J. Phys. Chem. 1991,95, 3819-3823
also operates when the micelles are swollen with 0 i 1 . ~ ~ In ~ ' ~both the binary and ternary systems, a maximum in R2 was found as a function of temperature while a minimum in the surfactant diffusion constant, coinciding with the R2 maximum, was observed. It was concluded that at temperatures above the R2 maximum exchange through fission-fusion processes was more rapid than aggregate reorientation. In the present system R2 was also measured at 2 OC and was found to be much larger than at 8 OC (cf. Table I). This difference is too large to be due to the temperature dependence of thermal motions only, assuming structure, length scales, and interactions to remain unchanged. For a 20 wt % solution in the CI2E5-water system, the fission-fusion processes appear to contribute to the spin relaxation even at lower temperatures (4 OC)'O far below the clouding temperature ( e 4 0 "C).Since the clouding temperature for the present sample is about 16 OC,it is reasonable to assume that this is also the case in this sample at the two temperatures 2 and 8 "C. Another possible contribution to the increase in R2 with decreasing temperature is a growth of the micellar length. If the fission-fusion processes provide the dominating contribution to R2,then the large difference in R2 at the two temperatures reflects a strong temperature dependence in the intermicellar interactions. This is not inconsistent with the upper consolute boundary, found in these types of systems, indicating that interactions are becoming progressively attractive with increasing temperature. Measurements of Rl and R2at the highest field strengths (39 and 55 MHz) were also performed at three other compositions ( 5 , 10, and 40 wt %) in the Ll phase. For all samples, R 1was found, within the experimental uncertainty, to be the same as for the 20 wt % ' sample, indicating that the local molecular motions
3819
are similar at all concentrations. Moreover, R2 was found to be much larger than R I at these concentrations as well, and we can therefore conclude that large aggregates, presumably rodlike micelles, are formed in the whole concentration range studied. In the present system of rod-shaped micelles the isotropic surfactant dynamics are much more rapid (1-2 orders of magnitude) than what is found in concentrated systems with ionic surfactant containing very long rod-shaped micelle^.^' Also, the zero shear viscosity appears to be significantly lower and no low-frequency viscoelasticity could be detected. (This can be qualitatively detected by observing the recoil of trapped air bubbles in the solution after swirling the sample.) However, to obtain visually detectable shear birefringence and viscoelasticity in systems of the present kind, the lifetime of the aggregates has to be in the millisecond range (or longer). As argued above, the lifetime of the CI2E4micelles is in the microsecond regime; therefore, no such effects are observed. Finally, in solutions of rodlike micelles an exponential stress relaxation is often observed@ which cannot be explained by the reptation mechanism.4I It has recently been suggested that breaking of rodlike micelles may play an important role for the relaxation of the transient netw0rk.4~.~~ In this context, it is possible that spin relaxation of surfactant nuclei can be an important technique for estimating the time scale for breaking and recombining of rodlike micelles in solution.
Acknowledgment. This work was supported by the Swedish Natural Science Research Council. We also want to thank Peter Stilbs for the use of his curve-fitting programs. Registry NO. C12E4,5 2 1 4 4 8 4 .
(38) Olsson, U.; Nagai, K.; Wcnncrstrijm, H. J. Phys. Chem. 1988, 92, 6675. (39) Olsson, U.; JonstriSmer, M.; Nagai, K.; SBdcrman, 0.; Wennerstrijm, H.; Klose, G. Prog. Colloid Sei. 1988, 76, 75.
(40) (41) (42) (43)
Rehage, H.; Hoffmann, H.J. Phys. Chem. 1988, 92, 4712. de Gennes, P.-G. J . Chem. Phys. 1971,55, 572. Cates, M. E. Mueromolecules 1987, 20, 2289. Cates, M. E. J . Phys. (Les Ulis, Fr.) 1988, 49, 1593.
Fluorescence and Phosphorescence Study of AOT/H,O/Alkane Systems in the L2 Reversed Mlcellar Phase R.J6hannsson, M. Almgren,* and J. Alsins The Institute of Physical Chemistry, University of Uppsala, S-751 21 Uppsala, Sweden (Received: May 14, 1990; In Final Form: September 28, 1990)
Time-resolved fluorescenceand phosphorescence quenching measurements were made to determine the structure and dynamical behavior of micelles in oil-continuous microemulsions stabilized by aerosol OT, (AOT). In particular water/AOT/dodecane and water/AOT/isooctane systems were studied. It was found that reversed micelles, or water droplets stabilized by the surfactant, formed clusters in the AOT/alkane/water systems. The average cluster size was determined in the L2phase. The clusters were polydisperse in size whereas the micelles were not. Cluster formation increased with the concentration of micelles and with the chain length of the alkane solvent. It was not possible to determine whether the processes of exchange within a cluster was due to fusion-fission or some other process. Exchange between different clusters, however, seemed to be very slow.
Introduction Aerosol OT is well-known to form reversed micelles or water-in-oil microemulsions. The reversed micelles in the isotropic solution phase, L2, have been studied by dynamic and quasi-elastic light scattering (QELS),'I small-angle neutron scattering (SANS),C6 ~ltracentrifugation,'~J'and static and time-resolved fluorescence quenching e~periments.'J*'~ All these methods show that the micellar size increases with the molar concentration ratio R = ~ a t e r / A O T , ' - ~ *but ~ ~ ~the ' ' increase in size is almost independent of the volume fraction 4 of the dispersed phase (Le., AOT To whom correspondence should be addressed.
0022-3654/91/2095-38 19$02.50/0
+
H2O),I3at least outside the critical region beyond which phase separation into two reversed phases occurs. Different experimental (1) Day, R.; Robinson, B. H. J. Chem. Soe., Faraday Tram. I 1979,75, 132. (2) Zulauf, M.; Eike, H. F. J . Phys. Chem. 1979, 83, 480. (3) Huang, J. S.;Kim, M. W. Phys. Rev. Le??.1982, 47, 1446. (4) Cabos, P. C.; Delord, P. J. Appl. Crystallogr. 1979, 12, 502. (5) Kotlarchyk, M.;Chen, S. H. J . Phys. Chem. 1982, 86, 3273. (6) Robinson, B.;Toprakciogiu, C.; Dore, J. J. Chem. Soc., Faraday Tram. I 1985, 80, 13, 431. (7) Atik, S. S.; Thomas, J. K . J . Am. Chem. Soc. 1981, 103, 3543. (8) Eicke, H. F.;Borkovec, M.; Das-Gupta, B. J. Phys. Chem. 1989, 93. 314.
0 1991 American Chemical Society
3820 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
techniques give different suggestions on what happens in the critical region. Light-scattering methods3 indicate that in the neighborhood of the cloud point, the hydrodynamic radius Rhbegins to increase dramatically from about 100 A to several thousand angstroms. It is also observed that the intensity correlation function is nonexponential near the cloud point. This together with the fact that the scattering intensity obeys the Orstein-ZernikeDebye relation suggests that the microemulsion contains a polydisperse, highly distorted droplet system in the neighborhood of T,.3 Kotlarchyk et al.5 have performed a number of experiments on water/ AOT/alkane systems using a small-angle neutron scattering (SANS) technique. These workers had access to a large Q range for the scattered intensity distribution and performed a polydispersity analysis assuming a spherical water core. Kotlarchyk et al. came to the conclusion that the microemulsion behaves like a collection of polydisperse spheres when it approaches the critical point. These results contradict what is suggested by QELS. They also concluded that the S A N S data give radii that are smaller by a factor of 2 than the QELS hydrodynamic size. Electrical conductivity m e a s ~ r e m e n t s ~in~AOT/water/isooctane *'~ solutions indicate that the increase in conductivity is due to percolation in clusters formed when the solution approaches the phase limits and that the percolation and thereby the cluster formation increase with temperature. To explain the conductivity of the droplets before the percolation threshold, Eicke et a1.* assumed that the droplets could bear a net charge. This idea was scrutinized by Halle? who also concluded that attractive forces between charged and neutral droplets and between oppositely charge droplets may induce the formation of droplet pairs and further aggregation. Lang et al.I3 performed a comprehensive study of the fluorescence deactivation of Ru(bpy),Z+ (bpy = 2,2'-bipyridyl) by K3Fe(CN)6 in several AOT/alkane/water systems. These workers interpreted the results in terms of a steady increase in both micelle size and rate of exchange of the micellar contents on approach of the phase line. The exchange process, assumed to proceed via collision and coalescence of droplets followed by fission into two new droplets as suggested by Robinson et al.,10 became very fast, according to these results; so fast, in fact, that the self-consistency of the model must be questioned. If the droplets fuse on every encounter, as these results suggest, and the contents become mixed before fission occurs, then there must be a polydispersity of droplets present, which was not observed in the measurements. We found it important to resolve this problem and have therefore studied the same system with both more long-lived and more short-lived probes. In the long-time studies, phosphorescence quenching (PQ) of C r ( b ~ y ) was ~ ~ +measured, and for the short time scale (ca. 100 ns) fluorescence quenching (FQ) of 1,4,6,9-pyrenetetrasulfonate(PTSA) was measured. It will be shown that the choice of the probe molecule is very important in these systems, as was pointed out earlier by Verbeeck et al.II This is particularly important when measurements are taken over long time scales. The results from (PQ) studies showed this behavior to be due to clustering and that the clusters were polydisperse in size and were smaller in more diluted solutions.
Theory It has been shown by Infelta et aLm that the fluorescence decay
JBhannsson et al.
I
0.2c
0
2 0
2
4
time
6
E
10
(microseconds)
Figure 1. Schematic graph of decay curves of phosphorcsccnce decay in a cluster system with and without quencher.
curves from fluorescence quenching experiments in a micelle system are of the form F(t) = A , exp(-A,r + A3(exp(-A4t) - 1)) (1) were F(t) is the fluorescence intensity at time t and Ai are constants that depend on the system. If no migration of quencher molecules occurs*I between micelles, the Infelta equation (1) becomes In ( F ( t ) / F ( O ) )= - t / ~+ ~n(exp(-k,t) - 1)
(2)
where F(0)is the fluorescence intensity at t = 0, n is the average number of quenchers in the micelle, kq is the first-order quenching constant in the micelle, and T~ is the lifetime of the probe with no quencher molecules present. If clusters occur in the reversed micelle systems, then it is likely that the observed decay kinetics will be similar to that observed for quenching in normal micelles. The quenching process within a cluster depends upon the time taken for an excited probe and a quencher to encounter in the same droplet after a random transfer from droplet to droplet. The detailed kinetics of the process depends on both the size of the cluster and its connectivity. If it is assumed that the migration of a probe and a quencher between the micelles in a cluster can be approximated by a first-order rate constant, k, (which can be looked upon as the average of the number of jumps required for an encounter multiplied by the jump frequency), then the equation for the decay kinetics in a reversed micellar system can be expressed as In ( F ( t ) / F ( O ) ) = + / T o n(exp(-kqt) - 1) + (n, - n)(exp(-k,t) - 1) (3)
+
where n, is the average number of quenchers in a cluster and k, is the first-order quenching constant in the cluster. Since k, is about 100 times larger than k (vide infra) and the solution contains sufficiently small micaes, eq 3 can be simplified, for long times (subscript It), to In ( F ( t ) / F ( O ) ) , , - f / Q - n + (n, - n)(exp(-k,t) - 1) (4) since lim exp(-k,t) = 0 1-m
(9) Halle, B. Prog. Colloid Polym. Sci. 1990. 82, 21 1. (10) Howe, A. H.; McDonald, J. A.; Robinson, B. H. J . Chem. Soc., Faraday Trans. I 1987,83, 1007. (11) Verbeeck, A.; De Schryver, F. C. Lungmuir 1987, 3, 494. (12) Ganz, A. M.; Boegcr, B. E. J . Colloid Interface Sci. 1985, 109, 504. (13) Lang, J.; Jada, A.; Malliaris, A. J . Phys. Chem. 1988, 92, 1946. (14) Eicke. H. F.; Rehak, J. Hefu. Chim. Acra 1976, 59, 2883. (15) Eickc, H. F.; Hilfiker. R. Chem. Phys. Left. 1985, 120, 272. (16) Eicke. H. F.;Geiger, S.; Sauer, F. A.; Tomas, H. Eer. Eensen-Ges. Phys. Chem. 1986,90, 872. (17) Streyler, D.C.; Tack, R. D. J . Chem. Soc., Faraday Trans. I 1979, 75, 481. (18) Baker, B. R.; Mehta, B. D. Inorg. Chem. 1965, 4, 848. (19) Maestri, M.; Bolletta, F.; Moggi, L.; Balzani, V.; Henry, M. S.; Hoffman, M. Z. J . Am. Chem. Soc. 1978, 100, 2694,
The average number of quenchers per micelle, n, can thus be determined from the drop in initial intensity when compared to an unquenched curve. When the intracluster quenching reaction has decayed, k,t >> 1, eq 4 becomes In ( F ( O ) / F . ~ O ) )=I ~- t / T O - n,
(5)
F(0)is the luminescence intensity at time zero, and Fm(0)is the intensity from clusters containing no quencher molecules, at t = (20) Infelta, P. P.; Gritzel, M.; Thomas, J. K. J . Phys. Chem. 1974, 78, 190. (21) Infelta, P. P. Chem. Phys. Lerr. 1979, 61, 88.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3821
AOT/H20/Alkane Systems
0, and is determined by extrapolating the exponential part of the decay at long times back to t = 0. From this drop in intensity, n,the average number of quenchers per cluster, and n, the average number of quenchers per micelle, can be determined and distinguished since the difference in the rate constants is large. Any of difference between the slope of In (F,(t)) and the luminescence decay of the system in which the quencher is absent provides evidence for exchange of quencher molecules between clusters or between the clusters and the surrounding solution. Figure 1 shows a decay curve that corresponds to eq 4 and an unquenched decay. The quenched curve starts with an initial drop due to the intramicellar quenching and gives the average number of quenchers per micelle, n. Next comes quenching within the clusters (I) with corresponding decay constant k and the curve ends with an exponential tail, the straight line%, which is parallel to the unquenched curve, with intensity difference n,. At short times or on the fluorescence time scale, eq 3 can be approximated by an expression of the same form as that given in eq 1. At sufficiently short times, the intermicellar decay exponent exp(-k,t) can be approximated as 1 - k,t (the first two terms in the series expansion of the exponential function). Equation 3 then becomes
In (F(t)/F(0))s, -( 1/q,+ (n, - n)k,)t
+ n(exp(-k,t)
- 1) (6)
The subscript st stands for short-time approximation. From a fit of the fluorescence quenching decay curves to this equation n, k,, and n,&, can be determined. Polydispersity Effects Several earlier studies"J3 as well as our own FQ results indicate that the micelles have a rather narrow size distribution. It is very likely, however, that there is a distribution of cluster sizes. The theory of effects of polydispersity for micelles was worked out by Almgren and LBfroth22and was further developed by Warr and Grieser.2 The Q-average aggregation number, ( N ) @for micelles has the form
( N ) Q ( N ) w - f/zcw2r]+ ' / 6 K 3 v 2
(7)
where ( N ) , is the weight-average aggregation number: lim (N)Q= ( N ) , IrO
and c2 is the variance or width of the distribution, r] is the ratio between quencher and surfactant, [Q]/[S], and K~ is the third cumulant, which gives the skewness or asymmetry of the distribution. This theory may be extended to the case of clusters. The Q-average number of micelles in clusters is given by
(Nc)Q (Nc)w - !!2'JCw2Na,r]+ k3Nagtq2
(8)
where ( N , ) , is the weight-average number of micelles in a cluster, N,, is the aggregation number of the micelles, and ecw2and K , ~ are the variance and the third cumulant of the weight distribution of clusters. Experimental Section The probes sodium 1,4,6,9-pyrenetetrasulfonate (PTSA, Eastman) and ruthenium bipyridyl ( R ~ ( b p y ) , ~ +G., Fredrick Smith Chemical Co.) were used as supplied, the phosphorescence probe [Cr(bpy)3](C104)3was synthesized by the method of Baker and Mehta.l* The photophysics of C r ( b ~ y ) ~is ~well + described by Maestri et a1.I9 The quenchers KI (Merck, analytical grade) and K3Fe(CN)6 (Merck analytical grade) were used as supplied. The surfactant aerosol OT, obtained from Sigma, and the solvents isooctane (Merck analytical grade) and dodecane (Merck synthesis grade) were used as supplied. (22) Almgren, M.; Lafroth. J.-E. J. Chem. Phys. 1982. 76, 2737. (23) Warr. G. G.; Grieser, F. J. Chem. Soc., Faraday Trans. 1 1986,82, 1813.
\
\
2t
80
90
dodecane
Figure 2. Phase diagram (plotted to scale as volume fraction) for the H20/AOT/dodecanesystem at 25 O C ; cp is the critical point. Reprinted from ref 10 with permission from the Royal Society of Chemistry. The solutions examined are marked with points in the phase diagram.
Most of the experiments were performed in solutions where the molar concentration ratio R = [H,O]/[AOT] was 8.3. C, the molar concentration of AOT, was 0.194 mM, which corresponds to 3% water in a 0.2 mM AOT/alkane solution. The dispersed phase was studied in both dodecane and isooctane. The quencher concentration was varied from 0.2 to 3.0 mM of total solution. In all measurements the concentration of probe was between 1 X and 7 X lov5M. Phosphorescence was studied by using an XeF excimer laser (Lambda Physik EMG-100) to excite the probe, (Cr(bpy)?+), in air-equilibrated solution, to the triplet state, in a 1-cm fluorescence cell. The phosphorescence signal was collected as close to the cuvette as possible with a 5-mm light guide (Oriel Corp.) provided with Schott filters WG 360 (2 mm) to reduce scattered laser light (351 nm) and RG 5 (2 mm) to isolate the phosphorescence emission. The detector was a Hamamatsu R 928 photomultiplier with a reduced number of active dynodes. The signals were captured with a Tektronics 7912 digitizer, provided with 7B90P time base. System control and signal processing were performed with a AT-compatible computer. Fluorescence decays were determined by using a picosecond single-photon-counting apparatus, using a mode-locked Nd:YAG laser (Spectra Physics, Model 3800) to synchronously pump a cavity-dumped dye laser (Spectra Physics Model 375) as an excitation source. The set up has been described earlier by Almgren et al.24 Results and Discussion The phase diagram for the water/AOT/dodecane system is shown in Figure 2. The boundary between the L2 phase and the 2L2 two-phase area is shown as well as the compositions used in the experiment. If water is added to a solution, the composition is brought closer to the water corner of the triangle. When the dispersed phase (the reversed micelles) is diluted with the solvent (dodecane in this case), the composition is brought toward the dodecane corner. Phosphorescence Measurements. Figure 3 shows the timeresolved phosphorescence decay of Cr(bpy)?+ for a variety of KI (quencher) concentrations. In general there is an initial drop in fluorescence intensity, as quencher is added to the system, due to intramicellar quenching (shown as I in Figure 1). At long times the decay exhibits an exponential character (shown as I1 in Figure 1). There is some difference between the slope of the curve without quencher and the curves at long time (II), and the slopes of I1 appears to be independent of quencher concentration. The decay rate I after the initial drop also depends on the concentration of quencher. If In F,(t,) or the initial intensity for [Q] value is subtracted from In F,(O), the initial intensity of the unquenched (24) Almgren, M.; Alsins, J.; van Stam, J.; Mukhtar, E. Prog. Colloid Polym. Sei. 1988, 76, 68.
Jdhannsson et al.
3822 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
4 t
0
I
2
6
4
E
10
12
time (microseconds)
time (microseconds)
Figure 3. Phcephorcscencedecay of Cr(bpy);+ in the presence of a range of concentrationsof quencher KI in microemulsion of R = 8.3 and C = 0.194 M in dodecane (3% H 2 0 in 0.2 M AOT in dodecane). Solid line, no quencher; dashed line, KI = 0.2 mM; dotted line, KI = 1.0 mM; dashed/dotted line, KI = 2.0 mM.
Figure 4. Effect of dilution of micelles on phosphorescence decay of Cr(bpy)t+ in the presence of a range of concentration of quencher KI in microemulsion in dodecane, with constant R = 8.3. Solid line, no quencher; dashed line, C = 0.194 M, KI = 2.0 mM; dotted line, C = 0.097 M, KI = 1.0 mM.
TABLE I: Aggregation Number, N for Micelles, Number of M i c e k in Cluster, (Nc),,, and the %e Constant for Intermicellar Quenching, k Obtained for Micelles in Dodeune (C = 0.197 M, R = 8.3 and in $armtheses C = 0.1 M, R = 8.3) and for Isooctane (C = 0.197 M, R = 8.3) witb Phosphorescence and Fluorescence Quenching Metbods (NJw 10"k,, s-I method NIsr PQ (n-ciz) 80 5 8.38 (87 f 5 ) (5.65) PQ (iso-Cs) 70 5 2.55 FQ (n-Ci2) 92A 3 2.5
*
I ,
0
TABLE II: Intermicellar E x c h g e Rate Constant, k , for Various Values of QuMeher Coocentratioas, in Dodecane and Isooctane
quencher concn, mM
dcdecane (0.2 M)
0.1
IOdk,, s-I dodecane (0.1 M)
isooctane (0.2 M)
0.83
0.2 0.5
0.78
1 .O
1.5
2.0 3.0
2.1
1.6 2.3
3.2 3.2 3.1
curve, the average number, n, of quenchers in a micelle is obtained, and N, can be calculated. The number of micelles per cluster, n,,can deduced in a manner similar to that for n in the ordinary nonexchange Infelta equation since eq 5 is valid. Nonlinear fittings were performed on these curves, and the results for N , , the aggregation number, and the weight average num%er of micelles in a cluster as obtained by using the first two terms in eq 8 (see Figure 8), are presented in Table I, together with Nass and k, from FQ measurements. The values for k , for various values of quenchers are presented in Table 11. Figure 4 shows the effect of dilution. The solution was diluted to half the concentration with dodecane, which is supposed'^'' not to affect the size of the micelles but only increase the distance between them. It is observed that the decay curves for different solvents have similar initial values, which confirms that the size is hardly dependent on the concentration of the dispersed phase. It is also noted that the n, value is much smaller in the dilute solution, indicating smaller clusters. In Figure 5 the effect of solvent is presented. The size of the clusters is strongly dependent on the properties of the solvent but not the size of the micelles. Curves for the same composition and quencher concentration give the same initial value but much smaller n, drop in isooctane than in dodecane. This means that the cluster size depends on the chain length of the solvent. A small difference is also observed in the aggregation number, N,=, of the micelles when curves are fitted. The micelles in dodecane are found to have N,= = 85 f 10 as compared to Nsee = 70 f 10 in isooctane.
,
,
'
l
2
I
.
.
I
4
,
,
,
I
.
6
1
1
1
,
,
8
.
1
,
10
,
,
12
time (microseconds)
Figure 5. Solvent effect on the phosphorescence decay of Cr(b~y),~+ in the presence of a range of concentration of quencher KI in a microemulsion of R = 8.3 and C = 0.194 M in dodecane and in isooctane. Solid line, no quencher; dashed line dcdecane; dotted line, isooctane. The quencher concentration is 2.0 mM in both cases. 1
2
1
time (nanoseconds)
Figure 6. Fluorescence decay of PTSA in presence of a range of quencher concentration in microemulsion of R = 8.3 and C = 0.194M in dodecane. Solid line, no quencher; dashed line, KI = 1.5 mM; dotted line KI = 3.0 mM.
Fluorescence Measurement. To check the Nagsobtained from phosphorescencequenching measurements, fluorescence quenching measurements were performed, using Ru(bpy)32+and PTSA as probes. The results of FQ in AOT/dodecane/water, presented in Figure 6, show the quenching of FTSA with KI. The intramicellar decay is well resolved, and the decay can be expressed by eq 6. The intramicellar process proves to be very quick, with kq = 2.5 X 108 s-' which agrees with the values obtained by Verbeeck et al.*l The aggregation number, Nw, was obtained as 92 f 3, in reasonable agreement with what was found in the phosphoresce quenching measurements. The value for k, can be estimated from (n,- n)kq assuming cluster size 8.3 to 2.3 X lo6 s-I, also in agreement with what was found in PQ measurements. It is interesting to
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3823
AOT/H20/Alkane Systems
a
centration of the clusters decreases. The cluster size and polydispersity is much less in isooctane, only 2.6 micelles/cluster, without observable polydispersity. Table I1 shows estimated values of k , versus the quencher concentration in droplets in dodecane as measured with the PQ technique. The simplest form of mechanism for the exchange between the micelles in a cluster assumes a first-order process for the droplet exchange. If we denote the exchange rate of a quencher or excited probe between any two micelles in a cluster k,,, then kq from exchange quenching can be expressed as k, = k,,/(N, - 1) (9)
0 5
time (microseconds)
Figwe 7. Fluorescence decay of Ru(bpy),*+in the presence of quencher (Fe(CN)61-]. Upper line, no quencher; lower line, with [Fe(CN)63-]= 2.5 mM. a-
I
I
L
0
0.m5
0.01
0.015
[QI/[Sl
Figure 8. Q-averaged number of micelles in cluster versus the quencher/surfactant ratio. Top line, dodccane, R = 8.3, C = 0.194; middle line, dodecane, R = 8.3, C = 0.097; bottom line, isooctane, R = 8.3, C = 0.194.
observe that the aggregation number is a slightly larger in dodecane than in isooctane. FQ measurements were also performed with Ru(bpy)?+, which has a fluorescence lifetime of 266 ns in the micelles. The results are presented in Figure 7. This graph shows the importance of choosing the correct time scale for the decay of the probe. The curve is hard to analyze since the intramicellar process is over after the first few channels, whereas the intracluster process occurs on a time scale comparable to the lifetime of the excited state, which results in deviation from an exponential decay. The measurements are very time consuming in the single-photoncounting method since the count rate is low. The use of this probe to study the short-time deactivation would not be practical, since there would be too few counts per second and channel if the time resolution were chosen as in the experiment in Figure 7. Fits made on the curves from R ~ ( b p y ) , ~measurements * did not give satisfactory results. The apparent cluster sizes obtained from phosphorescence quenching measurements at different quencher concentrations were analyzed by the polydispersity theory as presented in eq 8. The plot in Figure 8 shows the Q-averaged number of micelles in a cluster vs the [Q]/[S] ratio. Straight lines were drawn though the data points and from those lines ( N J Wand u, were estimated. The results show that in the case of dodecane at C = 0.2 M, the weight-average number of micelles in a cluster, (NC),, is 8.4 and cr, is 4.6. When the solution is diluted with dodecane to C = 0.1 M, ( N J Wreduces to 5.6 micelles/cluster and ucwto 3.9. That means that both the size and polydispersity decrease as the con-
where ( N , - l)-' is the probability that the probe and quencher will be in the same micelle after the exchange, given that they started in different micelles. This should result in a decrease in k , with cluster size, which is also observed. It is further found that the apparent value of k , varies with the quencher concentration. The reason is as follows: With polydisperse clusters, the excitation will predominantly select large clusters, because the probes are most likely to be found in those. The quenching will also occur predominantly in the large clusters when the quencher concentration is low and will therefore give small values of k,. At high quencher concentration, it is highly probable that if quenching does not occur directly, intramicellar, it will occur after the first transfer to another micelle. The large clusters are not singled out under these circumstances, and the k, will become high, approaching, the exchange-rate constant. The values of k for dodecane as solvent represented in Table I1 can be extrapolat4 in a plot vs [Q]-' to a value close to 3 X lo6 s-' for infinite concentration, in agreement with values estimated in isooctane. Linear extrapolates to [Q] = 0 in a plot vs [Q] yields limiting values for k which can be combined with the corresponding estimates of "PIC-,), to give k, = (3-5) X 106 s-' from eq 9, which, again is consistent with these results.
Conclusions From the present study we can conclude the following: The rapid exchange observed by Lang et al.I3 was probably mainly an exchange between micelles within a cluster and should rather be stated in terms of a first-order rate constant. Large clusters form in dodecane already rather far from critical point. In isooctane, the results indicate the presence of small clusters or maybe only pairs of micelles. It seems probable that this aggregation is a result of electrostatic interactions between droplets with net charge (either droplets with opposite charge, or one charged and the other polarized) as suggested by Halle.g The micelle size is constant at constant R; a small change between dodecane and isooctane was observed; the cluster size depends on both solvent and droplet concentration. Concerning the methods, it can be concluded that phosphorescence quenching is a good method to characterize reversed micellar systems along with the fluorescence quenching method. It is emphasized that it can be essential to examine longer time scales to fully analyze the behavior of the system, and in particular that the choice of probe is crucial for the successful use of these methods. For good resolution of the intramicellar quenching process a relatively short-lived probe is favorable. PTSA was very well suited, and the measurements were easy to perform on the time correlated single-photon-counting instruments. In the phosphorescence quenching measurements Cr(bpy)?+ is a good probe for measuring uslow" processes in water and in other polar solvents. Acknowledgment. We are grateful to Robert Urquhart for discussions and correcting the English of the text. This work was supported by the Swedish Natural Science Research Council.
