Langmuir 1993,9, 287S2882
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Intradroplet Exchange Rate and Activation Energy of Fusion in AOT Water/Oil Microemulsions in the Cluster Regime of the L2 Phase R. J6hannsson and M.Almgren' Department of Physical Chemistry, University of Uppsala, S- 751 21 Uppsala, Sweden Received April 15,1993. In Final Form: August 19, 1 9 9 9 Time-resolved phosphorescence and triplet absorption quenching measurementswere made to monitor the cluster structure on approach of phase separation, by increasing temperature, for AOT microemulsion systems in the L2 reversed droplet phase. The frequency and the activation energy of the droplet fusion is determined at different droplet sizes, with dodecane and octane as solvents. A decrease in fusion rate and an increase of activation energy are observed at increased droplet size. Introduction Microemulsion systems have attained a substantial interest, both regarding structure and other physical properties. Discrete water droplets persist over a wide composition range in waterloil (w/o) ternary systems formed by the ionic surfactant AOT, where AOT stands for sodium bis(ethylhexy1) sulfosuccinate. There are indications on the formation of clusters of droplets in these systems.14 The clusters show a fractal structure and exhibit percolation close to phase separation limits. The percolation phenomenon has been studied by conductivity measuremer~ts,'*~*~ electooptical Kerr effect measurements,2 and dielectric measurements4and further scrutinized by phosphorescence quenching meas~rements.~.~ Other physical properties of the droplet systems have been studied as well by light, X-ray, and neutron scattering methodsa17 and by fluorescence quenching m e t h o d ~ . ' ~ J ~ The formation of clusters is enhanced by approach to the haze point where a separation in two liquid phases occurs, by temperature increase, or by increasing w , the water/ surfactant ratio. When the temperature is raised, dielectric studies show4 that the clusters remain open and increasingly ramified toward the phase separation. Upon increase
* To whom correspondence should be addressed. e Abstractpublishedin
Aduance ACSAbstracts, October 15,1993. (1)Eicke, H.-F.; Hilfiker, R.; Thomas,H. Chem. Phys. Lett. 1986,125, 295. (2)Eicke, H.-F.;HiMker,R.; Thomas,H. Chem.Phys.Lett. 1986,120, 272. (3)Sager, W.;Sun, W.;Eicke,H.-F.Prog. ColloidPoZym.Sci. 1992,89, 284. (4)Eicke, H. F.; Geiger, S.;Sauer, F. A.;Thomas, H. Ber. Bensen-Ges. Phys. %hem. 1986,90,812. (5)Jbhannsson, R.;Almgren, M.; Alsins, J. J. Phys. Chem. 1991,95, 3819. (6)Almgren, M.; J6hannsso11,R. J. Phys. Chem. 1992,96,9512. (7)Maitra, A.; Mathew, C.; Varshney, M. J. Phys. Chem. 1990,94, 5290. (8) Zulauf, M.; Eicke, H.-F. J. Phys. Chem. 1979,83,480. (9)Day, R.; Robinson, B. H. J. Chem. SOC.,Faraday Trans. 1 1979, 75,132. (10)Huang, J. S.;Kim, M. W. J . Phys. Reu. Lett. 1982,47,1446. (11)Assih, T.;Larch& F.; Delord, P. J.Colloid Interface Sci. 1982,89, 35. (12)C a b , C.; Marignan, J. J. Phys. Lett. 1986,46,L-267. (13)Pileni, M.-P.; Zemb, T.;Petit, C. Chem. Phys. Lett. 1986,118, 414. (14)Kotlarchyk, M.; Chen, S. H.; Huang, J. S. J.Phys. Chem. 1982, 86,3273. (15)Kotlarchyk, M.; Chen, S. H.; Huang, J. S.; Kim, M. W. Phys. Reu. A, 1984,29,2054. (16)Kotlarchyk, M.;Chen, S. H. J. Phys. Chem. 1986,89,4382. (17)Robinson, B.;Toprakcioglu, C.; Dore, J. J. Chem. Soc., Faraday Trans. 1 1986,80,13,431. (18)Lang,J.; Jada, A.; Malliaris, A. J. Phys. Chem. 1988,92,1946. (19)Verbeeck, A.; De Schryver, F. C. Langmuir 1987,3,494.
in droplet concentration, a change from fractal clustering toward a compact cluster with glasslike packing of stable droplets has been r e p ~ r t e d . ~At l ~very * ~ ~high water-boil ratios the droplets collapse and a bicontinuous phase is formed in a narrow temperature range. Cluster formation has not been observed in microemulsions stabilized by nonionic surfactants like Triton X-100 or poly(oxyethylene) alkyl e t h e r ~ , 3 ,for ~ ~which , ~ ~ formation of a bicontinuous phase occurs earlier.3*25This maintenance of discrete dropleta in clusters rather than formation of bicontinuous structures indicates a rather high stability for the AOT w/o droplets. The exchange of droplet associated solutes between AOT w/o droplets in different solventshas been studied by stop flow and luminescencequenchingmeasurements?~6J8*x~1@ In the present study, we use triplet state quenching to study the intermicellar exchange in clusters of AOT stabilized w/o microemulsions. The effect of droplet size on the exchange rate between droplets and the activation energy for the droplet exchange process at different water/ surfactant ratios, both for droplets in octane and dodecane, is studied. Quenching i n Clusters of Droplets. The quenching in small isolated droplets has been described by Infelta and TachiyaZ7pz8 and an extended expression for exchange between droplets has been p r e ~ e n t e d . ~ l - ~ ~ When clusters of droplets are present, however, then after the rapid intradroplet quenchingprocess, there w i l l be clusters that contain an excited probe and possibly quenchersin one or more of the other dropletsparticipating in the cluster. Quenching will occur when P and Q meet in the same droplet. The most likely way of transport of P and Q is through fusion between neighboring6dropleta, but other mechanisms are possible. In this study PTSA is used as probe and ferrocyanide as quencher. Both have high negative charge and should therefore be effectively (20)Chen, S. H. Annu. Rev. Chem. 1986,37,351. (21)Atik, S. S.;Thomaa, J. K. J . Am. Chem. SOC.1981,103,3643. (22)Dederen, J. C.;van der Auweraer M.; De Schryver, F. C. Chem. Phys. Lett. 1979,68,451. (23)Almgren, M.; van Stam, J.; Swamp, S.; Ufroth, J.-E. Langmuir 1986,2,432. (24)Fletcher, P. D.I.; Howe, A. M.; Robinson, B. H. J. Chem. SOC., , Faraday Trans. 1 1987,83,985. (25)Clark, S.; Fletcher, P. D. I.; Ye, X.Langmuir 1990,6,1301. (26)Howe, A. M.; McDonald, J. A.; Robinson, B. H. J. Chem. Soe., Faraday Trans. 1 1987,83,1007. (27)Infelta, P. P.; Gratzel, M.; Thomas, J. K. J.Phys. Chem. 1974,78, 190. Infelta, P. P. Chem. Phys. Lett. 1979,61,88. (28)Tachiya, M. Chem. Phys. Lett. 1975,33,289.
0743-1463/93/2409-2879$04.00/00 1993 American Chemical Society
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2880 Langmuir, Vol. 9, No. 11, 1993
repulsed from the interface and situated in the aqueous core of the droplets. The exchange is therefore assumed to occur by fusion. Exchange within a Cluster. In a previous contribution! expressions for quenching of excited species by exchange processes in clusters of droplets were presented, for large compact clusters as well as for open and ramified ones; an expression for exchange in small clusters was presented earlier.5 Exchange in Large Clusters. The decay law for quenchingby exchange in large clusters was described as6 (1) F ( t ) = F(0) exp(-pS(k,t)) exp(-hot) where F(t) is the absorption or phosphorescence signal which is proportional to the amount of excited state at time t and S(k,t) is the number of distinct sites, droplets in this case, visited in a walk by the reactants at time t . The rate of jumps between droplets, k,, is assumed to equal the rate of droplet opening, and ko is the natural decay constant of the probe. When clusters with compact character are considered (Swiss cheese case, Staufferm), the number of sites visited can be expressed as
S(k,t) = a,(k,t) (2) where a2 is a constant depending on the lattice structure30 probably of the order of unity. In the case of open and ramified clusters, the clusters can be described as fractal clusters and S(k,t) takes the form3lr3,
S(k,t) = al(k,t)d*’2 (3) where a1 is a constant probably close to unity as well, and d , is the spectral d i m e n ~ i o n . ~For ~ .many ~ ~ fractal lattices, including percolating clusters, the spectral dimension has been suggested to be close to 4/3.33The measurementsin compact clusters give exponential decay constants proportional to the quencher concentration k2 = kl/[QI. The second-order deactivation constant kp is related to the walk frequency by
k, = u,k,/[Micl
(4)
where a2 is not known, but probably in the order of unity. Exchange in Small Clusters. Small clusters are fully explored after a certain time, i.e. ifthey contain quenchers. Those clusters which do not contain quenchers will only by quenched by exchange with other clusters ~ ( t=)F(O)exp(-k,t
+ p(e-kqt- 1) + p ( m - l)(e-kd - 1))
k, = k,/(m - 1)
(7)
This approximation is useful when mainly dimers and trimers are present, besides free droplets. In dimers k, = k,, in trimers k, = kw/2, etc. For small clusters the approximation k, = k, will be used. Measurements of the electrical conductivity have shown a percolative type of t r a n s i t i ~ n ’with ~ ~ ~increasing ~~~~~ temperature. In the first part of this contribution, the cluster formation on approach at phase separation by increasing the temperature is studied as monitored from the quenchingof phosphorescence by diffusionof quencher molecules. Secondly, a study of the quenching of the triplet state of PTSA (sodium 1,4,6,9-pyrenetetrasulfonate) by W e (CN)6 was performed in compact clusters and in small clusters, in both cases far from phase limits, and k,, the frequency of fusion,determined. If the assumption is made that the droplet size remains unchanged (as discussed below) at elevated temperature. Arrhenius plots for the droplet fusion can be made to determine the activation energy, E., for the fusion process. Experimental Section Materials. The probe sodium 1,4,6,9-pyrenetetrasulfonate (PTSA) (Eastman) was used as supplied; the phosphorescence probe [Cr(bpy)sl(C10d3was synthesizedby the methodof Baker and MehhU The photophysicsof Cr(bpy)ss+axe well described byM.Maeatxieta1.% ThequenchersKI(Merck,analyticalgrade) were used as supplied. The surfactant Aerosol-OT was obtained from Sigma, and the solvents octane (Merck analytical grade) and dodecane (Merck synthesis grade) were used as supplied. ExperimentalTechnique. Phosphorescence was measured using an excimer laser (Lambda Physik EMG-100) to excite the probes. The samples were freed from oxygen by bubbling with nitrogen (except for Cr(bpy)s8+which was used aerated), in a l-cm fluorescence cell. The phosphorescencesignal was collected as close to the cell window as possible by means of a 6-mm light guide (Oriel Corp.) provided with Schott fiiters WG 360 (2 mm) to reduce scatteredlaser light (351nm for XeF) and RG 5 (2 mm) to isolate the phosphorescence emission. When transient a b sorption was measured for the PTSA triplet state, light from a pulsed xenon lamp in a rectangular zone of approximately 1 X 1 X 10 mm was passed through the solution at right angles to excitation, just behind the cell window. Wavelength selection was done with a Zeiss MM 12 double momochromatorwith quartz prisms.
The detector was a Hamamatau R 928 photomultiplier with reduced number of active dynodes. The signals were captured with a Tektronica 7912 digitizer, provided with 7B90P timebase. System control and signal processing was performed with a AT-compatible computer.
(5)
where m is the number of droplets per cluster, k, the firstorder intradroplet quenching constant, k, the first-order rate constant for the interdroplet quenching in a small cluster containing one quencher, and p the average number of quenchers per droplet. When the decay is studied on a long time scale, however, the intradroplet quenching is over within 100 ns and eq 5 can be simplified, for long times to
F ( t ) = F(0) exp(-k,t - p + p ( m - l)(eJfJ- 1)) (6) l l ( m - 1) is the probability that the quencher meets a probe after the fiist fusion-fission event. An approximation for the relation between k, and k, can be made6 (29)Stauffer, D.Phys. Rep. 1979,54(1). (30)MontroIl, E.W.;We&, G. H. J. Math. Phys. 1965,6,167. (31)Rammd, R.;Toulouse, G. J. Phys. Lett. 1983,44, L-13. (32)Blumen, A.;Klafter, J.; Zumofen, G. Phys. Reu. B 1983,28,6112. (33)Alexander, S.;Orbach, R. J . Phys. Lett. 1982,43,L-625.
Results and Discussion Figure 1 shows the change in cluster structure as the temperature was increased for droplets in a microemulsion with w = 20 in dodecane and at the surfactant concentration, C = 0.1 M. The quenching of C r ( b ~ y ) 3 by ~ +Iis followed. ([&I = 0.05 mM, which corresponds to 0.14 quenchers per droplet). The top curve shows the quenching at the lowest temperature and the bottom curve that at the highest temperature. For direct comparison, the curves were freed from the influence of the natural decay (which changed with temperature) by dividing the quenchedcurves by the corresponding unquencheddecay curves. At low temperature, 17 OC (the top curve in the graph), the microemulsion is far from the haze point and only small clusters are observed. After the small initial (34)Baker, B. R.; Metha, B. D. Znorg. Chem. 1965,4,848. (36)Maestri, M.; Bolletta, F.; Moggi, L.;Balzani, V.; Henry, M. S.; Hoffman, M. Z. J. Am. Chem. SOC.1978,100(9),2694.
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Cluster Structure of AOT Microemulsion Systems
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Time (psec) Figure 1. The change in cluster structure observed by the quenching of Cr(b~y)3~+ phosphorescence (In scale) by I- at increased temperature, for droplets in microemulsion with w = 20 and surfactant concentration;C = 0.1 M. Top curve shows the quenching at the lowest temperature, bottom curve at the highest.
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i/[qx io3 ( ~ - 1 ) Figure 2. Arrheniusplots of the fusion-rateconstantfor droplets in dodecane at w = 8.5, 20, and 30. Table I. Activation Energy of Droplet Fusion in Dodecane and in Octane w
drop due to the intracluster quenching, a plateau is reached. The intensity difference between the plateau and the initial intensity gives an indication of the droplet number in the ~ l u s t e r .An ~ approximate value of 2.5 droplets per cluster was obtained at 17 O C . When the temperature was raised to 20.8 OC the clusters had grown so much that the cluster size could not be obtained. The clusters are irregular and open and the quenching now follows the fractal model for the diffusionof the quenchers.6 When the temperature is increased further, the clusters remain open and ramified until the cloud point is reached at =32 "C. A fit to a fractal model for the quenching in the percolating cluster at 30.8"Cwas performed for three quencher concentrations (0.14,0.28,and 0.56 quenchers per droplet). The spectral or fraction dimensionobtained was 1.3 f 0.1,in agreementwith the valued, = 4 / 3 , suggested by Alexander and O r b a ~ for h ~ a~percolating cluster. The effect of temperature on droplet size has to be considered before discussing the results for activation energy, both because the droplet concentration has to be known in order to obtain k, and because the value of k, depends on the droplet size,as discussed below. In a paper by Lang et a1.18 where the quenching of Ru(bpy)s3+was followed, an increase in droplet size was observed when the temperature was increased. These results contradict results for the droplet size obtained by SANS (smallangle neutron scattering) where no change or even a slight decrease in size was In the work by Lang et al. the exchange between droplets is accounted for by applying a correction on n,, the average number of quencher per droplet, due to the contribution of migrating quenchers, as formulated in a model by Almgren et al.23 In this model the migrational part adds to the natural decay, 1 / ~and , increases the slope of the exponential tail. In clusters, however, this is not the case. This does have the effect that the value obtained for the aggregation number will be very unsure when clusters, in particular large cluster, are found in the solution. For droplets in short chain solvents far from the critical line, however, only small changes in aggregation number were observed when the temperature was increased. We performed some fluorescence quenching of PTSA with KI, in the nanosecond time scale, for droplets at w = 8.3and with the droplet concentration3 mM indodecane which corresponds to a low extent of cluster formation. The temperature was increased from 20 to 35 "C. No increase in size was found. We assume, therefore, that the droplet size is independent of temperature.
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8.5 20 30 a
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E. (kJmol-l) 25 33
E. (kJ mol-') 25.5 34.6
w
8.5* 18.2*
47
The dropeta in octane are marked by an asterisk.
0' 0
10
20
30
40
Figure 3. Activation energy (kJ mol-') of droplet fusion as a function of w, the water-surfactantratio: 0, dropleta in octane; 0 , droplets in dodecane. Measurements of Activation Energy of Fusion. In Figure 2 the Arrhenius plots of the fusion rate constant for droplets in dodecane at three different w values are presented. The k, values are calculated from the decay rate in compact clusters according to eq 4. At the lowest water surfactant ratio, w = 8.5,the clusters are small, and the model for quenchingin small clustsre as presentad in eq 7 is applied. E a is then obtained from the change ink,, the intracluster quenching rate constant. The results are compared to activation energies obtained in octane at w = 8.5 and at w = 18.5. The resulting values for the activation energies are presented in Table I. An increase in activation energy with droplet size is observed. No significant difference is noted for droplets in octane at the same size. The increase in activation energy with w (and consequently the size) is presented graphically in Figure 3. The trend of increasein activation energy with w was also observed in a study by Fletcher et ~ 1 . :where ~ Eawas determined by a stop-flow technique for droplets in heptane. In the present study, however, considerablylower values for E, are obtained, a difference by a factor 2 is observed. The explanation for the difference is as follows; stop-flow measurementa are in the millisecond time range, and the rate of interdroplet exchange is determined by a combination of steps of
Jbhannaon and Almgren
2882 Langmuir, Vol.9,No. 11, 1993 6.5
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1/[vx lo3 (K-') Figure 4. Arrhenius plots of k, (upper curve) and ko (lower curve) for droplets in octane at w = 8.5 and C = 0.6 M.
encounter of the droplets and the actual droplet fusion on that time range. In heptane, the droplets are mainly free or in doublets at the surfactant concentrationsused. Since the exchange is a process of both encounter and droplet fusion, the activation energy calculated from stop-flow measurements will depend on both steps in the exchange process. If this is the case, the rate constant observed by the stop-flow technique should be the same as or at least similar to, the change in the decay constant ko of the exponentialtailin the smallcluster model.6 Note, however, that as presented in ref 5, ko in the model was 1/7. In the present measurement the natural lifetime of the probe was very long and ko now refers to the quenching due to exchange between clusters. We then compare the results for droplets at w = 8.5 in octane at C, the surfactant concentration 0.6 M, to the results obtained by Fletcher et al. The experimental curves followed the model for small clusters,with the small cluster size retained at higher temperatur es The resulting Arrhenius plot from a fit of the experimental curves to eq 6 are shown in Figure 4. The upper curve correspondsto k , = k,, lower curve to ko, the change in slope rate. Such calculationsfor the change in exponentialtail slope for droplets in octane at w = 8.5, where small clusters are present, were performed. From Arrhenius plots for ko, an apparent E. 69 kJ mol-' is calculated, which is close to the value -72 kJ mol-' obtained from stop-flow mea~urements.~~ Effect of w on Fusion Rate. In Figure 5 the rate of droplet fusion with increasing o is shown on a logarithmic scale, for the studies in dodecane and octane. The points were obtained both by quenching of Cr(bpyh3+phosphorescence with NOa- and with the quenching of PTSA triplet by Fe(CN)&. It is observed that the rate of fusion decreases with droplet size; the rate falls exponentially with w. An interesting result is that the rate of fusion does not depend on the solvent, only on the size of droplet.
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o = [H20]/[AOTl Figure5. Log of the rate of dropletfusionWithincreasing watersurfactant ratio, w , at 20 O C . These results are in line with the increasing activation energy needed for the droplet fusion when the droplet size increases. A plausible explanation for the small solvent effect is that the droplets participating in a cluster are in contact and not separated by the solvent molecules. Therefore, the rate of fusion does not depend on the solvent. The solvent chain length has, however, an important effect on the solubility of the droplets, since it influences the droplet-droplet and droplet-solvent interactions, and therefore the form and stability of the clusters (and consequently on the form of the phase diagram). Higher alkane solvents cannot solvate the droplets adequately and the clusters grow with increasingconcentration of the dispersed phase. This chain length effect can be understood from the difference in entropy of mixing; it is easier for a short chain solvent to mix with the surfactant tails, so that with increasing chain length it becomes more favorablefor the tailsto mix with those from other dropleta rather than with the solvent. When the temperature is raised the misingof oil and surfactant decreasesand cluster growth is enhanced.
Conclusion We report the activation energy involved in the fusion of AOT droplets in octane and in dodecane. An increase in activation energy with the droplet size is observed and a decrease in the rate of fusion as well. No difference in activationenergy or rate of fusion was observedfor droplets in octane vs dodecane. Long chain solvents are supposed to stabilize the droplet pair in an encounter and therefore increase the probability of fusion before separation. The rate of exchange between nonclustering droplets will increase due to this effect, when the droplets interaction become more attractive, from an increase of either temperature or the solvent chain length. Acknowledgment. This work was supported by the Swedish Natural Science Research Council.
