A thermodynamic analysis of the molar conductivity of the ternary system: Water-aerosol OT-isooctane

A Thermodynamic Analysis of the Molar Conductivity of the Ternary System: Water-Aerosol OT-Isooctane Because of their particular sensitivity and accuracy, conductimetric measurements prove to be frequently valuable in following shifts of adsorption equilibria, charging processes, and eventually ion pair formation of charged microphases in multicomponent systems containing amphiphilic electrolytes. The experimental results are plotted as the molar conductivity (A) against the square root of the concentrations of AOT and water (Fig. 1). Beyond a small region of jumplike increasing molar conductivities bounded by 5_ curves which correspond to [H20]/[AOT] = w0 = 44.5 and 15, respectively, the curves exhibit a certain regularity depending obviously on the amount of water added to the system. Small aliquots of water lead to an initially nonlinear, following steep linear increase of the conductivity (not all curves are shown), while larger aliquots of water produce an opposite effect, i.e., initially reducing the conductivity (linearly with the square root of the amounts of AOT and water), leveling offwith larger amounts of the added components. The above-mentioned regularity of the conductivity plot prompts one to offer a thermodynamic interpretation of the supposed underlying mechanism. Hence it is assumed that two different charging mechanisms are operative: (i) The first mechanism is closely related to a frequently proposed (see e.g., Ref. (1)) adsorption equilibr i u m of surfactants at solid surfaces and (liquid) oil/water interfaces, i.e.,

ward the oil/water interface increases as the water in the aqueous microphases approaches the property of"bulk"water (2). The proper charge production is then described by K'

( 1 / n ) S , + Sads ~- (l/n)S+, + S S ~

[2a]

and K"

( 1 / n ) S , + Saos ~- ( 1 / n ) S , , .

[2b]

On the right-hand side of Eq. [2b] the correct subscript should read n + 1; however, 1 has been neglected in view of the large value of n. Applying the mass action law to Eqs. [2], considering the electroneutrality and denoting [S~] and [S~] by c i (~- ionic concentration), one obtains cj = 1. v , / 2 ~ix, , adsl. , m cJ n ]13/2 [3] where K = K ' K " . This expression may be easily transformed into gnl2r,'n/2t

~.

[3a]

• ~,ds~wol $3/2

cJ

n3/2

if the conservation of mass is introduced. So is the added amount of surfactant plus an aliquot of water which is essentially bound to the surfactant. Hence it is assumed that in this region the added water does not act as an independent component. From Eq. [3a] the specific conductivity is derived to be K = ftFc, = u_F

gn/2gn/2/

,

~ ads~Wo) $3o/2

[41

Kads(n 0)

(1/n)S,,

~S~ds,

Sad~ = K~d~(wo)[S~] ~1/"),

[la] [lb]

where the left-hand side of Eq. [la] denotes the adsorption of the hydrated surfactant at the water/oil interface (within the surfactant aggregate with aggregation number n), while the right-hand side describes the adsorption of the hydrated surfactant at the electrodes (or eventually glass walls of the cell). Kad~(w0) is the equilibrium conslant governing the mutual adsorption processes. It is assumed that K~d~varies with the amount of water added to the system, increasing with decreasing aliquots of water. This property of K~d~ parallels the shift of the critical micellar concentration (CMC) toward smaller values with increasing amounts of added water (w0). It expresses the fact that the affinity of the surfactant to-

(~ is the mean mobility of the charge carriers, and F t h e Faraday constant) and, accordingly, the molar conductivity A

K n / 2 I,~,/2t ,,, ",,~ tz:" "~ H ads~ 3/2~0),,-- ~,0 c~P-.

[4a]

The latter equation displays indeed the experimentally observed relation between the molar conductivity and the square root of the surfactant and water concentrations in the system. Also in line with the experimental results is the increase of the slope of the curves with decreasing amounts of added water since gads should increase according to the above model (i) while n, the aggregation number, is decreasing with decreasing aliquots of water. (ii) At larger aliquots of water, the above proposed mechanism becomes invalid and another charging pro-

593 0021-9797/83 $3.00 Journal o f Colloid a n d Interface Science, Vol. 93, No. 2, June 1983

Copyright © 1983 by Academic Press, Inc. All rights of reproduction in any form reserved.

594

LETTERS TO THE EDITORS °

tz~

II II

Ii

/

/

~

E u "7

o/ •

l u

25

m

• -

<2"

30

!\ I I

\,

\

I

44.5

! ! ! /

011 0z(cAo,.,,o),,2

019

FIG. 1. Molar conductivity (A = K/CAoT + C~O)) against (CAoT+ Cn20) ~/2 of the ternary system: water, aerosol OT, iso-octane at 293°K. Parameter: added aliquots of water (w0 = [H20]/[AOT]).

cess becomes predominant. The transition region has to be located somewhere between 15 < w0 < 25 which again agrees well with analogous conclusions obtained from other experiments (3). The already mentioned linearly decreasing molar conductivity with the square root of the surfactant and water concentrations is attributed to the formation of ion pairs. In the present context these ion pairs in the sense of Bjerrum are dimers of charged mierophases. This is in line with the above model, i.e., Kads(wo) is decreasing with increasing Wo favoring the adsorption of surfactants at the oil/water interface and, hence, the formation of aqueous microphases. At higher surfactant and water concentrations the molar conductivity becomes constant, indicating that the specific conductivity of the system is proportional to the sum of the concentrations of surfactant and water. This may be straightforwardly visualized by referring to a model (4) which has been applied rather successfully to exchange Journal of Colloid and Interface Science,

V o l . 9 3 , N o . 2, J u n e 1983

processes between aqueous microphases (5, 6). We therefore write h*

2S, ~- S,+_~ + S~+,.

[5]

This equation simulates the physical exchange process of the dissociation products of the Aerosol OT between microphases. The latter is an anionic surfactant, hence the anion is amphiphilic which is added to a neutral aggregate to yield S, + S-. In contrast to case (i) this charging process proceeds within the oil continuous phase. The specific conductivity is, accordingly, from Eq. [51 K = ~*FKI/2[S,] [6] which may be written in view of the mass conservation as

K

So

A

K*I/2~*F

- - ,

n

[7]

595

LETTERS TO THE EDITORS where ~* is the mean mobility of the charged microphases and K* the dissociation constant of the AOT which is made up of two contributions, i.e., the dissociation within the aggregates and the charge separation (7). Equation [7] hence conforms to the experimental findings that the molar conductivity becomes constant for larger amounts of added surfactant and water aliquots. Considering the first part of the conductivity curves at small concentrations of surfactant and water, the linear decrease of A clearly resembles the behavior predicted by Kohlrausch's law for strong electrolytes. The experimentally observed slopes of the linear parts of the curves, however, are considerably larger when compared to the values calculated with the help of the Debye-Hfickel-Onsager theory. This phenomenon is well known (8) and is due--as mentioned above--to the association of charged microphases which could give rise in the present case to considerable dipole moments. Since the "radius of the ionic atmosphere" is large due to the relatively small concentration of charged microphases, a clear distinction between discrete "ion pairs" and ion cloud interactions cannot be obtained from these measurements. One may ask whether under these conditions Ostwald's dilution law for low degree of dissociation of the associated charge carders would fit better the experimental curves. The apparently linear initial part of the curves for higher aliquots of added water does not support this assumption. However, the leveling of the A curves at the higher concentrations to reach the above calculated value K*~/2ff*F/n could be better accommodated by Ostwald's law which is frequently used to describe ion association in nonpolar solvents. Hence there exists a certain ambiguity which cannot be solved with conductivity measurements alone. Finally it should be mentioned that the concentration region where the jumplike increase of the molar conductivities is observed corresponds to the so-called CMC region as concluded from other experiments (9). It is noteworthy that the conductivity displays correctly the shift of the critical surfactant concentration toward lower values as the aliquots of water are increased. The

absolute values of the CMC which are derived from these measurements coincide satisfactorily with data from other sources. ACKNOWLEDGMENT This work is part of the project 2.025.0.81 of the Swiss National Science Foundation. REFERENCES 1. Mittal, K. L., and Mukerjee, P., in "Micellization, Solubilization, and Microemulsions" (K. L. Mittal, Ed.), Vol. 1, p. 1. Plenum, New York, 1977. 2, Eicke, H. F., J. ColloidlnterfaceSci. 52, 65 (1975). 3, Eicke, H. F., in "Microemulsions" (I. D. Robb, Ed.), p. 17. Plenum, New York, !982; Chimia 36, 241 (1982). 4. Eicke, H. F., Shepherd, J. C. W., and Steinemann, A., J. Colloid Interface Sci. 56, 168 (1976). 5. Fletcher, P. D. I., and Robinson, B. H., Ber. Bunsenges. Phys. Chem. 85, 863 (1981); also in "Microemulsions" (I. D. Robb, Ed.), p. 221. Plenum, New York, 1982. 6. Robinson, B. H., Steytler, D. C., and Tack, R. D., J. Chem. Soc. Faraday Trans. 1 75, 481 (1979). 7. Eicke, H. F., and Denss, A., in "Solution Chemistry ofSurfactants" (K. L. Mittal, Ed.), Vol. 2, p, 699. Plenum, New York, 1979. 8. Kortfim, G., "Electrochemistry." Verlag Chemie, Weinheim, 1972. 9. Rehak, J., Ph.D. thesis, University of Basel, 1976. H. F. EICKE H. HAMMER1CH G. VASTA

Institute of Physical Chemistry University of Basel CH-4056 Basel, Switzerland Received July 14, 1982; accepted September 28, 1982

Journalof Colloidand InterfaceScience, Vol.93, No. 2, June 1983