Langmuir 1992,8, 409-413
409
A Comparison of the Counterion Binding to Ionic Micelles in Aqueous and Nonaqueous Systems Marie Sjoberg,*ptJ Mikael Jansson,? and Ulf Henrikssonf Institute for Surface Chemistry, P.O. Box 5607, S-114 86 Stockholm, Sweden, and Department of Physical Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden Received February 11, 1991. In Final Form: October 2, 1991 The counterion binding to hexadecyltrimethylammoniumfluoride (ClsTAF)micelles in three different solvents, water, formamide, and ethylene glycol, has been studied both experimentally and theoretically. Self-diffusion measurements by NMR spectroscopy was used as the experimental technique, and the counterion binding was determined for surfactant concentrationsup to 20 wt 5%. The degree of counterion binding was found to be very different in the three solvents: high in water and ethylene glycol but much lower in formamide, with an increase with concentration in the latter system. The Poisson-Boltzmann equation was used to calculate how the aggregation number and the dielectrical constant of the solvent effect the counterion binding. A comparison between experimental and calculated values of degrees of counterion binding indicates that the micelles are significally smaller in the nonaqueous systems. The concentration dependenceof the counterion binding in formamide was explained as aggregategrowth with increasing surfactant concentration. Introduction As amphiphilic molecules aggregate to from micelles, the critical micelle concentration (cmc) and the size of the aggregates will be determined by the balance between several different interactions. One important term for ionic surfactants is the electrostatic interaction between the headgroups. The effect of these interactions can be studied by looking at how strongly the counterions bind to the micelles. A large number of different techniques have been used to determine the counterion binding experimentally.lS2 Three different main classes of experimental techniques have been employed: thermodynamic measurements, transport measurements, and spectroscopic measurements. The three techniques probe the counterion-micelle interaction in different ways, which makes it important to distinguish between results obtained from different methods. The most frequently employed technique is to measure a transport property, either with use of conductance or with self-diffusion measurements: NMR self-diffusion or radioactive labeling. In order to investigate how different physical properties of the system, such as surface charge density, salt concentration, surfactant concentration, and temperature, affect the degree of counterion binding, the Poisson-Boltzmann equation has been used to calculate the distribution of counterions with regard to the micellar ~ u r f a c e Although .~ the PoissonBoltzmann equation contains some rather crude approximations, the agreement with both experimental results3v4 and results from Monte Carlo simulations is good.5 However, investigations of the counterion binding to micelles has to our knowledge only been done in aqueous systems so far. The aim of this study is to investigate the counterion binding tomicelles in other polar solvents, such as formamide and ethylene glycol, and to give account for
any observed differences in terms of aggregation numbers or dielectrical constants by using the Poisson-Boltzmann equation. The micellization of surfactant molecules in nonaqueous polar solvents such as formamide and ethylene glycol has been debated for some time. However, recently several different studies have demonstrated that some amphiphiles form micelles in these solvents, but under different conditions than in waterS6-l2We have previously studied the aggregation of hexadecyltrimethylammonium bromide, ClGTABr, in water, formamide, and ethylene glycol, utilizing frequency-dependent NMR relaxation measurements.12 These measurements were performed at a surfactant concentration of 5 times the cmc, and at 60 OC, which is above the Krafft point of the surfactant in these solvents. The data were fitted to the two-step model for the reorientation of the micelles,13and approximate micellar radii were calculated, showing that the micelles formed in the nonaqueous solvents have an aggregation number of approximately one-third of that in water. This is in agreement with other studies on similar ~ystems.~-ll In this study we have used NMR self-diffusion measurements to experimentally determine the degree of counterion binding to micelles of hexadecyltrimethylammonium fluoride, C16TAF, in these three solvents. Cl6TAF was used since the fluoride counterion is very suitable for NMR self-diffusion measurements. The experimental results have thereafter been compared with the degree of counterion binding calculated from the Poisson-Boltzmann equation, using aggregation numbers and cmc's obtained in the previously mentioned investigation.12 ~
* T o whom correspondence should be addressed. + Institute for Surface Chemistry.
* Royal Institute of Technology.
(1) Wennerstxom, H.; Lindman, B. Phys. Rep. 1979,52, 1. (2) Lindman, B.; Wennerstrbm, H. Top. Curr. Chem. 1980,87, 1. (3) Gunnarsson,G.; Jbnwon, B.; Wennerstrom, H. J.Phys. Chem. 1980, 84, 3114. (4) Johnson, I.; Olofsson, G.; Jonsson, B. J. Chem.Soc.,Faraday Trans. I 1987,83, 3331. (5) Linse, P.; Gunnarsson, G.; Jonsson, B. J. Phys. Chem. 1982, 86, 413.
0743-7463/92/2408-0409$03.00/0
~~
~
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(6) Rico, I.; Lattes, A. J. Phys. Chem. 1986, 90,5870.
(7) Auvray, X.; Petipas, C.; Anthore, R.; Rico, I.; Lattes, A.; AhmahZadeh Samii, A.; de Savignac, A. Colloid Polym. Sci. 1987, 265, 925. (8)Belmajdoub, A.; ElBayed, K.; Brondeau, J.; Canet, D.; Rico, I.; Lattes, A. J. Phys. Chem. 1988, 92, 3569. (9) Belmajdoub, A.; Boubel, J. C.; Canet, D. J. Phys. Chem. 1989,93, 4844.
(10) Lattes, A.; Rico, I. Colloid Surf. 1989, 35, 221. (11) Binana-Limbele, W.; Zana, R. Colloid Polym. Sci. 1989,267,440. (12) SjBberg, M.; Henriksson, U.; Wiirnheim, T. Langmuir 1990, 6, 1205. (13) Halle, B.; Wennerstrom, H. J. Chem. Phys. 1981, 75, 1928.
0 1992 American Chemical Society
410 Langmuir, Vol.8,No.2, 1992
SjBberg et al.
M a t e r i a l s and Methods Chemicals. Hexadecylammonium bromide CleTABr (Merck, 99%) was converted to the hydroxide form by ion exchange on ion exchanger IRA-400. The C16TAOH was immediately neutralized with HF to pH 4-5. The solution was vacuum freezedried, and the product was recrystallized once in ethanol. Ethylene glycol (Riedel-deHaen, 99.5%) was used as received, and formamide (Merck, 99.5 %) was dried with molecular sieves. Water was twice distilled. Hexamethyldisiloxane, HMDS, was purchased from Stohler Isotope Chemicals. NMR Measurements. Self-diffusion Coefficients were determined with the Fourier transform pulsed gradient spin-echo (FT-PGSE) technique, described in detail in ref 14. A JEOL FX-100 spectrometer was used for the water and the formamide systems, while a Bruker MSL-200 spectrometer equipped with a microimaging probe was used for the ethylene glycol system. Higher gradients were available on this latter spectrometer, which was necessary due to the higher viscosity and hence slower diffusion in the ethylene glycol system. 'H NMR was employed for the determination of surfactant diffusion coefficients, while I9FNMR was employed for the counterion. Since the l9F spinspin relaxation time is rather short in the water system, the time interval between the 90' and the 180' pulse was here taken as 70 ms, which is half the value used in the other systems. All measurements were carried out at 60 0.5 "C,i.e., well above the Krafft point for both systems.I5
*
Calculation Procedures Self-Diffusion Coefficients. The FT-PGSE technique has been shown to be an excellenttool for the investigationof different aggregation phenomena in surfactant systems, such as counterion binding.le19 The technique makes it possible to simultaneously follow the self-diffusion of several different components. Since the diffusion decreases drastically when the studied species participates in an aggregate, the self-diffusion coefficient will directly give information of the state of aggregation. The exchange of the species between aggregate and solution is much faster than the time scale of the experiment (-100 ms), and therefore the so-calledtwo-site model can be used in determining the different self-diffusion coefficients:
D,b is here the observed diffusion coefficient, Dmicthe diffusion coefficient of the micelles, Df,= the diffusion coefficient for the nonaggregated species, and p the fraction of aggregated species. Dmicis usually determined by solubilizing a hydrophobic probe into the micelles and determining the diffusion coefficient of the probe. We have here used hexamethyldisiloxane, HMDS, as a micellar probe in the water system. Since HMDS is slightly soluble in formamide and ethylene glycol, it is not suitable as a probe in these solvents. Other substances were also tried as hydrophobic probes, such as different hydrocarbons and fluorinated hydrocarbons, but none of these were found to be suitable for this application. Equation (1)can be rewritten for the two species amphiphile (+) and counterion (-) as
(3)
where Cmicand Cmic+are the micellar concentrations, D- and D+ (14) Stilbs, P. B o g . Nucl. Magn. Reson. Spectrosc. 1987, 19, 1. (15) Wiunheim, T.; Jonsson, A. J. Colloid Interface Sci. 1988, 125, 627. (16) Lindman, B.; Puyal, M. C.; Kamenka, N.; Rymdh, R.; Stilbs, P. J.Phys. Chem. 1984,88, 5048. (17) Stilbs, P.; Lindman, B. J. Phys. Chem. 1981, 85, 2587. (18) Lindman, B.; Kamenka, N.; Puyal, M. C.; Brun, B.; Jdnsson, B. J.Phys. Chem. 1984,88, 53. (19) Stilbs, P.; Lindman, B. J. Magn. Reson. 1982, 48, 132.
are the observed diffusion coefficients, and D-0 and D+oare the diffusion coefficients in solution for the counterion and the surfactant, respectively. We define the degree of counterion binding Bas
(4) Since it was not possible to determine the diffusion of the micelle in the formamide and the ethylene glycol systems, the range in which0 lies was calculated using two extreme values of Dmic.The maximum value of Dmic is set equal to D+,whereas the minimum value corresponds to Dmic= 0. The value of 0 is not very sensitive to changes in Dmicin the formamide system, so 6 can here be determined with good accuracy. However, the diffusion coefficients are smaller in the ethylene glycol system due to the high viscosity, and 0 is therefore determined with less accuracy in this system. The diffusion coefficients for the nonaggregated species, D-0 and D+o,are in some investigations corrected for the obstruction effect due to the excluded volume in the presence of micelles in the system. The observed diffusion coefficient has been found to decrease with a factor (1 + 0.5@)-', where @ is the volume fraction of micelles in the system, if the micelles are spherical.M However, it is not totally correct to make this kind of correction for the diffusion coefficients of the free counterions, since there is no sharp distinction between bound and free counterions, but a continuous distribution of ions from the micellar surface. Furthermore, these effects will not influence the 0 value to any large extent since the corrections will be made both in the nominator and in the denominator. The 0 values do not change by more than 5% at any concentration, if the Do values are modified according to the obstruction effect. No corrections for the obstruction effect have therefore been made in this work. Poisson-Boltzmann Calculations. The micellar solution has here been represented by a cell model.21 In the cell model, the micelle is treated as a sphere fixed in the middle of a larger sphere (the cell). The micelle is assumed to have a radius R,i, and a constant surface charge density. The radius of the cell, R,, is determined from the micellar concentration in the solution. Counterions and co-ions are considered to be able to move freely in the intervening space between the boundaries of the micelle and the cell. Variations in micellar sizeshave here been neglected, even though the polydispersity probably is higher in the nonaqueous systems than in water. The electrostatic interactions in the system can be described with the Poisson-Boltzmann e q u a t i ~ nwhere ,~ the mobile ions are treated as point charges:
c, is the permittivity of vacuum, C, is the relative dielectricconstant of the solvent, 9 is the electrostatic potential, F is the Faraday constant, zi is the valency, ci0 is the concentration of ion i for @ = 0, e is the unit charge, and kT is the Boltzmann factor. The solution of eq 5 yields the electrostatic potential as a function of the distance from the micellar surface, and thereby the ion concentration profile in the cell. The following boundary conditions are needed to solve the Poisson-Boltzmann equat i ~ n (i) : ~The electrostatic field V@ and the potential @ are zero at the cell boundary. (ii) At the surface of the micelle V@er = -u/c,e, = eN/4rRhC2where e, denotes the normalized radius vector, CT the surface charge density, and N the aggregation number. The detailed calculation procedures used to solvethe PoissonBoltzmann equation are given in ref 3.
Results and Discussion The self-diffusion Coefficients for the amphiphile and t h e fluoride counterion were determined at different concentrations of CIGTAFin formamide, ethylene glycol, and water. T h e diffusion Coefficients of t h e nonaggre(20) Jbnsson, B.; Wennerstrom, H.; Nilsson, P. G.; Linse, P. Colloid Polym. Sci. 1986, 264, 77. (21)Wennerstrdm, H.; Jonsson, B.; Linee, P. J . Phys. Chem. 1982,76, 4665.
Comparison of the Counterion Binding to Ionic Micelles
Langmuir, Vol. 8, No. 2, 1992 411
v1
cu'
E
0'
'
"'I
5
'
I
10
8
15
'
' 20
'
I
25
'
,I
4 30
.
cmc
H20
wt % C16TAF
Figure 1. Self-diffusion coefficients, D+*, for the CIeTA cation in formamide (O),in ethylene glycol (e),and in water (A)as a function of the surfactant concentration. The coefficients in ethylene glycol and in water are scaled with the viscosity as described in the text (temperature 60 "C).
gated species, D-a and D+O, were determined at a concentration below the cmc. The degree of counterion binding, j3, could then be determined from eq 4. Figure 1shows how the diffusion coefficient of the surfactant varies as the surfactant concentration increases in the three solvents. The diffusion coefficients in water and in ethylene glycol have here been scaled with regard to the solvent viscosity so that all three of them can be directly compared; that is, D*(H2O) = Dobs(H20)q(H20)/ q(FA) and D*(EG) = Dob"(EG)q(EG)/q(FA). It can be noted that the decrease in D+ above cmc is not as sharp in formamide and in ethylene glycol compared to the water system. Furthermore, the ethylene glycol system resembles the water system more than the formamide system, since the former immediately after cmc reaches a fairly constant level, while the latter decreases continuously, all the way up to 20 wt 7%. These observations indicate that the micellization process is very different in nonaqueous and aqueous systems. The micellization seems to be less cooperative in the nonaqueous systems; that is, the micellar size increases with increasing surfactant concentration. This effect is most pronounced in the formamide system, in agreement with the j3 data for formamide as will be discussed below. It is also interesting to note that the viscosity-scaled self-diffusion coefficient at 20 wt 7% is twice as large in ethylene glycol as in formamide, although the cmc values are very similar. The most obvious explanation is that the aggregates might be larger or the free surfactant concentration lower in formamide than in ethylene glycol at this concentration. It is, however, impossible to draw any definite conclusions since the electrostatic interactions are very different in the two systems, which influences the observed self-diffusion coefficients. The viscosity-scaleddiffusion Coefficientsof the fluoride ion are displayed in Figure 2. The reduction in the selfdiffusion coefficient above cmc is less sharp in the nonaqueous solvents compared to water, supporting the conclusion of a less cooperative micellization process in the nonaqueous solvents. The experimentally determined degrees of counterion binding, 8, are displayed in Figure 3-5 for the three different systems. The diffusion of the micelle could not be determined in the nonaqueous systems, as discussed in the calculation section. Therefore, maximum and minimum values of /3 are shown, taking into account this uncertainty. The binding of counterions in water (Figure 3) is fairly constant with concentration, in accordance with
cmc
'
'
I
5
'
'
I
10
I
15
'
9
20
'
I
'
25
30
H20 wt /o' C16TAF Figure 2. Self-diffusion coefficients,D-*, for the fluoride ion of ClsTAF in formamide (O),in ethylene glycol (01,and in water (A)as a function of the surfactant concentration. The coefficients in ethylene glycol and in water are scaled with the viscosity as described in the text (temperature 60 "C).
P
Ob6
1 wt % Ci6TAF
Figure 3. Experimentally determined degrees of counterion bindings, 8, for C16TAF' in water as a function of the surfactant concentration (temperature 60 "C).
0.0 0
5
10
15
20
25
30
wt % C16TAF
Figure 4. Experimentally determined degrees of counterion bindings, j3, for CleTAF in formamide as a function of the surcalculated with factant concentration. Maximum value of j3(0) Ddc = 0 and minimum value of j3 ( 0 )calculated with Dfic = D+ (temperature 60 "C).
studies made on other aqueous system^.^^-^* The observed value, 8 = 0.85, is high, but it is well known that halide ions bind strongly to micelles. The counterion binding of C16TABr in water at 33 OC has been determined to be 0.71 using the radioactive tracer technique for studying the bromide diffusion.'7 Figure 4 shows the j3 values in formamide, where two significant differences compared with water are observed. Firstly, the counterion binding is no longer constant, but ~
(22) h a , R. J. Colloid Interface Sci. 1980, 78,330. (23) Khan, A.; SMerman, 0.; Lindblom, G . J. Colloid Interface Sci. 1980, 78,217. (24) Vikingstad,E.J . CoZloid Interface Sei. 1980, 73,260.
412 Langmuir, Vol. 8, No. 2, 1992
Sjoberg et al. Table I. Experimental and Calculated Degleee of Counterion Binding for C16TAF in Three Different Solvents at 60 'Ca
0.6
P
4
0,4
-
0,2
-
0,o
I
EG (er = 31.5)
< 0
solventb Cnd, wt % 4.5 HzO (c, = 66.8) 20.0 FA (e, = 81.2)
5
10
15
20
25
30
wt Yo C16TAF
Figure 5. Experimentally determined degrees of counterion bindings, 8, for C16TAF in ethylene glycol as a function of the surfactant concentration. Maximum value of b (0) calculated with Dmie= 0 and minimum value of b ( @ )calculated with Dmic = D+ (temperature 60
20.0
N
Cfree,wt %
86
0.04P 4.OC 1.7d 4.W 4.5c 2.5d 4.5c
28 28 86 23 23
86
Bcal
BexD
0.82e 0.82 0.53 0.56-0.54 0.57 0.68 0.67 0.79-0.71 0.73 0.76
a The calculations have been performed for different aggregation numbers, N, total surfactant concentration, Cnd, and free surfactant concentration, Cfrw. FA = formamide, EG = ethylene glycol. Cf, = cmc for C16TABr in each solvent. Cfrw= a value less than cmc, calculated from a thermodynamic model.* e /3dfor the water system was fixed to the Be.,, value in order to determine the limiting potential.
OC).
obtained from fluorescence-quenching measurements in the same system at 50 OC?' The aggregation numbers in it increases with concentration, and secondly, the maxiformamide and in ethylene glycol were calculated to be 28 mum levels is -0.55, which is lower than in water. The and 23, respectively. Attempts were also made to deterincrease in @ with concentration can be due to an aggregate mine the aggregation numbers more accurately in the nongrowth, as mentioned earlier. Small aggregates will have aqueous systems with fluorescence-quenching measurelower values of @ than larger ones, since the surface charge ments. However, no clear results could be obtained using density of the micelle is lower. The sizes of the aggregates probes and parameters suitable for normal aqueous will be discussed below. systems. The data for the ethylene glycol system is shown in Two values were used for the concentration of free amfigure 5. The uncertainties in @ are here larger, so nothing phiphiles in solution. Firstly, the concentration was taken definite can be said whether @ is constant with concenas the cmc in the different solvents, previously determined tration or not. However, it can be seem that @ is with surface tension measurements for the formamide and considerably higher than in formamide (-0.75). the ethylene glycol system.12 Secondly, a lower value was The Poisson-Boltzmann equation can be used to used, calculated from a thermodynamic model: assuming investigate how the counterion binding changes with that the concentration of free amphiphiles decreases in aggregation number and dielectrical constant. This analthe same way as in water above cmc. This model is based ysis can be done in different ways. One model calculates on the Poisson-Boltzmann equation, and the calculated the diffusion coefficients of the counterion and of the surdecrease in the concentration of free amphiphiles after factant from the Poisson-Boltzmann equation, and these cmc in water has been found to be in good agreement with values can then be compared with experimentally obtained experimental r e ~ u l t s .The ~ decrease in free amphiphile data.25 Alternatively, the degree of counterion binding concentration at five times the cmc is approximately onecan be calculated directly from the Poisson-Boltzmann third of the cmc for Cl6TACl in water, so the calculated equation, assuming that a "two-siten model can be emdecrease from 4.0 to 1.7wt % in formamide and from 4.5 p10yed.~ We have chosen to use the latter alternative, to 2.5 w t % in ethylene glycol seems to be reasonable. The since the use of the former requires the diffusion coefficient calculated values of @ are, however, not very sensitive to of the micelle, Dmic. The micelles are small in these changes in the free amphiphile concentration, as can be systems, so the contribution of Dmic to the effective I. The dielectrical constant is strongly seen in Table diffusion coefficient may be significant. In our calculation temperature dependent, so all values have been interpoof @ from experimental diffusion data (eq 4),the diffusion lated to the experimental temperature of 60 OC.Z8 coefficient of the micelle is also needed. However, here Two different approaches can be used in calculating the result will not be very sensitive to changes in Dmic, the degree of bound counterions from the ion concentration since Dmicis present both in the denominator and in the profile obtained from the Poisson-Boltzmann equation. nominator of the equation. One approach is to consider the counterions closer to the The degrees of counterion binding have thus been than a certain distance, typically 3 A, as bound. calculated directly from the Poisson-Boltzmann e q u a t i ~ n . ~ micelle However, when comparing theoretical @ values with those The input data required in the calculations are the miobtained from self-diffusion measurements, it is more cellar radius, Rmic, the aggregation number, N, the total relevant to consider the counterions having an electrostatic surfactant concentration, Csurf,the concentration of free potential higher than a certain value to be bound.3 The amphiphiles, Cfree,and +. Micellar radii obtained from same approach of treating the data with a potential limit NMR relaxation rate measurements of C16TABr at 20 w t for the free/bound counterions has previously been done 96 surfactant were used:12 21 A in water, 14.6 A in forin ionic/zwitterionic mixed micellar systems in water, and mamide, and 13.6 A in ethylene glycol. Aggregation the agreement between calculated and experimentally numbers were calculated from these radii, taking the determined fractions of associated counterions was found volume of an amphiphile molecule as the volume of the to be very good.29 The C16TAF/water system was taken hydrocarbon chain, that is, 458 A3 as given by Tanford.26 as a reference system in order to determine this limiting This gives an aggregation number of 86 for Cl6TACl in water at 60 OC, in good agreement with the value of 89 (27) Malliaris, A.; Le Moigne, J.; Sturm, J.; Zana, R. J . Phys. Chem. (25) Jansson, M. Ph.D.Thesis,University of Uppsala, Uppsala, Sweden, 1988. (26) Tanford, C. The Hydrophobic Effect;Wiley: New York, 1980.
1985,89, 2709.
(28) Handbook of Chemistry and Physics, 65th ed.; CRC Press: Boca Raton, FL, 1984. (29) Jansson, M.;Linse, P.; Rymdbn, R. J.Phys. Chem. 1988,92,6689.
Comparison of the Counterion Binding to Ionic Micelles
0,8
1 I
I
0
5
10
15
20
25
30
Wt % C16TAF
Figure 6. Experimental results of the counterion binding of C16TAF in formamide (see Figure 4) compared with j3 curves calculated from the Poisson-Boltzmann equation using four different aggregation numbers. The concentration of free amphiphiles was taken as the cmc value (temperature 60 "C).
potential, that is, the potential where the experimental and calculated j3 values for water coincide. The limiting potential was thereby taken as 0.5kT, and j3 values for the other systems were calculated based on this value. The experimental and calculated j3 values are shown in Table I. For the formamide system, it can be seen that experimental and calculated j3 values agree very well, taking an aggregation number of 28. This holds both for a free surfactant concentration equal to the cmc and for a lower value. Using the same aggregation number as in water, 86,will on the other hand give a considerably higher j3 value, not in accordance with experimental findings. It can thus be concluded that an aggregation number around 30 seems to be reasonable for 20 w t % surfactant in formamide. Turning to the ethylene glycol system, the uncertainties in the experimental and calculated values is not as good as in the formamide system, but it is nevertheless quite satisfactory. The considerably higher j3 values in ethylene glycol compared to formamide can thus mainly be attributed to the much smaller value of cr in ethylene glycol. It is more difficult to say anything definitely about the aggregationnumbers in ethylene glycol. The uncertainties in experimental data are larger, and furthermore a change in the aggregation number does not affect the j3 value as much as in the formamide system. Finally, let us look more closely on the observed change in j3 with concentration in formamide. The calculated j3 curves plotted as a functions of the surfactant concentration are shown in Figure 6, using four different aggregationnumbers, 86,28,15,and 10. The concentration of free amphiphiles was taken as the cmc value. As can be seen, an aggregation number of 28 fits the experimental data over a rather wide concentration range, but at concentrations close to the cmc, lower aggregationnumbers have to be assumed. It is somewhat difficult to imagine
Langmuir, Vol. 8, No. 2, 1992 413 micelles of ClsTAF with aggregation numbers of 10 or less, but it might be possible that we observe some kind of premicellar aggregation at low concentrations. In this context, it is relevant to compare the concentration dependence of j3 in the formamide system with that of short-chained surfactants in water. These surfactants are known to form rather small aggregates close to the cmc, increasing in size with the concentration. Sodium n-octanoate is an example of such a surfactant that shows alower degree of cooperative micellization than normal long-chained Surfactants. The counterion binding for sodium n-octanoate in water has been determined with tracer self-diffusion studies. A concentration dependence was found, with j3 going from -0.25 to 0.6 as the concentration was increased.18 It was concluded that the increase in micelle size with concentration contributes to the increase in 6. In comparing this system with our nonaqueous systems, it would be justified to say that the micellization process in the nonaqueous systems probably is a gradual, less cooperative, process. This conclusion has also been proposed by Belmajdoub et al., who studied the aggregation of ClsTABr in formamide,3O and by Tiddy et al. from observations using ion-selective electrodes in systems of ionic surfactants in ethylene glycol.31 In conclusion, the agreement between experimentally determined counterion bindings and calculated values confirms that small aggregateswith an aggregationnumber around 30 are formed in the formamide and the ethylene glycol system a t high surfactant concentrations. Smaller aggregationnumbers can be explained by a less unfavorable contact between solvent and hydrocarbon at the micellar surface in the nonaqueous solvents compared to water. In comparing the concentration dependence of j3 of ClsTAF micelles in formamide with that of sodium n-octanoate micelles in water, they were found to be very similar. It can therefore be concluded that long-chained amphiphiles, such as C16TAF, in nonaqueous solvents have a micellization behavior similar to that of short-chained surfactants in water. This seems to be reasonable since the driving force for micellization, mainly determined by the unfavorable interactions between hydrocarbon and solvent, obviously is weaker in these nonaqueous solvents and the driving force will decrease in water if the length of the hydrocarbon chain is reduced. Acknowledgment. We are grateful to Cecilia Lindblad for the fluorescence measurements in these systems and to Per Linse for letting us use his program for solving the Poisson-Boltzmann equation. We also want to thank Peter Stilbs for practical help with the NMR spectrometer. Registry No. C16TAF,14002-56-3;F, 16984-48-8;formamide, 75-12-7;ethylene glycol, 107-21-1. (30) Belmajdoub, A.; Marchal,J. P.; Canet, D. New J. Chem. 1987,11, 415. (31) Garibi, H.; Palepu, R.; Tiddy, G . J. T.; Hall, D. G.; Wyn-Jones, E. J. Chem. SOC.,Chem. Commun. 1990,115.
