Langmuir 1995,11, 2893-2898
2893
Structure and Dynamics of Nonionic Polyoxyethylenic Reverse Micelles by Time-ResolvedFluorescence Quenching Marilena Vasilescu" and Agneta Caragheorgheopol Znstitute of Physical Chemistry, Romanian Academy, Splaiul Zndependentei 202, 77208 Bucharest, Romania
Mats Almgren, Wyn Brown, Jan Alsins, and Ragnar Johannsson Department of Physical Chemistry, University of Uppsala, Box 532, S-751 21 Uppsala, Sweden Received March 27, 1995@ The application of the time-resolved fluorescencequenching method (TRFQ)to study the structure and aggregation behavior of nonionic surfactant polyoxyethylene(4)lauryl ether (C12E4) in reverse micellar systemsis presented. Solutionsofdifferentconcentrationsin three nonpolar solvents(cyclohexane,n-decane, and n-dodecane), at different water content and temperature, employing R~(bpy)3~+-methylviologen, solubilized in the polar core of micelles, as probe-quencher pair, were studied. The aggregation number and fluorescence quenching rates were determined and the size and shape of micelles estimated; the dependence of their values on medium was evidenced. Dynamic light scattering was utilized as a complementary method in checking the hypotheses regarding micellar sizehhape. It was found that in cyclohexane, at the compositions studied, the micelles can be regarded as spherical, growing with the water content, with a constant area per head group of about 50 A2. Only at the lowest water content (3 water molecules per surfactant or less) is there a deviation with a larger area per surfactant. The radius of the polar core is then smaller than the length of the EO tail, and there is no free water that could allow the micelle to swell beyond this limit. The micelles in decane and dodecane appear to grow in a nonspherical way and become much larger with water addition.
Introduction Systems containing nonionic surfactants, in particular those of the polyoxyethylenic type, in nonpolar solvents and water (w/o microemulsions) have recently attracted considerable attention. The information regarding the structure of reverse micelles, especially their size and shape, is scarce; therefore studying them is important from a scientific as well as a n applied viewpoint. Scattered structural information on reverse nonionic systems has been presented in several studies carried out by calorimetric measurements,ll2 dynamic light scattering,3 NMR,4-6 neutron ~ c a t t e r i n g and , ~ visible absorpti or^,^,^ f l u o r e ~ c e n c e ,and ~ ~ -ESR13J4 ~~ probe spectroscopies. From among the physical methods, the fluorescence Abstract published in Advance ACS Abstracts, July 1, 1995. (1)Friberg, S.E.; Christenson, H.; Bertrand, G.; Larsen, D. W. In Reverse Micelles; Luisi, P. L., Straub, B. E., Eds.; Plenum Press: New York, 1984;p 105. (2)Olofsson, G.; Kizling, J.;Stenius,P. J . Colloid Interface Sci. 1986, 111, 213. (3)Kizling, J.;Stenius, P. J . Colloid Interface Sci. 1987,118,482. Friberg, S. E.; Larsen, D. W. J . Phys. Chem. (4)Christenson, H.; 1980,84,3633. (5)Seih, P. S.; Fendler, J. H. J . Chem. SOC.,Faraday Trans. 1 1977, 1480. (6) Kahlweit, M.; Strey, R.; Haase, D.; Kunieda, H.; Schmeling, T.; Faulhaber, B.; Borkovec, M.; Eicke, H. F.; Busse, G.; Eggers, F.; Funck, Stilbs, P.; Winkler, J.; Th.; Richmann, H.; Magid, L.; Soderman, 0.; Dittrich, A.; Jahn, W. J . Colloid Interface Sci. 1987,118,436. (7)Ravey, J.C.; Buzier, M.; Picot, J. C. J . ColloidZnterface Sci. 1984, 97,9. (8)Zhu, D.-M.; Schelly, Z. A. Langmuir 1992,8,48. (9)Zhu,D.-M.; Wu,X.; Schelly, Z. A. J.Phys. Chem. 1992,96,7121. (10)Almgren, M.;Lofroth, J. E.; van Stam, J. J . Phys. Chem. 1988, 90,4431. (11)Almgren, M.;van Stam, J.;Swamp, S.;Lofroth, J. E. Langmuir 1986,2,432. (12)Fendler, J.Acc. Chem. Res. 1976,9, 153. (13)Caldararu, H.; Caragheorgheopol,A,; Vasilescu, M.; Dragutan, I.; Lemmetyinen, H. J . Phys. Chem. 1994,98,5320. (14)Caldararu, H.;Caragheorgheopol, A.; Dimonie, M.; Donescu, D.; Dragutan, I.; Marinescu, N. J . Phys. Chem. 1992,96,7109. @
quenching technique was favored because it allows the determination of micellar size (see The first application of this method for the determination of micellar aggregation numbers was presented by Turro and Yekta20 using static fluorescence measurements. To ensure good resolution ofthe intramicellar quenching process, the probe-quencher pair has to be so selected that the quenching interaction is much faster than the natural decay of the probe fluorescence. Infelta et aZ.21 suggested that when the quencher moves between micelles during the lifetime of the excited probe, the fluorescence intensity decays according to the equation ln[F(t)/F(O)I = -A2t
+ A,[exp(-A&)
- 11
(1)
where
(3)
A, = k,
+ k-
(4)
Here k, is the first-order rate constant for quenching in a micelle, k- the exit rate constant of a quencher leaving (15)Lang, J. In The Structure, Dynamics and Equilibrium Properties ofColloidal Systems; Bloor, D. M., Wyn Jones, E., Eds.; Kluwer Academic Publishers: Dordrecht, 1990;pp 1-38. (16)Almgren, M. In Kinetics and Catalysis in Microheterogeneous Systems; Gratzel, M., Kalyanasundaram, IC,Eds.; Marcel Dekker: New York, 1991;p 63. (17)Almgren, M. Adv. Colloid Interface Sci. 1992,41,9-32. (18)Gehlen, M. H.; De Schryver, F. C. Chem. Rev. 1993,93, 199. (19)Van der Auweraer, M.; De Schryver, F. C. In Inverse Micelles Studies in Physical and Theoretical Chemistry; Pileni, M. P.,Ed.; Elsevier: Amsterdam, 1990;Vol. 65,pp 70-102. (20)Turro,N.J.; Yekta, A. J . Am. Chem. SOC.1978,100,5951. (21)Infelta, P. P.; Gratzel, F.; Thomas, J. K. J . Phys. Chem. 1974, 78,190.
0743-746319512411-2893$09.00/0 0 1995 American Chemical Society
Vasilescu et al.
2894 Langmuir, Vol. 11, No. 8, 1995
a micelle, ko the unquenched decay rate of the probe (the reciprocal of the lifetime TO), and n the average number of quenchers per micelle. There are also other conditions that the quencher and probe should fulfill.16 If k- is much less than k , and K O , eq 1 reduces to22
ln[F(W(O)I = -k,t
+ n[exp(-k,t)
- 11
(5)
This is the ideal case for determination of aggregation numbers. The most important features in the plot of eq 5 are the parallel linear tails of the curves, which suggest that no migration occurs and A2 = ko. Fitting the experimental data to eq 5, the following parameters are obtained: K O , n, and k,. The n values yield the micellar concentration [MI and the aggregation number N:
The “mic” subscript a t S and Q in eq 6 indicates the surfactant and quencher concentrations in micelles, respectively. The TRFQ method was initially applied to direct micelles and then to i o n i ~ ~and ~ - nonioniclO ~l reverse micelles. In this study the application of this method to nonionic reverse micelles is attempted, aiming a t obtaining information regarding the micellization process and the micellar size. The &E4 ternary systems in cyclohexane, decane, and dodecane with various water additions were investigated. The dependence of the aggregation number on solvent, temperature, and water concentration was also examined. The values of the polar core radius and the area per polar head were estimated. In the case of 15% Cl~E~cyclohexane/water (8 “C) and Cl2Eddecane/water (8, 11, and 25 “C) systems, the variation of the micellar hydrodynamic radius was determined by dynamic light scattering.
Experimental Section Polyoxyethylene(4)lauryl ether ( C ~ Z ENikko ~ ) , Chemicals,was used without further purification. Cyclohexane, n-decane, and n-dodecane were spectroscopic grade Merck reagents and were utilized as supplied in the preparation of micellar solutions. These were subjected to ultrasonic irradiation and used 24 h later. Various amounts of water, henceforth represented as W = [HzO]/[surfactant] molar ratio, were added to these solutions, and the samples were mechanically stirred. The water used was deionized. The phase limits were determined by visual observation of the turbidity at stepwise addition of water, while in the case of decane and dodecane solutions the samples were also inspected between crossed polarizers. Ruthenium bipyridyl (the dichloride salt of Ru(bpy)S2+)from G. Frederick Smith Chemical Co. was used as probe and methylviologen (Mvz+),Aldrich, analytical grade, as quencher. The probe and quencher were added with water by microsyringe; appropriate volumes of stock aqueous solution of probe and quencher were added. To avoid probe-quencher electrostatic (22)Infelta, P. P. Chem. Phys. Lett. 1979,61, 88. (23)Atik, S.S.;Thomas, J. K. J.Phys. Chem. 1981,85, 3921. (24)Atik, S.S.;Thomas, J. K. J.Am. Chem. SOC. 1981,103,3543. (25)Gelade, E.;De Schryver, F. C. J. Photochem. 1982,18,223. (26)Bridge, N.J.; Fletcher, P. D. J. Chem. Soc., Faraday Trans. 1 1983,79,2161. (27)Brochette, P.;Pileni, M. P. Nouu. J. Chim. 1986,9,551. (28)Verbeeck, A.; De Schry-ver, F. C. Langmuir 1987,3,494. (29)Lang, J.; Jada, A.; Malliaris, A. J.Phys. Chem. 1988,92,1946. (30)Lang, J.; Mascolo, G.;Zana, R.; Luisi, P. L. J.Phys. Chem. 1990, 94. 3069. (31)Johannsson, R.;Almgren, M.; Alsins, J. J. Phys. Chem. 1091, 95, 3819.
repulsion, the stock solutions contained NaCl so as to yield a 10-3 M NaCl final concentration in the samples. The quencher and 3 x concentration ranged within 5 x M, while that of the probe ranged between 5 x and M, so that [P]/[Q] , . , 10-2. Time-resolved fluorescence quenching measurements were made using a Nz laser to excite the probe in an air-equilibrated solution. The detector was a Hamamatsu R 928 photomultiplier. The signals were taken up with a Tektronics 7912 digitizer provided with 7B90P time base. System control and signal processing were performed with an AT-compatible computer. For some of the samples, time-resolved fluorescence decay data were collected with the single-photon counting technique as described earlier.32 The setup uses a mode-lockedNd:YAG laser to synchronously pump a cavity-dumped dye laser for the excitation using DCM as dye and a KDP crystal for frequency doubling. The excitation wavelength was 305 nm and, I,, was 650 nm. The results obtained with the two sets of equipment were comparable. Measurements were performed at different thermostated temperatures. Dynamic light scattering (DLS)measurements have been made using the apparatus and techniques described in an earlier ~ommunication.~~ Micellar hydrodynamic radius, RH,values were calculated using the Stokes-Einstein equation, RH = kT/ (GnrjQ),where D is the diffusion coefficient, k is Boltzmann’s constant, T is the absolute temperature, and 70 is the solvent viscosity. The particle is considered to be equivalent to a sphere with a solvation shell. Diffusion coefficients are calculated as D = T/g2, whereg is the scattering vector and r is the measured relaxation rate.
Results and Discussion I. C12E4/CyclohexaneAVater System. Most of the fluorescence quenching measurements were carried out in samples with 15%(0.41 mol/kg) surfactant. A solution with 7.7%(0.21molkg) surfactant was also measured for comparison. For initial calculations of N values, the concentration of free surfactant molecules([Sl,~, = [SI in eq 6) was disregarded; aggregation numbers systematically higher for 7.7% than for 15% (at the same w> were obtained. On the basis of these findings and the phase diagram (the oil-rich part of this diagram is shown in Figure l a ) the concentration of free surfactant molecules was taken as 2.5%. Measurements were conducted a t 8 “C. At higher temperatures the system solubilizes very small amounts of water, as one can note in Figure lb, which shows the solubility of water in micellar solutions versus temperature, for various C12E4 concentrations. The runs were repeated three to five times at constant W making use of the same or different quencher concentrations (care was taken to keep the [Ql/[Ml ratio sufficiently low). The resulting values were scattered at the extreme values of W at low W the N value is small, while a t high W, due to the slow quenching, one approaches the applicability limit of the method. In Table 1 the average values are reported. Figure Z shows, as a n example, the fluorescence decay curves of Ru(bpyIs2+ without quencher and with M V + quencher. One can note the parallelism of the tails of decay curves with and without quencher (i.e., k- ko is no longer fulfilled. This limits the micellar size that can be determined by this method with the probequencher pair selected. Moreover, the micellar growth may be usually accompanied by a change of shape and an increase of the po1ydispersity;l' probably because of these effects our attempts to measure at high W with another probe (phosphorescent Cr(bpy)g3+,whose z is much higher) did not yield satisfactory N values. 3 . N increases with W. Figure 3 shows the W dependence of N in solutions with 15% and 7.7% surfactant; Nvalues were calculated assuming that 2.5% &E4 is present as monomer in the oil. One can note that the data obtained a t the two concentrations superpose except for those at low W; this could mean that the concentration of free surfactant is larger a t low W. The radius of the polar core, Rpo and the surface area per polar head, Aph, were calculated by the equations
0.5 1.0 1.2 2.0 1.1 1.5 1.7 2.0 2.5 1.6 2.0 2.7 1.2 2.0 2.1 2.7 3.0 1.5 2.5 2.6 3.0 1.7 2.5 2.6 3.0 1.0 1.6 1.7 2.6 2.7 1.7 2.6 2.7 2.0
ko
k,
(106s-')
n
(106s-')
N
1.74 1.78 1.78 1.78 1.79 1.79 1.79 1.79 1.79 1.81 1.81 1.81 1.85 1.85 1.85 1.85 1.85 1.91 1.91 1.91 1.91 1.97 1.97 1.97 1.97 2.01 2.01 2.01 2.01 2.01 2.05 2.05 2.05 2.06
0.17 0.21 0.23 0.42 0.50 0.60 0.63 0.64 0.61 0.72 0.91 0.98 0.67 1.19 1.22 1.83 1.91 1.09 1.88 1.93 2.47 1.67 2.19 2.28 2.97 1.07 2.11 1.95 2.70 3.18 2.26 3.10 3.71 2.91
31.1 28.0 10.1 35.5 20.0 24.7 15.0 18.6 24.6 16.1 15.5 12.0 10.4 12.0 12.2 11.0 14.3 10.8 11.1 12.5 12.6 8.6 9.4 9.5 11.1 6.69 7.74 6.93 7.89 7.84 5.67 6.70 6.95 4.93
45 70 61 70 154 136 121 107 103 152 154 121 227 203 197 225 216 246 253 25 1 279 323 298 298 335 362 446 378 352 392 438 402 458 485
These W values were calculated considering the micellized surfactant concentration, [SI,i, = 12.5%.
4 3 % : (812) A,, = N with the assumption that all the water and the polyoxyethylene part of the surfactant lie within the polar core, which is spherical, monodisperse, and separated from the continuous oil phase by a monolayer of alkyl chains of the N surfactant molecules. VH~O stands for the molecular volume of water and VEOfor the volume of the polyoxyethylene chains. The R , andAphvalues are listed in Table 2. A plot ofR, versus W (Figure 4)is approximately linear; the solubilized water brings about an increase of N and micellar size (radius). If the variation ofthe hydrodynamic radius ( R H )from the dynamic light scattering is plotted versus W (Figure 41, one notes that R His systematically higher than Rpc. The broken line in Figure 4 is drawn with the same slope as the R,, line. The difference of 15 A is approximately the size of the hydrophobic shell of the micelle.'vg5 The results obtained at low Ware consistent with the assumption of spherical micelles with no water core. The R , values are close to the length of the fully stretched EO tail (18-20 A), and the Aph is close to 60 A2. When more water is added, a pool of free water is formed in the middle of the micelle and one could expect that the area per head group is smaller and remains independent of W. These were actually found in this system. 11. ClzEdDecaneMTaterSystem. The phase behavior with decane as solvent, Figure 5, is different from that (35)Nilsson, P.-G.; Wennerstrom, H.; Lindman, B. J.Phys. Chem. 1983,87,1377.
Vasilescu et al.
2896 Langmuir, Vol. 11, No. 8, 1995 500
10000
4001M)o
300
-
2 u. 200 .
100
In -100
100
500
300
700
900
t/ns
0
10
5
15
0
w Figure 3. Aggregation numbers,N , in C~~E~cyclohexaneJwater systems as a function of the watedsurfactant molar ratio, W (T= 8 "C).
a
*' ' 0
x
0
7
t0
U
U
100
20 100
100
700
Mo
300
5
t/ns
b 10
-4
1
5
0
10
15
w
y =+206x'+l20.v~ 0.486max dev.1.03
20
Figure 4. W dependence of R, (a) and RH (b) for micellar solutions in cyclohexane; [C12E41 = 15%; T = 8 "C. Table 2. Calculated N,R,, and Aph Values for 16% ClzEdOiyWater Systems at 8 "C
cyclohexane
E
%
H20 1
-12
- 16 0
yx)
1ocO
1500
2000
t Ins C
Figure 2. Time-resolved fluorescence curves for 15% C12E.d = cyclohexandwater solutions, at 8 "C: (a) W = 4.02,[W+] mol-kg-l; mol-kg-'; (b) W = 5.36,[W+] = 2.0 x 1.5 x (c) W = 8.04,[W+l = 1.2 x mol-kg-1 (curve 11, [W+l = 2.6 x mol-kg-l (curve 2).
with cyclohexane (we refer also to the oil-rich part of the diagram). More water is solubilized a t 25 "C than a t 8 "C; the amount of water solubilized a t 8 "C is much smaller than in cyclohexane. Furthermore, the phase that separates at 8 "C is in this case liquid crystalline, as evidenced by birefringent zones appearing a t demixing. The applicability of the TFRQ method was limited in this system owing to the size and structure of the aggregates. Thus, with water addition they become very large and the decay curves are no longer of the simple
2 3 4 5 6 7
8 9
RP
Aph
(A) (A2) 14.9 17.9 22.6 24.9 29.5 32.3 35.5 39.1 41.6
61.9 59.9 54.0 53.1 51.3 51.2 50.5 49.7 50.2
decane Rpc
N 45 67 121 142 213 256 313 386 433
Aph
(A) (Az) N 16.7 19.9 32.6 40.2
dodecane RP
Aph
(A) (A2)
54.3 64 18.2 51.8 96 24.5 35.1 380 35.4 31.4 647 48.3
N
49.6 84 42.0 200 32.4 484 26.2 1121
Infelta type, as shown comparatively in Figure 6, parts solutions a and b, which present the decay of 15% with W = 2.68 and 4.02. The decay curve a t the higher water content is reminiscent of the decays observed in long cylinder or large disk-like s t r u c t u r e ~ ; ~another ~J~*~~ possibility is that a migration of probes or quenchers occurs, as in the clusters of reversed AOT micelles studied earlier.36 Decays of a similar type were also obtained a t 25 "C a t W x 6 or larger, and although demixing occurred first a t W = 21 for [SI = 20%, the TRFQ method was not usefid above W = 6. (36)Almgren, M.; Johannsson, R.J.Phys. Chem. 1992, 96,9513.
Langmuir, Vol. 11, No. 8, 1995 2897
Nonionic Polyoxyethylenic Reverse Micelles decane
I50
o p
EO0
450 z
300 C12Eq % 150
c _
Figure 5. Oil-rich part of the phase diagram of the C12E4/
decandwater system, at 8 and 25 "C.
3
5
7
w Figure 7. Aggregation numbers,N , in the ClzEddecandwater system as a function of the waterlsurfactant molar ratio, W, at different temperatures.
-100
100
300
700
Kx)
900
VI-6 a
-200
200
1000
6M)
1wx)
t/ns b
Figure 6. The time-resolved fluorescence quenching curves for 15%ClzEddecane micellar solutions at 8 "C: (a) W = 2.68; (b) W = 4.02. Table 3. Selected Values for the ko,k,, and k- Rate Constants Obtained by Fitting of Fluorescence Decay Curves for 15%CiaEd Micellar Solutions at 8 "C
cyclohexane 4.02 cyclohexane 5.36 decane 2.68 decane 4.02
1.5 2.0 2.0 2.5
1.8 1.9 1.7 1.8
3.0 2.2 2.2 0.5
0.20 0.35 0.46 5.30
The decays shown in Figure 6a,b were evaluated using eq 1 yielding the ko, k-, and k, values listed in Table 3. For comparison, eq 1 was also applied to the two cyclohexane solutions shown in Figure 2a,b. Only in the case of Figure 6b is k- large compared to k,. The aggregation numbers reported below were all obtained assuming migration, i.e., using eq 1. It is likely that a change to rods or disks occurred as well as the demixing conditions were approached; since the liquid crystalline phase that appears there is probably lamellar,I disk-like micelles may be the preferred structure. In any
case, the true aggregation numbers may be much larger in this region. The aggregation numbers were determined by the TRFQ method in solutions of various surfactant concentrations (12%, 15%, 18%,and 20%), as well as a t various Wvalues and temperatures. Figure 7 shows the dependence of N on W and temperature. N decreases with increasing temperature. Within the experimental range of 12-20% the variation of surfactant concentration does not change sensitively the aggregation number at constant Wand T (25 "C), the concentration of free surfactant molecules being negligible when water is present, as Ravey et a1.I have suggested in their small-angle neutron scattering study on this ternary system. Comparison of data obtained with the solutions in decane and in cyclohexane shows that, a t the same temperature (8 "C), surfactant concentration, and W, decane, as solvent, favors aggregation to a greater extent, yielding higher N values. The R,, and Aph values were estimated a t various Ws, assuming spherical micelles. The values are listed in Table 2 for 15% surfactant and 8 "C. R,, (Figure 8a) increases with W, and the values are higher than those in cyclohexane. The marked variation of R,, and Aph a t W = 4.02 (3% water) supports the hypothesis that structural transformations have already occurred and the polar core is no longer spherical. This conclusion is confirmed by the results supplied by dynamic light scattering (Figure 8b). The RH)^,, values in decane are considerably larger than those in cyclohexane, and the variation with W is much stronger (the results were not improved by correcting the actual viscosities of the solutions and their variations with W). These effects can be due to changes in sizelshape andlor different interactions in the two solvents. The trends in RHin decane correspond closely to those in the aggregation number (Figure 7) determined by fluorescence quenching. Thus, taking the data together, the interpretation is that larger micelles exist in decane with a deviation in sizehhape as W is increased. 111. C12E4/Dodecane/WaterSystem. The aggregation numbers were determined a t various temperatures (8, 11, and 25 "C) in 15% surfactant solution; the results are shown in Figure 9. The aggregation numbers increase with W and decrease with temperature. The N values are higher than in decane a t the same T and W. It is worth recalling that the longer the chain, the more favored the aggregati0n.I
Vasilescu et al.
2898 Langmuir, Vol. 11, No. 8,1995 129
45
loo0
35
5
7 SO
z
&
500
25
250
5
3
0
W
1
2
4
3
5
a
W 100
Figure 9. Aggregation numbers, N, in the C~zEddodecand water system as a function of the water/surfactant molar ratio, W, at different temperatures.
75
The aggregation numbers and the radius of polar core increase with increasing W and decrease with increasing temperature. The micelle size, at the same water content and temperature, depends on solvent nature: when it is a linear hydrocarbon (decane, dodecane), aggregation is favored; whenever the chain is longer, the aggregation number and polar core radius are higher. All these dependences are in accord with the findings of Ravey et ale7for the same systems, using small-angle neutron scattering measurements. The experimental data obtained in cyclohexane solutions, supported by DLS measurements, point to a spherical shape for the micellar aggregates whose size varies between 30 A (at W = 1.34)and 60 A (at W = 13.4); the aggregation numbers range from 54 to 585, respectively. In the solutions with decane and dodecane the micelles are large; beginning from W = 4 the data are no longer consistent with a spherical shape; at W > 5.36 (at 8 "C) demixing occurs and a (lamellar) liquid crystal structure is noted. The aggregation numbers vary from 64.5 (at W = 1.34) to 647 (at W = 5.36) for decane and from 84 (W = 1.34) to 1120 (W = 5.36) for dodecane.
50
3 d 25
2.5
SD
7.5
1
W
Figure 8. W dependence of R , (a) and RH (b) determined for 15% ClzEJdecane micellar solutions.
R, andAphvalues, at various W, are listed in Table 2. R, increaseswith W. At W > 5.36 a liquid crystal structure is present as in decane, and the micelles begin to change structure a t even lower W. Comparison of Aph data in Table 2 for the three solvents shows that, for the same W, Aph decreases in the sequence cyclohexane > decane > dodecane, while for the same solvent, they decrease with increasing W. In the case of cyclohexane this decrease is small, while in decane and dodecane it is improbably high; at W > 4 it drops below a reasonable value, and it is likely that the micelles are no longer spherical.
Conclusions The TRFQ method was applied in nonionic reverse micelles to determine fluorescence quenching rates and aggregation numbers.
Acknowledgment. This contribution is the result of a cooperation between the Royal Academy of Sweden and the Romanian Academy. One of us, M.V., is greatfull for financial support from the University of Uppsala. LA950236U
