Self-diffusion in three-component, oil external microemulsions by forced Rayleigh scattering

Self-Diffusion in Three-Component, Oil External Microemulsions by Forced Rayleigh Scattering W I L L I A M D. D O Z I E R AND M A H N

WON KIM

Exxon Research and Engineering, Annandale, New Jersey 08801

P A U L M. C H A I K I N Exxon Research and Engineering, Annandale, New Jersey 08801, and University of Pennsylvania, Department of Physics, Philadelphia, Pennsylvania 19104

Received July 10, 1985; accepted April 15, 1986 The self-diffusionconstant of water droplets in a three-component, oil external microemulsion containing n-decane, water, and an anionic surfactant, sodium di-2-ethylhexylsulfosuccinate(AOT~) was measured by forced Rayleigh scattering. The droplet radius was kept fixed by holding the weight ratio of surfactant to water fixed at 3:5 and the diffusion constant was measured as a function of the minor component (water + AOT) volume fraction. The diffusion constant was observed to decrease about a factor of 3 from 10-16% volume fraction of water + AOT. From 16 to 60% the diffusion constant was independent of the volume fraction of water + AOT. These results, together with previous neutron scattering measurements on this system, suggest that a bicontinuous phase is not formed. A possible explanation involving dynamically percolating clusters of water droplets is discussed. © 1987Academic Press, Inc.

INTRODUCTION Microemulsions are mixtures o f water and oil stabilized by the presence o f a surfactant on the interface(s) between the two (1). Systems usually studied are those in which the m i n o r c o m p o n e n t forms droplets inside a continuous matrix o f the m a j o r c o m p o n e n t , with a layer o f surfactant on the surface o f each droplet. There can also be mixtures in which the m i n o r c o m p o n e n t forms disks, sheets, or rods, as well as systems which are bicontinuous (2, 3). The system investigated in this study is a "water-in-oil" microemulsion consisting o f water, decane, and aerosol-OT (AOT) surfactant. This is a t h r e e - c o m p o n e n t system requiring no "cosurfactant" to f o r m a microemulsion over a wide range o f water/oil ratios. Aerosol-OT (AOT) is a brand name of American Cyanamid.

The d e c a n e / w a t e r / A O T system has been studied by neutron (4) and light (5) scattering and by electrical conductivity m e a s u r e m e n t s (Bhattacharya et al., in preparation). Results from the n e u t r o n scattering show that the water forms moderately ( ~ 2 8 % half width) polydisperse, spherical droplets in decane and that the radius o f these droplets for the surfactant/water weight ratio used in this study (3/5) is ~ 5 0 A. T h e y also show that the size o f these droplets is independent o f the v o l u m e fraction (~b) o f water (in the range studied q5 < 25%), as long as the relative a m o u n t s o f water and A O T are kept constant. The c o n d u c tivity measurements show a sudden and sharp increase in conductivity beginning at ~b = 16%. This is suggestive o f the formation o f a bicontinuous phase (6) or the formation o f percolation clusters by the water droplets. The purpose o f this study was to use the "forced Rayleigh scattering" technique to gain an understanding o f the self-diffusion processes

545 0021-9797/87 $3.00 Journal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

Copyright © 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.

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in this interesting regime. Our results show that the self-diffusion constant (Ds) of the dye molecules drops by a factor of "~3 as ~bis increased from 10 to 16%. Forced Rayleigh scattering is an effective tool for measuring self-diffusion (7). A photochromic or photobleachable dye is placed in the system of interest. This dye experiences a marked change in index of refraction upon absorbing a photon at a certain wavelength. A laser beam of this wavelength is split and recombined in the sample, giving a pattern of interference fringes. This sets up a spatially periodic density of excited dye molecules. A second laser can then be Bragg scattered from what is effectively a diffraction grating. Since the first laser beam is only flashed on the sample a short time, the pattern begins to fade as the dye molecules diffuse and the density of excited molecules smears out. The diffracted spot from the second laser decays in intensity as this occurs, with the following time dependence:

1(0 oc (e-Dq~t+a)2+t32

[1]

where a is the noise mixing coherently with the signal and/3 is the background that mixes incoherently. This technique gives a direct measurement of the self-diffusion constant of the dye. This method is reminiscent of the typical way of measuring self-diffusion in solids by radioactive tracer. It has been used previously to study polymers (8), oil-in-water microemulsions (9), and charged polystyrene spheres in a colloidal liquid (10). The idea in this study is to use a dye that will stay in the water and then observe the diffusion of the dye. As long as the water is contained in droplets, the dye will be trapped inside and we will see the diffusion of the droplets by watching the dye. If a bicontinuous phase develops, though, we expect the dye to be freed of the droplets and to diffuse much more rapidly through the "pipes" formed by the continuous water phase. Furthermore, if the water phase is a percolating cluster we might see the anomalous diffusion characteristic of a random walk on a fractal (11). Journal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

EXPERIMENTS The samples were prepared with purified aerosol-OT surfactant, decane, and an aqueous solution of 0.3 mg/cc congo red. A stock solution of 32% minor component was prepared, and the other samples (except obviously the 60% one) were made by diluting this stock with decane containing 200 ppm AOT. The resistances of these samples were measured with a Hewlett-Packard 4274A LRC meter, and the results were similar to those obtained previously in samples without dye. Congo red is a dye of the azobenzene family which exhibits photochromism due to the cistrans isomerization of its azo linkage (12). It is quite water-soluble and is insoluble in decane. This was checked by adding decane to a solution of congo red in water. The two liquids immediately separated and there was no visible dye in the decane. Also, the interface exhibited the normal miniscus one would expect between water and decane. The "'writing" beam was from an argon-ion laser operating at 514.5 nm and a power of 100-400 mW. The fringe pattern is flashed upon the sample for 50-250 ms. A He-Ne laser was used for the "reading" beam, the diffracted beam being detected by a photomultiplier tube. A typical signal is shown in Fig. 1. The measurement is done for several fringe spacings and the relaxation rates are plotted against q2 (q = 2~r/d, d = fringe spacing). The

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SELF-DIFFUSION IN MICROEMULSIONS I

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FIG. 4. Self-diffusion constant as a function of minor component volume fraction.

slope of this line is the diffusion constant (1/r = Dsq2). One of these plots is shown in Fig. 2. To check for radiative transfer between dye molecules, samples were prepared at ~b = 30% in which the dye concentration was varied over an order of magnitude. No effect was observed in Ds as a function of dye concentration, indicating that we are not observing the diffusion o f the dye excitation.

conductance becomes measureable (R < 20 M~2) at 4~ = 16% and increases as a power law thereafter. The solid line is

RESULTS As stated above, the electrical resistance a was measured as a function of q~at a frequency of 1 kHz. The results are shown in Fig. 3. The 120

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with ~bc = 0.15 and x = - 1 . 7 . A plot of the diffusion constant for several volume fractions of minor component is shown in Fig. 4 and constitutes our main resuits. For small 4~, Ds is about 6 × 10- 7 cm2/ s, which corresponds to a droplet radius of about 50 A (using the Stokes-Einstein formula for the free diffusion of spheres and the viscosity of decane). This confirms the neutron scattering results. As q~ is increased the diffusion constant decreases more rapidly from 4~ 10-16%, and is then almost independent of ~b above 16%. For all 4~ we observe a q2 dependence of the relaxation rate indicating diffusive behavior. We did not observe an anomalous time dependence in the decay of the diffracted spot characteristic of diffusion on a fractal as might be expected if a percolation cluster had formed. The viscosity (n) of these samples was also measured to see if it would have behavior in c o m m o n with the self-diffusion or the conductivity. The samples were practically Newtonian, and the results of n as a function of q~ are shown in Fig. 5. This plot is similar to the results of the viscosity measurements of Ref. (9) and remarkably similar to the experimental Journal of Colloid and Interface Science, Vol. 115, N o . 2, F e b r u a r y 1987

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DOZIER, KIM, AND CHAIKIN I

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the continuous water phase and diffuse more rapidly, being freed of the relatively slowo moving droplets (Ds for the dye in pure water 8 is ~ 2 X 10 -6 cm2/s corresponding to a radius [] A D. o f ~ 2 0 ~,). On the other hand, Ds need not o 8 [] increase immediately upon the formation of the bicontinuous phase, as the channels of wa4 [] ter may be narrow and tortuously connected. [] o 2 Even so, as water is added to the system the o o o available free volume for diffusion would be 0 I I I I I I I 0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 increased as well as the connectedness of the water phase. So D~ should increase above ~bc FIG. 5. Viscosity as a function of minor component if the system becomes bicontinuous at the volume fraction. percolation threshold, even if there is not the expected sudden j u m p at ~bc. At low ~b, D~ slowly decreases with increasdata on hard spheres of Krieger (13). However, ing q~. As q~increases, D~ might be expected to in their diffusion measurements they did not decrease even more quickly due to the small observe the same behavior in D~ at high vol- attractive interaction between the droplets ume fraction of minor component. They (15). But D~ does not continue to decrease with found a continuous decline in Ds which was 4, as one would expect if the interactions were inversely proportional to n, similar to previous dominating the process. Since Ds becomes roughly independent of q~ at the higher conresults in charged polystyrene spheres (10). centrations, another mechanism is needed to explain the results. DISCUSSION Neutron scattering results (4) show that the It should be kept in mind that it was the microstructure of the microemulsion in this diffusion of the dye molecules that was mea- system stays constant up to at least a 24% volsured. There are three possible processes for ume fraction of water. That is, the droplet size this to occur. One is that the dye is a passenger ( ~ 5 0 A) is constant for ~b up to 24%. Also, in the water droplets, trapped inside. This is the viscosity measurements suggest no strucclearly the case in the dilute region, where Ds tural change at any point in the range mea6 × 10-7 cm2/s. This corresponds to the sured. Both of these show that the transport free diffusion of spheres of radius 50 .~. The of water in the microemulsion remains dropinitial slow decrease in Ds is similar to what let-like and no bicontinuous phase appears. A one would expect in any system at low q~from bicontinuous phase should not be expected in hydrodynamic effects (14). Another possible this system because if the bending energy of channel for the transport of the dye is for the the interface is large compared to kBT, the droplets to exchange their contents during droplets should retain the same radius even collisions allowing the dye to hop from droplet when phase separation occurs (16). This has to droplet. The third possibility is that a con- been seen to be the case in three-component tinuous water phase opens up and the dye AOT systems (4) like the one in this study. moves through it. As an aside, it should be mentioned that D~ is constant beginning at the same 4~where throughout this study the system was not near a begins to increase. As is stated above, the a critical point. The critical point for this sysincrease in conductivity suggests the possibility tem is at ~b = 8% and T = 309 K. So the samof a bicontinuous phase. In that event, one ples were always at least 10° from their critical would expect that the dye would remain in point. I

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Journal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

SELF-DIFFUSION IN MICROEMULSIONS The result that is most interesting and difficult to explain is the lack of concentration dependence of Ds at high volume fraction. It should be pointed out again that since we are directly measuring only the diffusion of the dye, the curve in Fig. 4 represents an upper bound for the diffusion constant of the water droplets. Clearly, the dye molecules (radius 20 A) must move at least as quickly as droplets having twice their radius. Some kind of exchange of dye between droplets can not be ruled out completely. When droplets collide, their contents may interchange (1 7). Also, the exchange of dye molecules solubilized in the decane by surfactant is also possible. Under such assumptions, though, one would not expect Ds to be independent of 05. Consider a droplet on such a percolation cluster. After a time ~-, the droplet detaches from the cluster and diffuses away. To find out how far the droplet travels before it reattaches (if at all), consider the intersection of a random walk (dimension dl) and the percolation duster (dimension d2). The probability P of intersection between the two after r steps are taken is (18) P oc r d-dl-d2

[3]

(d is the imbedding dimension, 3). If d - d l d2 < 0, then P is strongly weighted for small r and the droplet reattaches almost immediately. So if we write l2 Ds ~ -[4] -

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The conductivity and diffusion data suggest some kind of change at 05 -~ 15%. If the droplets do not have to mix contents to exchange charge, a cluster may form that connects across the sample, the conductivity will increase when this occurs. There are a couple of ways in which this might happen. Charged surfacrant molecules can be exchanged between droplets, allowing charge mobility without a mixing of contents between droplets and without the droplets carrying the charge themselves. Similarly ions may be exchanged through the oil phase if the droplets are sufficiently close. If such a percolated duster arises, then charge mobility is enhanced and rises. CONCLUSIONS We have measured the self-diffusion constant of water droplets in a three-component water-in-oil microemulsion by forced Rayleigh scattering. At low 05we observe diffusion characteristics of 50-A spheres in agreement with the neutron scattering results. Over the range of 05 = 10-16% the diffusion constant drops to a value about one-third of that for 05 = 0. Above 16%, Ds is independent of 05. The viscosity and diffusion measurements in this study, together with previous neutron scattering results, show that a bicontinuous phase does not appear in this system. A possible explanation of the independence of the self-diffusion coefficient on the concentration of droplets above 05 = 16% is the formation of dynamic percolation clusters.

we have for r the characteristic time during which the droplet is unattached and l will be ACKNOWLEDGMENTS the distance the droplet diffuses during r. Since it reattaches immediately, we can set l to be The authors acknowledge helpful discussion with H. on the order of a droplet radius. These param- Yu, F. Rondelez,P. Pincus, S. Alexander,S. Safran, and eters are independent of 05 so that after most J. Huang. droplets are attached to clusters (05 > 05o)D~ REFERENCES will be constant. Setting Ds = 2 X 10 -7 cmE/s 1. Robbins,M. L., in "MiceUization,Solubilizationand and l = 50 A, we get ~ 10 -6 S. In the case Microemulsions"(K. L. Mittal, Ed.), Plenum, New of this dynamic percolation model, droplets York, 1977. attach and escape from clusters so that on the 2. Seriven,L, E., in "Micellization,Solubilizationand time scale of these measurements ( ~ 1 min) Microemulsions"(K. L. Mittal, Ed.), Plenum,New no anomalous diffusion is seen. York, 1977. "-~

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3. De Gennes, P. G., and Taupin, C., J. Phys. Chem. 86, 2294 (1982). 4. Kotlarchyk, M., Chen, S. H., Huang, J. S., and Kim, M. W., Phys. Rev. A 29, 2054 0984). 5. Huang, J. S., and Kim, M. W., Phys. Rev. Lett. 47, 1462 (1982). 6. Cazabat, A, M., Chatenay, D., Guering, P., Langevin, D., Muenier, J., Sorba, O., Lang, J., Zana, R., and Paillete, M., in "Surfactants in Solution" (K. L. Mittal and B. Lindman, Eds.). Plenum, New York, 1984. 7. Rondelez, F., Hervet, H., and Urbach, W., Chem. Phys. Lett. 53, 138 (1978). 8. Chang, T., and Yu, H., Macromolecules 17, 115 (1984). 9, Cazabat, A. M., Chatenay, D., Langevin, D, Meunier, J., and Leger, L., in "Surfactants in Solution" (K. L. Mittal and B. Lindman, Eds.). Plenum, New York, 1984.

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10. Dozier, W. D., Lindsay, H. M., and Chaikin, P. M., Les Houches Winter School, J. Phys. Coll., C-3, 1985. 11. Rammal, R., and Toulouse, G., J. Phys. Lett. 44, L-13 (1983). 12. Brown, G. H., Ed., Techniques of Chemistry. Wiley, New York, 1971. 13. Krieger, I. M.,Adv. Colloid Interface Sci. 3, 111 (1972). 14. Batchelor, G. K., J. FluidMech. 131, 155 (1983). 15. Huang, J. S., Safran, S., Kim, M. W., Grest, G. S., Kotlarchyk, M., and Quirke, N., Phys. Rev. Lett. 53, 592 (1984). 16. Safran, S. A., and Turkevich, L. A., Phys. Rev. Lett. 50, 1930 (1983). 17. Fletcher, P. D. I., Robinson, B. H., Bennejo-Barrera, F., Oakenfull, D. G., Dore, J. C., and Steyler, D. C., in "Microemulsions" (I. D. Robb, Ed.). Plenum, New York, 1982. 18. Mandelbrot, B. B., "Fractals." Freeman, San Francisco, 1977.