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dichloroethane system
Power Law Behavior of Conductivity in the AOT/Dichloroethane System W. R. HEFFNER AND M. A. MARCUS A T & T Bell Laboratories, Murray Hill, N e w Jersey 07974 Received May 6, 1987; accepted September 30, 1987 In this paper we present electrical conductivity measurements on the AOT/dichloroethane system over more than four decades of surfactant concentration. The conductivity exhibits a power law dependence on the surfactant concentration over more than three decades, with an exponent of 0.73 +_ 0.02. Above the power law regime, the conductivity displays a m a x i m u m , which occurs at a weight fraction of 0.14. We also describe an apparatus with automatic dilution and m e a s u r e m e n t features which expedite the determination of conductivity vs concentration profiles in low conductivity solvents. © 1988 Academic Press,Inc. INTRODUCTION
Electrical conductivity measurements have been employed widely in the past to determine the critical miceUe concentration (cmc) of surfactants in aqueous solutions (1, 2). Generally the cmc is signaled by an abrupt change in the slope of the conductivity vs concentration curve, which is often seen as a break in the curve when the data are plotted on some appropriate axes. Conductivity vs concentration profiles have also been used to probe micellization in nonaqueous solvents (3-5), although this approach is far less commonly used than in aqueous solutions, possibly because of diiliculties associated with measuring the low conductivities in nonaqueous systems. Correspondingly, much less is known about the conductivity in these systems at low surfactant concentrations. On the other hand, conductivity has been extensively studied in inverse micellar systems at much larger surfactant concentrations, near the percolation threshold (6-14). Many of these studies have been performed on systems employing the surfactant aerosol OT (AOT) (11-14). AOT forms inverse micelles (both with and without added water) in a number of nonaqueous solvents, and a great deal of structural and related information is known about the micelles in some of these solutions (15-27). 617 Journalof Colloidand InterfaceScience,Vol. 124,No. 2, August1988
In this paper we present measurements of the electrical conductivity in the AOT/dichloroethane system over an extended range of surfactant concentrations. Our interest is to include the low concentration regime where a cmc signature might be expected to appear. To facilitate these measurements we have developed a method which lends itself to computer automation of the dilution and collection of data. With this method it is convenient to obtain a greater density of conductivity data than are usually determined, providing more precise information for such features as the cmc~ Results using this method on the AOT/ dichloroethane system are also compared with those using a more conventional conductivity cell, with good agreement. Interestingly, the data do not exhibit a cmc signature. Instead we observe an anomalous power law dependence of the conductivity on the surfactant concentration over more than three decades of concentration and a maximum in the conductivity near the percolation threshold. EXPERIMENTAL
Automation of the Experiment The technique employed in determining conductivity a vs concentration profiles often involves preparing a series of solutions of vat0021-9797/88 $3.00 Copyright© 1988by AcademicPress,Ine, All rightsof reproductionin any form reserved.
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ious dilution and then measuring their conductivities in a conductance cell employing some sort of bridge circuit. This process, especially preparing the dilution series, can be slow and tedious. The number of data points thus obtained is often a compromise between the desired precision and the patience of the experimenter. To circumvent this limitation, we have designed a conductivity cell appropriate for automatic dilution and computeraided automation of data collection and analysis. The automated cell design allows a periodic monitoring of cell conductivity while surfacrant-rich material is progressively added to the cell. A sketch of our apparatus is shown in Fig. 1. The apparatus consists of three main systems: the pump, the cell, and the currentmeasuring circuitry. All of these systems are under the control of an LSI- 11 computer. The pump is a positive displacement piston type (Micro r-petter, Fluid Metering, Inc., Oyster Bay, NY) capable of accurate delivery of microliter volumes. The conductivity cell consists of a copper base with a glass cylinder wall (2 cm diameter) and a brass stirring "foot." The stirring action is achieved through a solenoid attached to the end of this foot. A spring maintains the foot in its down position, where it is held apart from the base by three glass rods imbedded in the copper base. The glass rods extend approximately 100/~m above
LS' I
COMPUTER
FOOT
CURRENT AMP
SURFACTANTRICH SOLUTION
FIG. 1. Schematic representation of the apparatus used to automate the conductivity measurements. The stirring "foot" also serves as one of the electrodes. In this way we achieve a very large cell constant while providing good mixing. Journal of ColloM and Interface Science, Vol. 124, No. 2, August 1988
the base. Conductivity measurements are made while the foot is held against these spacers. By pumping a dye solution into the cell, we have observed that adequate mixing occurs for fluid volumes up to 3 ml. The special feature of this new cell is that the stirring foot doubles as the upper electrode. With this design we achieve both a large cell constant (approximately 0.6 m) and proper mixing of the materials within the cell. The copper base doubles as the other electrode. The base is also provided with a heating element so that temperature control is possible, though measurements in this study have all been carfled out at room temperature. Another feature of the cell is the small sample volume required for a complete a vs concentration determination (approximately 1 ml). This feature is especially significant for experiments where minimal solvent or surfactant is available. A typical sequence would be as follows: The cell is filled with approximately 1 ml of pure solvent and a surfactant-rich solution is loaded into the pump reservoir. The pump is activated so that a small aliquot (typically a few microliters) o f a surfactant-rich solution is delivered to the contents already in the cell. Following this delivery, the foot is pumped several times to achieve good mixing and then a measurement is taken of the current flowing through the cell. After this reading is taken by the computer, the cycle is repeated. A lock-in amplifier (PAR 5204) technique is used to measure the in-phase and quadrature component of the current. A fast current amplifier has been built which has essentially no phase shift below 50 kHz. The circuit utilizes the fast FET operational amplifier LH0032 (National Semiconductor). The stirring foot electrode is maintained at virtual ground. In this way, grounded guard shields can be employed to keep stray currents and noise at the input to a minimum. Using this instrumentation and our large cell constant, we are able to measure conductivities as low as 10-11 S/ m. The large cell constant minimizes the relative error introduced by stray capacitive currents.
CONDUCTIVITY IN AOT SOLUTIONS The cell constant was determined by measuring the quadrature current for several liquids of known dielectric constant. A cell constant of approximately 60 cm was obtained. All data reported were measured at a frequency of 1 kHz and an applied voltage of 100-200 mV. Measurements were also made at other voltages to verify that the conductivities are independent of field. For comparison, we have also used a commercial conductivity probe (YSI Instruments), with a nominal cell constant of 1.0 cm.
Sample Preparation The A O T surfactant (sodium di-2-ethylhexyl sulfosuccinate) was obtained from Fluka (purum grade). This material was further purified as follows: The A O T was first dissolved in methanol. This cloudy solution was centrifuged at 5900g for a half hour, and the clear supernatant was retained. This solution was heated to boiling until m u c h of the methanol was removed. The remaining methanol was
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removed by heating the solution to 120°C in a vacuum oven for one hour. The solution bubbled and frothed during the initial heating, but by 120°C all activity had subsided, leaving a foamy cake. The purified material was white and had no odor. This procedure removed a methanol-insoluble contaminant, possibly sodium bisulfite. The 1,2-dichloroethane (reagent grade) was used without further purification. A O T is very soluble in dichloroethane. For the automatic dilutions three surfactant-rich master solutions were used to cover the range from 10 - 4 to 0.3 weight fraction AOT. For the commercial (YSI) probe, a separate series of AOT/dichloroethane solutions were prepared by successive (1:1) dilutions o f a 4 wt% master mixture down to 10 -5 weight fraction AOT. RESULTS In Fig. 2 we present the conductivity results obtained from the automatic dilution appa-
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FIG. 2. Conductivity vs concentration on a log-log scale for the AOT/dichloroethane system at room temperature. Data from three separate automatic dilutions are shown (e, A, O) together with corroborative data obtained using a commercial probe ((3). The solid line has a slope of 0.73. Journal ofColloid and Interface Science, Vol. 124, No. 2, August 1988
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HEFFNER AND MARCUS
ratus together with those obtained from the YSI probe. The conductivities have been plotted vs the concentration (q~)of AOT in weight fraction on a log-log scale. The conductivities indicated are the solution conductivity minus the conductivity of the pure solvent. The pure solvent conductivity (1. I × 10-6 S/m) has been subtracted so that the data plotted reflect the contribution to the solution conductivity from the surfactant added. For all but the first few concentrations, the conductivity of the pure solvent is quite negligible in comparison. The accuracy of the measurements is limited by the reproducibility of the cell spacing, which is less than 2%. The automatic dilution data in this figure were obtained from three separate dilutions of master solutions. There is good agreement between the regions of overlap. The figure also indicates excellent agreement between conductivities measured using the automatic dilution apparatus and measurements made on separate solutions using the commercial YSI probe. Two features are apparent in this graph. First, there is a distinct maximum in the conductivity at 0.141 weight fraction, and second below this maximum the data exhibit a power law (~ oc ~t) dependence over more than three decades in concentration. An exponent t = 0.73 _ .02 was obtained from a least-squares fit to the data below q5 = 2 X 10 -2. Although the conductivity of the solvent was subtracted from the data, it was not a fitting parameter. Rather, it was measured and used without adjustment. It is not possible to adjust this value to make the exponent appreciably different from 0.73. Note that the quantity raised to the power is ~, not ~ - ~b0,where q~ois some critical concentration (28). If there is such a ~o it must be small compared to 10 -5 . There does not appear to be a cmc within the concentration range evaluated, as indicated by the absence of any breaks in slope in this curve. Solutions with weight fractions below 10 -5 become increasingly difficult to evaluate because their conductivities approach that of the pure solvent. Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
DISCUSSION
AOT is known to form inverse micelles in many nonaqueous solvents. Conductivity in these solutions has been studied extensively in regard to percolation phenomena (1 l - 14, 28). Earlier investigations (7, 8) have identified two thresholds in inverse micellar systems. One threshold occurs around 0.3 volume fraction and is associated with dense packing of the spherical micelles (7, 8). Another, lower threshold has been observed to occur in many systems (7, 8, 11-13), at approximately 0.1 volume fraction. This lower threshold is associated with percolation. The percolation threshold occurs at a volume fraction below that predicted for noninteracting hard spheres. Grest and co-workers (29, 30), and others (1113, 28), have attributed this lowering to clustering that occurs as a result of attractive interactions. Because the maximum in our data occurs near the percolation threshold, it is reasonable to suspect that it is due to the onset ofmicellar interaction, possibly repulsion. Such intermicellar repulsion would be manifest by a dramatic fall off in the mean free path of the micellar species. The viscosity would likewise increase. In this case, the conductivity, if due to micelles, should turn down. Lalanne et al. (27) have studied the transport properties in inverse micellar AOT/carbon tetrachloride solutions. They also observe a decrease in the thermal conductivity of their solutions at around 0.1 volume fraction AOT. This observation is consistent with the notion that micellar repulsion may be responsible for the maximum in conductivity observed in our AOT/dichloroethane system. An alternative explanation is that a structural change occurs near the maximum. In a recent paper Georges and Chen (2) reported a similar maximum to occur in the conductivity of aqueous sodium dodecyl sulfate systems at about the same concentration as in our system. In that case, the maximum was attributed to a phase transition between an oil-
CONDUCTIVITY
IN AOT
in-water and a water-in-oil structure. In a somewhat related set of experiments. Chen et al. (31) have observed a precipitous drop in the conductivity as water was added to a didodecyldimethyl ammonium bromide/H20/ alkane system. They speculate that this behavior occurs as the result of a transition from an interconnected network of tubes to a spherical microemulsion structure. The question as to whether, indeed, there are micelles in our solutions is central. Initial efforts to observe micelles in dynamic light scattering has shown no appreciable signal in the micellar size range for a 0.6 wt% solution. Lalanne et al. (27) also obtained "no significant signal" in the case of dry AOT/carbon tetrachloride solutions, although micelles were clearly seen in their wet AOT/water/carbon tetrachloride solutions. We feel that neither their results nor ours on the dry AOT solutions are conclusive because poor contrast (i.e., good index match) between the AOT and the solvent could mask the micellar structure, if present. The refractive index of AOT is 1.470 (32), while those of 1,2-dichloroethane and carbon tetrachloride are 1.444 and 1.460, respectively. Conductivity and light scattering in wet AOT/dichloroethane solutions might contribute additional insight into this question, but that work has not been completed. The other interesting aspect of our data concerns the power law behavior observed at concentrations below the maximum. One might have anticipated a linear dependence of the conductivity on the surfactant concentration, based on a micellar model of conductivity. Consider the model where conductivity is predominantly through the drift of charged micelles. Above the cmc, the total number of micelles should be proportional to the total surfactant concentration. For spherical micelles of radius r, the micelle density is given by 3~/47rr 3, where • is the volume fraction. If the fraction of micelles ~ which are charged can be assumed to remain a constant, then the carrier density would be proportional to the total number of micelles and thus the total
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SOLUTIONS
surfactant concentration. This, of course, also assumes the micelle size to be independent of concentration. Elementary application of Stokes law to this model yields the following form for the conductivity .Z 2
87r2~r4 ~, where n is the viscosity and Z is the micellar charge. Such a simplistic model is clearly inadequate to explain the sublinear power law behavior observed in our experiments. This model might be salvaged if the micellar radius increases with increasing concentration, but a corresponding power law dependence of the radius would be required. In studies made on micellar size in nonpolar solvents and at larger concentrations (16, 21), the micelle size is usually independent of concentration. In a study made at low concentration, Assih et al. (18) observed a size increase of the micellar radius with dilution in the AOT/H20/dodecane system. Thus there is little precedent to support the idea of micellar growth with increasing concentration. Further, we are not yet certain that micelles are present at all within the low concentration regime of our system, especially since no cmc signal was observed in the conductivity and light scattering showed no micellar signal in the power law regime. One might reasonably suspect surface conductivity as another possible explanation for the sublinear behavior. If such was the case, the measured conductivity would depend greatly on the particular geometry of the conductivity cell used, especially among cells with different surface to volume ratios. We find no such difference between our results using two cells with cell constants differing by almost three orders of magnitude. Further, a third confirming set of measurements was carried out in another laboratory, using an entirely different apparatus and cell, and the results were identical. We therefore do not believe that the effect is due to surface conductivity. Sublinear behavior could also occur if the carriers arose from dissociation of the surfacJournal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
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t a n t m o n o m e r s . T h e n one m i g h t expect a n e x p o n e n t o f 0.5 r a t h e r t h a n the one observed. Also, such b e h a v i o r is u n l i k e l y to o c c u r over three decades. In a n effort to c o m p a r e o u r results with c o n d u c t i v i t y d a t a in o t h e r inverse m i c e l l a r solutions, we have f o u n d t h a t experi m e n t a l d a t a o n the conductivities o f solutions far b e l o w p e r c o l a t i o n is sparse. M o s t o f the p r e v i o u s studies have focused o n c o n d u c t i v i t y n e a r percolation. T h e origin o f the p o w e r law behavior in o u r d a t a r e m a i n s unclear, although similar p o w e r law b e h a v i o r has b e e n o b s e r v e d in a c y a n o b i p h e n y l solvent (33). T h e r e a n exp o n e n t o f 0.6 was reported to describe the d a t a over two decades in c o n c e n t r a t i o n . CONCLUSIONS W e have d e s c r i b e d a m e t h o d w h e r e b y sol u t i o n c o n d u c t i v i t i e s c a n b e m e a s u r e d while surfactant-rich material is a u t o m a t i c a l l y a d d e d to the solution. T h e c o n d u c t i v i t y o f A O T / d i chloroethane solutions have been so obtained. W e have d e m o n s t r a t e d t h a t this m e t h o d gives g o o d a g r e e m e n t with d a t a o b t a i n e d b y m o r e conventional methods. T h e A O T / d i c h l o r o e t h a n e solutions show two interesting features. O n e is a m a x i m u m in the c o n d u c t i v i t y at a weight fraction which m i g h t be associated with m i c e l l a r i n t e r a c t i o n s or an otherwise u n o b s e r v e d structural transf o r m a t i o n . T h e o t h e r feature is a p o w e r law d e p e n d e n c e o f the c o n d u c t i v i t y o n the surfacrant c o n c e n t r a t i o n w h i c h occurs o v e r m o r e t h a n three decades b e l o w the m a x i m u m . T h e p o w e r law b e h a v i o r occurs with an e x p o n e n t o f 0.73 a n d with a negligible critical c o n c e n tration. T h i s b e h a v i o r is in c o n t r a d i c t i o n to the usual m o d e l s associated with c o n d u c t i v i t y in surfactant solutions. T h e d a t a r e m a i n an a n o m a l y , a n d further e x p e r i m e n t s into the n a t u r e o f t h e c o n d u c t i o n m e c h a n i s m , as well as the m i c r o s t r u c t u r e o f the solution, are needed. ACKNOWLEDGMENTS We thank E. Rietman for confirming our conductivity measurements on his apparatus, and P. Wiltzius for sharing Journalof Colloidand InterfaceScience,Vol.124.No. 2. August1988
his preliminary light scattering results. We are also indebted to F. Unterwald, M. van Dijk, W. van Saarloos, R. Cava, and B. Vyaz for useful comments and discussions. REFERENCES 1. Mukerjee, P., and Mysels, K., "Critical Micelle Concentrations of Aqueous Surfactant Systems," NBS Bulletin NSDS-NBS 36. Washington, DC 1971. 2. Georges, J., and Chen, J. W., J. Colloid Interface Sci. 113, 143 (1986). 3. Eicke, H. F., and Shepherd, J. C., Helv. Chim. Acta. 57, 1951 (1974). 4. Eicke, H. F., and Arnold, V., J. Colloid Interface Sci. 46, 101 (1974). 5. Eicke,H. F., Hammetich, H., and Vasta, G.,J. Colloid Interface Sci. 93, 593 (1983). 6. Lagues, M., J. Physique 40, L-331 (1979). 7. Lagues, M., Ober, R., and Taupin, C., J. Physique 39, L-487 (1978). 8. Lagourette, B., Peyrelasse, J., Boned, C., and Clausse, M., Nature (London) 281, 60 (1979). 9. Cazabat, A. M., Chatenay, D., Langevin, D., and Meunier, J., Faraday Discuss. Chem. Soc. 76, 291 (1982). 10. Chatenay, D., Urbach, W., Cazabat, A. M., and Langevin, D., Phys. Rev. Lett. 54, 2253 (1985). 11. Kim, M. W., and Huang, J., "Transport Properties of Microemulsions" in Statistical Thermodynamics of Micelles and Microemulsions (H. Chen, Ed.). Springer-Verlag, New York, in press. 12. Kim, M. W., and Huang, J., Phys. Rev. A 34, 719 (1986). 13. Bhattacharya, S., Stokes, J., Kim, M., and Huang, J., Phys. Rev. Lett. 55, 1884 (1985). 14. van Dijk, M. A., Phys. Rev. Lett. 55, 1003 (1985). 15. Peri, J. B., J. Colloidlnterface Sci. 29, 6 (1969). 16. Zaluf, M., and Eicke, H. F., J. Phy. Chem. 83, 480 (1979). 17. Wong, M., Thomas, J., and Nowak, T., J. Amer. Chem. Soc. 99, 4730 (1977). 18. Assih, T., Larche, F., and Delord, P., J. Colloid Interface Sci. 89, 35 (1982). 19. Kotlarchyk, M., and Chen, S., Phys. Rev. Lett. 53, 941 (1984). 20. Kotlarchyk, M., Huang, J., and Chen, S., J. Phys. Chem. 89, 4382 (1985). 21. Kotlarchyk, M., Chen, S., Huang, J., and Kim, M., Phys. Rev. A 29, 2054 (1984). 22. Chen, S. H., and Huang, J., Phys. Rev. Lett. 55, 1888 (1985). 23. Huang, J., Safmn, S., Kim, M., Grest, G., Kotlarchyk, M., and Quirke, N., Phys. Rev. Lett. 53, 592 (1984). 24. Peyrelasse, J., Boned, C., and Matin, G., ColloidPolyre. Sci. 264, 143 (1986). 25. van Dijk, M. A., Broekman, E., Joosten, J. G. H., and Bedeaux, D., J. Physique 47, 727 (1986).
CONDUCTIVITY IN AOT SOLUTIONS 26. Day, R. A., and Robinson, B. H., J. Chem. Soc., Faraday Trans. 1 75, 132 (1978). 27. Lalanne, J. R., Pouligny, B., and Sein, E., J. Phys. Chem. 87, 696 (1983). 28. Eicke, H. F., and Hilfiker, R., Chem. Phys. Lett. 125, 295 (1986). 29. Grest, G., Webman, I., Safran, S., and Bug, L. Phys. Rev. A 33, 2842 (1986).
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30. Safran, S. A., Webman, I., and Grest, G. Phys. Rev. A 32, 506 (1985). 31. Chen, S. J., Evans, D. F., Ninham, B. W., Mitchell, D. J., Blurn, F. D., and Pickup, S., J. Phys. Chem. 90, 842 (1986). 32. Rogers, J., and Windsor, P. A., J. Colloid Interface Sci. 30, 247 (1969). 33. Heffner, W. R., and Marcus, M. A., unpublished.
Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
Electrical conductivity measurements have been employed widely in the past to determine the critical miceUe concentration (cmc) of surfactants in aqueous solutions (1, 2). Generally the cmc is signaled by an abrupt change in the slope of the conductivity vs concentration curve, which is often seen as a break in the curve when the data are plotted on some appropriate axes. Conductivity vs concentration profiles have also been used to probe micellization in nonaqueous solvents (3-5), although this approach is far less commonly used than in aqueous solutions, possibly because of diiliculties associated with measuring the low conductivities in nonaqueous systems. Correspondingly, much less is known about the conductivity in these systems at low surfactant concentrations. On the other hand, conductivity has been extensively studied in inverse micellar systems at much larger surfactant concentrations, near the percolation threshold (6-14). Many of these studies have been performed on systems employing the surfactant aerosol OT (AOT) (11-14). AOT forms inverse micelles (both with and without added water) in a number of nonaqueous solvents, and a great deal of structural and related information is known about the micelles in some of these solutions (15-27). 617 Journalof Colloidand InterfaceScience,Vol. 124,No. 2, August1988
In this paper we present measurements of the electrical conductivity in the AOT/dichloroethane system over an extended range of surfactant concentrations. Our interest is to include the low concentration regime where a cmc signature might be expected to appear. To facilitate these measurements we have developed a method which lends itself to computer automation of the dilution and collection of data. With this method it is convenient to obtain a greater density of conductivity data than are usually determined, providing more precise information for such features as the cmc~ Results using this method on the AOT/ dichloroethane system are also compared with those using a more conventional conductivity cell, with good agreement. Interestingly, the data do not exhibit a cmc signature. Instead we observe an anomalous power law dependence of the conductivity on the surfactant concentration over more than three decades of concentration and a maximum in the conductivity near the percolation threshold. EXPERIMENTAL
Automation of the Experiment The technique employed in determining conductivity a vs concentration profiles often involves preparing a series of solutions of vat0021-9797/88 $3.00 Copyright© 1988by AcademicPress,Ine, All rightsof reproductionin any form reserved.
618
HEFFNER AND MARCUS
ious dilution and then measuring their conductivities in a conductance cell employing some sort of bridge circuit. This process, especially preparing the dilution series, can be slow and tedious. The number of data points thus obtained is often a compromise between the desired precision and the patience of the experimenter. To circumvent this limitation, we have designed a conductivity cell appropriate for automatic dilution and computeraided automation of data collection and analysis. The automated cell design allows a periodic monitoring of cell conductivity while surfacrant-rich material is progressively added to the cell. A sketch of our apparatus is shown in Fig. 1. The apparatus consists of three main systems: the pump, the cell, and the currentmeasuring circuitry. All of these systems are under the control of an LSI- 11 computer. The pump is a positive displacement piston type (Micro r-petter, Fluid Metering, Inc., Oyster Bay, NY) capable of accurate delivery of microliter volumes. The conductivity cell consists of a copper base with a glass cylinder wall (2 cm diameter) and a brass stirring "foot." The stirring action is achieved through a solenoid attached to the end of this foot. A spring maintains the foot in its down position, where it is held apart from the base by three glass rods imbedded in the copper base. The glass rods extend approximately 100/~m above
LS' I
COMPUTER
FOOT
CURRENT AMP
SURFACTANTRICH SOLUTION
FIG. 1. Schematic representation of the apparatus used to automate the conductivity measurements. The stirring "foot" also serves as one of the electrodes. In this way we achieve a very large cell constant while providing good mixing. Journal of ColloM and Interface Science, Vol. 124, No. 2, August 1988
the base. Conductivity measurements are made while the foot is held against these spacers. By pumping a dye solution into the cell, we have observed that adequate mixing occurs for fluid volumes up to 3 ml. The special feature of this new cell is that the stirring foot doubles as the upper electrode. With this design we achieve both a large cell constant (approximately 0.6 m) and proper mixing of the materials within the cell. The copper base doubles as the other electrode. The base is also provided with a heating element so that temperature control is possible, though measurements in this study have all been carfled out at room temperature. Another feature of the cell is the small sample volume required for a complete a vs concentration determination (approximately 1 ml). This feature is especially significant for experiments where minimal solvent or surfactant is available. A typical sequence would be as follows: The cell is filled with approximately 1 ml of pure solvent and a surfactant-rich solution is loaded into the pump reservoir. The pump is activated so that a small aliquot (typically a few microliters) o f a surfactant-rich solution is delivered to the contents already in the cell. Following this delivery, the foot is pumped several times to achieve good mixing and then a measurement is taken of the current flowing through the cell. After this reading is taken by the computer, the cycle is repeated. A lock-in amplifier (PAR 5204) technique is used to measure the in-phase and quadrature component of the current. A fast current amplifier has been built which has essentially no phase shift below 50 kHz. The circuit utilizes the fast FET operational amplifier LH0032 (National Semiconductor). The stirring foot electrode is maintained at virtual ground. In this way, grounded guard shields can be employed to keep stray currents and noise at the input to a minimum. Using this instrumentation and our large cell constant, we are able to measure conductivities as low as 10-11 S/ m. The large cell constant minimizes the relative error introduced by stray capacitive currents.
CONDUCTIVITY IN AOT SOLUTIONS The cell constant was determined by measuring the quadrature current for several liquids of known dielectric constant. A cell constant of approximately 60 cm was obtained. All data reported were measured at a frequency of 1 kHz and an applied voltage of 100-200 mV. Measurements were also made at other voltages to verify that the conductivities are independent of field. For comparison, we have also used a commercial conductivity probe (YSI Instruments), with a nominal cell constant of 1.0 cm.
Sample Preparation The A O T surfactant (sodium di-2-ethylhexyl sulfosuccinate) was obtained from Fluka (purum grade). This material was further purified as follows: The A O T was first dissolved in methanol. This cloudy solution was centrifuged at 5900g for a half hour, and the clear supernatant was retained. This solution was heated to boiling until m u c h of the methanol was removed. The remaining methanol was
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removed by heating the solution to 120°C in a vacuum oven for one hour. The solution bubbled and frothed during the initial heating, but by 120°C all activity had subsided, leaving a foamy cake. The purified material was white and had no odor. This procedure removed a methanol-insoluble contaminant, possibly sodium bisulfite. The 1,2-dichloroethane (reagent grade) was used without further purification. A O T is very soluble in dichloroethane. For the automatic dilutions three surfactant-rich master solutions were used to cover the range from 10 - 4 to 0.3 weight fraction AOT. For the commercial (YSI) probe, a separate series of AOT/dichloroethane solutions were prepared by successive (1:1) dilutions o f a 4 wt% master mixture down to 10 -5 weight fraction AOT. RESULTS In Fig. 2 we present the conductivity results obtained from the automatic dilution appa-
10-3
IE t0 -4 b
t0-5
ill
t0-5
i
I
I
LIIIl]
L
10-4
I
I
Llilll
L
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10-3
IIII1[
I
10-2
I
(
LIIIli
I
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FIG. 2. Conductivity vs concentration on a log-log scale for the AOT/dichloroethane system at room temperature. Data from three separate automatic dilutions are shown (e, A, O) together with corroborative data obtained using a commercial probe ((3). The solid line has a slope of 0.73. Journal ofColloid and Interface Science, Vol. 124, No. 2, August 1988
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ratus together with those obtained from the YSI probe. The conductivities have been plotted vs the concentration (q~)of AOT in weight fraction on a log-log scale. The conductivities indicated are the solution conductivity minus the conductivity of the pure solvent. The pure solvent conductivity (1. I × 10-6 S/m) has been subtracted so that the data plotted reflect the contribution to the solution conductivity from the surfactant added. For all but the first few concentrations, the conductivity of the pure solvent is quite negligible in comparison. The accuracy of the measurements is limited by the reproducibility of the cell spacing, which is less than 2%. The automatic dilution data in this figure were obtained from three separate dilutions of master solutions. There is good agreement between the regions of overlap. The figure also indicates excellent agreement between conductivities measured using the automatic dilution apparatus and measurements made on separate solutions using the commercial YSI probe. Two features are apparent in this graph. First, there is a distinct maximum in the conductivity at 0.141 weight fraction, and second below this maximum the data exhibit a power law (~ oc ~t) dependence over more than three decades in concentration. An exponent t = 0.73 _ .02 was obtained from a least-squares fit to the data below q5 = 2 X 10 -2. Although the conductivity of the solvent was subtracted from the data, it was not a fitting parameter. Rather, it was measured and used without adjustment. It is not possible to adjust this value to make the exponent appreciably different from 0.73. Note that the quantity raised to the power is ~, not ~ - ~b0,where q~ois some critical concentration (28). If there is such a ~o it must be small compared to 10 -5 . There does not appear to be a cmc within the concentration range evaluated, as indicated by the absence of any breaks in slope in this curve. Solutions with weight fractions below 10 -5 become increasingly difficult to evaluate because their conductivities approach that of the pure solvent. Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
DISCUSSION
AOT is known to form inverse micelles in many nonaqueous solvents. Conductivity in these solutions has been studied extensively in regard to percolation phenomena (1 l - 14, 28). Earlier investigations (7, 8) have identified two thresholds in inverse micellar systems. One threshold occurs around 0.3 volume fraction and is associated with dense packing of the spherical micelles (7, 8). Another, lower threshold has been observed to occur in many systems (7, 8, 11-13), at approximately 0.1 volume fraction. This lower threshold is associated with percolation. The percolation threshold occurs at a volume fraction below that predicted for noninteracting hard spheres. Grest and co-workers (29, 30), and others (1113, 28), have attributed this lowering to clustering that occurs as a result of attractive interactions. Because the maximum in our data occurs near the percolation threshold, it is reasonable to suspect that it is due to the onset ofmicellar interaction, possibly repulsion. Such intermicellar repulsion would be manifest by a dramatic fall off in the mean free path of the micellar species. The viscosity would likewise increase. In this case, the conductivity, if due to micelles, should turn down. Lalanne et al. (27) have studied the transport properties in inverse micellar AOT/carbon tetrachloride solutions. They also observe a decrease in the thermal conductivity of their solutions at around 0.1 volume fraction AOT. This observation is consistent with the notion that micellar repulsion may be responsible for the maximum in conductivity observed in our AOT/dichloroethane system. An alternative explanation is that a structural change occurs near the maximum. In a recent paper Georges and Chen (2) reported a similar maximum to occur in the conductivity of aqueous sodium dodecyl sulfate systems at about the same concentration as in our system. In that case, the maximum was attributed to a phase transition between an oil-
CONDUCTIVITY
IN AOT
in-water and a water-in-oil structure. In a somewhat related set of experiments. Chen et al. (31) have observed a precipitous drop in the conductivity as water was added to a didodecyldimethyl ammonium bromide/H20/ alkane system. They speculate that this behavior occurs as the result of a transition from an interconnected network of tubes to a spherical microemulsion structure. The question as to whether, indeed, there are micelles in our solutions is central. Initial efforts to observe micelles in dynamic light scattering has shown no appreciable signal in the micellar size range for a 0.6 wt% solution. Lalanne et al. (27) also obtained "no significant signal" in the case of dry AOT/carbon tetrachloride solutions, although micelles were clearly seen in their wet AOT/water/carbon tetrachloride solutions. We feel that neither their results nor ours on the dry AOT solutions are conclusive because poor contrast (i.e., good index match) between the AOT and the solvent could mask the micellar structure, if present. The refractive index of AOT is 1.470 (32), while those of 1,2-dichloroethane and carbon tetrachloride are 1.444 and 1.460, respectively. Conductivity and light scattering in wet AOT/dichloroethane solutions might contribute additional insight into this question, but that work has not been completed. The other interesting aspect of our data concerns the power law behavior observed at concentrations below the maximum. One might have anticipated a linear dependence of the conductivity on the surfactant concentration, based on a micellar model of conductivity. Consider the model where conductivity is predominantly through the drift of charged micelles. Above the cmc, the total number of micelles should be proportional to the total surfactant concentration. For spherical micelles of radius r, the micelle density is given by 3~/47rr 3, where • is the volume fraction. If the fraction of micelles ~ which are charged can be assumed to remain a constant, then the carrier density would be proportional to the total number of micelles and thus the total
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surfactant concentration. This, of course, also assumes the micelle size to be independent of concentration. Elementary application of Stokes law to this model yields the following form for the conductivity .Z 2
87r2~r4 ~, where n is the viscosity and Z is the micellar charge. Such a simplistic model is clearly inadequate to explain the sublinear power law behavior observed in our experiments. This model might be salvaged if the micellar radius increases with increasing concentration, but a corresponding power law dependence of the radius would be required. In studies made on micellar size in nonpolar solvents and at larger concentrations (16, 21), the micelle size is usually independent of concentration. In a study made at low concentration, Assih et al. (18) observed a size increase of the micellar radius with dilution in the AOT/H20/dodecane system. Thus there is little precedent to support the idea of micellar growth with increasing concentration. Further, we are not yet certain that micelles are present at all within the low concentration regime of our system, especially since no cmc signal was observed in the conductivity and light scattering showed no micellar signal in the power law regime. One might reasonably suspect surface conductivity as another possible explanation for the sublinear behavior. If such was the case, the measured conductivity would depend greatly on the particular geometry of the conductivity cell used, especially among cells with different surface to volume ratios. We find no such difference between our results using two cells with cell constants differing by almost three orders of magnitude. Further, a third confirming set of measurements was carried out in another laboratory, using an entirely different apparatus and cell, and the results were identical. We therefore do not believe that the effect is due to surface conductivity. Sublinear behavior could also occur if the carriers arose from dissociation of the surfacJournal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
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t a n t m o n o m e r s . T h e n one m i g h t expect a n e x p o n e n t o f 0.5 r a t h e r t h a n the one observed. Also, such b e h a v i o r is u n l i k e l y to o c c u r over three decades. In a n effort to c o m p a r e o u r results with c o n d u c t i v i t y d a t a in o t h e r inverse m i c e l l a r solutions, we have f o u n d t h a t experi m e n t a l d a t a o n the conductivities o f solutions far b e l o w p e r c o l a t i o n is sparse. M o s t o f the p r e v i o u s studies have focused o n c o n d u c t i v i t y n e a r percolation. T h e origin o f the p o w e r law behavior in o u r d a t a r e m a i n s unclear, although similar p o w e r law b e h a v i o r has b e e n o b s e r v e d in a c y a n o b i p h e n y l solvent (33). T h e r e a n exp o n e n t o f 0.6 was reported to describe the d a t a over two decades in c o n c e n t r a t i o n . CONCLUSIONS W e have d e s c r i b e d a m e t h o d w h e r e b y sol u t i o n c o n d u c t i v i t i e s c a n b e m e a s u r e d while surfactant-rich material is a u t o m a t i c a l l y a d d e d to the solution. T h e c o n d u c t i v i t y o f A O T / d i chloroethane solutions have been so obtained. W e have d e m o n s t r a t e d t h a t this m e t h o d gives g o o d a g r e e m e n t with d a t a o b t a i n e d b y m o r e conventional methods. T h e A O T / d i c h l o r o e t h a n e solutions show two interesting features. O n e is a m a x i m u m in the c o n d u c t i v i t y at a weight fraction which m i g h t be associated with m i c e l l a r i n t e r a c t i o n s or an otherwise u n o b s e r v e d structural transf o r m a t i o n . T h e o t h e r feature is a p o w e r law d e p e n d e n c e o f the c o n d u c t i v i t y o n the surfacrant c o n c e n t r a t i o n w h i c h occurs o v e r m o r e t h a n three decades b e l o w the m a x i m u m . T h e p o w e r law b e h a v i o r occurs with an e x p o n e n t o f 0.73 a n d with a negligible critical c o n c e n tration. T h i s b e h a v i o r is in c o n t r a d i c t i o n to the usual m o d e l s associated with c o n d u c t i v i t y in surfactant solutions. T h e d a t a r e m a i n an a n o m a l y , a n d further e x p e r i m e n t s into the n a t u r e o f t h e c o n d u c t i o n m e c h a n i s m , as well as the m i c r o s t r u c t u r e o f the solution, are needed. ACKNOWLEDGMENTS We thank E. Rietman for confirming our conductivity measurements on his apparatus, and P. Wiltzius for sharing Journalof Colloidand InterfaceScience,Vol.124.No. 2. August1988
his preliminary light scattering results. We are also indebted to F. Unterwald, M. van Dijk, W. van Saarloos, R. Cava, and B. Vyaz for useful comments and discussions. REFERENCES 1. Mukerjee, P., and Mysels, K., "Critical Micelle Concentrations of Aqueous Surfactant Systems," NBS Bulletin NSDS-NBS 36. Washington, DC 1971. 2. Georges, J., and Chen, J. W., J. Colloid Interface Sci. 113, 143 (1986). 3. Eicke, H. F., and Shepherd, J. C., Helv. Chim. Acta. 57, 1951 (1974). 4. Eicke, H. F., and Arnold, V., J. Colloid Interface Sci. 46, 101 (1974). 5. Eicke,H. F., Hammetich, H., and Vasta, G.,J. Colloid Interface Sci. 93, 593 (1983). 6. Lagues, M., J. Physique 40, L-331 (1979). 7. Lagues, M., Ober, R., and Taupin, C., J. Physique 39, L-487 (1978). 8. Lagourette, B., Peyrelasse, J., Boned, C., and Clausse, M., Nature (London) 281, 60 (1979). 9. Cazabat, A. M., Chatenay, D., Langevin, D., and Meunier, J., Faraday Discuss. Chem. Soc. 76, 291 (1982). 10. Chatenay, D., Urbach, W., Cazabat, A. M., and Langevin, D., Phys. Rev. Lett. 54, 2253 (1985). 11. Kim, M. W., and Huang, J., "Transport Properties of Microemulsions" in Statistical Thermodynamics of Micelles and Microemulsions (H. Chen, Ed.). Springer-Verlag, New York, in press. 12. Kim, M. W., and Huang, J., Phys. Rev. A 34, 719 (1986). 13. Bhattacharya, S., Stokes, J., Kim, M., and Huang, J., Phys. Rev. Lett. 55, 1884 (1985). 14. van Dijk, M. A., Phys. Rev. Lett. 55, 1003 (1985). 15. Peri, J. B., J. Colloidlnterface Sci. 29, 6 (1969). 16. Zaluf, M., and Eicke, H. F., J. Phy. Chem. 83, 480 (1979). 17. Wong, M., Thomas, J., and Nowak, T., J. Amer. Chem. Soc. 99, 4730 (1977). 18. Assih, T., Larche, F., and Delord, P., J. Colloid Interface Sci. 89, 35 (1982). 19. Kotlarchyk, M., and Chen, S., Phys. Rev. Lett. 53, 941 (1984). 20. Kotlarchyk, M., Huang, J., and Chen, S., J. Phys. Chem. 89, 4382 (1985). 21. Kotlarchyk, M., Chen, S., Huang, J., and Kim, M., Phys. Rev. A 29, 2054 (1984). 22. Chen, S. H., and Huang, J., Phys. Rev. Lett. 55, 1888 (1985). 23. Huang, J., Safmn, S., Kim, M., Grest, G., Kotlarchyk, M., and Quirke, N., Phys. Rev. Lett. 53, 592 (1984). 24. Peyrelasse, J., Boned, C., and Matin, G., ColloidPolyre. Sci. 264, 143 (1986). 25. van Dijk, M. A., Broekman, E., Joosten, J. G. H., and Bedeaux, D., J. Physique 47, 727 (1986).
CONDUCTIVITY IN AOT SOLUTIONS 26. Day, R. A., and Robinson, B. H., J. Chem. Soc., Faraday Trans. 1 75, 132 (1978). 27. Lalanne, J. R., Pouligny, B., and Sein, E., J. Phys. Chem. 87, 696 (1983). 28. Eicke, H. F., and Hilfiker, R., Chem. Phys. Lett. 125, 295 (1986). 29. Grest, G., Webman, I., Safran, S., and Bug, L. Phys. Rev. A 33, 2842 (1986).
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30. Safran, S. A., Webman, I., and Grest, G. Phys. Rev. A 32, 506 (1985). 31. Chen, S. J., Evans, D. F., Ninham, B. W., Mitchell, D. J., Blurn, F. D., and Pickup, S., J. Phys. Chem. 90, 842 (1986). 32. Rogers, J., and Windsor, P. A., J. Colloid Interface Sci. 30, 247 (1969). 33. Heffner, W. R., and Marcus, M. A., unpublished.
Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988