J. Phys. Chem. 1991, 95, 4552-4556
4552
Sizes and Aggregation Numbers of SDS Reverse Micelles in Alkanols Obtained by Fluorescence Quenching Measurements E. Rodenas* and E. Pirez-Benito Departamento de Quimica Fisica, Universidad de Alcalci de Henares, Alcal6 de Henares, Madrid, Spain (Received: October 18, 1990)
The aggregation numbers and sizes of SDS reverse micelles in alkanols have been obtained by steady-statefluorescence quenching measurements using 4 4 1-pyreny1)butyricacid as probe and N-cetylpyridinium chloride as static quencher (PBA/CPyC, probe/quencher). The validity of this system is discussed by comparing the results for SDS aqueous solutions with those using the system pyrene/CPyC. The obtained results show that the radii of the water pools of the reverse micelles are mainly determined by the water content, although they also depend on water/surfactant and surfactant/alcohol ratios. Aggregation numbers only depend on the amount of surfactant in the mixtures. The minimal water content and SDS/surfactant ratio needed for reverse micelle formation are evaluated. Droplet surface electrical potential and ion distribution inside the droplet have been obtained according to the Poisson-Boltzmann nomlinearized equation.
Introduction Fluorescence quenching measurements are very important tools for the study of such physical properties of micellar systems’ as micellar aggregation number?.’ cmc? polarity? microviscosity,6 and substrate partitioning between aqueous and micellar phases.’ In determinations of micellar aggregation number, one of the main problems is to find the appropriate probe/quencher system for which both probe and quencher are located in the same environment of the micelles. Various systems have been used for aqueous micellar solutions: tris(bipyridine)ruthenium(II)/9methylanthracene,8 pyrene/N-cetylpyridinium chloride,”’ and 1-methylpyrene/N-tetradecylpyridiniumchloride.12 Pyrene and hydrophobic quenchers, e.g., 2,5-dimethyl-2,4hexadiene,I3 have been employed with reverse micelles, although the probe location is not clearly determined. It is suggested that pyrene is solubilized into the organic phase at low surfactant concentrations and displaced to a more polar position, near the interface, a t high water content. Different pyrene derivatives, bearing polar groups that solubilize the probe in the micellar interface, e.g., the 1-pyrenesulfonate ion (PSA), have been used with different ionic quenchers: Br-, I-, Cu2+,and methylviologen(2+) (MV2+).I4 Other systems have been used, e.g., sodium nitrate in AOT reverse micelles for quenching of hydrated elect r o n ~ and ’ ~ Ru(bpy)32+and MV2+ for water-in-oil microemulsions.I6 In this paper, we discuss aggregation numbers and sizes of SDS reverse micelles in alkanols, from steady-state fluorescence quenching measurements using 4 4 1-pyrenyl)butyric acid as probe and N-cetylpyridinium chloride as quencher. Materials and Methods Muteriuls. The probe 4 4 1-pyrenyl)butyric acid (PBA) (Aldrich), the surfactant sodium dodecyl sulfate (SDS) (Sigma), the alkanols I-hexanol (Sigma) and 1-octanol (Merck), and sodium hydroxide volumetric standard solutions (Aldrich) were of the highest available punty and were used without further purification. The quencher N-cetylpyridinium chloride (CPyC) (a pyrene static quencher”) was recrystallized from MeOH/diethyl ether mixtures. PBA is insoluble in water and soluble in organic solvents, so it was used in [NaOH] = 0.01 M solution in order to attach it to the micellar interface of the reverse micelles. The compositions of the systems (percentage by weight) are shown in Table I, according to the phase diagram given in ref 18. The solutions were a set of systems with the same water/SDS ratio and different amounts of alcohol. Merbods. The fluorescence measurements have been carried out with a Perkin-Elmer spectrofluorimeter, LS-SB, at 25 f 0.1 OC. The emission was integrated for 69 s, and the reported data To whom correspondence should be addressed.
0022-3654/91/2095-4552S02.50/0
are mean values from several measurements. The emission spectra of PBA were similar in all the systems considered. Excitation was performed at 340 nm, the wavelength corresponding to the absorption maximum. Micellar aggregation numbers were determined by measurement of the fluorescence intensity in the presence and absence of CPyC, at the fourth peak of the emission spectra (398 nm), which is the least sensitive to the experimental conditions. In these measurements, analytical concentrations of probe and quencher were in the ranges 1 X 10d-5 X 10” and 0.001-0.01 M, respectively, corresponding to effective concentrations of probe and quencher 3 X l v - 5 X 1Ws and 0.005-0.05 M in the aqueous phase in the reverse micelles, respectively. The specific conductivities were measured at 25 f 0.1 “Cby using a CRISON 525 conductimeter. Theoretical Treatment Quenching of Fluorescence. The theoretical treatment is that developed by Turro and YektaZfor determination of aggregation numbers of SDS micelles in water with Ru(bpy):+ as probe and ( 1 ) Kalyanasundarm, K. Photochemisfry in MicroheterogeneousSysfems; Academic Prcss: New York, 1987. (2)Turro. N. J.; Yekta, A. J. Am. Chem. Soc. 1978,100, 5951. (3)Yekta, A.;Aikawa, M.; Turro, N. J. Chem. Phys. Letf. 1979,63,543. Almgren, M.; Swarup, S.J. Colloid Inferface Sci. 1983,91,256. Lianos, P.; Zana, R. Chem. Phys. Lerr. 1980,76,62. Infelta, P.P. Chem. Phys. Lerr. 1979,61,88. (4)Hara, H.; Suzuki, H.; Takisawa, N.J. Phys. Chem. 1989,93,3710. (5) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977,99,
2039. (6)Shinitzky, M.; Dianoux, A. C.; Gitler, C.; Weber, G. Biochemistry 1971,10, 2106. Keh, E.;Valeur, B. J. Colloid Interface Sei. 1981, 79,465. (7)L.issi, E.;Abuin, E.; Rocha, A. M. J . Phys. Chem. 1980,84, 2406. Abuin, E.; Lissi, E. J. Colloid Inferface Sci. 1983,95,198. (8)Almgren, M.; Lofrbth, J. E. J . Colloid Inferface Sei. 1981,8J,486. (9)Malliaris, A. Prog. Colloid Polym. Sci. 1987,73, 161. (10)Pbez-Benito, E.;Rodenas, E. An. Quim. 1990, 86,126. (1 1) PCrez-Benito, E.;Rodenas, E. J . Colloid Interface Sci. 1990,139,87. (12)Boens, N.;Luo, H.; van der Auweraer, M.; Reekmans, S.;de Schryver, F. C.; Malliaris, A. Chem. Phys. Leu. 1988, 146,337. Luo, H.; Boens, N.; van der Auweraer, M.;de Schryveer, F. C.; Malliaris, A. J. Phys. Chem. 1989,93,3244. (13)Backer, C.A.; Whitten, D. G. J. Phys. Chem. 1987,91,865. (14)Verbeeck, A.; de Schryver, F. C. Langmuir 1987,3,494.Verbeeck, A.; Voortmans, G.; Jackers, G.; de Schryver, F. C. Langmuir 1989,5,766. (15)Pileni, M. P.;Brochette, P.; Hickel, B.; Lerebours, B. J. Colloid Interface Sei. 1984, 98,549. (16)Atik, S. S.;Thomas, J. K. J. Am .Chem. Soc. 1981, 103, 3543. (17)Malliaris, A,; Lang, J.; Zana, R. J . Chem. Soc., Faraday Trans. I 1986,82, 109. (18)Jobe,D. J.; Dunford, H. B.; Pickard, M.; Holzwarth, J. F. In Reactions in Compartmental Liquids; Knoche, W . ,Ed.; Springer Verlag: Heildelberg, Germany, 1989.
0 1991 American Chemical Society
Sizes and Aggregation Numbers of SDS Reverse Micelles
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4553
TABLE I: Values of Density (d.), Number of Water Pools per Liter of Aqueous Phase (n,,,), Water Pool Radius (r,,,), Cell Radius (r,), and Anmcnrtion Number (N)for SDS/AUunol/Water Reverse Micelles at Different Commitions alcohol wt W H 2 0 wt W SDS wt 96 ROH [H20]/[SDS] d,, kg/L +, L-l rw, A r,, A N 1 -hexanol 35.0 15.0 50.0 37.4 0.91 3.5 19.0 28.8 25
I-octanol
28.6 21.0 27.5 22.5 19.0 14.6 9.9 22.7 15.7 12.0 8.1 5.0 17.8 14.5 9.5 6.4 20.0 10.4 7.0
12.3 9.0 19.3 15.8 13.4 10.2 6.9 24.1 16.7 12.8 8.7 5.3 29.0 23.7 15.2 10.3 20.0 10.4 7.0
59.1 70.0 53.2 61.7 67.6 75.2 83.2 53.2 67.6 75.2 83.2 89.7 53.2 61.8 75.3 83.3 60.0 79.2 86.0
9-methylanthracene as quencher. This treatment considers that both quencher and probe are solubilized into the micelles and that the substrate distribution into the micelles is given by Poisson statistics.19a The probability of finding micelles with i molecules of substrate is then given by the following equation pi =
i!
where ii is the average occupation number, ii = [Q]/[M], [MI the micelle concentration given by [MI = [Dn]/N, [Dn] the micellized surfactant concentration, and N the mean aggregation number. These statistics require a random distribution of solubilized molecules and the same occupation probability for all micelles. Now consider the following assumptions: (a) the residence times of both probe and quencher (immobile quencher) inside the micelles are much longer than the fluorescence lifetime of the probe; (b) the quenching is static and does not affect the fluorescence lifetime of the probe (quenching is much faster than probe decay); (c) the amount of quencher is small so that the probability of finding a micelle with more than one molecule of probe is negligible. If these assumptions hold, then the ratio of fluorescence intensities in the absence and in the presence of quencher is given by the fraction of micelles without quencher, Po. The logarithm of lo/lis then given by
The micellar aggregation number can be obtained from a plot of the left side of eq 2 against the quencher concentration. This treatment has also been used to provide physical parameters of reverse micelles and microemulsions.*' The same Poisson statistics can be used to describe quencher and probe distributions in reverse micelles. In this case, the mean occupation number is given by the number of quencher molecules per water pool, ii = [Q]/[Dn] = [Q]NA/nWp,where [Q] and [Dn] are the quencher and the micellized surfactant concentrations, [Q1is the effective quencher concentration per liter of aqueous phase in the micellar system, and n,,.is the number of water pools per liter of aqueous phase in the micellar system. Ion Distribution inside Water Pools According to the PoissowBoltzmann Equation. The electrostatic approach considers the total volume of reverse micellar solution divided into water (19) Hunter, T. F. Chem. Phys. Lerr. 1980, 75, 152. (20) Infelta, P. P.;Griltzel, M.J . Chem. Phys. 1979, 70, 179. (21) Almgren, M.:Grieser, F.: Thomas, J. K.J . Am. Chem. Soc. 1980, 102, 3188.
22.8
15.1
9.8
16.0
0.88 0.87 0.91 0.88 0.87 0.85 0.84 0.91 0.88 0.85 0.84 0.83 0.90 0.88 0.85 0.82 0.89 0.85 0.83
4.0 4.7 4.4 5.0 6.3 7 .O 7.8 7.0 8.7 13.1 10.0 19.4 8.5 8.9 14.7 16.3 6.5 12.0 14.3
18.2 17.1 17.6 16.8 15.6 15.1 14.5 15.1 14.0 12.2 13.3 10.7 14.1 13.9 11.8 11.4 15.5 12.6 11.8
30.1 31.6 28.8 30.1 30.1 31.7 35.2 26.3 28.3 27.6 34.7 33.1 26.9 28.8 28.8 32.5 27.4 28.2 30.6
23 19 34 29 24 21 19 32 25 17 22 12 40 39 23 20 32 13 15
pools with the corresponding surfactant molecules in the surface (aggregation number N), where the amount of alcohol and electrolyte is given by the whole concentration of the particular system. In our experimental conditions, we can assume that the water pools are spherical, with radii determined by the amount of water and the number of pools. The micellar charge is assumed to be uniformly distributed over the water-pool surface with a surface charge per unit area given by Ne g=(3) 417rw2
where N is the aggregation number, e the electron charge, and rwpthe droplet radius. The ions are distributed in the region 0 < r < rwpaccording to the nonlinearized Poisson-Boltzmann equation, which for spherical symmetry and monovalent ions in solution is expressed as ereo(l /g)d/dr(gd$/dr)
=
-F[c+o exp(-e4/kT) - c-0 exp(&J/kT)I (4) where cr is the relative permittivity which we have assumed is that corresponding to the aqueous phase, eo is the vacuum permittivity, Tis the absolute temperature, k is Boltzmann's constant, 4 is the ~ c, are the concentrations of electrostatic potential, and c + and positive and negative ions, respectively, at the center of the pool, where 4 = 0. We have neglected specific interactions of Na+ with the micellar surface. The boundary conditions are
4FO=0
(5)
and from electroneutrality of the cell (d4/dr)r=rv = -g/crto
(7)
The parameters cM and c, are related to the total number of positive and negative ions in the cell, n+ and n-, by the normalization conditions n+ = ~ + ~ ~ x ~ ' [ e x p ( - e d / k T ) ] ( 4 a r 'dr )
(8)
n- = c_dv,xr"[exp(ed/kT)](4arZ) dr
(9)
We solved eq 4 by using the fourth-order Runge-Kutta method by assuming initial values of cM and c, and optimizing them with all the boundary and normalization conditions (eqs 5-9). The integrals in eqs 8 and 9 were solved by using Simpson's rule.
Rodenas and Perez-Benito
4554 The Journal of Physical Chemistry, Vol. 95, No. I I , 1991
1
Ln
I?(
/-
3-
-P
I
I
:1_1
-2 -1 1
0 02
I
1.0
0.5
1.5 1Q1~105 (MI
0.06
-
[QI
Figure 1. (a, 0)Fluorescence intensity ratio of 4-(l-pyrenyl)butyricacid in the absence and presence of quencher (Io/I) versus quencher concentration, [Q], in SDS aqueous micelles. (b, 0 ) Variation of (-In ((I/Io)(l + Ro) - Ro) versus [Q] in SDS aqueous micelles.
Once the Poisson-Boltzmann equation has been solved, we consider the ions that neutralize the droplet surface to be in a layer with a thickness Ar = 4 A; therefore, the fraction of micellar groups neutralized by counterions is given by
B = (NA/NS
0.04
Figure 2. Logarithm of the 4 4 1-pyreny1)butyric acid fluorescence intensity ratio in the absence and presence of quencher versus effective quencher concentration per liter of aqueous phase with [HzO]/[SDS] = 15.1 and different [SDS]/[l-hexanol] ratios: 0,[SDS]/[ROH] = 0.160, 0, [SDS]/[ROH] = 0.0876; 0, [SDS]/[ROH] = 0.0603;0 , [SDS]/ [ROH] = 0.0370;m, [SDS]/[ROH] = 0.0209.
r w - A?
co+[exp(e~o/k~)1(4*~) dr
'w
(10)
where +o is the droplet surface potential. Ion distribution around micelles according to the PoissonBoltvnann equation has been used to describe physical properties of ionic micelles2' and to fit kinetic data.23
Results In order to test the ability of the PBA/CPyC pair, with PBA as the acid, to give aggregation numbers of micelles, the data were compared with those obtained by using the pyrene/CPyC pair. Our aggregation number for SDS micelles in water was ca. 55, at [Dn] = 0.027 M, which is slightly smaller than the value of ca. 60 obtained by using pyrene as a probe.12*24*2s When PBA is employed in a basic aqueous SDS solution, the probe partitions between aqueous and micellar phases and the ratio of the intensities in the absence and presence of quencher, Io/I, reaches a maximum value as quencher concentration increases (Figure la). These results can be explained by considering that all the quencher, CPyC, is in the micellar phase and acts only on the probe solubilized in the micelle. Under these conditions, Illovalues are given by I I, -=-=-
+ I-
R
+ Ro
IO
+ Iwo
1
+ RO
Imo
(1 1)
where R = &,/I,,,,,is the ratio of intensities for the probe solubilized in the micelles in the presence and in the absence of quencher and Ro = Iwo/Im0is the ratio of the intensities in the aqueous and in the micellar phases in the absence of quencher. If the quenching mechanism in the micellar phase follows the theoretical treatment given above (eq 2). R = e-", at high quencher 0, and eq 11 reduces to concentration R
-
which fits the fluorescence results. (Ro = 0.53 is shown as the (22) Mille, M.; Vanderkooi, G. J .Colloid Inrcrfaccr Sci. 1977, 59, 21 1. G u n n a m , 0.;J b m n , 8.;Wennmtrlim, H.J. Phys. Chcm. 1980,84.3114. Bratko, D.; Dolar, D. J. Chcm. Phys. 1984, 80, 5782. (23) Bunton, C. A,; Moffat, J. R. J. Phys. Chcm. 1986,90,538. Ortega, F.; Rodenas, E. J. Phys. Chcm. 1987, 91, 831. Rodenas, E.;Dolcet, C.;
Valiente, M.J. Phys. Chcm. 1990. 94, 1472. (24) Lianos, P.;Viriot, M. L.; Zana, R. 1. Phys. Chcm. 1984,88, 1098. ( 2 5 ) Almgrcn, M.;Swarup, S.In Surfucranrs in Solurion; Mittal, K.L., Lindman, B., Eds.; Plenum Press: New York. 1984; Vol. 1, p 613.
10
20
30 SDS w / w
Figure 3. Specific conductivity versus amount of surfactant at different [H,O]/[SDS] ratios (R):0, R = 25.5; 0, R = 9.8.
maximum value of Io/Iin Figure la.) Equation 11 can be rearranged to I -(1 IO
+ R,)
- Ro = e-"
(13)
and a plot of -In (1(1 + &)/Io - &) versus [Q] should be linear, from which the aggregation number can be obtained. The experimental results fit this theoretical treatment (Figure Ib) if we neglect the initial sigmoidal variation a t small R (that is within the experimental error). The aggregation number obtained is ca. 65, and a little higher than other reported value^."*'^*^^^^^ From Ro it is possible to calculate the binding constant, K,,of anionic PBA
so that, at the used [Dn] = 0.023 M, K, = 70. &/q5, corresponds to the ratio of probe intensities in the water and in the micellar phases and is ca. 1, according to our results. In the reverse micellar system, surfactant concentrations in terms of water content are 0.6-1 1 M, so it is safe to assume that the probe is wholly at the droplet surface adjacent to the quencher. Fluorescence quenching measurements in SDS reverse micelles in 1-hexanol follow the theoretical treatment described, and the logarithm of the ratio of intensities has a linear dependence on effective quencher concentration, as is shown in Figure 2, where some of the results are plotted. Similar straight lines have been obtained in all the systems studied. From the slopes, we calculate the number of water pools per liter of aqueous phase in the reverse micelles and, by considering a homogeneous distribution of surfactant molecules at the water-pool surface, the micellar aggregation number. These values are given in Table I. From the number of pools per liter of aqueous phase, we obtain the water-pool radius, r,,, assuming spherical pools (Table I).
Sizes and Aggregation Numbers of SDS Reverse Micelles
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4555
N 'WP
(A, 8
L
I
20
1
I
10
LH20J/[SDSI
I
20
30 '/e
SDS
-
W/W
Figure 4. Aggregation number versus amount of surfactant for the
SDS/l-hexanol/water reverse micelles at different [H,O]/[SDS] ratios (R):0, R = 37.4; 0, R = 22.8; 0,R = 15.1; @ R = 9.8.
~~
~~~
01
0.2
[SDS]/[ROH]
Figure 6. (a) Water-pool radius versus [SDS]/[l-hexanol] ratio for SDS/l-hexanol/water reverse micelles at different [H,O]/[SDS] ratios (R): 0, R = 37.4; 0 , R = 22.8; 0,R = 15.1; R = 9.8. (b) Intercepts at [SDS]/[l-hexanol] = 0 (rvo) versus [H,O]/[SDS] ratio.
20 -
I
.
40
1
I
10
20
I
1 I
I
30 Ye H2O
W/W
Figure 5. Water-pool radius versus water content for SDS/l-hexanol/
water reverse micelles at different [H,O]/[SDS] ratios (R):0, R = 37.4; 0 , R = 22.8; 0,R = 15.1; @ R = 9.8. The conductivity of these systems increases with surfactant concentration, and with the same amount of surfactant, conductivity increases with water content, as can be seen in Figure 3.
Discussion The data in Table I show that reverse micellar aggregation numbers are determined mainly by the surfactant concentration. This fact is stressed by plotting N versus percent SDS (Figure 4). This plot shows an almost linear correlation, with all the values in the same correlation, irrespective of the water/SDS and SDS/alcohol molar ratios. Extrapolation of these data to [SDS] 0 corresponds to the minimum aggregation number (No = 9) for the reverse micelle to be formed. According to the data given in Table I, the radius of the water pool depends mainly on the water content as shown in Figure 5 , where calculated radii at the different water/surfactant and alcohol/surfactant ratios are plotted versus water content. But contrary to the effect of aggregation number, there are also small variations, with a slight increase of rv with the water/surfactant ratio. This variation for SDS/1-hexanol reverse micelles is clearly shown in Figure 6a, where radii at different water/SDS ratios are plotted versus SDS/ I-hexanol molar ratio, giving parallel straight lines with different intercepts. The plot of these extrapolated values versus water/SDS ratio is linear (Figure 6b) with an intercept rwpO= 8 A, which corresponds to the mininum water-pool radius for the formation of reverse micelles. From these values rw; and No and by considering that the water-pool micrcdensity IS 1, it is possible to obtain a minimum number of water molecules per surfactant in the reverse micelles of ca. 8, so that at low water and surfactant content there are no real reverse micelles but only some hydrated surfactant molecules, which agrees with some other results in the literature." This ratio [H20]/[SDS] corresponds to one of the limits of the phase diagram. It is interesting to note that the interface area per 100 g of solution linearly depends on the amount of surfactant in the mixture (Figure 7a), with different slopes for each water/SDS
-
0.05
msos
F b i 7. (a) Interface area/100 g of solution of SDS/l-hexanol/water reverse micelles versus moles of SDS/100 g of solution, at different [H,O]/[SDS] ratios (R):0, R = 37.4; 0, R = 22.8; 0,R = 15.1; @ R = 9.8. (b) Slopes/N,, (interface area per surfactant molecule) versus
[H,O]/[SDS] ratio. ratio but with the same intercept independent of this ratio. From the slopes, it is possible to obtain the area per surfactant molecule at each water/SDS ratio, a value that increases with this ratio, which could be related to the amount of alcohol that goes to the surface of the water pool. A plot of these slopes versus water/SDS ratio is linear, from which the minimum surface area per surfactant molecule for the reverse micelles to be formed with [H20]/[SDS] = 8 can be obtained with a value near 60 A; this value agrees with other results for this hydrated surfactant head group.26 From this plot, it is possible to obtain the surface area per molecule of surfactant in the reverse micelle system with [H20]/[SDS] = 40, which corresponds to another limit in the phase diagram for this system; this area is 170 A. According to the results, reverse micelles form with areas per surfactant molecule that range between 60 and 170 A2: the lower value corresponds to the minimum hydrated surfactant area in the absence of alcohol, the water molecules reducing the electrostatic repulsion between the surfactant head groups; the other limit, 170 A, could be related to the minimum surfactant surface concentration that decreases the interfacial tension and stabilizes the system. The intercept in Figure 7b is the surface area occupied by a molecule of surfactant in the absence of water, with an apparent value of 17 A2. From these results, it appears that these systems are authentic microemulsions in which the alcohol acts as a cosurfactant. (26)Stigter, D.J . Phys. Chem. 1964, 68,3603.
4556 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 TABLE II: Calculated Val- of Droplet Surface POt&hl ( $ 0 ) and Fraction of Micellar Head Group Neutralized with Ions (B) for SDS/AUuwl/Water Reverse Micelles w t % w t % wt 5% [H,0]/ alcohol H20 SDS ROH [SDS] &, V fl I-hexanol 35.0 15.0 50.0 37.4 -0.0592 0.752 28.6 12.3 59.1 -0.0579 0.761 21.0 9.0 70.0 -0.0536 0.766 27.5 19.3 53.2 22.8 -0.0730 0.819 22.5 15.8 61.7 -0.0688 0.818 19.0 13.4 67.6 -0.0647 0.826 14.6 10.2 75.2 -0.0611 0.827 9.9 6.9 83.2 -0.0591 0.831 15.1 -0.0767 0.865 22.7 24.1 53.2 15.7 16.7 67.6 -0.0701 0.867 12.0 12.8 75.2 -0.0612 0.880 8.1 8.7 83.2 -0.0673 0.872 5.1 5.3 89.7 -0.0539 0.897 17.8 29.0 53.2 9.8 -0,0882 0.901 14.5 23.7 61.8 -0.0877 0.903 9.5 15.2 75.3 -0.0734 0.909 -0.0694 0.909 6.4 10.3 83.3 I-octanol 20.0 20.0 60.0 16.0 -0.0756 0.856 10.4 10.4 79.2 -0.0513 0.850 7.0 86.0 -0.0581 0.881 7.0
From nwpand by considering spherical symmetry of the cells that contain the water pool and the corresponding amount of alcohol and surfactant, it is possible to obtain the cell radius as 4 V 7 r C 3= (15) n,,(% H20/100)d, where d, is the macroscopic density of the reverse micelles and V is the volume of the micellar solution. The calculated radii, r,, are given in Table I. These radii for SDS reverse micelles are independent of SDS/water ratio and decrease with the SDS/1-hexanol ratio (Table I). It is interesting to note that at high SDS content the difference between the cell and water-pool radii (rc- rV) is smaller than the length of the surfactant molecules; that means the alcohol is not only a dispersant medium but also a component of the interface. The system SDS/1-octanol has been studied at a water/SDS molar ratio of 16 and different SDS/ 1-octanol ratios. The results (Table I) are nearly the same as for SDS/1-hexanol with the same water/SDS molar ratios, which means there are not significantly different micellar structures.
Rodenas and Perez-Benito TABLE III: Calculated Values of Droplet Surface Potential (9,) and Fraction of Micellar Head Groups Neutralized with Iow (8) for SDS/l-HexpnOl/Water Reverse Micelles with a Relative Permittivity c, = 50 wt%
wt %
wt 7%
HzO
SDS
35.0 28.6 21.0 17.8 14.5 9.5 6.4
15.0 12.3 9.0 29.0 23.7 15.2 10.3
ROH 50.0 59.1 70.0 53.2 61.8 75.3 83.3
[HzO]/ [SDS] 37.4 9.8
&o,V -0.0756 -0.0741 -0.0692 -0.107 -0,106 -0.0913 -0.0870
B 0.812 0.813 0.815 0.930 0.935 0.934 0.934
We also made a calculation of ion distribution inside the water pools according to the Poisson-Boltzmann equation, using the experimental radii and the aggregation numbers. The obtained results are given in Table 11. In the calculation, we neglected the small amount of NaOH used in the experiments, which does not affect the results. From these results, it appears that /3 only depends on the water/SDS molar ratio and it increases as this ratio decreases. The micellar surface potential decreases with the amount of alcohol for each water/SDS ratio. These results agree the conductivity measurements showing that the conductivity increases with the micellar ionization degree, a = 1 - 0 (Figure 3). Although the conductivity mechanism in these systems is not well established and should be mainly related to micellar collisions and ion transfer, it appears also to depend on micellar ionization. Taking into account our experimental evidence showing that reverse micelle formation produces a decrease in the apparent dielectric constant of the water pool?’ we repeated the calculation using t, = 50. The obtained results are given in Table 111. Both droplet surface potential and fraction of micellar groups neutralized slightly increase, and it is interesting to report that, in the third limit of stability of this system (alcohol amount near 50 wt %I*), the droplet surface potential depends on the ratio [H,O]/[SDS], but the free charge per unit area becomes nearly the same value, Nae/4*r2 = 0.017 C/mZ. Acknowledgment. We thank Prof. C. A. Bunton and Prof. E. Lissi for their corrections and comments on this paper. Registry NO. PBA, 3443-45-6; SDS,151-21-3;CPyC, 123-03-5;1hexanol, 1 1 1-27-3; 1-octanol,1 1 1-87-5. (27) Valiente, M.;Rodenas, E. J . Phys. Chem. 1991, 95, 3368.
