dodecane systems by time

Study of the structure of water/Aerosol OT/dodecane systems by time domain ... Dielectric Relaxation and Solvation Dynamics of Water in Complex Chemic...
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J . Phys. Chem. 1985, 89, 310-319

370

Study of the Structure of Water/Aerosol OT/Dodecane Systems by Time Domain Dielectric Spectroscopy J. Peyrelasse* and C. Boned UniversitP de Pau et des Pays de I’Adour, Laboratoire de Physique des MatZriaux Industriels. 64000 Pau, France (Received: April 18, 1984; In Final Form: September 17, 1984)

The dielectric complex permittivity of the system water/AOT/dodecane has been measured by time domain spectroscopy, at low molar ratio ( n = [water]/[AOT] 5 10). The data have been completed with a study of dynamic viscosity. The effect of salt content has also been studied and some indications are given on the effect of the oil type. The experimental data have been interpreted through a model based on a dielectric blending law applied to ellipsoids of revolution. The model assumes the electric charges to be on the surface of the dispersed objects. It is shown that, when the dispersed-phasevolume fraction 4 (water and AOT) tends to zero, there is practically no micellar aggregation, and the spherical model remains valid. As 4 increases, an apparent anisotropy may be observed for high enough n values. The model developed in the paper gives a good agreement between theoretical and experimental values. In the case where brine is used, one verifies that the interactions are decreased, and the spherical model applies whatever the 4 and n values.

Introduction A microemulsion is a macroscopically monophasic, low-viscosity fluid system, resulting from the mutual “solubilization” of water and “oil”. Such mutual solubilization requires the addition of one or several surface-active agents, and, according to the composition and nature of the components, microemulsions of water in oil (w/o) or oil in water (o/w) can be obtained. When two surface-active agents are required, we find most often an alcohol together with an ionic type surfactant, but there are no experimental ways to know the distribution of oil and alcohol between the continuous phase, the disperse phase, and the interfacial layer, except along a demixing line.’,* The validity conditions of the dilution method have been recently d i s c ~ s s e d . Therefore, ~ analyzing the results can often be difficult because the volume fraction $I of disperse matter is not generally known. If a single surface-active agent, such as sodium bis(2-ethylhexyl) sulfosuccinate (AOT) or sodium dipentyl sulfosuccinate (AY) is used, there is no more problem about locating the alcohol. When the critical micellar concentration (cmc) is much inferior to the concentration used (for the AOT, the cmc in the solvent generally ranges between and lo4 mol/dm3), it can be admitted that the whole surface-active agent is localized at the interface. If the oil penetration in the interfacial film is neglected, we can have a good evaluation of the disperse-matter volume fraction $I$+5 water and surfactant, since these types of systems behave as ideal solutions (the surface-active agents, oil and water volumes can be added6). Angel et al.’ have recently underlined the interest of studying the three-component microemulsions and have agreed that studying four- or five-component systems (brine) leads to theoretical and experimental difficulties hindering progress in the understanding of the properties of such systems. For example, in previous works, we carried out a studys on the dielectric properties of surface double active agent microemulsions (soap alcohol). In some cases, the dielectric increment is very

+

(1) Rosano, H. L.; Peiser, R. C.; Eydt, A. Reo. Fr. Corps Gras 1969, 16, 249-257. (2) Graciaa, A.; Lachaise, J.; Martinez, A,; Bourrel, M.; Chambu, C. C. R. Hebd. Seances Acad. Sci., Ser. B 1976, 282, 547-550. (3) Cazabat, A. M., J. Phys., Lett. (Orsay, Fr.) 1983, 44, 593-599. (4) Nicholson, J. D.; Doherty, J. V.;Clarke, J. H. R. In ‘Microemulsions”; Robb, I. D., Ed.; Plenum Press: New York, 1982, pp 33-47. (5) Kubik, R.; Eicke, H. F.; Jonsson, B. Helu. Chim. Acta 1982, 65, 170-177. (6) Rouviere, J.; Couret, J. M.; Lindheimer, M.; Dejardin, J. L.; Marrony, R. J . Chim. Phys. Phys.-Chim. Biol. 1979, 76, 289-296. (7) Angel, L. R.; Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1983,87, 538-540. (8) Boned, C.; Clausse, M.; Lagourette, B.; Peyrelasse, J.; McClean, V. E. R.:Sheppard, R. J. J . Phys. Chem. 1980, 84, 1520-1525.

0022-3654/85/2089-0370$01.50/0

high; in the case of the potassium oleate/water/hexanol/hexadecane system, a remarkable increase in the static permittivity can be observed near the demixing curve; we have qualitatively imputed it either to the existence of strongly anisotropic dispersed objects or to the aggregation of spherical globules. However, as we cannot know $I, it forbids us any attempt at quantitative theoretical interpretation. Therefore, we shall be considering in the present work a ternary system studied by time domain dielectric spectroscopy (viscosity measures come as a complement) for which we can hopefully analyze the experimental results, as we know the disperse-matter volume fraction. We have selected the water/AOT/dodecane system, which has already been extensively studied, and we will recall the main results that have already been obtained, insisting on observations carried out when the molar ratio n = [water]/[AOT] is close to IO, which corresponds to our experimental conditions. We will also mention the previous results concerning the microemulsion dielectric relaxation. Review of Previous Studies Studies on Water/AOT/Oil Systems. The monophasic water/oil transparent area obtained through water solubilization with AOT has been the subject of structural studies using different techniques. Such studies seem to reveal that for water concentrations with a molar ratio n greater than 10, those phases are constituted of spherical or almost spherical inversed micelles delimited by an AOT film with water at a bulk state in the core. With n 5 10, the system would rather be a suspension of hydrated AOT aggregates as the water is strongly bound because of Na+ ion solvation. Such a situation can also be found with systems with two a m p h i p h i l e ~ . ~ , ~ As for the micellization threshold of water/AOT/hydrocarbon ternary systems, it seems to be a value close to 10 which is to be considered. As an example, we find the values 9 and 10 that have been put forward by Eicke et al.sosllfor the water/AOT/isooctane system, the value 8 of Rouviere et aL6 for the water/AOT/nhexane system, the value 8 for the water/AOT/n-heptane system studied by NMR,s2 and the value 12 for the water/AOT/nheptane and water/AOT/dodecane systems studied by fluorescence dep01arization.I~ As for US,^ we have found the value 11 for the water/AOT/dodecane system. Assuming that, along the (9) Boned, C.; Peyrelasse, J.; Heil, J.; Zradba, A,; Clausse, M. J. Colloid. Interface Sci. 1982, 88, 602-604. (10) Eicke, H. F.; Rehak, J. Helu. Chim. Acra 1976, 59, 2883-2891. (11) Zulauf, M.;Eicke, H. F. J. Phys. Chem. 1979, 83, 480-486. (12) Wong, M.; Thomas, J. K.; Nowak, T. J. Am. Chem. Sot. 1977, 99, 4730-4136. (13) Wong, M.; Thomas, J. K.; Gratzel, M. J. Am. Chem. Sot. 1976, 98, 2391-2397.

0 1985 American Chemical Society

Structure of Water/AOT/Dodecane Systems “micellization line”, the system corresponds to a monodisperse population of w/o swollen spherical micelles and that the whole surfactant is incorporated inside the interfacial film, we have ~ b t a i n e d ~a, ’rough ~ estimation of the micelle radius on this line, that is to say 30 A, which leads us to a water core radius of about 20 A, thus being in accordance with other estimations (Zinslils for the water/AOT/isooctane system, Zulauf et al.” for the water/AOT/isooctane system with n = 8 and 9, Day et a1.16 for the water/AOT/cyclohexane, toluene, chlorobenzene system with n = 8). However, recent studies show that the value of n, corresponding to existence of water with normal properties within the micelles, is still creating a problem. The water vapor pressure for the water/AOT/isooctane system shows,5 a t fixed temperature, a pronounced inflection near n N 8 and the curves of apparent molecular weight that have been obtained by combining several experiments (light scattering, ultracentrifugation, proton chemical activity (shifts), bandwidth in NMRI7) corroborate the previous conclusions. However, the experiments of Day et a1.I6 concerning the water/AOT/oil (cyclohexane, toluene, benzene) systems with n 5 10 show that the average aggregation number increases with n and that the size remains unchanged if n remains unchanged, and it seems that only when n 5 3 is water not comparable to “bulk water”. It seems to be the same for Zinsli‘s re~u1ts.I~ Studies on Microemulsion Dielectric Relaxation. Among all the different methods implemented for the study of microemulsions, dielectrometry has been generally used as an auxiliary technique. The literature gives us disparate results as far as the permittivity of microemulsion type systems is concerned. An extensive review of this subject has been recently published.18 It seems that there is a very limited number of studies presenting relaxation spectra of the complex permittivity e* = e’ - je” (jz = -1, e’ is the real permittivity, and e” the loss factor). As for the w/o systems, we noticed for the 4’( 4 )curves either a Davidmn and Cole or a Cole-Cole distribution with a frequency spread parameter, observed with both ioniclg~zO and nonioniczhz2 surfactants, or the superposition of two Cole-Cole distributions with a frequency spread parameter of average value.z3 As for interpretation, the Looyenga lawz4 used by some authors25J6is a symmetric relation inconsistent with a spherical model of microemulsion; it may be used, for instance, for a Scriven type bicontinuous structure.z7 At present, the most elaborated modelz3 considers interfacial polarization (Maxwell-Wagner effect), the detergent film between water and oil, as well as the polarization of the electric double layer. Yet, it cannot explain the high values of static permittivity. Thus, the model gives el < 4.5 while experimental values can reach 25. Experimental Techniques The measuring techniques of dielectric properties by time do(14) Clausse, M.; Peyrelasse, J.; Boned, c . ; Heil, J.; Zradba, A.; Nicolas-Morgantini, L. In ‘Surfactants in Solution”; Mittal, K. L., Lindman. B.. Eds.: Plenum Press: New York. 1984: Vol. 3. OD 1583-1626. (is) Zinsli, P. E. J . Phys. Chew. 1979.83: z23-3231.(16) Day, R. E.; Robinson, B. H.; Clarke, J. H. R.; Doherty, J. V. J . Chew. SOC.,Faraday Trans. 1 1979, 75, 132-139. (17) Ekwall, P.; Mandell, L.; Fontell, K. J . Colloid Interface Sci. 1970, ~

33, 215-234. (18) Clausse, M. In ’Encyclopedia of Emulsion Technology”;Becher, P., Ed.; Marcel Dekker: New York, 1983; Vol. 1, pp 481-715. (19) Hanai, T.; Koizumi, N. Bull. Insr. Chem. Res., Kyoto Univ. 1%5,45, 342-351. (20) Clausse, M.; Boned, C.; Peyrelasse, J.; Lagourette, B.; McClean, V.

E.R.; Sheppard, I. In ‘Surface Phenomena in Enhanced Oil Recovery”;Shah, D. O., Ed.; Plenum Press: New York, 1981; pp 199-228. (21) Peyrelasse, J.; Boned, C.; Xans, P.; Clausse, M. C. R. Hebd. Seances Acad. Sci., Ser. B 1975, 284, 235-237. (22) Peyrelasse, J.; Boned, C.; Xans, P.; Clausse, M. In ‘Emulsions, Lattices and Dispersions”, Becher, P., Yudenfreund, M.N., Us.; Marcel Dekker: New York, 1978, pp 221-235. (23) Chou, S. I.; Shah, D. 0. J . Phys. Chew. 1981, 85, 1480-1485. (24) Looyenga, H. Physica (Amsterdam) 1965, 31, 401-406. (25) Eicke, H. F.; Kubik, R. Ber. Bunsenges, Phys. Chew. 1980,84,36-41. (26) Sjoblom, J.; Nylander, C . ; Lundstrom, J. Colloid Polym. Sci. 1982, 260, 89-92. (27) Scriven, L. E. Nature (London) 1976, 263, 123-125.

The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 371 TO ;A ;

Figure 1. Phase diagram in weight of water/AOT/dodecane system. Blank area is the monophasic domain w/o.

y

/

\

I

5

10

-

E’

Figure 2. ColeCole plot ~ ” ~ ( t ’for ) water/AOT/dodecane system = 0.293, n = 3.6). Frequencies in MHz.

(6

main spectroscopy have been recently developed and have numerous advantages compared with classical measurements in the frequency domain. First of all, rapidity: a few minutes are enough to completely obtain a dielectric relaxation spectrum. Besides, the important number of obtained experimental points allows an excellent definition of the relaxation domain. The development of our experimental apparatus has already been treated in two technical article^.^*-^^ It is a compact Tektronix WP 1200 unit with a reflectometer and a digital processing oscilloscope monitored by a calculator. The “total reflection” method has been used for the present work since it enables us to determine simultaneously the dc conductivity x and the complex permittivity e* according to the frequency v of applied field. The S m-*. precise e* determination is possible as long as x < Here, covering the 2-400-MHz range is generally enough to characterize the microemulsion relaxation. Studying alcohols with well-known properties, we have checked that the relative uncertainty of e‘ and e‘‘ is about 3%. Such precision is much better than that of many classical systems in the same frequency range (up to 10% for e’ and 15% for e”). The study at low frequencies of the AOT dielectric properties has been carried out with a Hewlett-Packard 4192A impedance meter monitored by the calculator. The sample kinematic viscosity has been determined by using a Lauda automatic viscosimeter with Ubbelohde type tubes. The density has been systematically measured with a DMA 45 densimeter. All such experiments have been carried out at 25.0 f 0.1 O C . We have used dodecane (Fluka AG purum), isooctane (Fluka AG puriss), cyclohexane (Fluka AG purum), and benzene (Fluka AG purum). Classical methods have been used for AOT (Fluka AG purum) p ~ r i f i c a t i o n . ~In~some cases, we have used solutions of sodium chloride (Prolabo Norma pur). All samples are characterized by the disperse-matter (water and AOT) volume fraction 4 and by the molar ratio n = [water]/[AOT]. The water volume fraction will be reported as cpw. (28) Peyrelasse, J.; Boned, C.; Le Petit, J. P. J. Phys. E 1981, 24, 1002-1 008. (29) Boned, C.; Peyrelasse, J. J . Phys. E 1982, 15, 534-538. (30) Eicke, H. F.; Christen, H. J. Colloid Interface Sci 1974.48, 281-290.

Peyrelasse and Boned

372 The Journal of Physical Chemistry, Vol. 89, No. 2, 1985

“‘t

TABLE I: Results of Fitting by Eq 1 for Various Systems AOT/ AOT/ AOT/ AOT/ water/ AY/ water/ water/ cyclo- water/ water/ isooctane isooctane hexane dcdecane benzene 0.3 0.3 0.3 0.3 0.18 9 Cl €h

u,, MHz a

rms L’ rms c”R I

I

5

8

7

I

I

-

9 log I

Figure 3. Variations of the real permittivity e’ and loss factor C”R vs. frequency u for water/AOT/dodecane system (9 = 0.293, n = 3.6); frequencies in MHz: (+, a) experimental data; (-) calculated curve (eq 1) with €1 = 11.48, = 2.75, U, = 17.1 MHZ, CY = 0.364.

Experimental Results Phase Diagram. Figure 1 represents, within the ternary diagram (expressed in mass fraction), the monophasic area of the water/AOT/dodecane system established at 25 OC. The maximum molar ratio is M = 25 and maximum solubilization seems to vary little with the AOT proportion at least if the latter is less than 0.8. The value M N 25 seems to be in accordance with previous studies demonstrating that M decreases when the number of carbons increases6 (M= 70 with heptane and 50 with decane). The line corresponding to n = 10 has also been represented in the figure. Determination of Electric Properties. General Information. For all studied samples, we have established the existence of a relaxation and a conduction absorption. The complex permittivity t* can therefore be written as follows: E*(u)

=

t*R(’)

-jx/(,Ow)

where x represents the dc conductivity, eo is the vacuum relative permittivity, w = 2 ~ isu the electric field angular frequency, j 2 = -1, and = e’(u) - j ~ ” ~ ( vrepresents ) the term related to relaxation. The conductivity varies increasingly as 4, and can S m-l, e*(v) cannot be become very important. When x > properly measured anymore with our equipment. Actually, we have been limited to 4 = 0.18 for n = 10 (cp, = 0.057). Figure 2, relating to n = 3.6 with C#J = 0.293 (cp, = 0.042), indicates that the =At’) is a semicircle centered under the t’ axis. Studying the t ’ ( u ) and E ” ~ ( U ) curves indicates that the distribution of relaxation times is of Cole-Cole type. Therefore, we can write

In this relation u, represents the frequency of the maximum absorption, q and e,, are the permittivities at low and high frequencies with respect to uc, and a is the frequency spread parameter characteristic of the eccentricity of the circular arc. A fitting method enables one to determine the t I th, uC, cy quantities, starting from experimental values. As for Figure 2, we get el = 11.48, t h = 2.75, u, = 17.1 MHz, a = 0.364. The mean square deviations (rms) between experimental values and resulting representations are always less than experimental uncertainties (for Figure 2, rms e’ = 0.04, rms = 0.04). Figure 3 shows the agreement between experimental and calculated values. Besides, it is to be noted that the representation by relation 1 is correct whatever the n and 4 values. In order to determine the limits of relation 1, we have altered the system constitution. We replace dodecane first by isooctane and then by cyclohexane. The results are given in Table I. The oil nature appears to have a prevailing influence over relaxation parameters, yet relation 1 is still valid, such as demonstrated by the very low values of mean square deviations. We also made some measurements on the water/AY/benzene system. Figure

6 16.9 2.20 25.2 0.44 0.08 0.02

4.4 12.50 2.45 42.9 0.36 0.1 1 0.05

n

6 4.85 2.85 362 0.22 0.04 0.02

4.4 14.8 2.80 16.8 0.40 0.09 0.08

6 31.8 2.70 10.5 0.39 0.27 0.21

5

I

^^

/

0

I

I

5

10

Figure 4. Cole-Cole plot

\

I

15

*

E’

for water/AY/benzene system (9 =

0.18, n = 4.4). Frequencies in MHz.

i

30i 20-

10-

n“ I 0

L

L

0.1

012

0:3

Figure 5. Variations of the low-frequency permittivity c, vs. 9 at various n values (water/AOT/dodecane system): (A)0, ( 0 )2, ( X ) 3.6, (B) 4.4, (0) 6.9, (+) 7.0, (A) 10.0.

4 represents obtained with n = 4.4, C#J = 0.18 1, cpw = 0.03 1. Like, Eicke and Shepperd3’ we get a typical diagram of a relaxation time distribution, which can be represented in our experiments by relation 1 (Table I). For the same system, Eicke and Shepperd have used a Davidson-Cole distribution. The difference probably arises from the mistake that they made between permittivity at high frequencies and benzene permittivity. Considering the presence of water and surfactant, this is not correct and leads to underestimation of the exact t h value. Besides, the maximum value of their experimental frequency (10 MHz) is not large enough to describe properly the dielectric relaxation. Yet, there is a case23(isobutyl alcohol, dodecane, water + 0.5% NaCl, petroleum sulfonate) where the representation given by the authors corresponds to the superposition of two Cole-Cole distributions with moderate frequency spread parameter (0 < a < 0.22), but figures indicate a poor fitting. The observation of two hardly differentiated peaks on the PR(log v) curves is probably due to the poor accuracy of the equipment. The authors indicate uncertainties of 10% for E’, and 15% for €’IR. (31) Eicke, H. F.; Shepperd, J. C. W. Helu. Chim. Acta 1974, 57, 1951-1963.

The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 373

Structure of Water/AOT/Dodecane Systems

Eht

r;(MHz:

t

100

\

d

0 .‘20

0 .‘IO

m

0 .‘30

Figure 8. Variations of the high-frequency permittivity q, vs. 6 for two values of n (water/AOT/dodecane system): ( 0 ) n = 2; (+) n = 6.

50

‘t

.

‘09

0

0 .I10

0

.bo

0 (30

a,

Figure 6. Variations of the frequency v, of maximum absorption vs. 6 at various n values (water/AOT/dodecane system): (0) 2, (X) 3.6,(M) 4.4, (0) 6.0,(+) 7.0,(A) 10.0. I‘

b

t

I

5

0

10

-

ps

Figure 9. Variations of the dc conductivity x vs. salinity p , (in percent) (water/AOT/dodecane system, 6 0.308,n = 4.4).

0

I

0 10

I

0 20

I

0 30

040

-

0

Figure 7. Variations of the frequency spread parameter a vs. 6 for two values of n (Water/AOT/dodccane system): (+) n = 3.6;(0) n = 6.

In our opinion, the microemulsion relaxation is best represented by relation 1 whatever the nature of the constituents may be. Beyond the results that have just been described, a similar behavior (with high a values) has already been observed for w/02*22 (quaternary or with nonionic surfactants) or o/w32*33 systems; all such systems have been studied by classical measurement methods. Influence of n and 4. Figure 5 represents cl variations according to 4 for different n values. When n 6 4.4, tl varies increasingly as 4, and when n 2 6,a maximum can be observed in the explored volume fraction interval. The frequency uc of maximum absorption decreases with 4 when n 6 4.4, whereas when n 2 6,vc reaches a minimum for a smaller volume fraction 4 as n is bigger (Figure 6). The large u, variations according to 4 (from 150 to 3 MHz, for example, for n = 4.4) should be noted. The variations of the a parameter are similar to those for el. As an example, Figure I represents the cases when n = 6 and n = 3.6. Much more difficult is the study of the 4 effect on q, considering its very low variations and the uncertainties in its determination by fitting. Yet, q,can be estimated as varying increasingly as n and 4 (Figure 8). Influence of Water Salt Content. To study the influence of water salt content, we have kept constant the n and 4 quantities (n = 4.4, 4 = 0.308, vw = 0.052)and we got the salt weight percentage p s to vary in the solution. Figure 9 indicates that x decreases very rapidly as p s increases. To highest salt concen(32) Foster, K.R.; Epstein, B. R.;Jenin, P.C.;Mackay, R.A. J. Colloid Interface Sci.1982, 88,233-246. (33) Epstein, P. R.; Foster, K.R.; Mackay, R.A. J. Colloid Interface Sci. 1983, 95, 218-227.

“i30i I

litMHz1

1150

- 100

- 50

I

0

5

10

*I PS

Figure 10. Variations of the low-frequency permittivity t, and the frequency u, of maximum absorption vs. salinity p , (in percent) (water/ AOT/dodecane system, 6 = 0.308,n = 4.4).

trations this conductivity is very low: x = 8.5 X lo4 S m-’ when p s = 10.5%. In the same way, tl decreases when ps increases and seems to tend toward a limit near to 3 (Figure 10). On the other hand, the frequency Y, increases with p , (Figure 10). Study of Viscosity. We have determined the dynamic viscosity t) of the systems considered according to the disperse-matter volume fraction 4 and to the molar ratio n. If the latter is kept constant, t) is an increasing monotonic function of 4. On the other hand, when 4 is constant, t) reaches a maximum when n increases, a maximum as important as 4 is bigger (Figure 11). (As the equipment could allow it, we have reached n = 20.) For systems with brine, viscosity as well as conductivity can be seen to decrease very rapidly with salt content (Figure 12).

Discussion AOT Perm’ttiuity. A proper discussion of results will be possible only if the dielectric features of each components are well-known.

374 The Journal of Physical Chemistry, Vol. 89, No. 2, 1985

H a n a P gets the following expression, valid for large volume fractions:

l%P!

LO

30

Peyrelasse and Boned

(-)-=-

q * - €2* €I* - € *

J

O /

I

I

1 (1 - 4)3

€21

where e* is the complex permittivity of the system, el* the complex permittivity of the dispersed medium, and e2* the complex permittivity of the continuous medium. Experience shows that this law accounts well for the dielectric properties of various disperse systems18J5and up to volume fractions of about 0.8 (demonstrating that relation 2 does not require any hypothesis on polydispersity). It should be reported that the Hanai law is asymmetrical when the part of phase 1 and 2 is permuted, which reveals the existence of discontinuities observed with emulsions at phase inversion. Limiting laws obtained when the frequency tends to zero or to infinity in eq 2 enable one to calculate the mixture dc conductivity x as well as the permittivities t h and el at high and low frequencies. If x1and x2 are the conductivities of the phases, t l h and '2h their permittivities at high frequencies, we get

i

'*Vr---

e*

@=0.180

1

D=0.106

*

I

5 10 15 n Figure 11. Variations of the dynamic viscosity T vs. n at various 4 values

0

3 x - XI

(water/AOT/dodecane system).

;)

= 3( e2s - Cls + x2 -

x1

2) -2 x - XI

x2

(3)

cis and e2 being the static permittivities of phases 1 and 2. This last relation is valid only if x2 (and x) is different from zero. If x2 4 to take into account the hydration of the surfactant heads in water. In our case, where oil is the most extensive phase, one could imagine oil penetration in the interfacial layer, but calculations show that one would need very high values of the apparent volume fraction 4’. For example, for tl = 40 = 2.008 and n = 4.4, 4 = 0.308), one would get 4’ 2 0.63, close to the value corresponding to a compact piling of identical spheres. (c) Salt Influence. Figure 10, where q variations are represented according to salt content, for n = 4.4 and 4 = 0.308, shows that static permittivity tends at the highest salt concentrations to the value anticipated by the spherical model. Figure 13 represents the variations of dynamic viscosity according to 4 for samples constituted with brine (n = 4.4 and ps = 10.5%). The interpretation can be based on a modification of the Brinkham law, which considers the increase in viscosity due to collisions between hard spheres4I (9) where qo represents the dynamic viscosity of the continuous phase (for dodecane qo = 1.36 cP). For a compact piling of identical spheres distributed at random, viscosity should tend to infinity. The value of 4 at compact piling is (phi = 0.637, which involves h = 0.895. Figure 13 shows the good similarity between the values calculated from eq 9 (with h = 0.895, qo = 1.36 cP) and the experimental values. In this way, at high salt concentrations, the studied systems seem to behave as random dispersions of identical hard spheres without any other interactions than collisions. It should be noted that this remains true up to important values of 6. Besides, assuming that system conductivity is due to the electrophoretic motion of micelles, Figure 9 shows clearly that the average micelle charge must tend to zero when ps increases since conductivity tends as well to very low values. Therefore, we understand why relation 9, which does not account for electroviscous phenomena, satisfactorily applies when the salt concentration is high. Spherical Model Considering the Surface Charges. A simple spherical model does not apply except at high salt concentrations, since it does not consider electric charges trapped at interfaces. They can be taken into account in the following way. ( a ) Schwarz To explain dielectric properties of colloidal suspensions in electrolytic solutions, Schwarz has de~~~

(38) Goset, G.These de 35 Cycle, Pau, France, 1978. (39) Schwan, H.P.; Schwarz, G.; Maczuk, J.; Pauly, H. J . Phys. Chem. 1962, 66, 2626-2635.

(40) Peri, J. B. J . Colloid Interface Sci. 1969, 29, 6-15. (41) Dvolaitzky,.M.;Guyot, M.; Lagues, M.;Le Pesant, J. P.; Ober, R.; Sauterey, C.; Taupin, C. J . Chem. Phys. 1978, 69, 3279-3288. (42) Schwarz, G. J . Phys. Chem. 1962, 66, 2636-2642.

376 The Journal of Physical Chemistry, Vol. 89, No. 2, 1985

;1(

Peyrelasse and Boned I /

i /

/ /

/ / / / /

10-

ogLl-'I'

,

- c 7.0

I

-0 15

1

-0 10

I

-005

I

/

+/

t-g C

Figure 14, Variations of log (e,) vs. log (1 - #) at various n values (water/AOT/dodecane system): (+) 0, (A)2, ( X ) 3.6, (W) 4.4, ( 0 )6 (a) limiting law, e, = e2s/(l - 4)3(eq 4).

veloped a model which takes into account both a surface current due to the charge movement (linked to the surface) through the action of the electric field, and a diffusion current tending to reestablish random distribution. The equivalent permittivity of a sphere is then given by the following expression: E,* = At,*

+

0 1

b

Ei

0:3

0:2

0.1

0

b

9.4

Q,

/ /

2.50

where tsO*represents the sphere equivalent permittivity in the absence of charges and where Ats* is given by 2.30.

where eo is the electron charge, a the sphere radius, uo the superficial density of charges a t random distribution (number of charges per unit area), k the Boltzmann constant, and T the temperature. r' is a relaxation time defined by

2.10.

r' = a 2 / ( 2 u k T )

where u is the mechanical mobility of surface charges. Relation 10 indicates that At,* is characteristic of a Debye type dipolar dispersion. Like Schwarz we can assume the existence of afl.') distribution function related to a distribution of the surface charge mobility. Therefore, we shall assume that

TO/

= a2/(2uokT)

that is, a Cole-Cole distribution. ( b ) Case of Water/AOT/Dodecane Systems. First of all, let us assume that the previously indicated phenomenon occurs a t the level of the separation surface between water core and coat (which is the hypothesis of Chou and Shahz3). Therefore, we have

Relation 6 enables the calculation of e,*, and the dispersion complex permittivity E* is then given by relation 2. Obviously, considering the limit value of eq 7 for t I sthe introduction of the electrical layer a t the water-soap interface does not bring any improvement concerning the cI value. We can also form the hypothesis that the phenomenon described by Schwarz remains valid at the AOT/oil interface. This would suggest the existence of charges at the micelle surface, which is apparently confirmed by the viscosity and conductivity measurements. In this case, the maximum t/ value will be limited by t2,/( 1 - &)3 (this is true for the two hypotheses: swollen micelles and hydrated micelles); however, calculation showed us that this hypothesis deserved detailed discussion. (c) Comparison with Experiments. Figure 14 represents the log tI variations according to log (1 - 4) for several n values (the

0

0.02

0.04

0.06

(I,

Figure 15. (a) Variations of the low-frequency permittivity e, vs. 4 at n = 3.6 (water/AOT/dodecane system): (+) experimental data; (-) limiting law, e, = ez/(l - $)3 (eq 4). (b) Idem, small 4 values.

curves for n 2 6 have not been transcribed so as not to encumber the figure). The same diagram also indicates the variations of log CI as deduced from eq 4. We can see that the model may apply if n 6 2. For n > 2, curves draw near the eq 4 limit law (obtained ' ) ta(l + 2j)/(l -j)) if e&zuo/(eokQ >> tz and e ~ a u o / ( t o k 7>> if 0. Figure 15, a and b, related to n = 3.6 shows that, at low 4 values, the system actually behaves like a sphere dispersion since the el, >> t2, approximation is compiled with, and relation 4 is then checked. However, viscosity cannot be represented anymore by eq 9 , which does not consider the electroviscous phenomena resulting from surface charge. Figure 16 shows the gap a t small & between experimental 7 values and the values deduced from eq 9 and from the Einstein law: 7 = qo( 1 + 2.54). For n = 2, we have been able to interpret properly the results concerning dielectric relaxation for all 4 values with the previous model. Figure 17 enables a comparison of theoretical or experimental results for q(4) and vc($) with auo = 5.629 X lo7 MKS; a 2 / u o = 2.45 X MKS; a' = 0.36 Figure 18, which corresponds to 4 = 0.40, indicates, for the complex permittivity variations, the agreement with calculations. It should be noted that the model makes only one relaxation domain appear. This arises from the fact that the prevailing relaxation caused by the Maxwell-Wagner effect in the case of swollen micelles (eq 6-8) has a much lower amplitude. It is also

-

The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 377

Structure of Water/AOT/Dodecane Systems

already been pointed out for similar systems: oblate or prolate revolution ellip~oids,6*~~ disks.40 (a) Model of Dielectric Properties of Revolution Ellipsoid Dispersions. In the case of qspermittivity ellipsoids, dispersed at random in a ea permittivity environment, the following relation, can be obtained43for low volume fractions:

1

. r - T - - - - -

ul

0.05

0

Figure 16. Variations of the dynamic viscosity q vs. &I at n = 3.6 (water/AOT/dodecane system): (+) experimental data; (-) eq 9 and Einstein law.

where Ak is the depolarization factor along the k axis and is such = as = 1. In the case of the sphere, a = b = c, = A3 = /3. The extension of relation 11 at high volume fraction can be carried out by using the static permittivities as per the Bruggeman method and using a generalization at complex perm i t t i v i t i e ~ . ~A~ ,general ~~ relation is obtained. In the case of revolution ellipsoids of a, b, c, semiaxes with b = c, we get A2 = A3 = A =

Al=1-2A= If b

0 0 .I 0.2 0.3 0,4 @ Figure 17. Variations of the low-frequency permittivity tl and the frequency yo of maximum absorption vs. &I at n = 2 (water/AOT/dodecane system): (+, 0)experimental data; (-) theoretical curve with uuo = 5.629 X lo7 MKS, a2/uo= 2.45 X MKS,and a’ = 0.36 (point fitting, q5 = 0.4, n = 2).

+

+

ab2 ds s)3/2(b2+ S)

(+)

U

2 sin3 8

< a, prolate ellipsoid

A = - - -1 2 sin2 6

0

Jm2(a2

+

> a, oblate ellipsoid A=

If b

ab2 ds l m 2 ( b 2 s)~(s a2)1/2

cos2 e 4 sin3 8

with cos 8 = b

cos 8

[

+

1 sin e ] 1 - sin 0

b with cos 8 = a

In that case the general relation gives45*46 (1

- 4) =

($)’”(

el*

‘I*

- e*)[ - ‘2*

‘2

* (1 + 3A) + q*(2 - 3A)

“(1

+ 3A) + q * ( 2 - 3‘4)

d = A(l - 2A)/(2 - 3A) 3K = 2(1

’i

- 3A)(1

+ 3A)]

Assuming the presence of surface charge leads to an important additional Aq*, dielectric increment, then lel*l >> Ie2*I when v 0. Hence, we get

-

280

7 - 0

I

0

- 3A)’/[(2

I

3K

2

4

6

E/

\ 0

w t’

Figure 18. Cole-Cole plot t f f R ( ~for ’ ) water/AOT/dodecane system (&I = 0.4, n = 2); frequencies in MHz: (+) experimental data; (-) theoretical curve with abo = 5.629 X lo7 MKS, a2/uo= 2.45 X loF2*MKS, and a’ = 0.36.

to be noted that relation 2 provides for dispersion a relaxation frequency obviously depending on the value of the disperse-phase relaxation time (here, mainly 74;that is, 5.3 M H z for the frequency) but also of 4 and on the e2s value. In this way, we get for 4 = 0.4, v, = 10 MHz, but vc = 39 MHz for = 0.1. This is to prove that, except in very particular cases,the relaxation time of the disperse phase must not be mistaken with the one to be measured for the mixture. Finally, the large value of the a parameter corresponds to a distribution of mobility of surface charge. Model of Anisotropic Dispersion. The spherical dispersion model with or without surface charge only allows one to explain some experimental observations: those corresponding to n 5 2, those obtained when 4 0, as well as those corresponding to the case of concentrated salty solutions. That is why, in this section, we shall consider the influence of the deformation of disperse objects. The existence of micelles or anisotropic groupments has

-

= ‘ZS/(l - 4)1/3d

When a / b remains constant, the log

(12)

curve according to log (1

- 4) is a -1/3d slope line passing through the 0, log e2s point.

(b) Comparison with the Experiment. Figure 14 shows that the log e/ curves according to log (1 - $), plotted for n = 3.6 and 4.4, actually have a linear part passing through the 0, log (2.008) point, in compliance with relation 12 predictions. Yet, we find a gap at low 4 values which we can attribute to a / b variations (a/b 1 when 4 0). For n 5 6, the linear part does not exist any more, and the log el =fllog (1 - 4)] curve shows a maximum. As we know e2,, el, and 4, relation 12 enables the calculation of d, hence A , and we can trace back the value of the a/b ratio in the case of the two hypotheses: oblate or prolate ellipsoid. Figure 19, a and b, represents a / b variations with 4 for the different n values in the case of the two hypotheses. We can see that for n 5 6 the anisotropy of disperse objects reaches a maximum according to

-

-

(43) Bostock, T. A.; Boyle, M. H.; McDonald, M. P.; Wood, R. M. J . Colloid Interface Sci. 1980, 73, 368-372. (44) Dukhin, S. S. In “Surface and Colloid Science”;Matijevic, E., Ed.; Wiley-Interscience: New York, 1971; Vol. 3, pp 83-165. (45) Boned, C.; Peyrelasse, J. J. Phys. D 1983, 16, 1777-1784. (46) Boned, C.; Peyrelasse, J. Colloid Polym. Sci. 1983, 261, 600-612.

Peyrelasse and Boned

378 The Journal of Physical Chemistry, Vol, 89,No. 2, I985

0

I

I

I

I

*

0 .‘IO o.>o 0 .I30 0.’40 (P Figure 20. Variations of the frequency vC of maximum absorption vs. 4 at n = 3.6 and n = 6 (water/AOT/dodecanesystem): experimental data, ( X ) n = 3.6, (0) n = 6; (-) theoretical curve (two-point fitting: n = 6, 6 = 0.12;and n = 3.6, 6 = 0.23).

that the frequency spread parameter CY for the model shows little variation and that the frequency of the maximum absorption v, reaches a minimum as already experimentally observed. Figure 20 represents v, variations according to for n = 3.6 and n = 6. We see that there is a good qualitative agreement between measured and calculated values and that the v, minimum to be observed experimentally must be linked to the anisotropy variation.

+

The a / b values are deduced from the prolate ellipsoid model (relation 12) by using the e, and + experimental values. We have investigated the qs,t l h , T’, and a’ values best fitted to the experimental results for = 0.12, n = 6 and = 0.23, n = 3.6. The values of tis, f l h , T’, and a’ are kept constant; if + varies, we see

Conclusions The proposed analysis has been made possible by the knowledge of the exact volume fraction of the dispersed phase. The analysis of the experimental results leads to the following general conclusions: (i) For n 5 2, the surface charge shows little effect, and the electric interactions between the dispersed objects are not high enough to lead to aggregation, and the model of charged spheres applies (Figures 17 and 18). Yet, we cannot make conclusions on the exact structure of the objects; however, considering the low n values, we are most probably dealing with hydrated AOT micelles. (ii) For n 5 3.6 and sufficient volume fractions of disperse matter (50.05),high values of the dielectric increment appear to be interpreted only by the existence of anisotropic objects. However, after dilution, that is for small values, we see that the surface charge remains important but that the system behaves again like a dispersion of spheres. This result is in agreement with studies using light scattering or neutron scattering of various microemulsions obtained by d i l ~ t i o n . ~ ~It, ~seems * difficult to assume that the system dilution alone involves very important modifications in the micelle shape. Most likely, because of electric interactions, the spherical micelles form, at sufficient concentration, anisotropic aggregates which we compared to ellipsoids from a dielectric point of view. Such structures are undoubtedly fluctuating and an average effect is to be observed. The aggregation hypothesis is supported by the following fact: salt addition, as it decreases the charge and interactions of micelles, causes a decrease of apparent anisotropy, and at highest salt concentrations, the spherical model is satisfying up to important disperse-phase concentrations (Figure 13). (iii) When the dispersephase volume fraction is kept constant, the n increase involves the decrease of the available total soap quantity in the system in favor of the water quantity. Then the

(47) Berthod, A.; Georges, J. J . Chim. Phys. Phys.-Chim. Bioi. 1983.80, 245-249.

(48) Assih, 35-39.

0

I

I

I

0.2

0.1

0.3

* cf,

Figure 19. Variations of the a / b ratio vs. Q at various n values (water/AOT/dodecane system). (a) Prolate ellipsoids: (*) 2, (0) 3.6, (+) 4.4, (0) 6, (X) 7, (A) 10. (b) Oblate ellipsoids: (*) 2, (A)3.6, (+) 4.4, (0) 6, ( X ) 7, (M) 10.

+. For + 5 0.18, it is the same according to n and with I#J constant.

The maximum deformation to be observed when is kept constant according to n should be correlated with the maximum viscosity to be observed under identical conditions (Figure 11). It should be noted that the existence of this maximum cannot be explained by a change in the water/oil F! oil/water structure as this has been done for some systems,47since studied systems are clearly of water/oil type, because of their composition. We have also studied the predictions of this model according to frequency. We have admitted that the presence of surface charge is expressed for the disperse phase by an equivalent permittivity: €,*

=

e,,

+ 1 + C-j W€fl)hl - a ’ €1,

(analogous with the Schwarz model) with €1,

+

>> €2,

+

+

T.;Larche, F.;Delord, P.J. Colloid Interface Sci. 1982, 89,

The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 379

Structure of Water/AOT/Dodecane Systems number of dissociated soap molecules must reach a maximum, for which the interactions, hence the aggregation phenomenon, could reach a maximum, therefore involving a maximum apparent anisotropy. On the other hand, with n = constant, when increases, anisotropic aggregation can occur first of all; then, when is sufficient, because of the overcrowding increase, there could be as well successive aggregation on existing entities tending to reduce the surface/volume ratio. Therefore, it would result in a decrease of apparent anisotropy. One may also consider another explanation: the anisotropy maximum observed at constant n and increasing 4 is related to the fluctuating nature of the aggregates. At small 4 values, a spherical micelle may be solicited by an aggregate only in its neighboring area. As 4 increases, the probability of an aggregate encountering a free spherical micelle (and then growing) will increase (as a/b). However, as becomes large, a free micelle will be solicited by several aggregates in its neighboring area at the same time. There will be some kind of compensation, and the micelle will take part of no aggregate. That effect will increase with 4, and the fluctuating aggregates will get less and less spherical micelles. So there is a value giving a maximum anisotropy. One may also consider that only the increasing part of the curves corresponds to aggregation. The maximum corresponds then to a bicontinuous structure where conducting matter paths may be defined in terms of chaotic interconnected conduits which are dynamic in nature. Such a structure has been recently postulated by Chen et al.49 for three-component ionic microemulsions. In the case of our experiments, however, one may question whether the low cpw values are compatible with such a model. However, we acknowledge the fact that such explanations can be discussed, though the el maximum according to 4 with n constant is an experimental point. At last we have to point out the good qualitative agreement obtained when one uses the model of charged ellipsoids of revolution (Figure 20), in order to interpret the dielectric properties of these systems. (iv) We must also mention a very recent study by Sj6blom et al.50951about the static permittivity of sodium octanoateln-de-

+

+

+

+

(49) Chen, S.J.; Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1984.88, 1631-1634.

canol/water systems, They found a large increase in the dielectric constant as the concentration of reversed micelles is increased. This behavior could not be explained by means of a model based on spherical aggregates. They extended the spherical model to involve nonspherical aggregates and show that the increase in the macroscopic dielectric constant may be explained by a moderate asymmetrical growth of the micelles (axial ratio n, 3). They also found that at low concentrations of reversed micelles a spherical geometry can explain experimental data. Their relation is obtained by solving the Laplace equation in a spheroidal coordinate system. (That is a particular case of a in the general case of demonstration already made by us45,46 ellipsoidal coordinates. The reader is also referred to Stepin’ss2 paper on stratified ellipsoidal systems, that is, the model utilized by Sjomblom et al.) That relation is only valid at low 4 values; at high values (30.1) it is ~ e l l - k n o w n *that * ~ ~it ~is~necessary ~ to take into account the interactions between dipoles equivalent to each dispersed particle. That is not the case in their demonstration. Besides, they made measurements only at 1 MHz50 so they cannot explore the relaxation phenomenon. The high values of the frequency uc are in our opinion generally linked to the existence of a surface charge. Nevertheless, our measurements agree qualitatively with theirs as far as the variations of the static permittivity are concerned. (v) The results obtained with totally different systems show that microemulsion dielectric relaxation is represented by a Cole-Cole type relaxation. The values of amplitude, frequency of maximum absorption, and spread frequency parameter mainly depend on the nature of the present components. A systematic study of such phenomena is under way. The presence of surface charges seems to play a very important part but the features of a spherical dispersion seem to appear when the volume fraction tends to zero.

+

Acknowledgment. We are indebted to the Societt Nationale ELF-Aquitaine (P) for the financial support of this work. Registry No. AOT,577-11-7; dcdecane, 112-40-3; water, 7732-18-5. (50) Sjablom, J.; JBnsson, B.; Nylander, C.; Lundstrbm, I. J . Colloid Interface Sci. 1983, 96,504-516. (51) Sjablom, J.; JBnsson, B.; Nylander, C.; Lundstrom, I. J . Colloid Interface Sci.1984,100, 21-32. (52) Stepin, L. D. Zh. Tekh. Fiz. 1965, 35, 996-1001.