920
Langmuir 1990, 6, 920-928
Dielectric Properties of Anionic and Nonionic Surfactant Microemulsionst Marcia A, Middleton,$ Robert S. Schechter,* and Keith P. Johnston The Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712 Received June 9, 1989. In Final Form: November 15, 1989 The dielectric permittivities of anionic and nonionic oil-continuous microemulsions have been measured with varying water content, temperature, alkane carbon number, and electrolyte concentration. The data confirm the hypothesis that underlying phase behavior and consequent morphology have a profound effect on the dielectric properties of microemulsions. The results make it abundantly evident that it is not possible to understand permittivity by use of a simple drop model for microemulsions. It is proposed that water-in-oil domains coexist with oil-in-water domains even at low water concentrations and low electrical conductivities and that the dielectric constant is sensitive to the fraction of each type of domain present in a system. A mean field approximation is used to evaluate the fraction of water-in-oil domains that coexist with oil-continuous domains in these predominately oil-in-water microemulsions.
Introduction The permittivity behavior of microemulsions has been the subject of some study. Comparison of the reported experimental results indicates considerable consistency among these results, attesting to their basic reliability. The overwhelming bulk of the data relate to systems composed of anionic surfactants, water, and hydrocarbon at compositions below the conductivity percolation threshold. Thus, in a sense, these systems can be considered water-in-oil (W/O) microemulsions. While many researchers have investigated essentially the same systems and obtained wide agreement in the experimental trends, fundamental differences persist in the interpretation of trends. A common interpretation involves calculating dielectric constants of equivalent heterogeneous material~.l-~ The Maxwell-Wagner equation predicts the dielectric constant of a composite of noninteracting spherical particles dispersed in a Models for the dielectric constants of heterogeneous materials have been derived that also account for the effects of particle shape or conductivity, which causes interfacial polarization. In many cases, the experimentally measured dielectric constants of oil-continuous (i.e., nonconducting) microemulsions are much greater than can be fit to these models. Eicke et ala5have suggested that fractal clusters form that create an effective volume fraction of reverse micelles larger than the actual micelle volume fraction. Van Dijk et a1.6 have proposed a clustering model to explain the + Presented a t the symposium entitled "Thermodynamics of Micellar Solutions", American Institute of Chemical Engineers Spring National Meeting, Houston, April 2-7, 1989. Westvaco Corp., 11101 John Hopkins Rd., Laurel, M D 20723. (1) Maxwell, J. C. A Treatise on Electricity and Magnetism, 3rd ed.; Clarendon Press: Oxford, 1892; Vol. 1, p 440. (2) Wagner, K. W. Arch. Elektrotech. 1914,2, 371. (3) Clausse, M. Dielectric Properties of Emulsions and Related Systems. Encyclopedia of Emulsion Technology; Becher, P., Ed.; Marcel Dekker: New York, 1983. (4) Dukhin, S. S. Dielectric Properties of Disperse Systems. Surface and Colloid Science; Matijevic, E., Ed.; Wiley-Interscience: New York, 1971; Vol. 3. (5) Eicke, H.-F.; Geiger, S.; Sauer, F. A.; Thomas, H. Ber. BunsenGes. Phys. Chem. 1986,90, 872. (6) van Dijk, M. A.; Broekman, E.; Joosten, J. G. H.; Bedeaux, D. J. Phys. (Les Ulis, Fr.) 1986, 47, 727.
*
increases in dielectric constant and conductivity with temperature of an AOT/water/isooctane system. They postulate the existence of an energy barrier to clustering that is more easily overcome as temperature increases. This explanation is not intuitive since attractive forces become less important with increasing temperature. In addition, data are presented here showing that dielectric constant and conductivity decrease with increasing temperature in a nonionic microemulsion. This observation is exactly opposite to the anionic case but does correspond to well-known trends in phase behavior for the differing systems. The justification for the idea of clustering originates in interpretations of light-scattering experiments on oilcontinuous microemul~ions.~~S Osmotic compressibilities measured by light scattering led Agterof et aL7 to hypothesize the existence of attractive interactions between reverse micelles. They suggest the interactions could be due to long-range van der Waals forces between the aqueous cores. However, the authors point out that the Hamaker constant necessary to account for the data is over 100 times larger than predicted by Lifschitz's t h e ~ r y . ~ Agterof et al. suggest that perhaps the overlap of the long surfactant tails may contribute to the attractive interactions. This interpretation has gained wide acceptance.loJl Also, conductivity percolation, which is very dependent on the system variables, is observed in many microemulsion systems. The argument that closely associated reverse micelles can percolate is not persuasive when considering the existence of water-in-oil microemulsions with high disperse-phase volume fractions that do not exhibit electrical conduction. An AOT/DzO/decane system has been studied via freeze-fracture microscopy by Jahn and Strey.12 The micrographs show densely packed micelles in oil continua, which incorporate up to 40% (7) Agterof, W. G. M.; van Zomeren, J. A. J.; Vrij, A. Chem. Phys. Lett. 1976, 43, 363. (8) Calje, A. 4.; Agterof, W. G . M.; Vrij, A. In Micellization, Solubilization, and Mtcroemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2, p 779. (9) Ober, R.; Taupin, C. J.Phys. Chem. 1980, 84, 2419. (10) Brunetti, S.; Roux, D.; Bellocq, A. M.; Fourche, G.; Bothorel, P. J. Phys. Chem. 1983,87, 1028. (11) Huang, J. S.; Safran, S. A.; Kim, M. W.; Grest, G. S.; Kotlarchyk, M.; Quirke, N. Phys. Reu. Lett. 1984, 53, 592.
0 1990 American Chemical Society
Dielectric Properties of Microemulsions
Langmuir, Vol. 6,No. 5, 1990 921 s
,C)
Tspe II Syrlem
Figure 2. Winsor phase diagrams showing inversion zone (shaded area) and conductivity precolation threshold (solid line).Zl S = surfactant, W = water, and 0 = oil. Doma!" 1, W O
~
"
B
~
W
)
Figure 1. Proposed morphology. Coexisting W/O and O/W domains having same composition.
water and 20% AOT a t 15 "C without becoming conduct ing. However, these microemulsions do conduct at higher temperatures when, presumably, the morphology changes so that charged species can migrate in solution. Not all researchers subscribe to the above-outlined view of clustering, recognizing that the inversion from waterin-oil to oil-in-water cannot occur ~uddenly.'~-'~Boned et al.13 have reported using conductivity and dielectric constant data to detect structural transitions in a potassium oleate/hexanol/water/hexadecane system. No attempt was made to model the data quantitatively, but the concept of structural transitions is an important one. Robbins" has proposed a model which postulates the coexistence of water- and oil-continuous domains. In a similar fashion, Lamla has proposed that a microemulsion may be viewed as a mosaic of W/O and O/W domains. In this paper, we review the morphology and phase behavior of microemulsions and then present a systematic experimental study of the dielectric constants of these systems as a function of water content, temperature, alkane carbon number (ACN), and electrolyte concentration. The data demonstrate that the fundamental trends in the dielectric properties of anionic and nonionic microemulsions are related to phase behavior. They confirm the hypothesis that the underlying phase behavior and consequent morphology have a profound effect on the dielectric properties of the microemulsions. We propose, as did Lam et al.,I0 that within the phaseinversion zone a microemulsion is a mosaic of W/O and O/W domains having the same composition, as illustrated by Figure 1. If p is defined as the fraction of the microemulsion that is water continuous, then p will increase (12) Jahn. W.; Strey. R. J. Phys. Chem. 1988,92,2294. (13) Boned, C.; Clausse, M.; Lagoluette. B.; Pepelme, J.; McClean, V. E. R.; Sheppard, R. J. J. Phys. Chem. 1980,84,1520. (14) Robbins, M. L. In Mieellization, Solubilization, and Micmemulsions; Mittal, K.L., Ed.; Plenum Press: New York, 1977; Vol. 2, p 713. (15) m e r , E.; Bennett, K. E.; Davis, H. T.; Scriven, L. E. J. Chem. Phys. 1983,79,5673. (16) Chang, N. J.: m e r , E. Longmuir 1986.2, 184. (17) Robbins, M. L.; Bock, J. Colloid Interface Sei. 1988,124,462. (18) Lam, A. C . Dissertation, The Univemityof Teras at Austin, 1986. (19) Lam, A. C.; Falk, N. A,; Sehechter, R. S. J. Colloid Interface Sci. 1988, 120 (I), 30.
at a given volume fraction of water whenever the formulation variables are changed so as to yield a transformation from oil continuity to water continuity. Since permittivity is sensitive to changes in morphology, the fraction of each type of domain present will affect the dielectric constant and the characteristic dielectric relaxation.
Review of Morphology There is as yet no coherent theory relating the submicroscopic morphology of microemulsions to their physical properties.20 A t the extreme of either large volume fraction or small volume fraction of water are found oilswollen micelles or water-swollen reverse micelles, respectively. Under certain conditions, it is possible to continuously vary the water-to-oil ratio while maintaining a single-phase, isotropic, thermodynamically s t a b l e microemulsion. This continuous variation may extend from one side of the phase diagram to the other as shown by Figure 2. Thus, in some cases there exists a continuity of isotropic states, each differentially different from the preceding one, that extends from micelles to reverse micelles. This implies that there are intermediate states for which the classifications water and oil continuous are meaningless. Neither term can adequately describe the microstructure of these microemulsions. In Figure 2, states in which the submicroscopicmorphologies are neither water nor oil continuous are depicted as shaded regions. The position of these regions, or phase-inversion zones, will change depending on the underlying phase behavior, as depicted by Figure 2. For a Winsor type I system, the inversion zone is positioned near the surfactantoil leg of the ternary diagram. The inversion zone shifts toward the surfactant-water leg of the triangle as the system is varied from type I to type 11. This change can be accomplished by altering any one of a number of formulation variables.*O These are listed in Table I. The influence of temperature on the ,phase behavior of surfactantjwaterJoi1 systems differs depending on whether the surfactant is anionic or nonionic. Systems composed of ionic surfactants are relatively insensitive to temperature, although increasing it tends to promote type I to type I1 transitions.20.21 On the other hand, (20) Bourrel, M.;Sehechter, R. S. Microemulsionr and Related Systems; Marcel Dekker: New York, 1988.
922 Langmuir, Vol. 6, No. 5, 1990
Table I. Factors Inducing Type I to Type I1 Transition decreasing alkane carbon number decreasing temperature for ionic surfactants increasing temperature for nonionic surfactants increasing electrolyte concentration increasing surfactant lipophile length increasing branching of surfactant nonionic surfactant systems are quite temperature-sensitive, and increasing it produces an opposite trend.22-25 This distinct difference in the temperature behavior is a key factor that will support the contention that the dominant feature of dielectric properties of microemulsions is the underlying phase behavior. The extent of an inversion zone is not now known. Although in Figure 2 it is depicted as a rectangular region, this picture should not be accepted as correct since the extent of the zone should certainly depend on a number of factors.'g Furthermore, several different types of measurements will be required to define its extent. It is contended, however, that the portion of the inversion zone to the right of the conductivity percolation threshold (shown as a vertical line) can be mapped by using dielectric measurements. As a corollary, the deviation of the dielectric behavior of microemulsions from that exhibited by a collection of conducting spheres is due to the onset of inversion behavior.
Experimental Section The anionic surfactant sodium bis(2-ethylhexyl) sulfosuccinate (AOT) was obtained from Fluka and purified by dissolving one part AOT in three parts hexane and adding one part activated charcoal. The mixture was filtered through a 0.45-1m filter and the hexane evaporated. The purified AOT was stored in a vacuum desiccator over Drierite. The water-to-AOT molar ratio was 25. The disperse phase volume fractions, = @water + ~ A O T ,were calculated assuming PAOT = 1.14 g/mL. Note that dw = 18WSdd/(390+ 18W,), so for W, = 25, dw= 0.536dd. The choice of a nonionic surfactant is a difficult one. Microemulsions prepared with pure nonionic surfactants are extremely sensitive to changes in temperature. The range of the singlephase region may extend only a few degrees Celsius and may move with changes in other formulation variables. Because blends of nonionic surfactant form microemulsions that are much less temperature-sensitive and that exhibit much wider singlephase regions, the solubilization properties of several commercially available surfactant blends were studied, and a polyethylene glycol surfactant Cll-14E05 obtained from Shell Development Co. (Westhollow Research Center, Houston, TX (Reference No. 15114-59)) was selected for study. It has an alkyl chain length distributed between 11 and 14 carbons and an average of five ethylene oxide groups, and it was used as received. From conductivity experiments on aqueous solutions of this surfactant, it was determined that ions are present in the surfactant mixture. Additional experiments were performed with the monomerically pure nonionic pentaethylene glycol dodecyl ether, C12E05, which was obtained from Nikkol Chemicals, Ltd., Japan, and used as received. All alkanes except for undecane were obtained from Sigma and used as received. Undecane was obtained from Philip Petroleum bottled with molecular sieves and used as received. Distilled water was further purified in a Technic Lab 5 ionexchange apparatus. The experimental apparatus consists of a cylindrical stainless steel capacitance cell attached via a coaxial cable to a Hewlett(21)Winsor, P.A. Chem. Rev. 1968, 68, 1. (22)Kunieda, H.;Friberg, S. Bull. Chem. SOC.Jpn. 1981,54, 1010. (23) Bourrel, M.;Salager, J. L.; Schechter, R. S.; Wade, W. H. J. Colloid Interface Sci. 1980, 75, 451. (24)Bourrel, M.;Koukounis, C.;Schechter, R. S.; Wade, W. H. J. Dispersion Sci. Technol. 1980, 1 , 13. (25)Kahlweit, M.J. Colloid Interface Sci. 1982, 90,197.
Middleton et al. 120 I
100
1
1 I \
t
4
I
6
I
0
8
I 2
I4
GCN
Figure 3. Maximum water-to-AOT molar ratio, We*,at 25 OC in a series of alkanes, ACN = 6 to ACN = 12. Packard 4192A impedenceanalyzer.% The HP 4192A is equipped with an IEEE-488 interface bus that is connected to a Metrabyte IEE-488 expansion board on an IBM-XT. A BASIC program accesses the interface controlling the instrument settings and stores the data automatically. The cell is filled with the sample by immersing it in a large test tube containing the solution. The test tube is then placed in a water bath with temperature controlled to within 0.1 OC for the AOT and Shell surfactant experiments and to within 0.05 "C for the Nikkol surfactant experiments. The complex admittance of the cell and cable assembly is measured at frequencies between 100 kHZ and 13 MHz. To calibrate the measurements, the complex admittances of liquids with known permittivities are measured, and then the dielectric constants are plotted versus the observed capacitance ( B / w ) for each frequency. The calibration Ycurvesnare linear, and from them the permittivities of the microemulsions are determined. The dielectric constants are accurate to hO.1 unit for nonconducting solutions. When conductivities are greater than 50 pQ-l/cm, the measuring circuit is dominated by the inductance and the susceptance is no longer capacitive, so the dielectric constants calculated by this method will be low. Conductivities of the AOT microemulsions were measured with a Beckman conductance bridge. Conductivities of the nonionic microemulsions were measured with a Cole-Parmer conductance meter with temperature compensation. The meter is accurate to AO.01 WQ-l/cm for conductivities less than 10 WQ-l/cm and 0.1 pQ-l/cm for conductivities between 10 and 100 pQ-l/cm.
Results and Discussion Figure 3 shows the maximum amount of water that can be solubilized at 25 "C in a solution composed of an alkane and 10 wt % ' AOT. The maximum solubilization of water is found in an octane system. Systems containing less water than the maximum amount shown by Figure 3 are clear, single-phase, solutions. These are the solutions tested here. The dielectric constants of the octane, decane, and undecane microemulsions are plotted versus water-plus-AOT volume fraction (dw = 0.536&) in Figure 4. For given fractions of water, the octane system exhibits the lowest dielectric constants while the undecane system exhibits the highest. In all cases, the specific conductivities were less than 2 pW-l/cm and did not show any trend. Figures 5 and 6 show the results of varying the temperature with C$d = 0.15 (& = 0.078). The solution remains clear throughout the experiment and does not have the bluish tint of a middle-phase microemulsion. In Figure 5, the dielectric constants at 0.1 MHz are plotted versus the temperature. We see that as temperature increases, both the conductivity and the permittivity increase. (26) Middleton, M. A., at Austin, 1988.
Ph.D. Dissertation, The University of Texas
Langmuir, Vol. 6, No. 5, 1990 923
Dielectric Properties of Microemulsions 9,
.
A
octcne
0
decane
:t
0 undecane
0
5
6
I
O
A
hexone
0
octane
decane
0
I
0
600
005
010
015
020
15
025
Figure 4. Dielectric constant versus volume fraction of waterplus-AOT for octane, decane, and undecane solutions at 25 "C; W. = 25, &+. = 0.5364d. ,100
30
25
-6
I
=24 7
-
-E u
-
:
20
Lo
IO
:
0 V
v
5
-
"aJ
.i
n
2 c
-Ea
-
...
.
r
IO
G
:I
m 0
5 -
0
I
30
20
40
50
60
Temperature ( " C )
Figure 5. Dielectric constant and conductivity versus temperature of AOT/water/decane solution: dd = 0.0781, w. = 24.7, 25 "C. Note: the dielectric constants at 49 and 52 "C are experimental artifacts and not the true values. 23'C
50 -
40 A
30°C *
350c
0
44T
+
.....e..
40°C A
35
45
55
Temperature l ° C )
Volume Fraction (water + A O T )
.AOT/Woter/Decone W/S
25
e...*....*e.e.ee~
iiiiiiiiiPiiiiPiiP P i i i i i P i i i i b a I06
Frequency (Hz)
Figure 6. Permittivity versus frequency of AOT/water/ decane solution: & = 0.0781, W , = 24.7, 25 "C. Note that the dielectric constant appears to reach a maximum. This same type of behavior was also observed by van Dijk27928 and by Peyrelasse and Boned.29 In our case and also apparently in van Dijk's case, the apparent maxima are spurious, artifacts of the experimental method. The practical conductivity limit of the apparatus is 50 pW/cm. As conductivity rises above 50 p W / cm, the dielectric constants measured are increasingly (27) van Dijk, M. A.; Caateleijn, G.; Joosten, J. G. H.; Levine, Y. K. J. Chem. Phys. 1986,85 (l),626. (28) van Dijk, M. A. Phys. Rev. Lett. 1985,55 (9),1003. (29)Peyrelasse, J.; Boned, C. J . Phys. Chem. 1985, 89, 370.
Figure 7. Dielectric constant versus temperature. Shell nonionic surfactant (40 wt %)/water (10 wt %)/alkane (50 wt %). underestimated. Van Vijk30 also mentions this limitation when describing his experimental setup. This can also explain why Peyrelasse and Boned observed apparent maxima in the critical frequencies of dielectric relaxati~n.~~ In Figure 6, the permittivity is plotted versus frequency. Dielectric relaxation appears in the frequency range 0.1-1 MHz for temperatures greater than 44 "C. For both the 49 and 52 "C solutions, the observed permittivities are decreasing at the lowest frequencies scanned. This is a clear indication of electrode polarization and shows that the solutions have connected water filaments; ions in the solution are sufficiently mobile to polarize oppositely charged electrodes. The steep increase in the conductivity and the onset of electrode polarization lead us to conclude that continuous paths through water regions extend from one electrode to the other at about 49 OC. Therefore, a transition from type I1 to type I phase behavior is observed as temperature increases in this anionic system, which is as expected (see Table I). The effect of temperature on the phase behavior of nonionic microemulsions is also well-known (see Table I).2o As the temperature increases, the entropy and the natural radius of curvature favor decreasingly sized water regions. The hydrogen-bonding energy of the ethoxylates with water decreases, thereby causing the system to become more convex toward water. This corresponds to phase behavior tending from type I to type 11. The dielectric constants and conductivities of three Shell C11-14E05/water/alkane microemulsions are plotted versus temperature in Figures 7 and 8. The dielectric constants decrease with increasing temperature and appear to be approaching a plateau value around 4.7. In Figure 8, conductivities are compensated for the increase of ionic mobilities due to increased temperatures. The conductivities compensated to 25 "C all decrease monotonically. Therefore, a transition from type I to type I1 is observed as temperature increases in this nonionic system. A similar trend for both ionic and nonionic micelles is observed when decreasing the alkane carbon number. Smaller alkanes are better solubilized among the surfactant tails and cause the interface to become increasingly concave toward water; thus, the dielectric constants decrease. In Figures 4 and 7, similar trends for both ionic and nonionic microemulsions are observed when decreasing the alkane carbon number. (30)van Dijk, M.A. Dissertation, University of Utrecht, The Netherlands, 1986.
924 Langmuir, Vol. 6, No. 5, 1990
Middleton et al. Table 11. C,Values for Multiple Theory.
1
39,
t
"
Temperature - Compensated o o
0.2258$,(1- &) 0.0500&(1- 4,) 0.01002~,(1-0.7518&) 0.002962~,(1- 4,) 0.0007361$,(1 + 2.6774,) 0.0001835@,( 1 - &) 0.00004583$,(1+ 1.0784,) 0.00001145@,(1- &) 0.000002862r$,(l- 0.99944,)
33
a
!,,,,,,,,,,,,,I 25
i?
35
30
40
Temperature
50
45
0
01 '5
A
I0 w l % wafer
0
2 0 w t % woter
0
"
"
25
"
Temperature
1
'
55
45
35
("Ci
Figure 9. Dielectric constant versus temperature. Shell nonionic surfactant (40 wt %)/water/alkane.
= 0.7405.
(1- k)[3 + 2(t2/tl - 1)1- 241(t2/tl- 1)
I
t
$Jm
There are a number of theories for the dielectric constant of a composite system of spheres randomly dispersed in an insulating medium. The Maxwell-Wagner theory1g2 shows the dielectric constant of a dispersion of noninteracting spheres to be a function of the volume fraction of the disperse phase and the respective dielectric constants of the dispersed and continuous phases. Bruggeman extended the Maxwell-Wagner theory to concentrated solutions by using a mean-field approximati0n.3~The Bruggeman equation and Hanai's extension of it to include complex p e r m i t t i ~ i t i e sare ~ ~ frequently used to represent composites with spherical inclusions. Gunther and Heinrich derived a formula on the basis that any distribution of charge can be represented by a system of multipoles.33 Their result for the dielectric constant of a monodisperse system of spherical particles with dielectric constant t1 and volume fraction $1 randomly distributed in a dielectric medium with dielectric constant €2 is t =
_ "t
where
Permittivity Theory
55
1°C)
Figure 8. Conductivity versus temperature; temperaturecompensated. Shell nonionic surfactant (40 wt %)/water (10 wt %)/alkane (50 wt %).
I
$Jr =
cz (1- k)[3 + 2(+1-
1)1+ 41(& - 1)
where
Temperature. Compensaled
fL 1=1
0'1 23
'
'
25
30
35
Temperature
40
45
(1)
5c
( O C 1
Figure 10. Conductivity versus temperature; temperaturecompensated. Shell nonionic surfactant (40 wt %)/water/ alkane. In Figures 9 and 10, dielectric constants and conductivities are plotted versus temperature for octane solutions of 40 w t % Cll-14E05 and lo%, 20%, and 30% water. Increasing the water concentration increases the dielectric constant dramatically. The plots for the 20% and 30% water solutions end abruptly a t 35 and 42.5 "C, respectively, where the mixtures become turbid. The dielectric constant of a 40 wt % C11-14E05/60 wt % octane solution a t 25 "C was measured and is 3.03. The conductivity of the 30% water solution decreases by nearly 3 orders of magnitude as the temperature increases from 23.3 to 35 "C, indicating a definite phase inversion from water continuity to oil continuity.
1+
l(1 + 1)C,
E('2 - 1) 21 + 1
tl
and CI values are related to the radial distribution function. For a random distribution, the values of CIcalculated by Gunther and Heinrich are given in Table 11.The dielectric constant given by eq 1is in general agreement with the Bruggeman equation at small to moderate disperse-phase volumes (see Figure 11). This equation is expected to be highly accurate because of the few assumptions imposed in its derivation. It shows that the dielectric constant depends only on the dielectric constants of the disperse and continuous phases, respectively, and the disperse-phase volume fraction. There are no other parameters. The concept of accounting for the presence of the counterions inside reverse micelles and their effect on the permittivity behavior of water-in-oil microemulsions was introduced by Chou and Shah.s4 They have incorporated Schwarz's theory of double-layer p ~ l a r i z a t i o ninto ~ ~ Max(31) Bruggeman, D. A. G. Ann. Phys.,Ser. 5 1935,24,636. (32) Hmai, T.KoEloid-Z. 1960, 171, 23; 1961, 175,61. (33) Giinther, K.; Heinrich, D. Z. Phyzik 1965,185, 345. (34) Chou, S. I.; Shah, D. 0. J. Phys.Chem. 1981,85, 1480. (35) Schwarz, G. J. Phys. Chem. 1962, 66, 2636.
Langmuir, Vol. 6, No. 5, 1990 925
Dielectric Properties of Microemulsions
I
00
01
0.2
03
0 4
0
oc!one aecane
0 5
41
Figure 11. Ratio of the dielectric constant of a suspension of conducting spheres to the dielectric constant of the continuousphase versus disperse-phasevolume fraction. van Dijk data for AOT/isooctane/water at 35 O C , W. = 25; from ref 6.
well-Wagner theory, considering the interfacial double layer within the reverse micelle as a thin shell and calculating two relaxation times. De Rozieres et al.36 have adapted this method and have calculated both the polarizability and the critical frequency of an isolated reverse micelle in an oscillating electric field. They find that micelles are highly polarizable due to the mobility of the counterions in the micelle interior. Thus, the value of the polarizability corresponds to that of a conducting metal sphere. Furthermore, the critical frequency reported by de Rozieres et al.36represents the point at which the diffusion rate of the ions through the aqueous interior becomes a limiting process. Since swollen reverse micelles are highly polarizable, it might be thought that the dielectric constant of the system will be comparable to a random dispersion of highly conducting spheres. The dielectric constants of an Aerosol OT/water/isooctane system with a water-to-AOT molar ratio of 25 and temperature of 35 OC6 are shown as a function of the particle volume fraction (dwater for a W/O microemulsion) in Figure 11 and compared with predictions of the three theories outlined here. This comparison is typical. Except for very small volume fractions, the ,measured values of the dielectric constant are substantially larger than predicted by the equations. Plots for other systems and other conditions reveal the same difficulty in applying the Bruggeman equation to microemulsions. Also shown in Figure 11 are the data for a dispersion of mercury drops in castor Notice that the dielectric constant of the dispersion of mercury drops is less than that of a microemulsion containing the same volume fraction of water. This is a striking result. The Gunther and Heinrich equation and the Bruggeman equation predict permittivities which compare well with the experiment for a dispersion of conductors but underestimate the dielectric constant of microemulsions even though it has been shown that reverse micelles are essentially conducting spheres. It seems, therefore, that the model of a microemulsion composed of a dispersion of spherical drops must be rejected.
Proposed Model As was discussed above, investigators have proposed attractive interactions between micelles to explain lightscattering spectra, but this cannot fully explain the dielectric behavior. Furthermore, we have found that the dielec(36) de Rozieres, J.; Middleton, M. A.; Schechter, R. S. J. Colloid Interface Sci. 1988, 124 (2), 407. (37) Guillien, R. Ann. Phys. 1941, 16, 205.
Volume Fraclion Woter
Figure 12. Volume fraction of O/W domains versus volume fraction of water as determined from the model for the AOT/ water/alkane experiment reported in Figure 4.
tric constants of anionic microemulsions increase with increasing temperature while for nonionic microemulsions dielectric constants decrease with increasing temperature. These findings leads us to conclude that submicroscopic changes in the structural morphology, not strong interactions between reverse micelles, are the origin of the dielectric phenomena observed. It has been assumed previously that the disperse phase consists only of reverse micelles, that all the water is contained within an oil-external domain; however, the data indicate an apparent water fraction that is much larger than the fraction of water actually in the microemulsion. This paradox may be understood by taking into account the possibility of water-external domains containing large amounts of oil. Figure 1 illustrates the proposed idea. The domains A and B contain X, volume fraction of water. Domain A is water-in-oil (W/O) and will exhibit a low dielectric constant while domain B is oil-in-water (O/W), of as yet undefined morphology, and will exhibit a high dielectric constant. Suppose that B domains comprise 25% of a solution and A domains the other 75%, as pictured. The solution is macroscopically oil continuous, but the large O/W domains (B) are dispersed in a continuum that is not 100% oil. The overall dielectric constant of the solution will be affected by this change in morphology. With our model of microemulsion morphology as a mosaic of O/W and W/O regions, we can calculate from the data the fraction of the volume in each microemulsion that must be water continuous. The fraction of O/W domains, p, is determined by applying the equations of Gunther and Heinrich.33 The calculation of the macroscopic dielectric constant uses an extended mean-field approximation in which eq 1 is applied a t two levels. The first entails determining the dielectric constant of a W/O phase containing dispersed water drops. By applying eq 1 with $1 = 4water, €2 = toil, and €1 = twater, we define tcont. This is the effective dielectric constant of the phase which surrounds the water-continuous zones until the percolation threshold is attained. Equation 1 is again applied, this time with €2 = tcont, to determine the volume fraction of the watercontinuous regions. The ~$1 is adjusted until the calculated dielectric constant is the same as that measured. This 41 is then taken to be equal to 0. Care should be taken in applying this model near the conductivity percolation limit because the dielectric constant becomes infinite, and inordinately large values of ,8 may result. The /3 values calculated for the AOT/water/alkane microemulsions are plotted in Figures 12 and 13. Notice
926 Langmuir, Vol. 6, No. 5, 1990
Middleton et al.
i i r
1
1I
bOT/water/decane
00""' ' 2c 25
'
I
3c
"
"
'
'
" "
35
-emperctdre
45
coi
'
5:
23
'
' 30
'
'
Tempera1 u r e ("C
("C
Figure 13. Fraction of domains that are water continuous (8) versus temperature as determined from the model for the AOT/ water/decane system reported in Figure 5.
50
hexone
o
octane
1
.
..........'.
30
-
3
I
25
35 Tevgerafure
C5
22 50c 25-C
.
0
30'C
35°C
i_
90.
c\
20 3 o c
x
*.= .o
L
0
0,
Figure 15. Volume fraction of O/W domains versus temperature. Shell nonionic surfactant (40 wt %)/water/octane. 0
1
-I -
'
,
40
105
106
10'
IC@
LL
Frequency l t i z )
_I
1°C'
Figure 14. Volume fraction of O/W domains versus temperature. Shell nonionic surfactant (40 wt %)/water (10wt %)/alkane (50 wt %). in Figure 13 that the p values are very small for dw = 0.025 and increase with increasing &. The /3 for the dodecane system increases most rapidly. In Figure 13, P is plotted versus temperature for the AOT/ water/decane experiment with dW = 0.078. It appears to be approaching an asymptote at 44 "C, and p is large, equal to 0.6. Conductivity experiments indicate that the Shell product contains ionic species; therefore, the water phase is conducting, and its dielectric constant is taken to be infinite. (In a pure nonionic system, the water phase will not be conducting and will have a finite dielectric constant of about 80. In this case, a spherical water droplet will have polarizability of 0.92, and the dielectric constant of the system will be slightly lower.) As long as the microemulsion remains nonconducting, W/ 0 domains will predominate and will constitute the continuous phase surrounding the O /W domains. The dielectric constant of the 40 wt 9% surfactant in octane solution was measured and found to be 3.03. This value is taken to be equal to the dielectric constant of the oil, 62. The p values for the nonionic microemulsions are plotted in Figures 14 and 15. The few reports of dielectric experiments with nonionic microemulsionsconfirm the trends found in this study. The observed changes correspond to variations in phase behavior and hence to changes in the submicroscopic morphology. (38) Kahlweit, M. J. Colloid Interface Sci. 1987,118, 436. (39) Peyrelasse, J.; Boned, C.; Xans, P.; Clausse, M. In Emulsions, Lattices, and Dispersions; Becher, P., Yudenfreund, M. N., Eds.;Marcel Dekker: New York, 1978; p 221. (40)Bostock, T. A.; Boyle, M. H.; McDonald, M. P.; Wood, M. W. J. Colloid Interface Sci. 1980,73,368.
Figure 16. Permittivity versus frequency,temperatures in O C . Shell nonionic surfactant (40 wt %)/water (20 wt %)/octane (20 wt %).
Permittivity is plotted versus frequency in Figure 16 for the nonionic systems. With ionic microemulsions, dielectric relaxation is attributed to the migration of counterions in the disperse water phases.36 The Shell Cll-14EO6 surfactant mixture is contaminated with electrolyte, so the relaxation observed in these systems may be due to migration polarization. This is clearly evident at 20.3 "C, where the effect of electrode polarization is manifested at. the lowest frequencies in the decreasing value of and inflection in the curve of permittivity. However, we have measured the frequency response of the permittivity of a microemulsion composed of the Nikko nonionic surfactant (C12E05)and observed relaxation in the same range as the impure Shell surfactant. This unexpected result is not yet fully understood. Furthermore, waterfree solutions of the nonionic surfactants in alkane do not exhibit relaxation in the range of frequencies studied here. Thus, one must consider that either there are sufficient electrolyte impurities in the Nikko surfactant to exhibit saturation effects because of restricted ion movement or that the response of the ethylene oxide units in water (but not in oil) to the variation of electric field becomes limited in the frequency range 0.1-1 MHz. The critical frequency for dielectric relaxation in the AOT systems is related to the time it takes to fully polarize the material. The polarizability of the water domains is due to the presence of ions in solution. The ions have finite mobility and a limited space in which to travel. The critical frequency is that intermediate frequency where the ions move continuously back and forth across the domain causing maximum energy dissipation (due to friction). The larger the distance the ions can travel, that
Langmuir, Vol. 6, No. 5, 1990 927
Dielectric Properties of Microemulsions is, the larger the water domain, the longer it takes to polarize the domain and the lower the critical frequency will be. De Rozieres et al.36 have derived an equation for the critical frequency which is a linear function whose slope, m, depends on the ratio of the permittivities t1/t2: -fc 2*a2 = b 'ion
+ m(
N*g,e2 4aatot,kT
)
(3)
where Nagsis the number of surfactant head groups on the reverse micelle surface, Dionis the diffusion coefficient of the counterions, e is the elementary unit of charge, and b is the intercept. From their plot for e l / t 2 = 35, we find b i= 8 and m i= 2. We know that the AOT head group covers approximately 69 A of interfacial surface m2/s and area a t 25 0C.20 Using the value D = 2 X substituting appropriate values for the constants, we find 2.5 X lo-' 9.1 (4) a a2 where f c has units of hertz and a has units of meters. Assuming that the relation holds approximately for the water domains, then the critical frequency characterizes the average distance across the water domains. In our model, as the system becomes bicontinuous, more and more domains are water continuous, and the likelihood of O / W domains being adjacent increases, so the observable size of the O/W regions increases. Therefore, we expect decreasing critical frequencies with increasing disperse-phase volume fraction and with increasing temperature because these changes in the formulation variables induce phase inversion. This trend has been found experimentally. For a AOT/water/dodecane ( W S= 10) system, Peyrelasse and Boned29 measured the critical frequencies, which decrease precipitously as the fraction of water increases. They were apparently unable to measure critical frequencies for the lowest volume fractions (& < 0.024), but the values span a 2-decade range from 2 to 105 MHz. Applying eq 4 to these data, we can estimate the sizes of the O/W domains. For C # J ~= 0.024 (t = 3.84), the average size of the O / W domains is about 900 A. For & = 0.030 (t = 7.68), the size of the domains has increased to 1600 A. For @w = 0.041 ( t = 19.5), the size increases to almost 0.1 pm a t the percolation limit. Because eq 3 was derived by considering a single inverted micelle in an electric field, it is not known what errors are incurred in applying eq 4 to determine the domain size; however, the values found here appear quite reasonable. It is desirable to confirm these values by some independent experimental means. At very low volume fractions where /3 is nearly zero, one may expect to find no relaxation in the frequency region (
