levels corresponding to the hydrophobic core and the outer hydrophilic layer. The values of model parameters were determined by solving the equations simultaneously which related to the morphological parameters, under the assumption of the uniform thickness of the hydrophilic layer. A relatively good agreement between experimental and calculated X-ray intensities has been obtained. However, the volume of the hydrophobic core was too small to be consistent with Tanford's theory. Besides this, the electron density of the core was considerably lower than that of molten paraffin. The hydration could not be reasonably explained by this micelle structure. Since the problem seemed to occur from the approximation of hydrocarbon core by a single electron density level, we have analyzed the micelle structure based on the three-shell model which considered a lower electron density region at the central part of the hydrocarbon core corresponding to the localized methyl group. The three-shell model has given better agreements in X-ray intensity data and shown reasonable micelle structures. We have also investigated the polydispersity in the micelle size based on the model calculation, in which the distribution of micelle volume was approximated by the Gaussian function. The significant improvement in X-ray intensity data could not be observed by the introduction of polydispersity. This fact indicates that the polydispersity is small and the results obtained by the monodispersive model calculation are appropriate for the sucrose ester micelles. 2. Materials and Methods 2.1. Detergent and Its Solubility in Water. The sucrose esters were synthesized by the method of Osipow et al.' at Mitsubishi ~~
(13) Reiss-Husson, F.; Luzzati, V. J . Phys. Chem. 1964, 68, 3504. (14) Reiss-Husson,F.; Luzzati, V. J. Colloid Inrerfice Sci. 1966,21, 534. (15) Sardet, C.; Tardieu, A.; Luzzati, V. J. Mol. Biol. 1976, IOS, 383. (16) Osborne, H. B.; Sardet, C.; Michel-Villaz, M.;Chabre, M. J . Mol. Biol. 19l8, 123, 177. (17) Wise, D. S.; Karlin, A.; Schoenborn, B. P. Biophys. J. 1979,28,473. (18) Cabane, B.; Duplessix, R.; Zemb, T. In Surfacronrs in Solurion; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 1 , p 373. (19) Chen, S.H. Annu. Rev. Phys. Chem. 1986.37, 351. (20) Sheu, E. Y.; Chm, S. H.; Huang, J. S. J. Phys. Chem. 1987,91, 1535. (21) Timmins, P. A.; Laonhard, M.;Weltzien, H. U.; Wacker, T.; Welte, W. FEBS Leu. 1988, 238, 361.
Kawaguchi et al. Y Roc
w PHC'
oblate
prolate Figure 1. Illustration of the ellipsoidal three-shell model proposed for micelle structure and notations for structural parameters.
Chemical Industries Ltd. (Yokohama, Japan). The respective products contained about 80% monoester. Most of the impurities were diester (17-19%) and triester (1-3%) types. The products were purified by column chromatography with silica gel and thus pure samples of almost 100% monoester were obtained. The solubility of sucrose monoester into water was examined by the measurement of turbidity. The turbidity of 0.2% (w/v) solution was measured by using a spectrophotometer (Shimadzu UV-ZOOS) with the integrating sphere attachment. In this method, the turbidity is represented by Td/Ttin percentage, where Td and Tt are transmittance of diffused light and total transmittance, respectively. 2.2. X-ray Experiment. Nickel-filtered Cu Ka radiation (A = 1.542 A) from an X-ray tube (Toshiba Co.) was used with a small-angle camera of three-slit system (Rigaku Denki Co.). The X-ray generator (Rigaku Denki Co., RAD-11) was operated at 40 kV and 40 mA. Scattering X-rays were detected by a linear-position-sensitive counter of delay-line read-out type (Rigaku Denki Co.). The monoester samples were dissolved in 50 mM sodium phosphate buffer solution (pH 7.0) containing 100 mM NaCl in X-ray measurements. The contrast was varied by changing the electron density of the solvent with sucrose. The sucrose concentrations were 0, 7, 14, 21, 28, 35,42, and 49% (w/v), which correspond to the electron density levels of 0.3381,0.3453,0.3532, 0.3614, 0.3686, 0.3768, 0.3836, and 0.3905 e/A3, respectively. The sample was put in a cell having windows covered by about 10 r m mica (in thickness) for X-rays to pass. The thickness of the cell was so determined that the intensity of X-rays passed through the specimen became about l / e of the incident beam, and was 1 mm. The X-ray experiments were carried out separately in two small-angle regions: the low-angle region (0.0026 A-' C s < 0.03 A-I; s = 2 sin B/A, where 28 is the scattering angle and A is the wavelength of X-ray) and the intermediate-angle region (0.016 A-' < s C 0.09 A-'). The distance from sample to the plane of registration and the width of second slit were 315 and 0.1 mm for the low-angle measurements and 180 and 0.2 mm for the intermediate-angle measurements, respectively. When the electron density contrast becomes small, the scattering intensity a t low-angle region becomes very weak and the experimental errors increase considerably. Also,the scattering intensity was weak at the intermediate-angle region. Consequently, relatively high detergent concentrations were adopted: 5% (w/v) for the low-angle measurements, and 10% (C,,$E, C12SE, C14SE) and 7% (C16SE) for the intermediate-angle measurements. The intensity data were obtained with good statistics in the counting time of 2 X IO4 s (low angle) and 1 X 10's (intermediate angle). All the X-ray measurements were done at 20 f 1 OC. The subtraction of the background scattering was made by using the buffer solution with the same concentration of sucrase as the micelle solution. The background subtracted intensity curyes were desmeared by the procedure described by Glatter.22 The data were corrected for the intermicellar interference effect as described in Appendix I. The conversion of measured X-ray intensity into (22) Glatter, 0. J . Appl. Crysiallogr. 1974, 7, 147.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3839
Micelle Structure of Sucrose Ester the one on the absolute scale was made by using Lupolen according to the procedure of Kratky et al.23as described in Appendix 11. The calculations were carried out on the PDP 11/34 computer (DEC) . 2.3. Model Calculation. 2.3.1. Model Building. For the reason described in the Results section, the micelle structure was modeled by the ellipsoid of revolution which had three different electron density levels in its internal structure as shown in Figure 1 , rather than the two-shell model. The parameters y, y’, and 7’’ are axial ratios of the whole micelle, the hydrophobic core, and the terminal methyl group region, respectively. The y’ is related with y by Rpo - RHc = ~ R p o- y’RHc = L (1)
Chain-length (CnSE)
so that the hydrophilic layer has a uniform thickness L. Further, 7’’ is related with y’ by
RHC - RHC’ = 7’RHc - 7”RHC’ = L’
(2)
Then, the following relations are obtained: RHc = Rpo - L
determined by solving the simultaneous equations. 2.3.2. X-ray Scattering Function of Models. The intensity i,(s,po)scattered by one micelle at a solvent electron density of po can be written24as
y’RHC = ~ R p o -L RHC’ = RHC - L’ = Rpo - L - L’ 7“RHC’ = y’RHc - L’ = ~ R p o- L - L’
(3)
The electron densities of the polar group layer, the hydrocarbon core, and the methyl group region are denoted as ppo, PHC, and pHC’,respectively. Thus, the micelle structure can be defined by the seven structural parameters of Rpo, yR=, L, L’,ppo, ~ H C and , PHC’.
The morphological parameters of micelle volume uI, average electron density pl, radius of gyration of micelle shape R,, second moment of the electron density distribution a, square average of the electron density distribution ( A P ~ ) and ~ , half of maximum dimension, D-/2, can be expressed by the structural parameters as follows: UI
= 4*yRpo3/3
(4)
PI = {Y”RHC‘3PHC‘ + (Y’RHC’ - Y”RHC’3)PHC + (*/RPG37’RHC3)pPG)/ yRPG3 ( 5 )
+
R, = {(2Rpo2 y2Rpo2)/5)’j2
(6)
{MHC’bHC’ - PI) + (MHC - MHC’) (PHC - PI) + (MPG - MHC)(Pffi - P l ) ) / u l (7)
a
where
+ ~T”’’RHC”/ 15 MHc = 8Ty‘R~c’/15 + 4Ty”R~c’/ 15 Mpo = 8*yRpoS/15 + 4ry3RpoS/15
MHC’= ~ T ~ ” R H c ”15/
= b H C ’ - P1)2Y”RHC’3 + (PHC - PI)’(Y’RHC3 ~”RHc”)+ (PFG - Pd2(YRpo3 - Y’RHC~))/YRFG~ (8) for oblate type D,,,/2 = Rpo = yRpo for prolate type (9) Equation 9 seems to be useful to estimate Rffi or 7Rpo at first sight. However, D,, has considerable error as mentioned later. Therefore, the structure analysis was performed by using eqs 4-8. In the case of the two-shell model, the expressions of pl, a, and (Apl)* are obtained by substituting RHC’ = ?‘‘RH=’ = pHC‘= 0 in q s $7, and 8, respectively. The equations for uI and R, are the same as eqs 4 and 6, respectively. The structural parameters of the two-shell model (Itpo,yRW, L,ppo, and hC) can be directly (23) Kratky, 0.;Pilz. 1.; Schmitz, P. J. J. Colloid Interfie Sci. 1966,21, 24.
Figure 2. Turbidity of 0.2% (w/v) alkyl sucrose ester solution as a function of the chain length of the fatty acid moiety. The turbidity was determined at 550 nm wavelength.
and
= (47r/3)yRpo3(ppo - pO)d(2xsRpo(sin2B + y2 cos2 /3)1/2) + (4T/3)Y’RHC3(pHC - pPG)d(2TsRHC(sin2 6 + ’y”2 COS’ ( ~ T / ~ ) Y ” R H c ’ ~ ( ~-H c ’ p~c)c$(2TSR~c’(Sin~ fl + y’l2 cos2 @)I/’) (1 1)
Fl(S,PO)
+
where +(x) = 3(sin x - x cos x)/x3. In the case of the two-shell model, Fl(s,po)is obtained by substituting RHC’ = 0 in eq 11. The R factor is useful to evaluate objectively the agreement between the observed and calculated il(s,po)or the autocorrelation functions. We have used the R factors given by Luzzati et al.2s as
R = CS2lil(0bs)- il(cal))2/cs2il(,b)2
(12)
for intensity curves, and
R = C$(Ao, - &J2/C$Aob2
(13)
for the autocorrelation functions, respectively. Where, A(r,po) is the autocorrelation function and described as A(r,po) = 2 ~ i l ( s , p o ) ( s / r )sin (27rrs) ds
(14)
The relation between A(r,po)and the distribution function D(r,po) is given by D(r,po) = $A(r,po).
3. Results 3.1. Turbidity of Micelle Solution. Figure 2 shows the relation between turbidity and chain length of fatty acid at 20 OC. The turbidity increases drastically from CI6SEto CI8SE,indicating that C18SEcan hardly dissolve in water at 20 OC. The detergents of C,,$E, CI2SE,and CI4SEdissolved easily in water over 20% (w/v) concentration. In the case of CI6SE,it dissolved up to 14% but 20% solution could not be obtained. 3.2. X-ray Scattering Data. The X-ray scattering intensity I(s,po) from the micelle in the aqueous solution was obtained after background subtraction and correction for collimation distortions as described in section 2.2. All the curves were also corrected with the interference function obtained in Appendix I. The I(s,po) curves obtained in the low-angle region could be fitted well wlth (24) Guinier, A. Ann. Phys. 1939, 12, 161. (25) Luzzati, V.; Tardieu. A.; Aggerbeck, L. P. J. Mol. B i d . 1979, 131, 435.
Kawaguchi et al.
3840 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 I
I
I
3.52
(a) - 3.08 n
,-" O b
-2.64
U
CI
3 2
2
U
U
-2.2
-1.0
-0.8
$
-1.76
.-
y
14
- 0.6
- 1.32
21
- 0.4
- 0.88
28
- 0.2
- 0.44
iso
so
4 2 3 4 9 0
2
6
4
$ .-
s (lo-2w1)
t
( b)
42.1 11.8
- 1.5
- 1.2 - 0.9
14
- 0.6 21 28 359 4 2 0
- 0.3 2
6
4
(10-2a-1) s (lO-*i-l) Figure 3. X-ray intensity il(s,po) scattered by monoester micelle in 0, 7, 14,21,28, 35,42 and 49% (w/v) sucrose solutions: (a) Cl$E (b) Cl2SE (C) Cl4Sk (d) C16SE.
TABLE I: Morphological Parameters parameter
irl. e 1 ~ 3 ul/m1I2, A3/e1/2 Rv, A a, e/A ul, 104 A3 mi10'3 e2/A6 Dllux* SI*, 10'2 A-1 RO(Sl*),
A
Cl$E
Cl2SE
Cl4SE
C16SE
0.3870 484 20.3 8.8 6.9 5.77 54*7 2.90 24.7
0.3813 605 23.1 11.6 10 5.27 60*7 2.59 27.6
0.3778 726 26.1 15.6 14
0.3735 888 29.5 19.8 20
5.4
5.00
68i7 2.35 30.4
84i7 2.12 33.7
those in the intermediate-angle region at the overlapping range 0.016 A-1 < s < 0.03 A-1 by a suitable scaling. From this result, it is suggested that I(s,po) contains no systematic error. Figure 3 demonstrates X-ray scattering curves at eight sucrose concentrations. In Figure 3, X-ray experimental curves I(s,po) are transformed into the intensity curves scattered by one micelle il(s,po) following the procedure described in Appendix 111. Each il(s,po) has one or two maxima which shift toward lower angle from C,&E to CI6SEmicelles. An isoscattering point where the intensity is practically independent of p0,l2 as indicated by an arrow, is observed in Figure 3. This point is the first isoscattering point sl* and its value is listed in Table I. 3.3. Morphological Parameters. On the basis of the theory described by Luzzati et a1.,26 we analyzed the data presented in
Figure 3 under the following three assumptions. 1. The micelles are monodisperse with the aggregation number n. The polydispersity in n is treated in section 4.2. 2. The boundary between micelle and solvent can be clearly discriminated and the shape of the micelle is well-defined by the (26) Luzzati, V.; Tardieu, A.; Mateu, L.; Stuhrmann, H. B. J. Mol. Biof. 1976,101, 115.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3841
Micelle Structure of Sucrose Ester I
4- \
I
t
i
shape function uI(r) which is 1 inside the micelle and 0 outside. 3. The sucrose used to raise the electron density of solvent does not change the micelle structure by penetrating into uI(r). The validity of assumptions 2 and 3 will be discussed later. First, we analyzed the intensity data in the Guinier region. The extrapolation of Guinier plot to s = 0 gives the meangle intensity I(O,po), which was converted to the sample intensity i,,(O,po) (cf. Appendix 11). Second, (in(0,po)/ce}1/2 were plotted as functions of po in Figure 4. The linear relations between two quantities are expected by the following equation.Is Iin(0,d/ce11’2 = u l ( ~ I- po)/m1/2
(15)
-’ I -2A
tb
‘49
20
do
$0
&I
41
.-
c
!
I
I
$0
io do
(A)
r
h
io i o
I
I
I
(c)
5 3
g
//
- 2
\\
-I
1
Q0 where c, is concentration in number of electrons of solute per I number of electrons of solution, ui volume of one micelle, p i 0 average electron density of the micelle (pl = Spl(r) dur/ul, pl(r) 0 is electron density distribution in the micelle), and m number of electrons of one micelle unhydrated. The value of pI is given by -1 po at which the sample intensity becomes zero and the slope of the straight line gives ul/m1/2.Obtained values of p i and ut/ml/2 are listed in Table I. A good linear relationship means that the -2; 20 io $0 80 $0 i o $0 Sb ,do value of p 1 is identical even if the micelle is polydisperse in size. r (A) The radius of gyration R(po)was determined from the slope of the Guinier plot. Figure 5 shows R ( ~ Oas)functions ~ of (bo)-’. Figure 7. Distribution function D(r,po) calculated with the intensity data in Figure 3: (a) Cl$E; (b) Ci2SE; (c) C14SE(d) C16SE. The dependence of R(p,J2 on Apo is given byI5 L-
Y
b
R(PO)* = Rv2 - a/&o
- b/(APo)2
(16)
where R, is radius of gyration of the shape function of micelle, a second moment of the electron density distribution (a = S9(pl(r) - p i ] dur/ul), and Apo electron density contrast (Apo = po - pl). The result indicates that b = 0 and, thus, the center of gravity of pl(r) coincides with the center of gravity of the shape function ui(t). The data points lie approximately on a straight line except one point (closed by parentheses) for CI6SEmicelle. The R(po)2 at (ApJ’ = 0 gives R: and the slope of the straight line gives the coefficient a. The obtained values of R, and a are also listed in Table I. The positive a indicates that the regions of higher electron density are preferentially located toward the outside of the micelle. As shown in Figure 5 , of C16SEmicelle departs fibm the straight line at 49% sucrcse concentration. The result suggests that the structural change of the Ci6SEmicelle occurs at higher sucrose concentration than 42%. Since the data point at 49% does not deviate from the straight line in Figure 4, this structural change does not cause the variation of pl. The turbidity of C16SEsolution decreases with increasing the sucrose concentration in solution. This result is due to the decrease of the difference between the
refractive indexes of Cl$E micelle and solvent and suggests that the aggregation among micelles does not occur at high sucrose concentration. From these results, it is presumed that the structural change correlates the variation of the electron density distribution p I (r). The linear relations presented in Figures 4 and 5 support assumptions 2 and 3. Furthermore, the existence of well-defined s,* in Figure 3 is an indication of the validity of these assumptions, as reported in the previous paper.I2 Next, several parameters were obtained from the intensity data in 0 I s I0.074 A-’. The value of invariant P(0,p0)was calculated by P(O,po) = 4?r~s2Z(s.pO)ds.%J7Then,Q(po) was obtained from P(O,po)divided by Z(O,po). The values of Q(po) were plotted as functions of ( A P ~ ) -in~ Figure 6. The relation between the two quantities is given by26-27 Q(Po) = P(O,PO)/WAPO) = l/ui
where
-
+ ( A ~ i ) ~ / u i ( l / ( A ~ o )(17) ~)
is square average of the electron density distribution
(27) Tardieu, A.; Mateu, L.;Sardet, C.; Weiss, B.; Luzzati, V. J . Mol. Biol. 1976, 101, 129.
Kawaguchi et al.
3842 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 TABLE 11: Micelle Constituents parameter C,SE CdE m, 10‘e 2.0 2.7 n
a nw, ( ~ 1 0 ~ ) nwln v l / n , IO2 A3
76 0.31 6.4 8.4 9.1
96 0.39 11 11
IO
C,SE
C16SE
3.7 122 0.43 16 13 12
5.1 161 0.47 24 15 13
((Ap# = .f’{pl(r) - p J 2 du,/u,). According to eq 17, uI is given by l/Q(po) at ( A P ~ ) -=~0, and the slope of the straight line and ul give ( A P ~ )The ~ . obtained values of uI and ( A P ~are ) ~listed in Table 1. The logarithm of uI shows an excellently linear dependence on the length of hydrocarbon chain. Figure 7 shows the distribution function D(r,po)calculated with the data given in Figure 3 . The D(r,po)is the Fourier transform of the intensity curve il(s,po) and is given by D(r,po) = 2 ? ~ i l ( s , p o ) ( s / rsin ) ( 2 ~ s rds )
(18)
The D(r,po)is useful to estimate the size of micelle: the maximum dimension D,, of micelle can be determined by the position where D(r,po)tends to zero.28 In Figure 7 , D(r,po) tends to zero at practically the same r. The value of D,,,, however, contains considerable error because of the truncation effect. According to the sampling t h e ~ r e m , ~the ~ ”truncation ~ effect is presented by s,Ar = 1/2, where, s is maximum s in the truncated il(s,po) and Ar is error in D,,,. Since Ar = 6.8 A in our data ,,s(, = 0.074 A-1),D,,, of the respective micelles have the error of f 7 A. The obtained values of D,,, are listed in Table I. The D(r,po)represents the correlation of the electron density distribution and is also useful to search the internal structure of micelle. The positive peak near the origin corresponds to the sum of correlations within the hydrophobic core and the hydrophilic layer, respectively. The negative peak means the correlation between the hydrophobic core and the hydrophilic layer. The second positive peak is due to the correlation between the hydrophilic layers. The D(r,po)are similar for the four micelles as shown in Figure 7 , indicating that the general features of micelle structure are similar except the size. Some other parameters are obtained from the parameters listed in Table I. (1) The number of electrons of one micelle unhydrated, m, is determined from uI and u l / m l / * . ( 2 ) The aggregation number, n, is determined by n = m/N,, where Ne is the number of electrons of one detergent molecule: 268 for Cl&3E, 284 for CI2SE,300 for C14SE,and 316 for C16SE.( 3 ) The micelles have bound water and the hydration ratio CY can be calculated by CY = u l p l / m- 1 . ( 4 ) The number n, of the bound water molecules in one micelle were determined as n, = am/lO, where 10 is the number of electrons of one water molecule. The obtained values of the respective parameters are listed in Table 11. The number n,/n of bound water molecules per detergent molecule and the volume u l / n occupied by one detergent molecule are also listed in Table 11. 3.4. Micelle Shape. The parameters closely related to the size and shape of micelle in Table I are the radius of gyration of outer shape 4,the maximum dimension D-, and the first isoscattering point sI*. In order to get some idea on the deviation of micelle shape from sphere, we tentatively assume that the micelles are spherical. Then, the three radii Ro of the micelle are obtained from R,, D,,,, and sI*independently. We denote the radius related with R, by & = (5/3)1/2Rv as &(R,). The radius related with D,, is D,,/2. The R&*) is given by the relation 2?rsl*& = tan (217sI*R0). &(R,), D,,/2, and &(sl*)must be the same, if the micelle is spherical in shape. On the other hand, if the micelle is not spherical, we have the relation of D,/2 > &(RJ > &(si*). The former relation is easily proved in the case of the ellipsoid of revolution. The value of Ro(sl*)decreases by anisometry in contrast with D,,/2 and Ro(R,),as reported in the (28) Porod, G . Kolloid 2.1951, 124, 83. (29) Moore, P. B. J. Appl. Crystallogr. 1980, 13, 168. (30) Taupin, D.; Luzzati, V . J . Appl. Crysrallogr. 1982, IS, 289.
TABLE III: Stnrctunl Parameters of Two-ShellModel parameter CISE CI,SE C,SE CInSE oblate oblate oblate prolate 11.6 28.9 19.7 0.682 17.3 8.1 0.468 0.421 0.207
11.9 33.1 21.8 0.659 21.2 9.9 0.467 0.416 0.230
11.7 37.9 23.1 0.609 26.2 11.4 0.435 0.4 19 0.245
12.5 31.2 49.0 1.57 18.7 36.5 1.95 0.416 0.257
previous paper.12 The degree of deviation from spherical shape corresponds to the difference among three radii. Table I shows the relation of 0 - / 2 > &(R,) > &(s,*). This result indicates that the micelles are not spherical in shape. The differences among the three radii are small for the micelles of Cl,,SE, C12SE,and CI4SE but relatively large for the CI6SE micelle. The ellipsoid of revolution can be a good approximation for the micelle shape of sucrose esters, if the deviation from spherical shape is not so large. 3.5. Shape of the Hydrocarbon Core. From the positive a and the feature of the distribution functions, it can be said that the sucrose ester micelles consist of a hydrophobic core and a hydrophilic layer covering the core. Furthermore, if the hydrophilic layer has approximately uniform thickness as pointed out by T a n f ~ r d , the ~ ’ shape of the hydrophobic core is considered to be also the ellipsoid of revolution. Tanford discussed the shape of the hydrophobic core on the basis of the volume of the hydrocarbon chain and the aggregation number na3I The volume u, of a chain having n( carbon atoms, in A’, is given by u, = 27.4 + 26.9n;. Then total volume of chains in one micelle is given as nu,. The maximum length I,, for the chain having q’carbon atoms, in A, on the other hand, is expressed as l,, = 1.5 + 1.265t1,‘.~~ Even if all of the hydrocarbon chains contribute to formation of the hydrophobic core, the core cannot be spherical to satisfy the obtained aggregation number. 3.6. Results of Model Calculations. 3.6.1. nveShell Model. In the case of the two-shell model, the micelle structure is defined , pHo by the five structural parameters of RPG,y R m , L,p p ~ and They can be directly determined by solving the simultaneous equations. Two solutions which correspond to the oblate and prolate ellipsoids, respectively, have been obtained. Since the curves il(s,po) and D(r,po)calculated on both oblate and prolate shapes were similar for y > 0.6 or y < 1.7, the decision of shape could not be done visually. However, R factors have shown a systematic difference between oblate and prolate for both il(s,po) and A(r,po). The structural parameters of the two-shell model are listed in Table 111. Since the R values were in the order of 1V2,the tweshell model seemed superficially to be suitable for micelles of sucrose esters. However, the several points were found to be unreasonable. (1) The volume of the hydrophobic core is too small to be explained by Tanford’s theory. If the above volume is accepted, the polar group layer must contain 5-6 units of -CH2- of the hydrocarbon chain. (2) The dependence of hydration, nJn, on the chain length contradicts the fact that the electron density ppg and thickness L of the polar group layer are almost the same for the four micelles. ( 3 ) The electron density of hydrophobic core, p is considerably lower than that of molten paraffin (0.27-0.28 e / x ).I3 If we put pHc at 0.274.28 e/A3, the volume of hydrophobic core was close to the reasonable value but the agreement between the observed and calculated i,(s,po) became worse. 3.6.2. Three-Shell Model. It seems due to the localization of terminal methyl group that the two-shell model was not suitable for the sucrose ester micelles. Therefore, we have adopted the three-shell model as shown in Figure 1. The values of Rpg and yRm are determined from eqs 4 and 6. The electron density of
F,
(31) Tanford, C. The Hydrophobic Eflecr: Formation of Micelles and Biological Membranes, 2nd ed.: Wiley: New York, 1980.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3843
Micelle Structure of Sucrose Ester TABLE I V Comparison of R Values for Oblate and Prolate Three-Sbell Modela il @*Po)
CISE
SC. 0 0 7 14 21 28 35 42 49 0 7 14 21 28 35 42 49 0 7 14 21 28 35 42 49 0 7 14 21 28 35 42 49
oblate 0.065 0.069 0.074 0.077 0.062 0.043 0.025 0.009 0.038 0.040 0.040 0.030 0.024 0.017 0.01 1 0.009 0.038 0.041 0.041 0.034 0.030 0.017 0.01 5 0.007 0.050 0.057 0.062 0.065 0.053 0.039 0.033 0.048
prolate 0.067 0.072 0.079 0.086 0.071 0.051 0.029 0.014 0.049 0.057 0.066 0.068 0.065 0.057 0.045 0.041 0.056 0.072 0.086 0.091 0.086 0.065 0.059 0.035 0.040 0.043 0.045 0.047 0.037 0.027 0.025 0.045
A(~,Po) oblate prolate 0.064 0.066 0.070 0.067 0.077 0.072 0.084 0.075 0.069 0.060 0.050 0.041 0.028 0.024 0.014 0.009 0.049 0.038 0.056 0.039 0.065 0.039 0.068 0.029 0.065 0.023 0.057 0.016 0.045 0.01 1 0.009 0.040 0.037 0.055 0.041 0.071 0.040 0.086 0.090 0.033 0.027 0.085 0.017 0.065 0.014 0.058 0.007 0.035 0.049 0.039 0.057 0.042 0.062 0.044 0.064 0.046 0.052 0.037 0.039 0.027 0.032 0.025 0.047 0.045
TABLE V Structural Parameters of Three-Shell Model Darameter CAE CI,SE CdE oblate oblate oblate 9.4 9.9 10.3 10.5 8 9.7 37.9 28.9 33.1 23.1 21.8 19.7 0.609 0.682 0.659 28.4 19.5 23.2 13.6 11.9 10.3 0.479 0.528 0.5 12 16.9 11.5 13.5 2.1 2.3 2.2 0.124 0.200 0.163 0.426 0.420 0.420 0.285 0.285 0.285 0.166 0.166 0.166
ClnSE prolate 11.4 14 31.2 49.0 1.57 19.8 37.6 1.90 5.8 23.6 4.07 0.415 0.285 0.166
the methyl group region, pHC’,was put at 0.166 e/A3, equal to the electron density of CH3- group.” The value of PHC was varied from 0.270 to 0.295 e/A3 In steps of 0.005. The other three parameters (L,L’,and ppo) were varied within reasonable extent. Then, the pl, a, and ( A P , ) ~were calculated by using eqs 5 7 , and 8. The sets of L,L’, p p o , and pHCwhich give the experimental values of p , , a, and (Ap,)l were sought for each micelle. Then, il(s,po) and D(r,po)functions were calculated for all the micelle structures thus obtained. The choice of the best model was done by using R factors as criteria. Table IV lists the R values of the best models for both oblate and prolate ellipsoids. The il(s,po) and D(r,po)curves of the models presented in Table IV are shown in Figures 8 and 9, respectively. For Cl$E, C12SE,and CI4SE, R values of the oblate ellipsoid models are less than the prolate ones, indicating that these micelles are oblate. On the other hand, the CI6SEmicelle shape seems to be prolate, judged from the R values. The structural parameters of the three-shell model are listed in Table V. The several parameters derived from the structural parameters given in Table V were calculated and are listed in Table VI. The
TABLE VI: Volumes and Surface Areas of Polar Group h y e r , HvdroPbobic Core. and Terminal Methyl CrouD Region8 parameter Cl$E Cl6SE CISE C12SE 5.3 7.3 9.3 13.8 770 860 760 690 4.6 6.2 2.7 1.6 370 380 220 280 2.5 3.3 1.3 1.7 17 21 21 18 11 17 6.6 8.6 87 89 90 106 2.8 4.0 5.9 8.0 41 48 50 37 1.8 1.4 0.87 1.2 11 12 15 8.6
“upo, uHC, and uHC’ are volumes of polar group layer, hydrophobic are core, and methyl group region, respectively. spa, sHC,and sHC’ surface areas of whole micelle, the hydrophobic core, and the methyl group region, respectively.
vpG/n, vHC/nr and sHc/n (n is the aggregation number) increase with increase of the length of hydrocarbon chain, but spG/nis almost the same for the three oblate micelles.
4. Discussion 4.1. Micelle Structure. As shown in Table I, the micelle volume vI becomes larger by about 40% for the increase of every two -(CH2)- units in the fatty acid chain. If the aggregation number remains unchanged, the increment of v1 is expected to be less than 10% and then the packing mode of the detergent molecules must change largely. Actually, the aggregation number and anisometry increase (Table 11). Therefore, it is necessary that the aggregation number and the anisometry of micelle shape increase with the chain length in order to keep the same packing mode. The hydration water per detergent molecule, &/n, also increases with the chain length. This suggests the slight change in the packing mode. The effective increase of hydrocarbon chain layer is about 60% of the value expected and correspondingly the cross section of a chain increases, by Occurrence of the gauche-trans-gauche (kink) sequence of hydrocarbon chain as described later. This increase of the surface area per detergent molecule at the hydrophobic core, sHC-n, may cause the increase of the space between the polar groups and hence, n,,./n. The logarithm of n shows an excellently linear dependence on the chain length. A similar relation between n and the chain length was reported in the micelles of zwitterionic betaine.32 This suggests that a specific relation might exist among the hydrophobic interaction, the hydrophilic interaction, and the hydration. Since the hydrophobic part has low electron density, the average electron density pI decreases with increase of the volume of the hydrophobic core. But the second moment of the electron density distribution, a, increased as seen in Table I. This is reasonably explained by the localization of the hydrophobic core at the center of micelle and the farther separation of the hydrophilic layer from the center of micelle with the increase of chain length. First, we have analyzed the micelle structure based on the two-shell model and obtained the models fitting well with the observed X-ray data (Table 111). However, the several unreasonable points concerning vHC, hydration, and pHC were found as mentioned in section 3.6.1. (1) The vHCis too small to be explained by Tanford’s theory. The value of nd derived vHC = n(27.4 26.9n,’) is 4.0 (C,$E), 6.2 (CIISE), 9.0 (CI4SE), and 11.3 (CI6SE). From these values, I,, ( e l . 5 + 1.265n:) was obtained as 6.5, 9.3, 12.8, and 15.8 A, respectively. If the hydrocarbon chains are in the liquidlike state in the core, the minor semiaxis (Y’RHcfor oblate, RHc for prolate) is expected to be less than or equal to lmax. However, the obtained minor semiaxis is 8.1, 9.9, 11.4, and 18.7 A, respectively (Table 111), and greater than the calculated l, value except C I S E . (2) Since the electron density of water (0.333 e/A3) is considerably lower than that of
+
(32) Swarbrick, J.; Daruwala, J. J . Phys. Chem. 1970, 74, 1293.
Kawaguchi et al. (a)
prolate
oblate
I
- 1.4
bblate
R
-i+?O h
v
s
(b)
-4
(lo-2A-1)
oblate
s
prolate
i
i+?
1.8
U
35 42
3 0
(d 1 0
- 2.1 wn
@ .,
!?
prolate
(lo-*%-')
oblate
prolate
- 4.9
t
H
n N
-4.2
2
4
-1.5
n
-3.5
-1.2
z
-2.8
9
- 0.9
- 2.1
- 0.6
- 1.4
- 0.3
- 0.7
6
," s? U
Y
0
2
4
n
$
6
s (lo-2P) s (109%1) Figure 8. Calculated il(s,po) of oblate and prolate three-shell models: (a) C,$SE; (b) C & E (c) C&E; (d) C16SE.
sucrose, the increase of nJn must bring about both decrease of the electron density pm and increase of the thickness L of the polar group layer. However, ppG and L are almost same for the four micelles (Table 111). ( 3 ) The value of pHCis considerably lower than that of molten paraffin. Therefore, second, we have tried the analyses of X-ray data based on the three-shell model. Although the agreement between the observed and calculated data had not been improved significantly, the three-shell models got rid of the unreasonable points in the two-shell model. In the three-shell model, the minor semiaxis is comparable to the 1- ( n l n, - 1) for the four micelles. This suggests that the hydrocarbon chains are packing in relatively parallel in the micelle core and, therefore, the terminal methyl groups may be localized at the micellar center. Recently, it was found by the ESR spin label method that the order parameter of hydrocarbon chain in the sucrose ester micelle is greater than Ammonyx LO (dodecyldimethylamineoxide) micelle.ll Our result is consistent with this. From small-angle neutron scattering experiments, Bendedouch et al.33have deduced a distribution of the terminal methyl group showing a peak at the micellar center. Our result also supports the localization of methyl groups in the sucrose ester micelles. For Cl&E, C12SE,and CI4SE,the minor semiaxis increases with the chain length but the increment does not correspond to the length of -CH2- units. It could be explained if the degree of radial fluctuation of detergent molecules would increase with the chain length. But it was denied by the fact that L,pHC,and p p were ~ almost the same. This result is reasonably explained
-
(33) Bendedouch, D.; Chen, S. H.; Koehler, W. C. J. Phys. Chem. 1983, 87, 153.
by the increase of kink in linear alkyl chains. The change in shape has been observed between CI4SE and C16SE,judged by R factors. However, X-ray scattering curves seem to indicate the Coexistence of both oblate and prolate micelles in C16SEsolution. Since the melting point of CI6HMchain (18.2 0C)31is close to the temperature of the sample (20 "C), the above transition may be related to the flexibility of hydrocarbon chains. In fact, the minor semiaxis of C16SE micellar core becomes considerably longer than C14SEand close to the length of the all-trans conformation. The surface area of hydrophobic core per detergent molecule, sHc/n, increases with the chain length. This result is not consistent with that for betaine.34 On the other hand, the surface area of whole micelle per detergent molecule, spG/n,is about 90 A2and almost constant against the change of chain length except for the C16SEmicelle. The cross-sectional areas estimated from the molecular model are about 50 A2for sucrose molecule and 12 A2 for water molecule. Since the cross section of all-trans alkyl chain is about 21 A2in the crystalline state,3l the hydration water exists near the boundary between hydrophobic core and hydrophilic layer but cannot penetrate into the hydrophobic core. The increment of um/n with increase of the chain length equals the change of n,/n, taking the volume for one water molecule to be 30 A'. The volume V (V = n(27.4 26.9%')) for the hydrophobic core is equal to uHCwhen Y is calculated with n,' n, - 1 = n - 2 (n = 10, 12, 14, 16) for each of the four micelles. This result indicates that about one unit of fatty acid, -CH2-, is included in the polar group layer. A similar result is also obtained from um/n and nJn by (um/n - (360 3 0 ~ / n ) ) / 2 7where , 360 and
-
+
+
(34) Tanford, C. J. Phys. Chem. 1972,76,3020.
The Journal of Physical Chemistry, Vol. 9.5, NO. 9, 1991 3845
Micelle Structure of Sucrose Ester I
I
I
I
I
oblate
tt
S.C. (%) Y
I
1
I
I
(c)
prolate
I
I
I
I
I
oblate
1
I
prolate
1
- 1
2
i
Y
0 0 -1
-4
20
do
60
20
80
I
I
I
60
80
-21
Id0
io
lo
60
b
80
I
I
2b l o
el0
Id0
l o $0 eb
Id0
60
(11
r I
I
I
pro late
oblate
1
c S.C. (%)
$’ 2‘
lo
(A)
r
Y
- 1
ao
i
Y
0 0 -1
-21
20
do
60
d
80 r
20
lo
60
sb
-2;
ld0
20
lo
60
A
60
(1)
r
20
(8)
Figure 9. Calculated D(r,po) of oblate and prolate three-shell models: (a) Cl$E (b) C&E; (c) CI$E (d) C16SE.
27” are the volumes of sucrose molecule and -CH2- unit in A), respectively. The fact that the some part of the hydrocarbon chain is included in the polar group layer determined by X-ray study is explained by ( I ) the hydrocarbon chains mixing with the polar groups around the boundary, and/or (2) the boundary shifting apparently into the hydrophobic core because of the approximation of the electron density distribution by the step functions. 4.2. Polydispersity in Micelle Size. The micelle size may If the degree distribute in the solution of a nonionic of distribution is significant, the micelle solution must be treated as a polydisperse system. Thus, we examined the degree of the polydispersity by means of the model calculation. We assumed that the distribution of micelle volume uI around the mean value (ul ) is expressed by the Gaussian function under the condition of the average electron density, pl. being constant12 Aul/(ul)) = expl-(1
, ... k...., 4 s (lO-*d-’)
I
0
2
6
- ul/(u1))2/2u2)/(2*)”2u
(19) where u is the standard deviation of uI/(uI). The average X-ray intensity is given by ipOly(s40) = ~ A u , / ( u I ~ ) i I ( s , P O , do1 uI)
(20) r
where il(s,po,ul)is the intensity scattered by a micelle with volume ul and obtained by using eqs 10 and 11. In the calculation of il(s,po,ul),we treated ppo, PHC, pHC‘, y, y’. and y” as constants and varied uw,U H C , and uHC’ in the proportion of u l / ( u l ) . We have calculated ipl,(s,p0)by using eq 20 from u = 0 to u = 0.5 in s t e p of 0.1. A significant improvement in X-ray intensity data could not be obtained by the introduction of polydispersity for all the micelles. As shown in the previous paper,12 the effect of polydispersity on the X-ray scattering curves was prominently recognized in the spherical micelle. In the case of the nonspherical model, the anisometry affects X-ray scattering curves in a similar way as the polydispersity. Although the present calculation does not exclude the polydispersity, the above fact indicates that the polydispersity is not so large and the monodispersive ellipsoidal (35) Tanford, C. J. Phys. Chem. 1974, 78. 2469. (36) Tanford, C. Proc. Natl. Acad. Sci. U S A . 1974, 71, 181 1.
4)
Figure 10. (a) il(S,49%) and (b) D(r,49%) of CI6SEmicelle: observed data (-), the model in Figures 8 and 9 (---), and the modified model
.
(. .).
model used in the analyses is not bad for the sucrose ester micelles. 4.3. Structural Change in C,$E Micelle. The structural change in C16SEmicelle was observed a t 49% (w/v) sucrose concentration. The discrepancy between the observed and calculated curves was remarkable at the low-angle region (0 < s < 0.02 A-I) rather than the intermediate-angle region. The deviation of R(po)2from the straight line at 49% indicated the decrease of a in the relation of R(p0)* = R$ - o/Apo, since u1 and 0-. and therefore R,,did not change. As o is the second moment of electron density distribution, the constancy of p1 suggested the change of pl(r), i.e., the intemal structure of micelle, at that concentration. The value of a was revaluated to be about 15.4 e/A.
Kawaguchi et al.
3846 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Acknowledgment. This work was supported in part by grants-in-aid for scientific research from the Ministry of Education, Science and Culture of Japan to T.H.
=.- : 3 C
Y
v
2
z h
$
Y
2 1
O -
0 1.2 CI
$ 1 ul
o.e 0.6
I
I
1
2
3
s (lo-zi-’) Figure 11. (a) Intensity curves of C1$E micelle in water normalized by detergent concentration c. The curves numbered 0-6 correspond to the detergent concentrations of 0, 1, 2, 3,4, 5,6% (w/v). The curve at 0% was obtained by extrapolating from 6% to 1% at different scattering angle as shown by inset.” (b) Intermicellar interference function at 5% (w/v) CIzSEobtained from the curves of 0% and 5% in (a).
-
O S
40F==7
Appendix I. Derivation of Intermicellar Interference Function The measured X-ray scattering intensity Zob(s,po) is distorted by the intermicellar interference due to the finite detergent concentration. For a system of nearly spherical particles with low polydispersity IobS(S9Po) a I(S,PO) %Po) (Ai) where Z(s,po) is the intensity at limit of zero concentration and S(s,po) is the intermicellar interference function.33 In the present work, S(s,po) was experimentally determined from the concentration dependence of intensity curve from 1% (w/v) to 6% concentration. Figure 1l a shows the result for CIZSEin water. The intensity curve at zero concentration was obtained by the extrapolation method.37 Figure 12 shows the concentration dependences of the radius of gyration ROb(po)and the zero-angle intensity (Ih(0,po)/c)1/2.The Rob(pO)and {Zob(O,po)/cjl/z show the same concentration dependence for the four homologous micelles in water and the CIZSEmicelle in 21% (w/v) sucrose solution. The interference functions of 5% solutions were obtained as the ratio of intensity curves at 0% and 5% solutions and are shown in Figure 11b for the case of CIzSE. Appendix 11. Conversion of Measured X-ray Intensity into the Absolute Intensity The zero-angle intensity i,(O,po) of the sample intensity curve can be obtained from I(O,po) of the observed intensity curve and scattering intensity of Lupolen as described below. In the case of infinitely long primary beam, the ratio of I(O,po) and the primary energy weakened by the sample Ps(po)is given by I(o,Po)/p~(Po)= K’I(O,Po)/&,iso A(1 / & % / A S (A2) where & l s o ~is the scattering intensity of Lupolen at the angle 28 = 35.3’ corresponding to a Bragg’s value of 150 A.z3 The parameter d is the distance from sample to registration plane. A, and A, are attenuation factors for X-ray of Lupolen and sample, respectively. K is a constant. Equation A2 is defined in units of area (cm2). According to Luzzati et a1.,26 i,(O,po) is described as in(0,PO) = I(O,PO)/ W E O (A31 where q is thickness of the sample in electrons per cm2. The parameter Y is a physical constant: Y = 7.9 X 10-z6A2(A is the wavelength of X-ray). Eo is the energy of the incident beam. Equation A3 is defined in the unit of solid angle. From eqs A2 and A3, we obtain the relation i n ( 0 d = A2d2I(O,p0) / v P , ( ~ o )
= (KA2dAc/sYA,)I(O,po)/~~,isoA (A41 On the basis of eqA4, thus, the value of in(O,po) can be obtained from I@,Po) and & , I ~ o A . c
O/O
(wlv)
Figure 12. (a) Radius of gyration Rh(pO) and (b) root of zero-angle intensity [I,,b(O,po)/c}l/zas functions of detergent concentration: (0) C,,,SE, (A) CI2SE,(a) C,,SE, ( X ) CI6SEin water; ( A ) CI2SEin 21% (w/v) sucrose solution. The structural parameters of C16SEmicelle in the 49% sucrose solution were determined by the same procedure described in section 2.3. The values of L,L’,ppo, pHc, and p ~ c were ‘ estimated to be 17.9 A, 7 A, 0.397 e/A), 0.2 e/A3 and 0.166 e/A3, respectively. The values of RHC,Y‘RHC,RHC‘,and ~ “ R H cwere ‘ obtained from L,L’,RE, and yRK to be 13.3, 3 1.1,6.3, and 24.1 A, respectively. The results are shown in Figure 10 and remarkable improvements are observed. The structural change is consequently explained by increase of L and decreases of L’,pH,-, and ppG. This may be due to the change in the packing mode of the detergent molecule and/or the distribution of the hydration water.
Appendix 111. Transformation from I (s,ppo)into il(s,ppo) The zero-angle intensity of il(s,po) is described as il(0,PO) = U l 2 ( P l - Po)2 (‘45) From eqs A5 and 15, we obtain the relation il(0,po) = min(O,po)/ce (A6) where the number of electrons of one micelle unhydrated, m, is the parameter listed in Tajle 11. The value of i,(O,po)/ce is obtained from I(O,po) and Zc,lSo~,as described in Appendix 11. The scale factor k of transformation from I(s,po) into il(s,po), therefore, is given by k = il(s,po)/I(s,po) = mi,(O,po)/cJ(O,po) (A71 Registry No. C,$E, 21837-26-9; ClzSE, 27837-24-1; C I ~ S E4483, 07-2; C16SE, 27837-27-0. ~
~~
(37) Pilz, I.; Goral, K.;Hoylaerts, M.;Witters, R.; Lontie, R. Eur. J. Biochem. 1980, 105, 539.
