3364
J. Phys. Chem. 1991, 95, 3364-3361
Ternary Water-in-Oil Microemulsions Made of Cationic Surfactants, Water, and Aromatic Solvents. 3. Self-Diffusion Studies in Relation to Exchange of Material between Droplets and Percolation Raoul Zana,* Jacques Lang, Institut Charles Sadron (CRM-EAHP),CNRS- ULP Strasbourg, 6, rue Boussingault, 67083 Strasbourg CPdex, France
and Daniel Canet Luboratoire de Mi?thodologie RMN (UA CNRS No. 406 LESOC), Universiti?de Nancy I , B.P. No 239, 54506 Vandoeuvre-les-Nancy CPdex, France (Received: June 29, 1990; In Final Form: August 19, 1990) Ternary water-in-oil microemulsionsusing alkylbenzyldimethylammoniumchloride (alkyl = dodecyl (N12), tetradecyl (N14), and hexadecyl (N16)) surfactants and benzene or chlorobenzene as oils have been investigated by means of electrical conductivity and NMR self-diffusion. The variations of the water self-diffusion coefficient with the [water]/[surfactant] molar concentration ratio w and with the volume fraction of benzene in the oil mixture in water/(benzene + chlorobenzene)/N16 microemulsions are well correlated with the changes of electrical conductivity, as expected from a model of microemulsions where the water cores of the droplets become increasingly connected above the percolation threshold. These connections, however, have a strongly dynamic character. This model permits us to explain the widely differing magnitudes of the changes of electrical conductivity, water self-diffusion coefficient, and rate of exchange of reactants between droplets upon increasing w. The self-diffusion coefficient of the oil has been found to be about half that of the bulk oil, as in studies reported by others.
Introduction The first part' in this series reported measurements of solubility of water in binary systems made of cationic surfactants and aromatic solvents. The results were interpreted in terms of the main effects that govern the stability of water-in-oil (w/o) microemulsions, that is, the curvature of the surfactant layer separating oil and water, and the attractive interactions between water droplets.*s3 The second part of our work4 reported results about water droplet sizes, interdroplet interactions, rates of exchange of material between droplets through collisions with temporary merging,5 and percolation of electrical conductivity in w/o microemulsions based mainly on water, chlorobenzene (CIBz), or benzene (Bz) and the benzalkonium chloride surfactants C,HM,(C6HSCH2)N+(CH3)2C1-with m = 10, 12,14,16, and 18 (referred to as Nm). For these systems it was found that, as predicted by theoretical treatments of microemulsion droplet sizes and interdroplet interactions increase as the surfactant chain length, characterized by m,decreases. It was also observed that the second-order rate constant k, for interdroplet collisions with exchange of material increases very much when m decreases. It was further observed that percolation occurs only when k, is larger than the threshold value of (1-2) X lo9 M-'s-'. This condition was shown to hold for all systems where both k, values and conductivity data were available, irrespective of the nature of the surfactant (anionic, cationic) and of the oil (alkanes, arena), [water]/[surfactant] molar concentration ratio w, temperature, and number of components of the microemulsion.5-8 Also, the value of k, is well correlated to the magnitude of the attractive interactions between droplets. The existence of interdroplet collisons with temporary merging is a central point in the above reports. It allows the reactants enclosed in colliding droplets to be rapidly transferred from one droplet to another, in the fairly short time during which the
surfactant layers separating the water cores of two collided droplets remain "open". It is very likely that water molecules are also exchanged between droplets by the same mechanism. This effect should therefore show as an increase of the water diffusion coefficient, in the same way as the rate constant k, or the electrical conductivity increase when, for instance, the ratio w is in~reased.~This led us to undertake a study of the selfdiffusion of water in water-ClBz-Nm w/o microemulsions as a function of w . Some measurements of oil self-diffusion coefficients were also performed, and we investigated the effect of a progressive substitution of chlorobenzene by benzene. Indeed, water-Bz-N 16 microemulsions show a percolation effectgand large k, values contrary to water-CIBzN16 micro emulsion^.^ It should be recalled that NMR selfdiffusion has been very successfully used for investigating the structure and dynamics of micellar solutions and microemulsions.1*2' In several studies, the results showed an accelerated diffusion of one or the other of the components of the system (surfactant in the case of nonionic surfactant micellar solutions;2c26
( I ) Jada, A.; Lang, J.; Zana, R. J . Phys. Chem. 1990, 94, 381. (2) Hou, M. J.; Shah, D. 0. Longmuir 1987, 3, 1086 and references therein. (3) Leung, R.; Shah, D. 0. J. Colloid Interface Sci. 1987, 120, 320, 330. (4) Jada, A.; Lang. J.; Zana, R.; Makhloufi, R.; Hirsch, E.; Candau, S. J. J. Phys. Chem. 1990, 94. 388. (5) Fletcher, P. D. 1.; Robinson, B. H. Ber. Bunsen-Ges. Phys. Chem. 1981,
(18) Jonsson, B.; Wennerstrom, H.; Niluon, P.; Linse, P. Colloid Polym. Sci. 1986, 264, 77 and references therein. (19) Olsson, U.;Jonstromer, M.; Nagai, K.;Soderman, 0.; Wennerstrom, H . ; Klasc, G. Prog. Colloid Polym. Sci. 1988, 76, 75. (20) Olsson, U.; Nagai, K.; Wennerstrom, H. J. Phys. Chem. 1988, 92,
85, 863.
( 6 ) Jada, A.; Lang, J.; a n a , R. J. Phys. Chem. 1989, 93, IO. (7) Lang, J.; Mascolo, J.; Zana, R.; Luisi, P. J. Phys. Chem. 1990, 94, 3069. (8) Jada, A.; Lang, J.; Candau, S.J.; Zana. R. Colloids Surf. 1989, 38, 251.
0022-3654191 /2095-3364$02.50/0
(9) Chatenay, D.; Urbach, W.; Cazabat, A.-M.; Langevin, D. Phys. Rev. Lett. 1985, 54, 2253. (IO) George, J.; Chen, J. W. Colloid Polym. Sci. 1986, 264, 896; 1987, 265. 45.
( I 1) Dozier, W.; Kim, M. W.; Chaikin, P. J . Colloid InterfuceSci. 1987, 115, 545. (12) Cheever, E.; Blum, F. D.; Faster, K.; MacKay, R. J . Colloid Interface Sci. 1985, 104, 121. (13) Nilsson, P.; Lindman, B. J . Phys. Chem. 1982, 86, 271. (14) Warnheim, T.; Sjoblom, E.; Henriksson, U.; Stilbs, P. J . Phys. Chem. 1984.88. ~., ~~,5420. . (15) Almgren, M.;Van Stam, J.; Swarup, S.; LofrBth, J. E. Longmuif 1986, 2, 432. (16) Olsson, U.;Shinoda, K.; Lindman, B. J . Phys. Chem. 1986,90,4083. (17) Blum, F. D.; Pickup, S.;Ninham, B.; Chen, S. J.; Evans, D. F. J . Phys. Chem. 1985,89, 71 1. ~~
6675. (21) Olsson, U.;Strom, P.; Soderman, 0.;Wennerstrom, H. J . Phys. Chem. 1989, 93,4512. (22) Blum, F. D.; Evans, D. F.;Nanagara, B.; Warr, G. hngmuir 1988, 4 , 1257. (23) Billman, J.; Kaler, E. W. Longmuir 1990, 6, 611. (24) Nilsson, P.-G.; Lindman. B. J. Phys. Chem. 1984, 88, 4764. (25) Brown, W.; Pu, Z.; Rymden, R. J. Phys. Chem. 1988, 92, 6086.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3365
Ternary Water-in-Oil Microemulsions
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0.1
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20
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30
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Figure 1. Variations of the water self-diffusion coefficient D, in N16ClBz (+), N14-CIBz (0). NI2ClBz (O), and in N16-Bz (A)microemulsion systems as a function of w = [H,O]/C; C = 0.270 M, T = 20 i 0.5 OC. (-) Calculated curve for N16-CIBz (see text). The arrows indicate the onset of electrical percolation (see Figure 2 and ref 4, Figure 16).
water or oil in the case of micro emulsion^'^^'^^^^^^), which were interpreted in terms of exchange of material between colliding particules (micelles, microemulsion droplets). The results reported below do show that an increased selfdiffusion of water is associated with the Occurrence of percolation and the increase of k,. We also report conductivity data showing that percolation can be induced by progressively substituting chlorobenzene by benzene, all other parameters remaining unchanged.
Experimental Section The preparation and purification of the surfactants with m = 12, 14, and 16 used in the present work have been described elsewhere.'*' The benzene and chlorobenzene were of high purity. The conductivity measurements were performed as described previously.' N M R self-diffusion studies were performed using a modified Brucker WP-2OOO spectrometer and a new technique that makes use of a gradient of the radio-frequency (rf) field created by a dedicated p r ~ b e . ~ ~This , ~ *technique only involves rf pulses which do not disturb the NMR measurement, as do static field gradient pulses usually employed.B Accurate and reliable results are therefore expected. The gradient was calibrated by reference to D20whose selfdiffusion is known.27 It was found to be 2.03 G cm-'. The time interval between the two gradient pulses (see ref 28 for details of the sequence) was generally set at 400 ms, whereas the length of the rf gradient pulses was varied in the range 0.5-12 ms; usually 15 values were employed. All the reported measurements were performed at 20 OC, as in parts 1 and 2 in this series. Results In our previous studies of the water-ClBz-Nm systems the surfactant aggregation number N, k,, and the electrical conductivity K were measured as a function of w! In the present work, in order to allow an easy comparison with these results the variations of the water self-diffusion coefficient, D,, were also measured as a function of w. The results are shown in Figure 1. For the N16-ClBz system D, decreases monotonically as w increases just like the electrical conductivity of this system (see Figure 16 in ref 4). The decrease of K was attributed to the increase of droplet size and the associated decrease of droplet concentration evidenced for this system upon increasing w.4 The D, vs w plot for the N 1K l B z system shows a minimum of small (26) Nilsson, P.-G.; Wennerstrom, H.;Lindman, B. Chem. Scr. 1985, 75,
67.
(27) Belmajdoub, A.; Boubel, J. C.; Canet, D.J. Phys. Chem. 1989, 93, 4844 and references therein. (28) Canet, D.; Diter, B.;Belmajdoub, A.; Brondcau, J.; Boubel, J. C.; Elbayed, K.J. Magn. Reson. 1989,81, 1. (29) Stilbs, P. Prog. NMR Specrrosc. 1987.19, 1 and references therein.
10-bl
0
1
I
I
10
20
30
* ,
Figure 2. Variation of the electrical conductivity K with w for the NlbBz microemulsion at 20 O C (+); C = 0.27 M. The systems at w < 6 were not monophasic at 20 OC so the measurements were performed at 25.5 O C for w = 3.8 and 4.6 and at 23 O C for w = 5.3. However, the temperature dependence of K was small. Thus for w = 5.3, K increased from 4.7 1 to 4.85 p S cm-' for T going from 23 to 25.5 O C .
amplitude and then an increase of D, with w at w > 30. Again this variation is similar to that of K with w : K first decreases as w increases from 10 to 30 because of increasing droplet size (decreasing droplet concentration) and then increases rapidly a t w > 30 when percolation takes place. Thus, for these two systems the variations of 0, and K are well correlated. At first sight such does not appear to be the case for the N12-ClBz and N16-Bz systems for which the D, values are high in the whole w range investigated and go through a minimum a t w = 10 and 20, respectively. As for the N14-ClBz system the initial decrease of 0,is due to the increase of droplet size. However, the position of the minimum in the 0,vs w plots does not correspond to the value of the percolation threshold obtained from the K vs w plots. Indeed, the threshold was found at w = 5 f 1 for both the N 12-ClBz and N 16-Bz systems! (The K vs w plot of the N 16-Bz system which had not been determined in our previous investigation is shown in Figure 2.) This difference obviously arises from the change of D, with droplet size below the percolation threshold and also somewhat above it. Indeed, in the semilogarithmic representation of Figure 1 it is seen that the initially decreasing parts of the 0,vs w curves due to the increasing droplet size run somewhat parallel for the four systems, at low w. On the other hand, even above threshold a significant amount of water is still present in the system under the form of isolated droplets or small droplet clusters, which contribute to D, by an amount decreasing upon increasing w. The measured 0,is the sum of this contribution, which varies with w as in the case of the N16-ClBz system (see Figure l), and of the percolation contribution which is very small below threshold and increases smoothly with w, above threshold. The resulting variation will thus show a minimum for an w value larger than the threshold and dependent on the system investigated, as experimentally observed. The w value corresponding to the threshold could be obtained by correcting the 0, vs w curves for the changes of droplet size with w, which are known, but one must also take into account the amoilnt of water in the form of isolated droplets or small droplet clusters. Unfortunately, this type of data is not available. At any rate such problems could be avoided by performing experiments at constant w (nearly constant droplet size) and increasing droplet concentration as in the recent study of Billman and Kaler.23 These authors reported equal values of the threshold as obtained from conductivity and self-diffusion. As a last remark concerning the results in Figure 1, it is to be noted that contrary to the fairly large increases of N and K' the increase of D, is moderate (factor up to 5 in the w ranges investigated). Moreover, the largest 0,value measured was only 4.5 X m2 s-I (N14-ClBz at w = 61.5), well below the value in the bulk, 2.5 X mz s-l, measured as part of this work. The results of Figure 1 indicate the possibility of inducing percolation in the N16-CIBz system by substituting ClBz by Bz, at constant o value, that is, at constant volume fraction of dispersed
3366 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991
Zana et al.
i A
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0.I 0
__----1
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0.2
0.1
1
0.6
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0.8
+Ex
1.0
Figure 3. Variations of the electrical conductivity (A) and water diffusion coefficients (B) as a function of the Bz volume fraction aBZ for N16-(Bz CIBz) systems with C = 0.268 M and w = 14.4 (+) and 34.4 (O), with C = 0.153 M and u = 34.4 (0).and with C = 0.113 M and u = 14.4 (X). T = 20 OC.
+
phase, CP. The electrical conductivity and D, were thus measured as a function of the volume fraction @Bz of Bz in the Bz-CIBz mixtures, all other parameters being unchanged. The results of Figure 3 clearly show the Occurrence of percolation, the increases being larger for w = 34.4 than for w = 14.4 and very much larger for K than for 0,. However, the changes of K with CPBr do not seem to be as steep as when percolation is induced by changing other properties, such as w or T.436-7*30 The percolation threshold @izhas been taken at the intercept of the extrapolated parts of the curve in the low CPBz range and in the range of rapid variation. The CPz ivalues from the D, plots appear to be larger than from the K plots. However, as for the results of Figure 1, the D, plots of Figure 3 should be corrected for the changes of droplet radius. From a qualitative point of view, one would expect this correction to increase the magnitude of the change of D, in going from ClBz to Bz, since R M increases with *B24.
Two additional series of conductivity measurements have been performed at lower surfactant concentration C, one at w = 34.4 and the other at w = 14.4. The results represented in Figure 3A show that aiz increases when C decreases (w = 34.4) and that the percolation disappears when Cis too small (w = 14.4). This is in agreement with results of other studies9where K was measured as a function of the volume fraction of the dispersed phase, at constant w . In other experiments not shown, performed with the N 16-Bz microemulsions at w = 34.4 and increasing C (that is, increasing a), we have found a threshold concentration of 7.1 X IO-* M, Le., CP = 0.076, close to that reported by others9 for the same system. Finally, Figure 4 shows the variations of the solvent (Bz and CIBz) diffusion coefficient D, with w , in the experiments corresponding to Figure 1. Three facts are noteworthy. First, the diffusion coefficients measured in the w range investigated are twice to thrice lower than for the pure solvent (DclBz = 3 X lo4 m2 s-I at 20 OC; DBz = 2.7 X m2 s-I at 25 OC, measured as part of this work). A similar finding has been reported in several with no explanation given. Second, the values of Dclez for the three Nm-CIBz systems fall on the same curve, within the experimental error. Finally, D, decreases with increasing w, for both Bz and CIBz, with a tendency to level off. (30) Lang, J.; Jada, A.: Malliaris, A. J . Phys. Chem. 19%8, 92, 1964.
I
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W
1
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Figure 4. Variation of the solvent diffusion coefficient 0, with w for the Nm/Bz (A) or ClBz (0, +, 0 ) systems; C = 0.270 M, T = 20 k 0.5 OC. Same symbols as in Figure 1.
.
The decrease of DpImm u w n increasine w (and volume fraction of the dispersed phase CP) cannot be d& oniy to the obstruction effect of the dispersed phase on the diffusing solvent molecules. Indeed, the theory predicts that the obstruction effect reduces the solvent diffusion coefficient at the most to 2/3 of its value in the absence of obstruction, the decrease being more or less steep depending on the particle shape.!* Clearly, DClez and D B are ~ reduced more than the theory predicts. Notice that attractive interzctions between solvent molecules and particles constitute another possible source of decrease of the solvent diffusion coefficient upon increasing 0 which cannot be discarded. . , . " a
o,5
I
Discussion Self-Diffusion Coefficient of Water and Aggregate Size in Nonpercolating Systems. The droplet radii can be calculated from the values of the surfactant aggregation numbers and the dimension of the surfactant ion, as previously indicated! The Stokes-Einstein equation can then be used to calculate the interaction-free diffusion coefficient Do of the micelles assumed to be spherical. In systems where interdroplet interactions are weak, the measured water self-diffusion coefficients D, should be close to the calculated D o . Our previous studies4 have shown that in the N16-CIBz system the interdroplet interactions are very weak as far as the mutual diffusion coefficient is concerned. We have therefore calculated the droplet diffusion coefficients for this system, using for the surfactant length a value 10 A shorter than the one calculated from bond lengths and angles since our previous measurements indicated a strong coiling of the alkyl chains of this surfactant in the interfacial layer.4 The calculated Do values, represented in Figure I by the curve in dotted line, are in excellent agreement with the experimental D, values at high w but are smaller than the D, values at low w. A qualitatively similar result has been found for the N14-CIBz system at w below the percolation threshold. Thus, the calculations yield Do = 5.7 X lo-" m2 s-l whereas D, = 9 X IO-" m2 s-I, at w = 20. The differences between Do and D, values may be thought to arise from a facilitated diffusion of water via droplet collisions with temporary merging. The contribution of this process is given byIS
D' = k,[M]dr/6 where [MI is the droplet concentration and d the center-to-center distance between two droplets. We have calculated [MI from the reported N values4 and obtained d assuming a cubic lattice of droplets.lS At w = 20 the calculations yield D'values of 2 and 0.45 X mz s-l for the N14-CIBz and N16-CIBz systems. Thus, facilitated water diffusion through collisions with merging may explain in part the difference found between Do and D, for the N14-CIBz system where the rate of collisions with merging is high4 but not for the N16-CIBz system where k, is much smaller. At this stage we note that these systems may contain a very small amount of water in the free state or hydrating free surfactant ion pairs or small surfactant aggregates. This water would nevertheless contribute at least in part to the difference between Do and D,, because of the very large value of the free water and/or free surfactant ion-pair diffusion coefficients with respect to typical droplet diffusion coefficients. Also, this contribution would decrease upon increasing w because the relative concentrations of
Ternary Water-in-Oil Microemulsions free water and of free surfactant ion pairs decrease upon increasing w. For the N16-CIBz system at w = 15, the concentration of free water required to increase the diffusion coefficient from 6.4 X IO-” m* s-I (calculated value) to 9 X lo-” m2 s-I (experimental value) is about 0.04 M. This value is equal to the solubility of water in chlorobenzene which was found to be of 0.04 f 0.015 M, as part of this work. Self-Diffusion of Water,Electrical Percolation, and Dynamics of Exchange of Material between Droplets. The three types of measurements used in the present study and ref 4, namely, time-resolved fluorescence quenching, electrical conductivity, and self-diffusion N M R probe the motion of the components of the water core: reactants (probe and quencher) solubilized in the water core, counterions, and water molecules, respectively. The results clearly show the correlation between the changes of k,, rate constant for exchange of material between droplets (motion of reactants) through collisions with temporary merging, electrical conductivity (motion of ions), and D, (motion of water). The occurrence of percolation affects all three properties. However, whereas it results in a very large and steep increase of K by a factor of lo2-lo3, it is seen only as relatively small changes (factor up to 5 ) of k,4 and 0,.These correlated increases of k,, D,, and K provide additional evidence that the exchange of material between droplets involves the opening of the double layer of surfactant which separates the water cores of two collided droplets or of droplets in contact in a droplet cluster. Indeed, above percolation threshold, an increasing amount of droplets are associated in clusters (including infinite clusters) which appear to be short-lived, constantly forming and breaking apart.9q”-31*32 However, in the clusters the droplets retain their identity in the sense that the interfacial surfactant layers coating them are not permanently open. (Time-resolved fluorescence quenching measures finite droplet sizes, even above percolation threshold?) The openings of these layers connect the water cores of neighboring droplets, thereby allowing a facilitated diffusion of the components of the water cores. The extent of connectivity, i.e., the number of adjacent “open” droplets in a cluster, increases with the frequency of opening of the surfactant layers. This frequency is directly obtained from time-resolved fluorescence quenching measurements as a first-order rate constant of reactant migration, k,. ( k , identifies as k, [MI when migration proceeds via collisions.) For most of the percolating systems investigated here km-l was found to be in the range 0.6-2 ps, the average time between successive openings. Another important quantity is the time to during which an open surfactant layer remains so. This quantity has been shown to be in the range of 1 ps for some systems.33 Clearly, the longer to and the larger k,, the longer the sequence of connected water droplets and the faster the diffusive motion of the water core components will appear to be. At this stage one must consider the time scale of the methods used to study these motions and the length scale probed. In time-resolved fluorescence quenching the time scale is given by the probe lifetime, Le., about 1 ps. The length scale is typically of a few droplet diameters, the distance over which probe and quencher in different droplets must diffuse to meet and react. In N M R self-diffusion the time scale is much longer, about 0.4 s, and as a result, the length scale is of several microns. Finally, in conductivity at the operating frequency of 1 kHz the time scale is of about 100 ps, intermediate between the other two techniques. This model of clustered droplets with aqueous cores temporarily connected permits the explanation of the difference between the changes of D,, k,, and K with w. Consider first D,. Below percolation D, corresponds to the droplet diffusion coefficient which is of about m2 s-’ at low w and (2-3) X m2 s-l at high w in the absence of percolation (see Figure 1). Close to and above the percolation threshold, an additional contribution (31) Guering, P.; Cazabat, A.-M.; Paillette, M. Europhys. Leu. 1986, 2, 953. (32) Fletcher, P. D.; Howe, A.; Robinson, B. H. J . Chem. SOC.,Faraday Trans. I 1987,83, 985. (33) Howe, A,; McDonald, J.; Robinson, B. H. J . Chem. SOC.,Faraday Trans. I 1987, 83, 1007.
The Journal of Physical Chemistry, Vol. 95, NO. 8, 1991 3367 comes from the diffusion of water in connected droplet cores. This contribution will progressively replace that associated with single droplets. As w increases and droplets in clusters become increasingly connected, D, increases and tends toward the value of the diffusion coefficient of water in the bulk (2.5 X lo+’ m2 SI). This situation corresponds to very high w values where experiments could not be performed because of the limited water solubility. As a result, only a moderate increase of D, was measured experimentally. We now turn to the migration of reactants (probe and quencher) solubilized in water cores. Recall that migration is monitored through the quenching of the probe fluorescence. We have noted that slightly below as well as above the percolation threshold k, [MI (or k,) is of the order of 106 s-I and changes only little with w or with the system. This result indicates that the quenching is limited by the rates of opening and closing of the surfactant layers whether it occurs via collisions with temporary merging of droplets (below threshold) or simple temporary merging of droplets in clusters (above threshold). During the lifetime of the excited probe, probe and quencher can diffuse over a distance that is several times larger than their average distance in different droplets of a cluster. The quenching reaction has ample time to occur every time there is an opening of the two surfactant layers separating a core containing a quencher and a core containing an excited probe provided they remain so a time to comparable to that required for diffusion. This appears to be the case. Indeed t is of about 1 ps,” whereas the time required to diffuse over 300 (that is 2-3 droplet diameters) is only 0.15 ps, assuming D N 10-9 m2 s-l. Finally, we consider the electrical conductivity. The enormous increase of K in going from the w percolation threshold to w values well above threshold is due to a change in the nature of the charge carriers. Below threshold the electrical charges are carried by the droplets which are in small number and diffuse slowly (low molar c o n d u ~ t i v i t y ) . ~Above ~ * ~ ~ threshold the counterions also act as carriers, and their contribution increases very rapidly with the connectivity of the droplets. Indeed, these new carriers are N times more numerous than the droplets ( N = surfactant aggregation number), and their molar conductivity is much larger than that of the droplets. As a result, at w slightly above threshold the conductivity becomes much larger than below threshold. As a last remark we note that our fluorescence studies of the above systems always indicated the existence of discrete droplets with a rate of interdroplet exchange of material rapidly increasing with w . Thus, these microemulsions are not bicontinuous, in the meaning usually given to this word, on the fluorescence time scale. Nevertheless, both K and D, increase above the percolation threshold as one would expect for an increasingly bicontinuous system. This however is the result of the highly dynamic character of the structures present in the system above threshold. Indeed the exchange of material (water, ions) between droplets occurs on the microsecond time scale, whereas electrical conductivity and N M R self-diffusion probe the systems on time scales of 100 ps and 0.4 s, respectively. For these methods therefore the systems are seen as b i c o n t i n u ~ u s . ~ ~ * ~ ~
8:
Conclusions We have shown that the self-diffusion coefficient of water in the ternary water-in-oil microemulsions investigated increases moderately above the percolation threshold, with the [water]/ [surfactant] molar concentration ratio or with the benzene volume fraction when benzene + chlorobenzene mixtures are used as oil, contrary to the very large and steep changes of electrical conductivity. These results as well as those concerning the interdroplet migration of reactants, previously investigated by time-resolved fluorescence quenching, have been explained by using a model of microemulsions where the droplet water cores become increasingly connected above the percolation threshold. These connections are ~ h o r t - l i v e d . ~ ~ (34) Eicke, H.-F.;Borkovec, M.; Das-Gupta, 9. J . Phys. Chcm. 1989, 93, 314. (35) Hall, D. G.J . Phys. Chem. 1990, 94, 429.
