J. Phys. Chem. 1993,97, 8590-8594
8590
Polydispersity of AOT Droplets Measured by Time-Resolved Fluorescence Quenching Mats Almgren' and Ragnar J 6 h a ~ s s o n Department of Physical Chemistry, University of Uppsala, S - 751 21 Uppsala, Sweden
Jan Christer Eriksson Department of Physical Chemistry, Royal Institute of Tecnology, S-10044 Stockholm, Sweden Received: May 18, 1993
The size and polydispersity of AOT water/oil microemulsions were measured by time-resolved fluorescence quenching. From the measured volume polydispersity the radius polydispersity was derived and calculated. An average polydispersity of 15.7% was obtained. No trends in polydispersity values at different droplet sizes or different solvent chain lengths were observed. The polydispersity values obtained are compared with values obtained by a new approach to theoretically estimate the polydispersity, and approximate values for the interfacial tension, y.., of the planar oillwater interface and the interfacial bending constant, K,were computed.
Introduction Microemulsions in the L2 phase of the AOT-oil-water system have been studied for years with numerous experimental techniques.'-lO In contrast to many microemulsions based on nonionic surfactants, or tertiary systems with alcohols as cosurfactants, the bicontinuousstates are not dominant; instead, closed water droplets persist over wide temperature and compositions ranges. Concerning the size of the droplets good consensus is at hand. Various experimental methods indicate that the size is determined by the water/surfactant molar ratio w (at surfactant and water concentrations large enough to make the fraction of molecularly dissolved water and surfactant molecules negligible), as if the surfactant molecules are present only at the water41 interface, always occupying the same area at the interface. As discussed by Bridge et al." and Howe et al.,7 there seem to be a certain size dependence, so that in small droplets (radius less than about 25 A) the packing at the headgroups (surface area -40 A2) determines the size, whereas for largedroplets thecrosssectional area in the tail region, about 65 A2, 7 8, from the headgroups, is the size-determining factor. High temperature and long-chain solvent molecules promote attractive interactions between the droplets, giving rise to a type of cloud point or haze point where two microemulsions phases are in equilibrium. Clustering of the droplets occurs upon approach to the phase separation conditions. High temperature and high droplet concentration lead to a percolative behavior of the electrical conductivity and eventually to formation of bicontinuous structures. Several other aspects of the L2 phase are more controversial, however. It has, for instance, been suggested that small "dry" reversed micelles coexist with the larger water droplets in the microemulsion.'*J3 Further obscure points are the mechanisms of electric conduction below, at, and above the percolation threshold, the importance of nonspherical shapes, and the magnitudes and rates of the size and shape fluctuations. The present contribution is concerned with size polydispersities, determined by a fluorescence quenching method. Analysis of SANS data has previously suggested that the relative radius polydispersity, u , / ( r ) , might be rather large, 0.25-0.35.1418 Recently, an interesting study by RiEka et a1.19 gave values of the polydispersity ranging between 0.10 and 0.14, based on two independent methods. Since the fluorescencequenchingmethod, as explained in detail below, measures the polydispersity of the To whom correspondence should be. addressed.
number of water molecules per droplet (i.e., volume polydispersity), it should easily discriminate between radius polydispersities of 0.14 and 0.25. Most theoretical treatments of microemulsions, leading to estimates of droplet size and polydispersities, have focused mainly on the curvature free energies of the interface.20-23 A few treatments have gone beyond that, including other free energies from surface thermodynamics, utilizing the efficient framework of classical chemical equilibrium for the description of the formation of surfactant-water aggregates.z4Z7 The differences between these various treatments have been discussed by Borkovec.** In the discussion of our results we have used a new expression for the polydispersity, based on a multiple chemical equilibrium approach for droplet microem~lsions.~5
Theory The determination of aggregation numbers from fluorescence quenching measurementsis based on the Infelta-Tachiya equation for quenching in monodispersed micelles,with nonmigrating probe and quenchers29-30
where 7 is the natural decay time of the probe, n is the average quencher per micelle and k, is the first-order rate constant for the quenching inside a micelle. From n the aggregation number, s can be evaluated
were the subscript mic stands for the concentration of surfactant, [SI,or quencher, [Q], in the micelles. The limitations and requirements of the method have been discussed in several recent reviews.31-34 The extension of the method to polydispersemicelle~35.~6 requires that the experimental decay curves develop an exponential tail with the decay constant 1/70, characteristic of the unquenched probe. Each subset of droplets with aggregation numbers s is assumed to have quenchers distributed according to the Poisson distribution, with the average number n, per micelle proportional to s.
(3) The number of droplets with aggregation number s, is M(s),
0022-365419312097-8590$04.00/0 0 1993 American Chemical Society
Polydispersity of AOT Droplets
The Journal of Physical Chemistry, Vol. 97, No. 33, 1993 8591
and that with x quenchers is
the I' distribution, for which a simple recursive formula for the moments is available
P(x,sq) is the probability of finding x quenchers in a droplet with averagequencher concentrationsg. For each sets, the decay will be given by eq 1, and the total decay is obtained by contributions from all droplets, assuming that the probability of finding an excited probe in a droplet of certain size is proportional to s.
(j"+') = (1 + w )(j")(r) (1 1) where y is the relative variance, and the relative radius polydispersity is then uJ(r) = fi.Insertion in eq 10 gives
To a good approximation for small y
F(tl
cq
This equation is too complex to be useful for direct fitting, but if a well-developed final exponentialportion with decay constant equal to that of the unquenched probe is obtained, the amplitude of the final decay can be determined and used to calculate the effective, q-average, aggregation number
.
2
sM(s)
S=Z
= 9 7 - 1077'
+ ...
(13)
Experimental Section Materials. The probe sodium 1,4,6,9-pyrenetetrasulfonate (PTSA, Eastman), the quencher KI (Merck, analytical grade), the surfactant Aerosol OT (Sigma), and the solvents octane (Merck analytical grade) and dodecane (Merck synthesis grade) were used as supplied. Methods. Fluorescencedecays were determined in 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 setup has been described earlier.37 The measurements were performed in air-saturated solutions at 25 OC.
Results and Discussion where F,(O) is the amplitude of the exponentialtail. Expansion of the exponential in eq 6 y i e l d ~ ~ ~ 9 ~ 6
(7) where (s), is the weight-average aggregation number, uW2the variance of the weight distribution, and ~3 the third cumulant of the distribution. The dependence of the apparent aggregation number on concentration can thus give information on both the width and the skewness of the droplet size distribution. The polydispersity measure obtained from the fluorescence quenching measurements has to be considered. The treatment of Warr and Grieser36 shows that the following moments, ,s of the number distribution are involved c q = z = - - - 2 is),
I
s2
where eq is a measure of the relative polydispersity. The method is based on three important assumptions: (i) The probability of finding an excited probe in a micelle with aggregation number s is proportionalto sf($),wherefls) is the frequency of occurrence of micelles of size s. (ii) The distribution of quenchers over the photoselected micelles is the same as over all micelles. (iii) The quenchersare distributed according to a Poisson distribution over micelles of each size class, with the mean number of quenchers per micelle proportional to s. In the present case, these assumptions are assumed valid with s taken as the number of water molecules in the reversed micelles, proportional to the volume of the aqueous core. In order to relate eq from eq 8 to the radius polydispersity, we use s 0: V a r3 and the relation between volume and radius distributions
f(V) dV=f(r)4a? d r
(9)
Thus e,+
1=
(rll)
(10)
(r8)2 To procecd, we follow the procedure of Ri6ka et al.19 and utilize
Before discussing these results theoretically, the error sources in the measurementsand the interpretation should be considered. Firstly, it is often observed that high apparent aggregation numbers are obtained at the lowest quencher concentration, as illustrated by the deviating value at the highest w in Figure 2. This is probably due to the fact that uncertainties in the measurements are largest under these conditions. The effect of the quencher is small, and the influenceof quenching impurities will be most important under these conditions. The effect of deviations from the assumed random distribution of probes and quenchers over the micelles would be expected to be most severe for small micelles and for high quencher concentrations. In the present case, employing a probe of charge -4 and a quencher of charge -1 at rather low concentration, the deviations would derive mainly from a tendency of the quencher to avoid micelles containing a probe. Note, however, that even in the smallest droplest studied here, about 35 sodium ions are present as counterions to the surfactant. This corresponds to a concentration of about 1 M in the aqueous core, and even if only a fraction of these ions are "free", the electrostatic interaction between probe and quencher must be rather well shielded. It is not possible to conclude how the error in the estimate would depend on the quencher concentration. The problem is further complicated if also the repulsion between the quencher ions becomes important. Bales and Stenland3*have shown that if a repulsion between the quenchers is assumed, the result will be a narrowing of the quencher distribution and a reduced number of micelles without quencher, i.e., an effect of opposite direction of that from probequencher repulsion. Our only firm conclusion at this stage, however, is that the effects from nonrandomness in the probe and quencher distributions would be seen most clearly for the smallest droplets and would tend to give too small estimates of the weight-average micelle size. In our work, measurements were performed on AOT droplets in dodecane with water-to-surfactant molar ratios, w = 12.3,8.4, and 4.9. The droplet weight ratio c, = (w s ) / ( w + s + 0 ) was 0.3, 0.15, and 0.084, respectively. For the microemulsion in dodecane with w = 12.4 the system is beyond the percolation limit as shown from conductivitymeasurements by Sager et al.39
+
Almgren et al.
8592 The Journal of Physical Chemistry, Vol. 97, No. 33, 1993 250 -3.0
A
'
>
I
'
1 5 x 1 0"
3 . 0 ~ O1 8
4,5x10-'
6 . O ~ 1 0 . ~7 . 5 ~ 1 0 "
c
150
A
50
E
01' 0
time (sec) Figure 1. Decay of fluroescence of PTSA quenched by I- in droplets in dodecane at y = 12.3. In the graph a fit to the Infelta model (q1) is shown as well, and the residuals from the fit are given in the graph on top. 250
4
k
'
'
'
I
'
'
'
'
'
I
'
1.o
.5
'
'
I
'
1.5
'
" 2.0
Figure 3. Same as in Figure 2,but solvent is Octane instead: circles, y = 12.3;boxes, y = 8.4.
TABLE I: Polydispersity of Reversed Micelles Obtained by Fluorescence Quenchinga ~
'
I
I
I
'
I
'
8
1
1
7
1
12.3 8.4 4.9 12.3* 8.4*
0
205 105 35 21 1 112
0.47 0.43 0.74 0.40 0.54
0.156 0.150 0.280 0.136 0.187
26.2 18.4 10.7 26.5 18.9
42 41 41 42 40
w is the molar water to surfactant ratio, (s), is the weight-average aggregation number, a,/ (s) is the weight-aggregation polydispersity, and u r / ~is the polydispersity of the droplet radius. The surface area u in is indicated in the last column. Droplets in Octane are indicated by *, Otherwise the droplets are in dodecane. @
100
1
1
1
c
0
4
.5
1 .o
1.5
2.0
q-averagedaggregationnumber (s),asa functionoftheaverage numberofquencherpermicellc [Q]/[S] X ( s ) ~ :circles, y = 12.3;boxes, y 5 8.4; triangles, y = 4.9. Solvent was dodecane in all cases.
-2.
and also studied by quenching of phosphorescencea In the other cases the solutions are below the percolation limit where the interactions between droplets is expected to be weaker. Verbeecket a1.9have studied thelimitations of the luminescence quenching method. They concluded that the probe PTSA quenched by I- is a good pair to determine the aggregation number of AOT micelles and can be used at water/AOT molar ratios up to 20. At higher ratios the micelle becomes too big for the quencher to explore the full volume during the short lifetime of PTSA, and the decays will not show a sufficiently well-developed exponential tail necessary to determine 7s in eq 6. It should also be noted that thevery short fluorescencelifetime of PTSA makes the time window of the measurements less than 100 ns. During this short time migration of quenchers and probes between the micelles can be neglected. Our measurements were made at molar water-AOT ratios below 15. In Figure 1 an example of experimental results with a fit to eq 1 is shown. In Figure 2 the q-average aggregtion number is plotted as a function of [Q]/[S]X (s), the quencher to droplet ratio, at three different w values for droplets dissolved in dodecane. The results obtained for droplets in octane are presented in Figure 3. As eq 7 shows, extrapolation to [Q]= 0 gives the weightaverage aggregation number, (s),, and from the slope uwzcan
be evaluated. The resulting values for aggregation number and u,/r from eq 13 are presented in Table I, together with values for the surface area. Note first that the area per surfactant at the interface of the water core is constant and apparently determined by the effective headgroup area. There is no indication that the estimate of the smallest droplet size should be in error due to a nonrandom distribution of probes and quenchers. With the exception for the smallest droplets, there is no trend in the polydispersity values. Both solvents give similar polydispersity (and radii), and there is no change with the size and concentration of droplets, not even for the system with the largest droplets in dodecane, which represents a system above the percolation limit. The exceptionally high polydispersity value obtained for the smallest droplets may be in error. As discussed above, the uncertainty of the method is largest in that case. Neglecting this value, the average polydispersity is 15.7%,which is rather close to the results obtained by RiEka et u1.,l9using hexane as solvent. A new theoretical estimate of the size polydispersity in microemulsion droplet systems has quite recently been made by Eriksson and Ljunggren,46 on the basis of a size distribution function derived earlier for the droplets in Winsor I1 w/o microemulsions,z~viz.,
Here 4 stands for the volume fraction, CFis a fluctuation-related constant, and y is the curvature-dependent interfacial tension that is supposed to vary with the droplet radius r in accordance with the quadratic expansion Y = Y..
+ k l / r + k2/?
(15)
where 7..denotes the interfacial tension of the coexisting planar,
Polydispersity of AOT Droplets
The Journal of Physical Chemistry, Vol. 97,No. 33, 1993 8593
TABLE Ik Calculations of the Relative Polydispersity, UJP, and of the Ratio C = y,r */keTBased on the Measurements Made by Aveyard et d.49 ?or AOT/Heptane/NaCI, Winsor II Svstems 0.0178 0.0316 0.0562 0.0708 0.0794
176 132 114 95 89
0.865 0.865 0.893 0.881 0.879
0.152 0.153 0.138 0.145 0.146 mean 0.147
1.00 1.00 1.42 1.20 1.18 mean 1.16
surfactant loaded oil/water interface, and the constants kl and k2 relate to bending of the interface at constantchemical potentials. The radius of the equilibrium droplet (for which the pressure drop across the interface is zero), rep. = -k1/2~-, is obtained by minimizing yr2. Furthermore, by directly comparing with the ordinary Helfrich expression, it is readily established that the two constants kl and kz are related to the bending constants K and k through the relation kl = -4K/rs and k2 = 2K k.25 The treatment due to Eriksson and LjunggrenM implies that the relative standard deviation of the droplet size distribution in a Winsor I1 system (w/o microemulsion with excess water phase) which is composed of three main components (water, oil, surfactant) is determined by the equations
the data collected by Aveyard et al. for Winsor I1 microemulsion systems with considerablylarger droplets, after converting these later data to relative widths as described above. Furthermore, Eriksson and Ljunggren have also considered the question as to how u / i might change when diminishing the water content and moving away from the two-phase line in the phase diagram into the one-phase microemulsion region. The size distribution will then tend to get somewhat more narrow, but at the same time the peak is shifted toward smaller radii. The net effect anticipated in this way of reducing the water content on the relative width of a microemulsion droplet size distribution is practically nil. In this context it is worth noting that the treatment of Eriksson and LjunggrenMshowsthat G y,r$/kTalwayscanbeobtained from ur/Fdata by employingthe followingexpression which results from combining eqs 16 and 17
+
This expression holds exactly for the Winsor I1 case, and in addition, it constitutes a good approximation also for one-phase microemulsions. In the Winsor I1 case the droplet size fluctuations occur in a parabolic free energy well, e(r), which is given by the expression
e(r) = 47r(y,A?
+ kZ- y,rq2)
(21) where Ar = r - rw Consequently, as a first approximation, the standard deviation of the size distribution can be estimated from ur =
where the parameter B denotes the ratio rq/i, f being the average value of the droplet radius or, more precisely, the radius where the distribution peak has its maximum. Normally, 8 is somewhat less than 1 for Winsor I1 microemulsions. In general, it may be a fairly good approximation to assume that y,rcs2 equals kBT (cf refs 47,48). Insofar as this condition actually is fulfilled, we can derive from eqs 16 and 17 that half of the relative width is simply given by numerical expression
which is in excellent agreement with our experimental results. Thus, for the AOT microemulsions that we have investigated it kBT. seems to hold that on the average y,re,2 Moreover, eqs 16 and 17 enable us to make an interesting comparison with the y , / i data recorded by Aveyard et (cf ref 44, p 421) for AOT Winsor I1 microemulsions. For this purpose we may rather write eq 17 as follows
Hence, by inserting the value for the interfacial tension y m measured for the surfactant-loaded oillwater interface and the associated average droplet size i, we can actually compute 8 = r q / i by means of eq 19, and then from eq 16 obtain u r / i . Upon employing this scheme and the data for water-AOT-heptane Winsor I1 microemulsions at 25 OC at different salinities from Aveyard et a1.,49 the results reported in Table I1 were obtained, with u r / i ranging between 0.138 and 0.153 for droplet sizes between?= 89and 176Awithameanof0.147. (Thesedroplets are too large for an experimental determination of the polydispersity by the fluorosecence quenching method, using PTSA as probe.) The corresponding average value of G = y,r,*/kBT was found to be 1.16. Our data on the polydispersityofcomparatively small AOT w/o microemulsion systems then closely agree with
and the corresponding relative standard deviation becomes
It is worth noting that no curvature-relatedconstants are involved in eq 22; in other words, ur is determined solely by the interfacial tension ymof the coexisting planar interface. However, there are some additional (negative) contributions to ur and ur/F of lesser (but yet important) magnitude which are due to the shape and surfactant packing density fluctuations and which are also accounted for by eqs 16 and 17. The major (formal) reasons why u,/F is found to be about 0.1 5 for many (- ternary) w/o microemulsion seem to be that the value of G = y-rss2/kBT as a rule is fairly close to unity and that u r / i depends rather weakly on G in this range, as readily verified by making use of eq 21. When viewed toward this background, the polydispersity ur/F = 0.12 f 0.02 derived by RiEa et a l l 9for water-AOT-hexane microemulsions appears to be somewhat on the low side since according to eq 20 it would yield G = 2.1. As a rather crude (order-of-magnitude)estimate of the overall volume fraction of droplets in a one-phasemicroemulsion, Eriksson and LjunggrenMhave derived the expression
where M is defined by
M = k,/k,T - G
(25) and where the fluctuation-related constant CF has the approximativevalue6.6 X 1036J md for a ternary microemulsion. Hence, by making use of the data recorded for &, i, and u r / i , it has been feasible for us (i) to qualify the corresponding values of G from eq 20 and (ii) to estimate k2 by means of applying eqs 24 and 25 with a computational precision of about *O.lkBT units. Furthermore, although it is excluded to make a complete
8594 The Journal of Physical Chemistry, Vol. 97, No. 33, 1993
TABLE III: Estimated Values of 7.. for a Very Large AOT Microemulsion Droplet and the Corres nding Interfacial Bending Constant, K,Obtained on the rmh of Eqs 20,24, and 25' iJA &, y,/mNm-l q r J i G klJkeT KJksT 26.2 18.4 26.5' 18.9'
0.225 0.106 0.214 0.100
0.6 1.3 0.9 0.5
0.156 0.150 0.136 0.187
I, Droplets in octane are indicated by dispersed in dodecane.
0.926 1.063 1.452 0.403
2.2 2.2 2.7 1.6
1.1 1.1 1.4 0.8
*, otherwise, the droplets were
quantification for a single-phase w/o microemulsion (including to obtain 8 = .r?/F-)without knowing the activity of the dispersed water phase, it is still possible to estimate 7 , from C = -y,.r:/kBT N y,P2/kBT to within f20%. Finally, by assuming that saddle-splaybending constant, E, is comparatively small lR/q IO.1, which is supportedby full model calculations for surfactant-loadedoil-water interfacesof spherical and cylindrical we are able to roughly estimate the rigidity constant as K N k2/2. The results of our calculations along these lines are collected in Table 111. It appears that 7.. is of the order of 1kBTfor octane as well as dodecane as solvent. The rigidity constants, K,obtained by other investigators for AOT monolayers between oil and water phases vary between 0 . 5 k ~ Tand 5kgT.41-44Binks et have recently determined K for AOT monolayers at oil-water interfaces by ellipsometry. Their results indicate that K is independentof added salt and has a value close to 1kBT for oil chain lengths up to 10;the value then falls abruptly to about 0.15k~Tfor dodecane and 0.05k~Tfor tetradecane. This means that, beyond a certain chain length, the interface would be strongly affected by the kind of oil employed and that the oil-surfactant interaction may strongly decrease its rigidity. In this work no such difference is observed between octane and dodecane; the bending constant, K,is much the same for the two oils used and for the different droplet sizes.
Acknowledgment. This work was supported by the Swedish Natural Science Research Council. References and Notes (1) Day, R.; Robinson, B. H. J . Chem. Soc.,Faraday Trans. I 1979,75, 132. (2) Zulauf, M.; Eicke, H.-F. J. Phys. Chem. 1979,83, 480. (3) Huang, J. S.;Kim,M. W. Phys. Rev. Lett. 1982, 47, 1446. (4) C a b , P. C.; Delord, P. J. Appl. Crystallogr. 1979, 12, 502. (5) Kotlarchvk. M.: Chen. S . H. J . Phvs. Chem. 1982. 86. 3273. (6j Robinso;, 8.;Toprakcioglu, C.; Dire, J. J. Chem: Sdc., Faraday Trans. I 1985, 80, 13. (7) Howe, A. H.; McDonald, J. A,; Robinson, B. H. J. Chem. Soc., Faraday Trans. I 1987,83, 1007. (8) Eicke, H.-F.; Borkovec, M.; Das-Gupta, B. J . Phys. Chem. 1989,93, 314. (9) Verbeeck, A.; De Schryver, F. C. Langmuir 1987, 3, 494.
Almgren et al. (10) Lang, J.; Jada, A.; Malliaris, A. J . Phys. Chem. 1988, 92, 1946. (11) Bridge, J. N.; Fletcher, P. I. D. J. Chem. Soc., Faraday Trans. I 1983, 79,2161. (12) North,A.N.;Dole,J.C.;McDonald,J.A.;Robinson,B.H.;Heenan, R. K.; Howe, A. M. Colloids Surf.1986, 19, 21. (13) CarlstrBm, G.; Halle, B. Longmuir 1988,4, 1346. (14) Kotlarchyk, M.; Stephans, R. B.; Huang, S.J. J. Phys. Chem. 1988, 92, 1533. (15) Kotlarchyk, M.; Chen, S.H.; Huang, J. S.;Kim, M. W. Phys. Rev. A 1984,29, 2054. (16) Robertus, C.; Philipse, W. H.; Joosten, J. G. H.; Levine, Y. K. J. Chem. Phys. 1989, 90,4482. (17) Robertus, C.; Joosten, J. G. H.; Levine, Y. K. Prog. Colloid Polym. Sci. 1988, 77, 115. (18) Kotlarchyk, M.; Chen, S.H.; Huang, J. S. J . Phys. Chem. 1982,86, 3273. (19) RiEh, J.; Borkovec, M.; Hofmeier, U. J . Chem. Phys. 1991, 94, 8503. (20) Safran, S.A. J. Chem. Phys. 1983, 78,2073. (21) Milner, S.T.; Safran, S . A. Phys. Rev. A 1987, 36, 4371. (22) Farago, B. Prog. Colloid Polym. Sci. 1990, 81, 60. (23) Farago, B. Phys. Rev. Let. 1990,65, 3348. (24) Overbeck, J. T. G. Prog. Colloid Polym. Sci. 1991, 83, 1. (25) Eriksson, J. C.; Ljunggren, S.Prog. Colloid Polym. Sci. 1990, 81, 41. (26) Borkovec, M.; Eicke, H.-F.; Ricka, J. J . Colloid Interface Sci. 1989, 131, 366. (27) Borkovec, M. J. Chem. Phys. 1989, 91, 6268. (28) Borkovec M. Ado. Colloid Interface Sci. 1992, 37, 195. (29) Infelta, P. P.; GrHtzel, M.; Thomas, J. K. J. Phys. Chem. 1974,78, 190. Infelta, P. P. Chem. Phys. Lett. 1979, 61, 88. (30) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (31) Almgren, M. Adv. Colloid Interface Sci. 1992, 41, 9. (32) a n a , R. In Zana, R., Ed. Surfactants Solutions: New Methods of Investigations;Surfactant Science Series; Marcel Dekker: New York, 1987; Vol. 22, p 241. (33) van der Auweraer, M.; De Schryver, F. C. In Pileni, M., Ed. Inverse Micelles. Studies in Physical and Theoretical Chemistry; Elsevier: Amsterdam, 1990; Vol. 65, p 70. (34) Almgren, M. In GrHtzel, M., Kalyanasundaram, K., Eds. Kinetics and Catalysis in Microheterogeneous Systems; Surfactant Science Series; Marcel Dekker: New York, 1991; Vol. 38, p 63. (35) Almgren, M.; LBfroth, J. E. J. Chem. Phys. 1982, 76, 2734. (36) Warr, G. G.; Grieser, F. J. Chem. Soc., Faraday Trans. 1 1986,82, 1813. (37) Almgren, M.; Hanson, P.;Mukhtar, E.;van Stam, J. Lungmuir 1992, 8, 2405. (38) Bales, B. L.; Stenland, C. J . Phys. Chem. 1993, 97, 3418. (39) Sager, W.; Sun,W.; Eicke, H.-F. Prog. Colloid Polym. Sci. 1992, 89, 284. (40) Almgren, M.; J6hannsson, R. J. Phys. Chem. 1992,96, 9512. (41) Richter, D.; Farago, B.;Huang, J. S . Phys. Rev. Lett. 1987,59,2600. (42) van der Linden, E.; Geiger, S.;Bedeaux, D. Physica A 1989, 156, 130. (43) Borkovec, M.; Eicke, H.-F. Chem. Phys. Lett. 1989,157, 457. (44) Binks, B. P.; Meunier, J.; Abillon, 0.;Langevin, D. Lungmuir 1989, 5, 415. (45) Binks, B. P.; Kellay, H.; Meunier, J. Europhys. Lett. 1991, 16, 53. (46) Eriksson, J. C.; Ljunggren, S. To be published. (47) Sicoli, F.; Langevin, D.; Lee, R. T.; Monkenbusch, M. Prog. Colloid Polym. Sci., in press. (48) Langevin, D. Acc. Chem. Res. 1988.21, 255. (49) Aveyard, R.; Binks, B. P.;Lawless, T. A. Can. J. Chem. 1988, 66, 303 1. (50) Eriksson, J. C.; Ljunggren,S. Paperpresentedat theECISConference in Catanzaro, Italy, 1990, to be published.
