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J . Phys. Chem. 1988, 92, 206-21 1
Two Percolation Processes in Microemulsions Michal Borkovec, Hans-Friedrich Eicke,* Holger Hammerich, and Bikram Das Gupta Institut f u r Physikalische Chemie der Uniuersitat Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland (Received: May 28, 1987)
We present an experimental study of an AOT-decane-aqueous 0.5% NaCl microemulsion in which the oil-to-water ratio can be arbitrarily varied. This allows an investigation of the structural inversion from an water-in-oil microemulsion into an oil-in-water microemulsion which happens completely continuously without any phase separation. ‘Conductivity,viscosity, and electrooptical Kerr effect data confirm the presence of two percolation processes. This structural inversion takes place in two stages: With increasing oil content, first a water continuous microemulsion transforms into a bicontinuous structure at roughly 20% oil (oil percolation threshold) and then at roughly 80% oil (water percolation threshold) and bicontinuous microemulsion turns into an oil continuous structure. These two percolations margin three structural regimes of a microemulsion: oil-in-water regime, water-in-oil regime, and a bicontinuous or oil and water continuous regime.
Introduction Since Schulman’ introduced the concept of a microemulsion such systems have attracted broad attention by experimentalists as well as Microemulsions are isotropic, thermodynamically stable mixtures of oil, water, and surfactant. In contrast, however, to a mixture of three miscible liquids which are homogeneous down to a molecular scale, the peculiarity of microemulsions lies in their molecular heterogeneity-they are divided into water and oil domain^.^-^ The occurrence of such domains is caused by the amphiphilic nature of the surfactant which resides on an interface in between the practically immiscible oil and water. To incorporate a macroscopic amount of surfactant, the interface separating the oil and water domains must be very large. The system can achieve this by forming regularly arranged layers or tubes of oil and water separated by a surfactant film. This, however, will be an anisotropic, liquid crystalline phase. An isotropic phase can be produced by formation of oil or water droplets or by generation of some random globular or tubular structures. In either case the characteristic size of these domains is given by the persistence length [, which is typically 50-500 A. The interface will appear flat on length scales small compared to [ and curved or wrinkled on larger length A more detailed characterization of the structure of these domains has been the subject of much discussion. It is generally a ~ c e p t e d that * ~ ~in~ a~ microemulsion containing a large fraction of water the oil is confined in small, isolated droplets, (nanodroplets) surrounded with a surfactant layer, Le., “swollen” micelles. In such an oil-in-water microemulsion the water is continuous. Analogously, on the oil-rich side the water is enclosed in isolated water nanodroplets (inverted swollen micelles). This water-in-oil microemulsion is now oil continuous. As one increases the oil-to-water ratio of a microemulsion, there must be some kind of structural transition by which the oil-in-water microemulsion inverts into a water-in-oil microemulsion. The nature of this inversion is quite controversial: an abrupt inversion, ( I ) Schulman, J.; Hoar, T. P. Nature (London) 1943, 152, 102. (2) Eicke, H. F. In Microemulsionr; Robb, I . D., Ed.; Plenum: New York, 1982. (3) Benett, K. E.; Hatfield, J. C.; Davis, H. T.; Macosco, C. W., Scriven, L. E. In Microemulsions; Robb, I . D., Ed. Plenum: New York, 1982. (4) Widom, B.; Dawson, D. A.; Lipkin, M. D. Physica A (Amsterdam) 1986, 140, 26. Safran, S.A,; Roux, D.; Cates, M. E.; Andelman, D. Phys. Rev. Lett. 1986, 57, 491. (5) De Gennes, P. G.; Taupin, C. J . Phys. Chem. 1982, 86, 2294. ( 6 ) Chen, S . H. Annu. Rev. Phys. Chem. 1986, 37, 351. Baker, R. C.; Florence, A. T.; Ottewil, R. H.; Tadros, T. F. J. Colloid Interface Sci. 1984, 100, 332. Gulari, E.; Bedwell, B.; Alkhafaji, S. J . Colloid Interface Sci. 1980, 77, 202. ( 7 ) Talmon, Y.;Prager, S. J . Chem. PhjJs. 1978, 69, 2984. (8) Jouffroy, J.; Levinson, P.; de Gennes, P. G. J . Phys. (Les LVif, Fr.) 1982, 43. 1241.
0022-3654/88/2092-0206$01.50/0
a phase separation, or a gradual change through bicontinuous structures has been p r ~ p o s e d . ~ ~ ~ ~ ~ As long as there is no phase separation and the system remains isotropic, percolation theoryl0 strongly supports the latter point of view. A microemulsion can be divided into imaginary cubes8 (or random polyhedra7) which are either filled with oil or water. If the water content of the microemulsion is high, the minor fraction of oil resides in small isolated oil clusters of these imaginary cubes. The water is found in a continuous, infinite water cluster that serves as a background. Increasing the oil content of the microemulsion, the isolated oil clusters will grow in size. At a particular point there will be a well-defined oil-to-water ratio (the oil percolation threshold) where an infinite oil cluster will appear for the first time. This oil percolation threshold is expected to appear at roughly 20% oil.Io With further increase of the oil content the fraction of oil in the finite, isolated clusters will decrease in favor of being found in the infinite cluster. At high oil content essentially no isolated oil clusters are present and the oil is found on the continuous, infinite cluster only. By symmetry, the role of oil and water can be interchanged and the same considerations apply to water clusters. Hence, starting at the oil-rich side and increasing the water content, a water percolation threshold appears at roughly 20% water (or 80% oil). Therefore, percolation theory strongly suggests that one expects three structural regimes of a microemulsion: A microemulsion containing up to roughly 20% oil is expected to be water continuous with isolated oil droplets, an oil-in-water microemubion. A microemulsion containing approximately more than 80% oil is expected to be oil continuous with isolated water droplets, a water-in-oil microemulsion. Finally, a microemulsion containing roughly between 20% and 80% oil will be water as well as oil continuous, a bicontinuous microemulsion. This can be pictured as a random intertwisted spongelike network. For clarity, these ideas are summarized in Figure 1. This interpretation where two percolation thresholds of water and oil margin three structural regimes of an microemulsion has already been ~onsidered.~ However, to our knowledge these important ideas have not received any attentioh since. The reason for this lies apparently in the fact that it is quite difficult to find surfactants forming microemulsions and at the same time allowing a continuous variation of the oil-to-water ratio. Frequently, changing the oil-to-water content over a wider range, the system becomes turbid; Le., two or more-often liquid crystalline-phases are formed. Unfortunately, at present very (9) Friberg, S.; Lapczynska, I.; Gillberg, G. J . Colloid Interface Sci. 1976, 56, 19. Bellcocq, A. A. M.; Biais, J.; Chin, B.; Lalanne, P.; Lamanceau, B. J . Colloid Interface Sci. 1979, 70, 524. Saito, H.; Shinoda, K. J . Colloid Interface Sci. 1970, 32, 647. ( I O ) See, for example, Zallen, R. Amorphous Solids; Plenum: New York, 1980; Stauffer, R. Rep. Prog. Phys. 1981, 5 4 , 1
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 1, 1988 207
Two Percolation Processes in Microemulsions oil percglation
S
water ,percolation
Figure 2. Gibbs triangle of a three-component system. The heavy line represents the Schulman line, the locus of a constant persistence length in a microemulsion. T k dotted line represents a cut at equal oil-to-water ratio.
'
I
I \
I
\ 1
\>nfinite cluster
\ I 0
00
1
I I 1
-- -
oil in bicontinuous water water in oil Figure 1. Schematic representation of the ihree structural regimes of a microemulsion margined by two percolations of water and oil as a function of relative amount of
few theoretical treatments4s5try to include the possibility of such liquid crystalline phases, which can be very prominent in real systems."-I4 Therefore, if one attempts to confront theoretical models of the structural inversion of the oil-in-water microemulsion into an water-in-oil microemulsion with experiments, one has to find systems that allow a continuous variation of the oil-to-water ratio. There are, generally, two ways to generate such systems. One way is to use multicomponent systems with increasing salinity which show phase separation to study progressively the properties of the lower, middle, and upper microemulsion phases. Such studies have been successfully p e r f ~ r m e d ~ . 'in~ *spite ' ~ of the conceptual and practical difficulties: for example, many parameters are changed simultaneously and one has no control over the composition of the microemulsion, not to mention the experimental problems involved. A second way to generate such systems has been suggested r e ~ e n t l y . ' ~ ,As ' ~ there is a considerable knowledge of phase behavior of surfactant systems one can effectively use such methods to find systems that form single-phase microemulsions. Actually, systems exist where a continuous variation of the oil-to-water ratio in a one-phase channel is possible. Unfortunately, such one-phase channels usually depend on temperature and exist in a rather narrow temperature interval such (1 1) Kunieda, H.; Shinoda, K. J . Colloid Interfuce Sci. 1980, 75, 601. (12) Kahlweit, M.; Strey, R. J . Phys. Chem. 1986, 90, 5239.
(13) Kahlweit, M.; Strey, R. Angew. Chem., Int. Ed. Engl. 1985, 24, 654. (14) Kaler, E. W.; Davis, H. T.; Scriven, L. E. J. Chem. Phys. 1983, 79, 5685. (15) Kaler, E. W.; Benett, K. E.; Davis, H. T.; Scriven, L. E. J . Chem. Phys. 1983, 79, 5673. (16) Thurston, G. B.; Salager, J. L.; Schechter, R. S.J . Colloid Interface Sci. 1979, 70, 517. (17) Kahlweit, M.; Strey, R.; Haase, D.; Kunieda, H.; Schmeling, T.; Faulhaber, B.; Borkwec, M.; Eicke, H.-F.; Busse, G.; Eggers, F.; Funck, T.; Richmann, H.; Magit, L.; Soederman, 0.; Stilbs, P.; Winkler, J.; Dittrich, A,; Jahn, W. J . Colloid Interface Sci. 1987, 118, 436. (18) Lichterfeld, F.; Schmeling, T.; Strey, R. J. Phys. Chem. 1986, 90, 5762.
that one has to change the temperature and the composition of the system simultaneously. Nevertheless, such studies can greatly contribute to the understanding of the structure of microemulsions. For example, a straightforward observation of the phase behavior will clearly show whether a particular system displays a continuous inversion from an oil-in-water into a water-in-oil microemulsion (appearance of a one-phase channel) or whether this inversion will proceed through an anisotropic phase. Here we present a study of the continuous inversion from an oil-tewater into a water-in-oil microemulsion. The present system allows a continuous variation of the oil-to-water ratio at constant persistence length. We show that during the inversion several transport properties behave in a very characteristic fashion which strongly support the appearance of two percolation processes of water and oil.
Schulman Line Since a microemulsion consists of oil and water domains separated by a monolayer of surfactant molecules, one can apply the above procedure and divide the sample into imaginary cubes of a length of side ,$ which are either filled with oil or water.8 As the orientation of neighboring surface elements will be mostly different, E must be chosen sufficiently large so that the surface appears wrinkled or curved on this length scale. Then the average interfacial area A per cube in which the surfactant must reside is related to the number of oil-water nearest-neighbor pairs of the cubes. Within the frame of a mean-field approximation, A = z,$2+,4w for a lattice with z next nearest neighbors where 4, and $,,, are the volume fractions of oil and water, respectively. Given the surfactant is in the saturated state, i.e., each surfactant molecule occupies a fixed surface Z, the total interfacial area per cube is A = ZNs = Z4,E3/u, where N , is the average number of surfactant molecules per cube which is related to the volume fraction of the surfactant q5s and to the volume of a single surfactant molecule us. Combining both expressions for A and introducing the length of a surfactant molecule a = u s / Z ,one
F
= z@04w/$s
or
E
a
@OdJW/A
(1)
Hence, a constant persistence length is achieved by keeping
@,,dW/&constant. For small surfactant concentrations &, the persistence length, ,$,is large and vice versa. If one attempts to vary the oil-to-water ratio (e.g., by changing &) at a constant persistence length, E, one has to vary the surfactant concentration according to
4s
(2)
+o+w
This is the Schulman line,8 which represents a parabolic cut through the Gibbs triangle from the water corner to the oil corner (heavy line in Figure 2). Let us consider the limit of the Schulman line when the microemulsion consists of mainly either oil or water. As we approach the oil-rich side (6, l), a constant, persistence length means a constant @,,,/& (water-to-surfactant ratio). Analogously, on the water-rich side (& 1), constant persistence length implies constant 4,/+, (oil-to-surfactant ratio). It is instructive to compare these ideas with experimental studies that determine the persistence length. In the high dilution domain
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The Journal of Physical Chemistry, Vol. 92, No. 1, 1988
the persistence length is approximately the diameter of the nanodroplets. It is well documented in oil-rich microemulsions that the water-to-surfactant ratio, @w/& (equivalent to wo),controls the size of the nan~droplets.~.'~ For 4o 1 and z = 6 we obtain from eq 1 = 6a4w/4s. Exactly this relation has been shown to predict the diameter of the nan0drop1ets.l~ Equation 1 has also been confirmed over a wide range of oil-to-water ratios by small-angle X-ray ~ c a t t e r i n g . ~ ~ J * For experimental work it would be ideal to be able to mix water and oil, add an appropriate surfactant, and study the properties of the resulting microemulsion along a Schulman line as one changes the oil-to-water content. Here we present a system that allows such a study.
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Experimental Section Materials. The microemulsions were prepared by mixing appropriate weight fractions of the three pseudocomponents: 0.5% aqueous sodium chloride solution (W), n-decane (0),and AOT (S). Volume fractions were calculated assuming ideal mixing behavior, using densities of brine (1.00 g ~ m - ~decane ), (0.73 g ~ m - ~and ) , AOT (1.14 g ~ m - ~ AOT ). (sodium bis(2-ethylhexyl) sulfosuccinate; Fluka) was purified by dissolving it in methanol with suspended active charcoal. The suspension was filtered and the solution of the surfactant dried in vacuo. We used bidistilled water; sodium chloride (Merck; p.a.) and n-decane (Fluka; purum) were used without further purification. Phase Diagrams. The samples were equilibrated by using a magnetic stirrer in an water-filled container that was thermostated within 0.02 K. Phase separation required a few minutes to several hours. The method becomes prohibitively slow only in regions of high dilution. Liquid crystalline phases were observed with crossed polarizers. Kerr Effect. The sample is thermostated in a quartz cell with two platinum electrodes. A laser beam polarized at 4 5 O with respect to the electric field enters the cell. The analyzer is crossed with respect to the polarizer so that no light is transmitted for an isotropic sample. If an electric field pulse induces birefringence in the sample, the light becomes elliptically polarized and the photodiode placed at the end of the beam registers an intensity that is related to the birefringence An. The latter is the difference of the refractive indices parallel and perpendicular to the field. The birefringence is related to the electric field E by the Kerr law20 An = XBE2
(3)
where X is the wavelength of the light used (633 nm). The Kerr constant B measures the amplitude of the response of the sample. The time lag between the applied field and the response of the birefringence is characterized by a rise time constant and a decay time constant. We determine these constants by fitting an exponential function to the time-dependent response. In our case: rise and decay time constants were approximately equal so that we focused on the rise time only. Using a X/4 device we found always a positive birefringence signal (An > 0). Our setup has been described in detail elsewhere.21 Viscosity. Kinematic viscosity Y was determined by using an Ubbelohde viscosimeter. Density p was measured by using an digital densitometer DMA 45 (Parr). The measured densites agree with calculated values assuming ideal mixing behavior. The dynamic shear viscosity 7 was obtained by using the relation 7 = pv. Conductivity. We use a cell with two platinum electrodes and an autobalancing bridge KONDUX 1 (Kamphausen) operated at 3 kHz or 380 Hz. (19) Zulauf, M.; Eicke, H.-F. J. Phys. Chem. 1979,83,480. Day, R. A.; Robinson, B. H.; Clarke, B. H.; Doherty, J. V. J. Chem. SOC.,Faraday Trans. I 1979, 75, 132. Assih, T.; Larche, F.; Delord, P. J. Colloid Interface Sci. 1982, 89, 35. (20) See, for example, O'Konski, C. T. In Molecular Electro-Optics; Krause, S., Ed.; Plenum: New York, 1986. (21) Hilfiker, R.; Eicke, H.-F.; Geiger, S.; Furler, G. J. Colloid Interface Sci. 1985, 105, 378.
Borkovec et al.
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Y 323 \
I-
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303
0.0 5
010
Figure 3. Phase diagram of the pseudoternary AOT-n-decane-aqueous 0.5% NaCl system as a function of surfactant fraction & and temperature T with equal amount of oil and water (@o = 4w). This cut is also shown in Figure 2 (dotted line). I
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1 - - _
-_-
-0-0
293. 0
4
c
.z
.8
1.0
Figure 4. Phase diagram of the pseudoternary AOT-n-decane-aqueous 0.5% NaCl system along the Schulman line where + o ~ w / & = 2.85 as a function of the oil volume fraction and temperature. The Schulman line corresponds to a constant persistence length of roughly 200 A. The dotted line is the one-phase channel where the composition of the microemulsion can be varied continuously and without any phase separation. This cut is also shown in Figure 2 (heavy line)..
Results Parts of the phase diagram of the present brine-decane-AOT system have been reported previously.l19l2 In Figure 3 a cut at an equal oil and water volume ratio ($o = &), varying the surfactant volume fraction &,is shown. For clarity the position of this cut is also shown in Figure 2 (dashed line). One can see (Figure 3) the typical triangular one-phase microemulsion regime (groove, 16) pointing toward the cut through the three-phase body13 (fish, 34). Above the groove one finds an upper oil phase in equilibrium with the microemulsion phase (24) and below a lower (water) phase in equilibrium with the microemulsion (24). The groove is split by the appearance of a liquid crystalline phase La.Such phase behavior is typical for many surfactant^.'^ The phase diagram along the Schulman line (cf. heavy line in Figure 2) is shown in Figure 4. Here we keep &&/& = 2.85 and vary $o, Le., the oil-to-water ratio. Note that as we change +o the surfactant volume fraction $s changes according to eq 2. For +o = 4wthe surfactant concentration stays approximately constant as one varies the oil-to-water ratio (see Figure 2). On the other hand, on the oil-rich side (40 1) one is diluting an oil-rich microemulsion with oil at a fixed water-to-surfactant ratio. Similarly, on the water-rich side ($o 0) we dilute the water-rich microemulsion with water at a fixed oil-to-surfactant ratio. In Figure 4 one can see a continuous one-phase channel that connects the oil-rich with the water-rich side (dotted line). In this one-phase channel one can change continuously the oil-to-water ratio and there is a continuous transition from a water-rich microemulsion (left side) to an oil-rich microemulsion (right side). Probably, the present microemulsion can be diluted on the water as well as on the oil side without any phase separation. As we follow the Schulman line, we expect the persistence length, E, to stay constant throughout the one-phase channel. Assuming a length of a single AOT molecule of 12 A and using eq 1, we estimate = 200 A.
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The Journal of Physical Chemistry, Vol. 92, No. 1, 1988 209
Two Percolation Processes in Microemulsions
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313 TIK 323 Figure 5. Semilog plot of the viscosity of the microemulsion as a function of temperature T at different volume fractions of oil bo along the Schulman line in the one-phase region.
- 5A ?5
h
c
m
Figure 7. Semilog plot of the viscosity of the microemulsion and its temperature coefficient as a function of volume fraction of oil along the one-phase channel (dotted line in Figure 4).
5
Qo
10
Figure 6. Semilog plot of the viscosity of the microemulsion as a function of volume fraction of oil boat different temperatures T. The heavy lines are interpolated from Figure 5 in the one-phase region. The dotted lines are eye guides only.
Nevertheless, an independent experimental determination of this quantity would be desirable. The water-rich side looks different from the oil side by the appearance of the liquid crystalline phases. Note that the phase diagram in Figure 4 (heavy line in Figure 2) intersects at +o = 0.46 and the phase diagram in Figure 3 (dashed line in Figure 2) at +s = 0.075. This one-phase channel is nicely suited for the study of the inversion process of an oil-in-water to a water-in-oil microemulsion. We have measured viscosity, electrooptical Kerr effect, and electrical conductivity. Unfortunately, the composition and temperature dependencies of the quantities of interest are somewhat complicated. Therefore, we focus at first on the viscosity data in some detail. Let us start with the viscosity data on the water-rich side. The viscosity as a function of temperature for a progressively increasing amount of oil in the one phase region is shown in Figure 5 . At low oil content the viscosity increases with temperature. For higher oil content the increase becomes steeper. At 4o = 0.2 the viscosity goes through a maximum as a function of temperature. Increasing the oil fraction even further, the viscosity is decreasing with temperature, steeply at first and flattening off later. A different way of presenting the data are cuts at constant temperature. Such a picture is shown in Figure 6. The data presented in Figure 5 were used to generate the left part of Figure 6; now we have included the complete data set covering the whole composition range. Again, as the single-phase region of the system depends on temperature, the curves are broken as the isotherms run outside the single-phase domain. On the water-rich side one can observe a pronounced maximum as a function of composition &, = 0.2, and it shifts with increasing temperature toward higher content of the minor component (oil). Remarkably, in a qualitative fashion the same behavior is observed on the oil-rich side. Again the viscosity passes through a second, flatter maximum near $o = 0.8. Now the effect of the temperature is the reverse, and the threshold shifts with increasing temperature toward smaller content of the minor component (water). It is
interesting to note that the isotherms at even lower temperatures than shown in Figure 6 would show a continuous increase of the viscosity with increasing water content. Such isotherms would run into the “dead-end channel” of the phase diagram. Still another way to present the data is to take a continuous cut through the one-phase channel along the dotted line shown in Figure 4. In this representation the system remains in a single phase throughout the whole composition range. However, the composition and temperature must be varied simultaneously. Even though the precise location of such a cut is somewhat arbitrary, the data along such a cut will represent the characteristics of the continuous transition of a water-rich into an oil-rich microemulsion. The viscosity data along this one-phase cut are shown in Figure 7. Again they show the characteristic double maxima, “camel hump”, structure. Below the temperature coefficient of the viscosity as a function of dois shown. This picture displays two characteristic oscillations and is similar to the derivative of the viscosity data with respect to do. In Figures 8 and 9 we present amplitude and relaxation time of the Kerr effect. Qualitatively the Kerr effect data look very similar to the viscosity data. For that reason we only present the data as a function of 4o along the one-phase cut (dotted line in Figure 4) together with their temperature coefficient. The maximum in the relaxation times on the oil-rich side is sharper than that for the viscosity data and is shifted toward higher oil content. The Kerr constant shows a similar behavior albeit the maximum on the oil-rich side is almost completely masked by the sharp maximum on the water side. Note the enormous magnitudes of the Kerr constant. In ordinary liquids one findsZavalues on V2m. Such large values of the Kerr constant the order of confirm the existence of extended structures in the microemulsion. Finally, in Figure 10 the conductivity as a function of temperature is shown, while Figure 11 presents the same data along the one-phase channel as a function of composition. The conductivity decreases very rapidly near &, = 0.8. This sharp drop shifts to higher oil content with increasing temperature, and the position of its inflection point correlates nicely with the maximum of the relaxation time.
Discussion The characteristic features of the transport properties of the microemulsion studied as a function of the oil-to-water ratio
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0
1.0
@o
313
318
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Figure 10. Semilog plot of the electrical conductivity of the microemulsion as a function of temperature fbr different volume fractions of oil in the one-phase region.
-1.0’ Figure 8. Semilog plot of the relaxation time of the electric birefringence (Kerr effect) of the microemulsion and its temperature coefficient as a function of volume fraction of oil along the one-phase channel (dotted line in Figure 4).
t 0
,Ai-,
c
c
^
,
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;1
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00
1.04 .C
o \
-A -l.O! Figure 9. Semilog plot of the Kerr constant of the microemulsion and its temperature coefficient as a function of volume fraction of oil along the one-phase channel (dotted line in Figure 4).
suggest that these properties are governed by two percolation processes: the percolation of oil at @o = 0.2 and percolation of water at do = 0.8. This hypothesis is supported by the following facts: first of all, the conductivity decreases abruptly at the water percolation threshold near 9, = 0.8. Such a sharp drop in the conductivity has been considered as the most important characteristic of a percolation transition.I0 Electrical conductivity traces qualitatively the fraction of water in the infinite cluster (see Figure 1). Obviously, the conductivity is unaffected by the oil percolation process as it is determined by the presence of the infinite water cluster. On the other hand, relaxation times and viscosity of the system should be equally affected by both percolation processes. The experimental data show indeed more or less pronounced maxima near the water as well as the oil percolation thresholds
10
Figure 11. Log plot of the electrical conductivity of the microemulsion and its temperature coefficient as a function of volume fraction of oil along the one-phase channel (dotted line in Figure 4). The arrow denotes the maximum slope observed (see Figure 10).
at @, i= 0.2 and & = 0.8. Birefringence amplitudes, relaxation times, and viscosity data follow qualitatively the volume fraction of isolated clusters which peak at both percolation thresholds (see Figure 1). This results in the characteristic double maximum structure of these properties when plotted as functions of the oil fraction. The fact that the maximum on the water side is higher than the maximum on the oil side hints toward a different nature of the interactions between surfactant monolayers in oil or water. This interpretation could be substantiated by self-diffusion studies which allow detailed conclusions about the connectivity of the net~ork.”~~~ Let us now compare the experimentally observed critical volume fraction of the percolation thresholds with theoretical estimates. We observe that both thresholds shift toward higher oil content with increasing temperature. This is caused by a strong variation of the interactions between the surfactant monolayers with temperature, which is also clear from the fact that the one-phase regime exists in a quite narrow temperature interval (Figures 3 and 4). The water percolation thresf ,Id is most accurately de(22) Kahn, A,; Lindstrom, B.; Shinoda, K.; Lindman, B. J . Phys. Chem. 1986, 90, 5799. Olsson, U.; Shinoda, K.; Lindman, B. J . Phys. Chem. 1986, 90, 4083. Geiger, S.; Eicke, H.-F. J . Colloid Interface Sci. 1986, 110, 181.
Two Percolation Processes in Microemulsions termined from the conductivity data. From Figure 10 one finds the critical value of 4o= 0.80 f 0.08 or of the minor component (water) 4w= 0.16 f 0.07, depending on the temperature. The oil percolation threshold can be well determined from relaxation times and viscosity, and one finds a volume fraction of the minor component (oil) +o = 0.18 f 0.02, again depending on the temperature. The fact that the threshold values of volume fraction of the minor component on the water side as well as on the oil side are in such close agreement is a further support for the symmetrical role of oil and water. These values can be compared with theoretical predictions. For noninteracting site percolation on a regular lattice as well as on random lattices in three dimensionsiOthe critical volume fraction of the minor component 4 is 4 = 0.16 f 0.02. Interactions decrease somewhat the critical volume fraction of the percolation.1° For the percolation of hard ~ p h e r e s ~the ~ qthreshold ~~ depends critically on an arbitrary shell thickness that must be introduced to define an overlap between the spheres. In the limit of narrow shells one finds23a very high percolation threshold at 4 = 0.35. For square well potential interactions there is a gradual lowering of the percolation threshold with increasing interaction strength down to phase separation at 4 = 0.13. However, the limit of narrow shells is possibly not physically relevant. Perhaps a more relevant case24where the thickness of the overlap shell is equal to the thickness of the attractive well shows a percolation threshold of 4 = 0.16 f 0.05. Definitely, the experimentally observed percolation threshold is in good accord with these theoretical estimates. Especially the agreement of both critical volume fractions with the value from site percolation is striking. We believe that the behavior observed is no peculiarity of the system studied but rather a general pattern characteristic for the continuous inversion of a water-rich into an oil-rich microemulsion. As discussed in the Introduction, the surfactant system will often separate into several phases as one attempts to change the oilto-water ratio over a wide range. Accordingly, only a few experimental studies of such an inversion e ~ i s t . ~ . ’ ~In- ~a *recent studyI7 rather similar results are found in an entirely different nonionic surfactant system, namely, C12E5-water-n-octane. The properties considered here show in the C12E5 system a very similar variation with the oil-to-water ratio. Even the “camel humps” on the water-rich side are higher than those on the oil-rich side although the difference is not as pronounced as in our case. The main difference is the temperature dependence of all the quantities, which is just the opposite to the present system. However, this is to be expected from the phase behavior: the nonionic surfactant system shows an upper oil phase at low temperatures (here at high T)whereas a lower water phase is seen at high temperatures (here at low r). A second important difference is the apperance of the plot of the Kerr constant as a function of the oil-to-water ratio. Whereas in our case Figure 9 strongly resembles “camel humps”, the Kerr constant of the Ci2E5 system peaks at a single maximum.I7 This difference is explained by the fact that in the case of C12E5 system the cut through the phase prism is chosen with a constant amount of surfactant.l’ This causes the correlation length E to peak near do = 0.5 with a varying oil to water ratio (cf. eq 1). As the Kerr constant increases strongly with the size of the particles so it will increase with the persistence length ( B (23) Bug, A. L. R.; Safran, S. A.; Webman, I . Phys. Reu. Lett. 1985,54, 1412. Safran, S. A.; Grest, G. S.; Webman, I. Phys. Rev. 1985, 32, 506. Haan, S. W.; Zwanzig, R. J . Phys. 1977, 10, 1547. (24) Netemeyer, S. C.; Glandt, E. D. J . Chem. Phys. 1986, 85, 6054. (25) Eicke, H. F.; Geiger, S.; Hilfiker, R.; Sauer, F. A.; Thomas, H. In Time Dependent Effects in Disordered Systems; Feder, J.; Riste, T., Eds.; Plenum: New York, 1987; in press. Eicke, H. F.; Hilfiker, R.; Thomas, H. Chem. Phys. Lett. 1985, Z20, 272. Bhattacharya, S.; Stokes, J. P.; Kim, M. W.; Huang, J. S. Phys. Rev. Lett. 1985, 55, 1884. Chen, S. J.; Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1984,88, 1631. Cabazat, A. M.; Chatenay, D.; Langevin, D.; Meunier, J. Faraday Discuss. Chem. SOC.1982, 76, 291.
The Journal of Physical Chemistry, Vol. 92, No. 1, 1988 211
= E3). This strong effect will mask the features of Figure 9, and the Kerr constant will peak at a single maximum. Unfortunately, this is difficult to verify as no one-phase channel is the C12E5 system along a Schulman line exists. The picture of two percolation processes that govern the structural inversion is further substantiated in the C12E5system by self-diffusion studies22which also confirm the symmetrical role of oil and water. Whereas the C,,E5 study is the only one on a three-component system, qualitatively similar results have been reported in more complicated system^.^,'"'^ Also “camel hump” like structure of viscosity, Kerr effect, and scattering data in the inversion regime of these microemulsions have been observed. As there are few studies that confirm the importance of both oil and water percolation processes, the water percolation on the oil-rich side has been studied in much detai1.2s21s25 However, the systems used in these studies do not allow a sufficiently high water content to observe the oil percolation on the water side. The situation is quite reminiscent of the present system as one approaches the water side at low temperatures: one gets caught in the dead-end channel of the phase diagram (see Figure 4). The water percolation is shifted to higher water content, the maximum in the viscosity is rather flat, and the viscosity keeps increasing with increasing water content. Its temperature dependence changes only once at the water percolation threshold. These observations point toward a somewhat different microscopic structure of the system in this part of the phase diagram. In summary, we present a study of the water-in-oil into an oil-in-water microemulsion inversion. Our system allows a continuous variation of the oil-to-water ratio at a constant persistence length, Le., along a Schulman line. We find that several transport properties are determined by two symmetrical percolation processes: an oil percolation on the water-rich side appearing at approximately 20% oil and a water percolation on the oil-rich side at 80% oil. These two symmetrical percolation thresholds play an important role in the inversion of an oil-in-water into a water-in-oil structure. This inversion is characterized by the succession of three structural types of a microemulsion. On the water-rich side with less than roughly 20% oil we have an oilin-water microemulsion. Here an infinite water cluster is present, but the oil is found in finite oil clusters. As we increase the oil content beyond the oil percolation threshold (approximately 20% oil), an infinite oil cluster is formed. Therefore between roughly 20% and 80% oil we have a bicontinuous microemulsion where two infinite clusters, an oil and a water cluster, are present simultaneously with a small fraction of isolated clusters. At a further increase of the oil content at water percolation threshold (approximately 80% oil), the infinite water cluster disappears. Therefore, for more than roughly 80% oil we have an water-in-oil microemulsion. Here the infinite oil cluster is present but the water is now found in finite water clusters. Throughout this structural inversion the microemulsion remains single phasic and the percolation transitions are not associated with any phase separations in the system. Note Added in Proof. Our manuscript was in print when we became aware of a self-diffusion study on a similar system.26 The results of this study support the picture put forward in the present paper. Acknowledgment. M.B. thanks Prof. M. Kahlweit and especially Dr. R. Strey for their kind hospitality during his visit at the Max-Planck-Institute for Biophysical Chemistry in Gottingen. This work has-been supported by the Swiss National Science Foundation. Registry No. AOT, 577-11-7; NaC1, 7647-14-5; decane, 124-18-5. Ceglie, A,; Lindman, B.; Shinoda, K. Langmuir 1986, (26) Carnali, J. 0.; 2, 417.
