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J. Phys. Chem. 1982, 86, 2533-2537
quently, this implies a rather unaltered average conformational behavior of the sn-1 and sn-2 chains in the mixed micelles. Only van der Waals solvent effects change upon mixed micelle formation with the quaternary surfactant molecules. This is clearly demonstrated by maximum differences in chemical shift for the methyl carbonsl6 reflecting the respective site factors.18 Logically, induced differences are most pronounced for mixed micelles containing less lecithin (Le., the 1:4 mixing ratio) and decrease toward the 4 1 mixing ratio. At the lowest ratio the lecithin undergoes the largest disturbing effect from the surrounding quaternary detergent molecules. This perturbation fades as the lipid concentration is raised to ratios
where the n-alkyl amphiphiles become the perturbed moieties in mixed micelles mainly containing lipid molecules (Le,, the 4:l mixing ratio). So, the possibility has been demonstrated to determine, at least approximately, to what extent n-alkyl detergents incorporated in DOPC micelles undergo additional chain bendings as compared with the single micelle solution. Acknowledgment. This investigation has been supported by the Netherlands Foundation for Chemical Research (SON) with financial aid from the Netherlands Organization for the Advancement of Pure Research (ZWO).
Mixed Micelles of GM1 Ganglioside and a Nonionic Amphiphile Marlo Cortl,' Downloaded by UNIV OF SUSSEX on August 31, 2015 | http://pubs.acs.org Publication Date: June 1, 1982 | doi: 10.1021/j100210a058
CISE Sp.A., 20090 Segrate, Milano, Italy
Vlttorlo Degiorglo, Istituto di Flsica Applicata, Universiti di Pavla, 27100 Pavla, Italy
Rlccardo Ghldonl, and Sandro Sonnlno Department of Biological Chemistry, The Medical School, University of Milano, Milano, Italy (Received: November 13, 1981; In Final Form: February 8, 1982)
Aqueous solutions containing a mixture of two amphiphiles, a nonionic surfactant, n-dodecyl octaoxyethylene glycol monoether (ClZEs), and a biological lipid, the ganglioside GM1, are investigated by static and dynamic light scattering. It is found that mixed micelles are formed in the whole range of investigated molar ratios. The theory of light scattering from solutions of homogeneous micelles is generalized to the case of mixed micelles. The final formula is used to derive from the experimental data the aggregation number of the mixed micelle. A simple phenomenological law is proposed to describe the dependence of the aggregation number on the molar ratio between the two amphiphiles.
Introduction The micelles formed in aqueous solutions of two amphiphiles contain usually both components and are in equilibrium with the two monomeric species in the aqueous phase. Several experimental and theoretical investigations have discussed the dependence of the monomer concentrations on the molar ratio between the two components and on the total amphiphile c~ncentration.'-~In particular,calculations of the mixed critical micelle concentration have been performed and compared with experimental data obtained through surface tension and electrical conductivity measurement^.'-^ Little information exists in the literature about the size and the aggregation number of the mixed micelles. We have recently reported experiments on mixed micelles of a biological glycolipid, the ganglioside GM1, and a commercial nonionic surfactant, Triton X-100.4 Such experiments were performed with the aim of establishing a correlation between the structural organization of lipid monomers and the activity of an enzyme which uses the GM1 as a substrate. Other authors (1) H.Lange and K. H. Beck, Kolloid 2.2.Polym. 251, 424 (1973). (2) J. Clint, J. Chem. SOC.,71, 1327 (1975). (3) D. N. Rubingh in "Solution Chemistry of Surfactants", Vol. 1, K. L. Mittal, Ed., Plenum Press, New York, 1979,. p 337. (4) M. Corti, V.Degiorgio, S. Sonnino, R. Ghldoni, M. Masserini, and G. Tettamanti, Chem. Phys. Lipids, 28, 197 (1981). 0022-3654/82/2086-2533$01.25/0
had previously studied mixed micelles of phospholipids arid Triton X-100 for similar biochemical application^.^^^ We present in this paper a light-scattering investigation of aqueous solutions containing the ganglioside GM1 and a pure nonionic surfactant, n-dodecyl octaoxyethylene glycol monoether (C12E8). From the point of view of a physicochemical study of mixed micelles, such a system is interesting because the molecular weight of the GM1 micelle is about 8 times that of the C12E8 micelle. This allows one to establish in a very direct way by the lightscattering measurement that the two amphiphiles form mixed micelles, as shown later on. Besides the fact that C12E8is a better characterized component than Triton X-100, there is a further advantage in using C12E8because the lower consolute temperature is considerably higher for C12E8 than that found for Triton X-100. This means that the temperature range over which the experimental results reflect the properties of the individual micelle instead of cooperative properties associated with the second-order phase transition is much larger for ClzE8 and includes, in particular, the room temperature. ~~~
~
(5) E. A. Dennis, A. A. Ribeiro, M. F. Robers, and R. J. Robson in 'Solution Chemistry of Surfactanh",Vol. 1, K.L.Mittal, Ed., Plenum Press, New York, 1979, p 175. (6) S. Yedgar, Y. Barenholz, and V. G. Cooper, Biochim. Biophys. Acta, 363, 98 (1974).
0 1982 American Chemical Society
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The Journal of Physical Chemistry, Vol. 86, No. 13, 1982
Corti et ai.
We have obtained both the hydrodynamic radius RH and the molecular weight M of the mixed micelle as a function of the molar ratio between the two components. Whereas the derivation of RH from the dynamic light-scattering data is straightforward, the relation which connects M to the average scattered intensity contains the monomer concentrations as unknown parameters. In order to gain information about the monomer concentrations, we have also performed surface tension measurements, The experimental dependence of M on the molar ratio is interpreted by introducing a model based on simple geometrical considerations which describes fairly well the data obtained.
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Light Scattering from Mixed Micelle Solutions The total intensity I, of the light scattered from the micellar solution is made up of two contributions, the first, I,, due to scattering from the solvent alone and the second due to the presence of micelles. For a single species of homogeneous noninteracting micelles of molecular weight M , the excess scattered intensity I, - I , is proportional to N [(dn/dC)M (1) where N is the number of micelles in the scattering volume and the quantity in brackets is proportional to the electric field amplitude scattered by the single micelle. The experiment described in this paper concerns solutions of two amphiphiles, so that in principle more than one type of micelle may be found in solution. We will consider the two extreme cases: (a) the two amphiphiles micellize separately; (b) the two amphiphiles form mixed micelles at all of the investigated molar ratios. For case a the relative normalized scattered intensity I, = (Z,- Iw)/Zwis simply given by the sum of the independent contributions from the two micellar species, that is 1, = A[(dn/dc)12Ml(cl - cod
+ ( d n / d ~ ) 2 ~ M 2-( cC~O Z ) ~ (2)
where c is the concentration and co is the critical micelle concentration, A is a calibration constant, dnldc is the refractive index increment, and M is the micelle molecular weight. Subscripts 1 and 2 refer to C&8 and GM1, respectively. considering now case b, we can say that the scattered amplitude from the individual mixed micelle is due to the sum of the contributions of each amphiphile present in the micelle weighted by its optical contrast represented by the refractive index increment. Consequently expression 1 becomes N[(dn/dc)lnlml
+ (dn/dc)2n2m2I2
(3)
where ml and m2 are the molecular weights of C12E8 and GM1 monomers, and nl and n2 are the numbers of C12E8 and GM1 monomers in the mixed micelle. The number N of mixed micelles is readily calculated from the total amphiphile concentration which goes into micelles and the mixed micelle molecular weight M as N = N*v(c - C,)/M (4) where NAv is Avogadro’s number, c is the total amphiphile concentration, and co is the total monomer concentration. Combining expressions 3 and 4, after some rearrangements, we obtain I , = gA(dn/dc)22M(c- c,) (5)
~~~
0.3 1
5
m~
10
50
100
C,,E8
Figure 1. Concentration of free C,,E8 monomers C,,,plotted as a function of the total concentration in an aqueous solution containing 0.8 mM GM1. The curve is calculated according to eq 8. The experimental surface tension u for the same solution is also reported.
with a = ml/m2,X = n1/n2, and = (dn/dc),/(dn/dc),. I t should be noted that g becomes equal to 1, independently of X,when the two amphiphiles have the same refractive index increment, that is, when p = 1. Equation 5 indicates that M can be derived from the measured I, only if g and co are known. The factor g depends on X, which is the molar ratio in the micelle and which does not generally coincide with the molar ratio in the solution because of the presence of free monomers. We recall that in the case of solutions containing a single amphiphile the concentration of free monomers in the micellar solution can be taken equal to the cmc. This amounts to saying that all of the amphiphile added to the solution in excess of the cmc goes into micelles. For the two-amphiphile system the situation is more complicated. We will refer here to Clint’s work2which treats the mixed micelle as an ideal mixture of its pure components. A more general approach was presented by Rubingh3 by introducing activity coefficients. The cmc of the mixed micelle C,, (we denote by capital C the molar concentrations) is connected to the cmc’s of the single components by the relation’s2 1/Ccm = 6/Cc1
+ (1 - 6)/Cc2
(7)
where 6 is the bulk molar fraction of C12E,. The treatment of Clint can also be used to calculate the monomer concentrations in the mixed micellar solution as a function of total amphiphile concentration. Equation 12 of ref 2 gives the free-monomer concentration of the amphiphile with the higher cmc as a function of the total concentration and of the amphiphile mole fraction. For the case of the experiments described in this paper, the equation may be simplified because Cc2N lo4 M is much smaller than C,, = 0.07 mM.’ Neglecting Cc2,the free-monomer concentration Col is given by Col = ((C + C,J - [(C + C,,)’ - 46CC,.]”2J/2
(8)
Figure 1 reports the behavior of C,, calculated according to eq 8 as a function of the C12E8 concentration with fixed (0.8mM) GM1 concentration. An interesting result is that Col does not level off until the concentration is much larger than the cmc value for the pure solution. For
where the dimensionless factor g is given by
1+pax g=( l+&)
(7) P. Becher, J. Colloid Sci. 16,49 (1961). Recent measurements by M. J. h n and co-workers (submitted for publication in J.Phys. Chem.) assign a higher value to the cmc of CI2Es,but this does not affect the present discussion.
Mixed Micelles of GM1 and a Nonionic Amphiphile
The Journal of Physical Chemistry, Vol. 86,
No. 13, 1982 2535
TABLE I: The Factor g Defined in Eq 6, the Relative Scattered Intensity I,, the Micelle Molecular Weight M, the Number of GM1 Monomers n, and C I 2 E ,Monomers n,,the Factor Y Defined as Y = n,/n,,+ nJn,,, the Diffusion Coefficient D, and the Hydrodynamic Radius R H of the Mixed Micelle Reported for Various GMl-C,,E, Aqueous Solutions at 1 5 "C 10-3~ Y 107D, cm2/s R H ,A C,, mM k? n, n2 C,, mM Ir 1 70.2 47 7 0 316 1.00 3.31 55.9 0 0.8 0.97 3.36 55.1 0.993 54.5 354 32 223 0.125 0.8 0.89 3.67 50.4 0.988 42.8 265 47 159 0.25 0.8 0.98 3.67 50.4 39.8 226 123 0.978 73 0.50 0.8 106 1.14 3.74 49.5 89 0.963 39 .O 192 1.oo 0.8 1.19 4.03 46.0 37.8 51 0.942 146 126 2 0.8 21 1.08 4.56 40.9 0.8 99 125 41.0 0.915 5 0.99 4.98 38 .O 0.8 77 119 8 57.9 0.897 12 4 0.8 0.888 122 1.00 5.41 35.8 92.6 25 12 142.3 123 1.01 5.65 35.8 2 0.8 0.883 50 70 5.67 33.4 66 1.00 0 0.878 0 12 123 41.8 0 6.09 33.4 66 1.00 0 0.878 50 123 128.3
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TABLE 11: Light-Scattering Data at 25 "C Ci, mM 0 0.125 0.25 0.50 1.oo 2 5 12 25 50 12 50
c,,
mM 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0
0
I, 66.9 53.3 41.5 38.1 37.8 35.8 40.1 57.6 93.7 142.8 41.8 133.4
TABLE 111: Light-Scattering Data at 37 "C CI, mM c2, mM Ir 0 0.8 61.9 0.125 48.1 0.8 0.25 40.1 0.8 0.50 37.2 0.8 36.4 1.oo 0.8 35.8 2 0.8 40.1 0.8 5 12 59.3 0.8 99.0 25 0.8 0.8 158.6 50 0 42.3 12 0 146.3 50
10-3~ 454 346 257 216 186 138 97 77 72 70 66 66
301 218 154 118 86 49 20 8 4 2 0 0
10-3~
n2
420 312 248 21 1 179 138 96 77 71 68 65 65
instance, when the C12E8concentration is 10 times Ccl, the C12E8monomer concentration in the mixed system is still only one-half of Ccl.
Experimental Results A description of the chemical composition and of the preparation procedure of the ganglioside solutions is given in ref 4. We recall here that the ganglioside GM1 was isolated from calf brain according to the method of Tettamanti et al.8 and purified following the indications of Sonnino et The C12E8was gas-liquid chromatographic-grade material from Nikko (Tokyo, Japan). The mixture of two amphiphiles was dissolved in 25 mM sodium phosphate5 mM Na2EDTAbuffer (pH 7.0) at room temperature. Surface tension measurements were performed with a standard stalagmometer. The light-scattering apparatus was equipped with an argon ion laser operating on the green 514.5-nm line and with a scattering cell temperature-controlled within a few (8) G. Tettamanti, F. B o d , S. Marchesini, and V. Zambotti, Biochim. Biophys. Acta, 296, 160 (1973). (9)S. Sonnino, R. Ghidoni, G. Galli, and G. Tettamanti, J. Neurochem., 31,947 (1978). (10)M. Corti and V. Degiorgio, Ann. Phys. (Paris), 3, 303 (1978).
n2
278 196 149 115 83 48 20 8 4 2 0 0
n,
Y
lO'D, cm2/s
R H ,A
0 32 45 70 103 119 123 119 122 123 123 123
1.oo 0.98 0.88 0.96 1.12 1.13 1.06 0.99 1.oo 1.01 1.oo 1.oo
4.27 4.33 4.87 4.92 4.92 5.14 6.15 6.58 7.08 7.33 7.31 7.69
57.3 56.5 50.3 49.7 49.7 47.6 40.1 38.0 36.2 36.3 34.0 34.0
n, 0 28 44 68 99 119 121 119 120 120 121 121
Y
lO'D,cm2/s
R H ,A
1.00 0.94 0.90 0.98 1.12 1.16 1.07 1.01 1.01 1.oo 1.00 1.oo
5.77 5.84 6.27 6.54 6.68 7.14 8.13 8.69 9.03 9.17 9.29 9.76
56.9 56.2 52.4 50.2 49.1 46.1 40.6 38.3 37.4 36.8 35.9 35.9
millidegrees. The solutions were filtered through a 0.2-pm Millipore filter directly connected with the scattering cell. The average intensity of the scattered ligth was measured at 6 = 90". The intensity correlation function was determined on the light scattered at 90" by a 108-channel digital correlator. Further details on the apparatus may be found in ref 9 and papers quoted therein. Surface tension data for 0.8 mM GM1 solutions at 25 "C are reported in Figure 1 as a function of the added concentration of C12Es. The surface tension CT starts from the value appropriate to GM1 micellar solutions (-60 dyn/cm)'l and drops to the value appropriate to C12E8 solutions (-30 dyn/cm) when C1 is about 5 mM, a value much larger than the critical micelle concentration of pure C12E8,CC1= 0.07 mM.' The measured values of the relative scattered intensity I , for 0.8 mM GM1 solutions at 25 "C are reported in Figure 2 as a function of the added concentration of CI2E8. The intensity I, at first decreases upon the addition of the nonionic surfactant. When the C12E8concentration is increased further, I , goes through a minimum and starts increasing. A similar behavior is observed for the data (11)M. Masserini, S. Sonnino, R. Ghidoni, and G. Tettamanti, Biochin. Biophys. Acta, 601, 282 (1980).
2538
The Journal of Physical Chemistry, Vol. 86,No. 13, 1982
Ir
1
2001
/'O
.'
I .
i
/
'
.
I
* . I
201
1
0.2
1
5
10
50 mM
concentration C,E, Flgure 2. Behavior of the scattered-light intensity I, from mixed GM1-C,g8micelles in 25 mM sodium phosphate/5 mM NagDTA (pH 7.0) at 25 OC as a function of C,& molar concentration with fixed 0.8 mM GM1 concentration. The dashed line represents the scattered-light intensity expected for unmixed micelles. The open dots represent data
corrected for intermicellar Interactions.
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Corti et al.
taken at 15 and 37 "C, as shown in Tables 1-111. The mass diffusion coefficient D is derived from the time-dependent part of the intensity correlation function by using the standard method.'O The hydrodynamic radius RH is calculated from D by the Stokes-Einstein relation.1° The values obtained are listed in Tables 1-111. Although the dynamic light-scattering measurements were not particularly aimed at an accurate study of micelle polydispersity, we could observe that the polydispersity of mixed micelles in the range of bulk molar ratios between 0.5 and 5 was considerably larger than for the pure Cl2E8 and GM1 micelles. Pure C12E8solutions with the same buffer were also investigated. The data reported in the last two rows of Tables 1-111 show that the excess scattered intensity I, 1 does not scale with the micelle concentration C1 - Celt thus giving an apparent molecular weight M' which decreases with the amphiphile concentration. We have assumed that this is due to intermicellar interactions, and we have derived a molecular weight M by postulating a linear dependence of M', on C1. A similar consideration was applied to the calculation of RH from the dynamic light-scattering data which give D. In order to derive M from I,, we have used the values of the refractive index increments (dn/dc)l = 0.134 cm3/g, as given in ref 7 , and ( d n / d ~=) ~0.143 cm3/g, as given in ref 12. We have neglected effects due to a possible temperature dependence of the refractive index increments.
Interpretation and Discussion The behavior of I, as a function of C1 constitutes clear evidence for the formation of mixed micelles having a molecular weight smaller than the weight of GM1 micelles. In fact the hypothesis of unmixed micelles would lead to a scattered intensity increasing monotonically with C1, as shown by the full line in Figure 2 which was calculated from eq 1 with A = 5.86 cm-3 (see ref 4), M1 = 66000, and Mz = 454000. By making the assumption that at a particular composition the micellar molar ratio X is the same for each micelle, one can calculate the molecular weight of the mixed micelle by means of eq 5. As discussed in the previous section, in order to apply eq 5, one should know independently the micellar molar ratio X and the freemonomer concentration co as a function of the total concentration c. It can be easily shown that the concentration (12) M. Corti, V. Degiorgio, R. Ghidoni, S. Sonnino, and G. Tettamanti, Chem. Phys. Lipids,26, 225 (1980).
F. 0.2
1
5
10
50 mM
concentration C,,E, Figure 3. Molecular weight M of mixed GM1-C,2E8 micelles in 25 mM sodium phosphate/5 mM NagDTA (pH 7.0) at 25 O C as a function of molecular concentration with fixed 0.8 mM GM1 concentration.
of free GM1 monomers is always negligible in the investigated range of amphiphile concentrations, since Cozis much smaller than the used GM1 concentration. Therefore co practically coincides with the C&8 monomer concentration col. We have calculated col by using eq 8. The obtained values are plotted in Figure 1. In order to derive M from I,, we have inserted into eq 5 the values of X calculated as X = (Cl - Col)/C2. It should be noted from Figure 1that col is much smaller than the total concentration c in the whole range of concentrations which we have investigated, so that the obtained values of M are not much different from those which one would obtain by using the drastic approximation co = 0. We note, incidentally, that by taking into account nonideality effects in the mixed micelle3one would even compute lower values of the C&8 monomer concentration. The surface tension data indicate that the theoretical formulas predict the correct order of magnitude for col, if one recalls that the difference between the surface tension at zero concentration and the surface tension at concentration c represents a measure of the free-monomer concentration at c. It should also be considered that intermicellar interactions are affecting the data obtained on mixed micelles. Since the effect of interactions becomes appreciable, in our case, only when the micelles are predominantly composed of C12E8 monomers, we can apply to our data the same corrections derived for pure C12E8 micelles. The magnitude of the effect can be appreciated by comparing full and open dots in Figure 2. The obtained values of M at 25 "C are plotted in Figure 3 as a function of the C12E8concentration. As expected, we find that M decreases smoothly from the value appropriate for the GM1 micelle to that typical of the ClzEs micelle. All of the results obtained at different temperatures are reported in Tables 1-111. Our molecular weight for the C12E8 micelle is in excellent agreement with the value of 65 000 obtained by Tanford et al.13 by sedimentation equilibrium in 0.1 M NaCl aqueous solution in the temperature range 15-25 "C. Good agreement is also shown with the light-scattering measurements of Becher7J4for heterogeneous compounds with dodecyl chains. The small sensitivity of the C12E8 micellar weight to temperature and salt concentration may be partially explained by the fact that the critical consolute temperature (the minimum of the cloud curve) is very high for this compound as compared, for instance, with C12E6. (13) C. Tanford, Y. Nozaki, and M. F. Rohde, J.Phys. Chem., 81,1555 (1977). (14) P. Becher, J . Colloid Sci., 17, 325 (1962).
The Journal of Physical Chemistry, Vol. 86, No. 13, 1982
Mixed Micelles of GM1 and a Nonionic Amphiphile
A discussion of this point may be found in ref 15. Our hydrodynamic radius for C12E8is consistent with the value RH = 36 A obtained from intrinsic viscosity
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measurement^.'^
The molecular weight of the GM1 micelle shows the same temperature dependence reported in ref 4, with absolute values 5% lower than in the previous investigation. This could be due to a slight difference in the lipid composition between the two samples. The ratio of the hydrodynamic radii of GM1 and C12E8 micelles is 1.67 at 15 OC, 1.69 at 25 "C, and 1.58 at 37 "C. Since the two micelles cannot have drastically different shapes, this ratio should coincide with the cubic root of the ratio of micellar volumes. From the measured molecular weights and from the known specific volumes of GM1 and C12E8micelles, we may calculate the ratio [(uM)~/(DM),]~/~ which is 1.80 at 15 "C, 1.77 at 25 OC, and 1.73 at 37 "C. The fact that these latter values are systematically larger than the ratios of the hydrodynamic radii indicates that the C12E8micelle is more hydrated than the GM1 micelle. The number of monomers of each component in the micelle can be determined from M by using the equation M = nlml n2m2 (9)
+
and by considering that the ratio n1/n2= X is known for each value of M . The molecular weights of the monomers are ml = 539 and m2 = 1510. The obtained values of n, and n2 are reported in Tables 1-111. With increasing C1, nl becomes, of course, larger, but the total aggregation number nl n2 becomes smaller. We are not aware of any theory which predicts the total number of monomers in the mixed micelle as a function of the molar ratio between the two components. It is interesting to note that the experimental results are rather well described by the relation
+
nl/nlo + n2/n20 = 1
(10)
for all values of C,. The numbers nloand n2, represent the aggregation numbers for pure C12E8and GM1 micelles, respectively. Relation 10 can be explained with the following geometrical picture in terms of the average curvature of the micelle surface. Such a picture represents an extrapolation of some considerations developed by Yedgar et al.6 In 47r sr C12E8alone accomodates n,, monomers and GM1 alone nm monomers. Therefore, the solid angle per monomer is 47r/?Ilosr for C12E8and 47r/nmsr for GM1. If we make the assumption that in the mixed micelle each (15) M. Corti and V. Degiorgio,
J. Phys. Chem.,
85, 1442 (1981).
2537
monomer takes the same solid angle taken in the homogeneous micelles, we obtain 4a = (47r/nlo)nl+ (4?r/nzo)n2, which coincides with eq 10. Our results suggest therefore that C12E8and GM1 monomers contribute on the average the same amount of surface curvature regardless of whether they are in the mixed micelle or not. Equation 10 can be rearranged to express the molecular weight M of the mixed micelle in terms of the ratio X = n1/n2as follows: 1+ ax M = m2n201 + yx where a = ml/m2and y = n20/nlo.The full line in Figure 3, drawn according to eq 11, confirms a reasonable agreement with the experimental data. We have verified that eq 11 adequately describes also the data on mixed GM1-Triton X-100 micelles reported in ref 4. Of course, we have chosen for our comparison the data taken at 15 "C, since micellar interactions affect considerably, for such a system, the data taken at higher temperatures. As we have mentioned above, another interesting example of mixed micelle formation is that of the system Triton X-100-sphingomyelin studied by Yedgar et a1.6 Sphingomyelin is a lipid which differs from GM1 by the fact that most of the molecule length is due to the hydrophobic portion, so that nearly parallel aggregation is favored leading to the formation of liposomes instead of micelles.16 The sedimentation measurements of ref 6 show a single, sharp peak a t Triton X-100 molar fractions between 0.32 and 0.79 ( X between 0.47 and 3.76), which indicates the presence of mixed micelles. At Triton X-100 molar fractions below 0.32, the mixed micelles coexist with sphingomyelin liposomes, and above 0.79 the mixed micelles coexist with Triton X-100 micelles. Yedgar et a1.6 find that the number of Triton X-100 monomers in the mixed micelle remains roughly constant when the molar fraction is changed. This is in agreement with eq 10 if we consider the particular case nm m; that is, the solid angle relative to the sphingomyelin monomer goes to zero. However, they find a number of Triton X-100 monomers in the mixed micelle larger than the aggregation number of the pure Triton X-100 micelle. This latter result is in disagreement with eq 10.
-
Acknowledgment. We thank G. Tettamanti for useful discussions. This work is partially supported by CNR/ CISE Contract no. 80.00016.02. (16) C. Tanford, 'The Hydrophobic Effect. Formation of Micelles and Biological Membranes", Wiley, New York, 1980.
