J. Phys. Chem. 1982, 86, 4756-4758
4756
following explicit expressions for the four quantities of interest (the symbols in parentheses on the left are those used by Noyes): which show that the modified version of the first relation in eq A14 also holds within the approximation considered. This relation allows one to construct the reaction probability for an imperfect sink from that pertaining to a perfect sink; calculating to first order in A/R, one finds a P l ( r o ) [ l - (1- a)P1(RO)]-I = cu(R/ro)[l+ A / R - (1 - a ) ( l - A/R)]-’ = (R/ro)a/[cu+ (2 - a ) A / R ] (AX) Thus, if one assumes from t h e outset that the relation corresponding to i in eq A14 must hold, the expression in As stated in our previous paper,3 Noyes deduced, from eq A16 must be identical with that for P(ro);it is readily purely formal reasoning, the relations seen that this requirement is met provided that w = a / ( 2 - a ) , a relation already established on other grounds. (i) p,,’ = aPo[1 - P + aB1-l (~14) Some Currently Accepted Relations. It can be verified (ii) Po’/’ = Po/P from their publications that Noyesl and Monchick6 use, statedly or implicitly, the following relations: and the question now arises whether the replacement of his quantities by those given in eq A13 creates a conflict Ro=R b=Lyuo/4 CY=W n=l with these relations. It should be kept in mind that Noyes (A171 D = uu2/6 = u01/6 identified Ro with R and did not have to face, as we do now, In our previous publication^,^^' we accepted these relations. the problem of discriminating between a and w (cf. eq 42). In this paper, we have shown that the first three relations It follows immediately that P(ro)/P(Ro)= Pl(ro)/Pl(Ro), given above must now be abandoned. Elsewhere: we have which corresponds to relation ii in eq A14; a straightforshown that the Lorentz model of random flights leads to ward calculation, where we use the relation a = 2w/(l + the relation u2 = 212,which implies that vu2/6 = D = u01/3. w ) in eq 42, further gives
Reactions in Mlcroemulsions. The Ion-Exchange Model Raymond A. Mackay Department of Chemistry, Drexel University, Phikdelphk, Pennsylvania 19104 (Received: April 4, 1982; In Final Form: July 14, 1982)
Reactions between interfacial substrates and ionic nucleophiles in oil-in-water microemulsions stabilized by ionic surfactant of the opposite charge have been treated by means of an ion-exchange model. This model, previously applied to similar reactions in normal micelles, considered that the concentrationsof free and bound counterion and coion (nucleophile)are related by an ion-exchange equilibrium constant KIE. When data for the reaction of a phosphate ester in a cetyltrimethylammonium bromide microemulsion are used, a value of KE of 0.1-0.2 is obtained for hydroxide and fluoride ion, comparable to the values obtained in aqueous micelles. The model is also shown to be consistent with pK data in an anionic microemulsion system.
Introduction In recent years, a pseudophase ion exchange (IE) model has been applied to reactions between substrates in micelles and aqueous ionic nuc1eophiles.l The model has a number of successes and a few partial failures.2 The binding of counterions and coions is treated from the point of view of an ion-exchange equilibrium, eq 1,where X and (1)See for example: (a) H. Chaimovich, J. B. S. Bonilha, M. J. Politi, and F. H. Quina, J.Phys. Chem., 83,1851 (1979);(b) C. A. Buton, L. S. Romsted, and C. Thamavit, J.Am. Chem. SOC.,102,3900(1980);(c) F. H.Quina, M. J. Politi, I. M. Cuccovia, E. Baumgarten, S. M. MartinsFranchetti, and H. Chaimovich, J.Phys. Chem., 84,361 (1980);(d) C. A. Bunton. L. S. Romsted. and L. SeDdveda. ibid... 84.2611 (1980). . . .. and references ‘therein. (2)(a) C. A.Bunton, L. S. Romsted, and G. Savelli, J.Am. Chem. SOC., 101,1253 (1979);(b) C. A. Bunton, J. Frankson, and L. S. Romsted, J. Phys. Chem., 84,2607 (1980). I
0022-3654/82/2086-4756$0 1.2510
Y represent the counterion and coion (e.g., nucleophile), and the subscripts b and f represent bound and free. The reaction “surface” is the region in which the bound ions reside, presumably the Stern layer. This model predicts that the rate constant in the micelle relative to that in water will depend not only upon the degree of dissociation ( a )of the micelle counterion, but also on the nature of the nucleophile. The other extreme, which may be called the effective surface potential (ESP) model, considers that the distribution of nucleophile depends only on CY and attributes any differences to the location of the reaction surface. Chemical reactions between a microdrodet bound substrate in an ionic oil in water (o/w) microemulsion and an Of the Same charge as the surfactant ionic should be amendable to a similar treatment. In this paper, 0 1982 American Chemical Society
Reactions in Microemulsions
we consider a method of extending the ion-exchange model to microemulsions.
The Journal of Physical Chemistry, Vol. 86, No. 24, 1982 4757
TABLE I : Degree of Dissociation ( a ) and Effective Surface Potential ( $ $) f o r the CTAB Microemulsion $d(F‘) iiim(OH-)
$a
Experimental Section The values of the degree of dissociation (a)were obtained from conductivity measurement^.^^^ Phase maps of the cetyltrimethylammonium bromide (CTAB)/l-butanol/hexadecane5 and polyoxyethylene(l0) oleyl ether (Brij 96)/ 1-butanol/hexadecane6 microemulsion systems have been published. The rate constants for the reaction of p-nitrophenyl diphenyl phosphate (PNDP) with hydroxide and fluoride ion in the CTAB and Brij 96 microemulsions as a function of phase volume ($) have been previously reported.’ The phase volume is the fraction of the total volume occupied by the microdroplets, and is determined here by 6 = 1 - wg, where w qand g are the weight fraction water and specific gravity of the microemulsion, respectively. Although there is some water also associated with the microdroplet, the ions are not effectively excluded from this volume, and the lower viscosity of this interfacial water need not be considered unless the reaction becomes diffusion controlled.s The pKa of l-methyl-4-(cyanoformyl)pyridiniumoximate was determined in a sodium cetyl sulfate (SCS)/lpentanol/mineral oil microemul~ion.~ Oxalate buffer in its mono- and dianion form was employed, and the unprotonated oximate determined spectrophotometricall9lO at 25 “C with a Cary 14 and a thermostated hollow metal cell holder. Results and Discussion Effective Surface Potential. A great deal of caution must be excerised when comparing a rate or equilibrium constant obtained in an o/w microemulsion with the corresponding value in water. The effective concentration of bound substrate is of course different, and there will also be a solvent effect due to the environment, as with normal micelles. Due to the larger size of the microdroplet, the location of the reaction surfaces can vary considerably. In addition, because of the high phase volumes, the aqueous nucleophile concentration will also be higher. A number of investigations employing the CTAB and Brij systems, as well as other similar microemulsions, have indicated that the intrinsic values of rate constants, pKs, and quantum yields are the same irrespective of charge type.” Therefore, if all of the substrate is solubilized in the microdroplet, the observed differences in rate constant for a reaction which is run in both an ionic (e.g, CTAB) and a comparable nonionic (e.g., Brij) microemulsionmay be ascribed to differences in local ion concentration due to the surface charge. In the case of hydroxide the actual nucleophile is butoxide, which is formed by reaction of hydroxide with 1-butanol in both Brij and CTAB microemul~ions.~ However, the equilibrium concentration of (3)R. A. Mackay in “Microemulsions”,I.D.Robb, Ed., Plenum Press, London, 1982. (4) R. A. Mackay and C. Hermansky, submitted for publication. (5) C. Hermansky and R. A. Mackay in “Solution Chemistry of Surfactants”, K. L.Mittal, Ed., Plenum Press, New York, 1979. (6) C. Hermansky and R. A. Mackay, J.Colloid Interface Sci., 73,324 (1980). (7)R. A. Mackay and C. Hermansky, J. Phys. Chem., 85,739(1981). (8) K.R. Foster, B. Epstein, P. C. Jenin, and R. A. Mackay, J. Colloid Interface Sci., 88,233 (1982). (9)R. A. Mackay, K. Letts, and C. Jones in “Micellization Solubilization and Microemulsions”,Vol. 2,K. L. Mittal, Ed., Plenum Press, New York, 1977. See also ref 3 for the phase map. (10)R. A. Mackay and E. J. Poziomek, J.Am. Chem. Soc., 94,6107 (1972). (11)R. A. Mackay, Adv. Colloid Interface Sci., 15, 131 (1981).
0.60 0.51 0.42 0.25
0.16 a
31 34 37 53
21
31 35 48 59
imb
a
29 32 36
0.10
50 5gc
0.12 0.14 0.17 0.19
B o t h t h e Brij a n d C T A B microemulsions c o n t a i n e d
90.1% emulsifier and 9.9% hexadecane initial ( w i w ) . T h e initial compositions were diluted with w a t e r to give t h e various phase volumes (@). T h e emulsifier compositions are 49.6% CTAB, 50.4% 1 - b u t a n o l ; 6 5 : 7 % Brij 9 6 , 3 4 . 3 % Average of $$values f o r OH-a n d F-,i n m V . 1-butanol. Extrapolated.
butoxide is controlled by the local hydroxide concentration, and the comparison is valid for hydroxide as well as fluoride ion. An effective surface potential ($,) may be defined from such rate constants. When the rate constants for the reaction between (completely solubilized) PNDP and hydroxide or fluoride measured as a function of 6 in both the CTAB and Brij microemulsions is used, $, is given eq 2. Here, e is the electronic charge, and the kze ~z,(CTAB)/~~,(BRIJ) = exp(e$,/kr) (2) are phase volume corrected rate constant^.^ Values of $# are given in Table I. I t may be noted that these values are the same to within f10% for both hydroxide and fluoride. This is of course in accord with the ESP model.lZ However, it must be remembered that both of these nucleophiles can have essentially the same ion-exchange equilibrium constant with respect to bromide.13 Therefore, we will proceed to develop the equations for the IE model and also apply it to the data. Ion Exchange Model. Neglecting activity coefficients, the ion-exchange constant (KIE)for eq 1 is given by 3, KIE = (xf) (Yb) / (xb) (yf) (3) where the concentrations within parentheses refer to actual concentrations in moles per liter of aqueous psuedophase, f, and moles per liter of reaction region volume, b. The stoichiometric concentrations in moles per liter of solution volume are indicated by brackets, and can be related to the actual concentrations by eq 4. Here & is the volume [XI, = (Xf)(1- 4) (44 [XI = (&)(I - 4) + (xb)$B (4b) fraction of the reaction region (e.g., Stern layer). Similar equations hold for the coion (nucleophile) Y. Using eq 4 and CY = [X]f/[X]in eq 3 and rearranging, we obtain [Yl/(Yb) = + &)/& (5) where K , = KE(l - ,)/a. It has been assumed above that the amount of bound nucleophile (Yb) is much less than the amount of bound counterion This will be the case if KE > [Y]. For the systems examined here, [XI 0.3 M and [Y] 0.01 M. Now, the overall second-order rate constant k2 = k,/[Y], where kl is the observed pseudo-first-order rate constant. Then the actual s u r f a c e rate constant kzs = k,/(Yb). Also, since the thickness of the surface reaction region (s) is much less
-
(&)a
-
(12)The ESP model is defined here as a limiting case in which the reaction rate is controlled by the nucleophile concentration at the surface (Gouy-Chapman),which is determined by the surface charge. Such a model has also been advanced as a possible explanation of the apparent failure of the psuedophase model in a reaction counterion micelle; C. A. Bunton, J. Frankson, and L. S. Romsted, J.Phys. Chem., 84,2607(1980). (13)J. X.Khym, “Analytical Ion-Exchange Procedures in Chemistry and Biology”, Prentice-Hall, Englewood Cliffs, NJ, 1974.
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The Journal of Physical Chemistry, Voi. 86, No. 24, 1982
Mackay
This may be compared with values of KIE for exchange between hydroxide and bromide counterion in CTAB micelles of O.08la and 0.05.1d Here k, C 1 (but not
