1844
The Journal of Physical Chemistry, Vol. 83, No. 14, 1979
F. H. Quina
and H. Chaimovich
Ion Exchange in Micellar Solutions. 1. Conceptual Framework for Ion Exchange in Micellar Solutions Frank H. Quina” and Hernan Chaimovich Group for Interfacial Studies (GIST), Instituto de Quimica, Universidade de SSio Paulo, Caixa Postal 20.780, SEio Paulo, S.P., Brasil (Received August 2, 1978: Revised Manuscript Received February 2, 1979)
The explicit consideration of ion exchange leads to a framework for the quantitative dissection and analysis of the influence of charged micelles on reactions which involve exchangeable ionic species. These include the following: (1) the binding of a reactive ion to the micelle in the presence or absence of salt and presence or absence of buffer; (2) the first-order reaction of an ionic substrate in the micelle; (3) the second-order reaction of an ionic nucleophile with a neutral substrate solubilized in the micellar phase; (4)the effect of micelles on the dissociation of weak acids; ( 5 ) the second-order reaction of the corresponding conjugate base. Model calculations based on the resulting mathematical expressions, which contain only experimentally accessible terms, are presented to exemplify the behavior patterns predicted by the model for each of these cases. These calculations illustrate the role that a given set of experimental conditions (unbuffered, buffered, added salt present, detergent concentration, etc.) plays in determining the concentration and kinetic behavior of exchangeable ionic reactants in the micellar pseudophase.
Introduction The effects of added salts on micelle-modified reactions can be quite varied, ranging from inhibition, the most commonly observed phenomenon,l to activation, observed in certain casesa2 Such effects have been shown to be strongly dependent on the nature of the detergent head group, the initial counterion present, and the total ionic content of the system.’ There is general agreement that these effects reflect the “local concentration” of reactive ions in the micellar p~eudophase.~ Various models which describe this problem , ~ - ~been proposed. in terms of ion binding to m i ~ e l l e s l ~have The relative success of some treatments has prompted many workers to attempt to generalize these approaches in order to arrive a t a fuller understanding of this phenomenon. Such an understanding has profound implications not only in micellar chemistry but also in the general sense of ion binding a t charged interfaces. To date, the two approaches most commonly employed to analyze ion binding to micelles treat the system either as a partition function of the type PI = PI, exp[-(+e/kT)I
+
where is the surface potential of the micelle and PI, accounts for the nonelectrostatic (hydrophobic ?) part of the interactiona4s6Recently, a semiempirical approach, based on a combination of phase ~ e p a r a t i o n land ~ , ~the (apparently valid) assumption that the degree of dissociation of the ionic micelle can be considered constant, has been put forward by Romstedlbv7and modified by Berezin5 As a part of our general effort directed toward the dissection and analysis of interfacial effects on reactions, we present here an approach to the treatment of ion exchange in micellar solutions that explicitly considers the consequences of ion-ion exchange. This approach permits the treatment of both buffered and unbuffered micellar systems within a single framework. Moreover, it permits one to analyze the effect that a given set of experimental conditions (unbuffered, buffered, added salt present, detergent concentration, etc.) will have on the concentration and kinetic behavior of exchangeable ionic reactants in the micellar pseudophase. +Contribution No. 2.
Ion Exchange in Micellar Systems If the charged micellar pseudophase were in reality a distinct bulk phase, it would be possible to describe ion exchange between the aqueous and micellar phases by an equilibrium of the type Kxiu xf + Yb e Xb + Yf
(1)
The corresponding selectivity coefficient would then be given by Kxly =
x by f
xf yb
where b and f refer, respectively, to bound and free exchangeable ions X and Y. Equation 2 has been utilized as a semiempirical expression by Romsted,lb as the selectivity ratio (f value) by Larsen and Magids and, indirectly, by Bunton in treating competitive inhibitiong by added salts and the binding of H+ to micellar sodium dodecyl ~ u l f a t e . ~ The fact that micelles are not a continuous macroscopic phase might lead one to question the applicability of eq 1to micellar solutions. That the ion-exchange process in such solutions can indeed be treated as if it were occurring between aqueous and micellar pseudophases is readily verifiable on the basis of either a mass-action or a statistical model. Either of these models becomes mathematically tractable for any given set of conditions, i.e., a t constant T and P for any fixed concentrations of total detergent (C,) or added ions, if one makes use of a limited set of approximations regarding the micellar species: (1)The distribution of aggregate sizes can be represented in terms of the most probable aggregation number N.’O (2) Ion-ion and ion-head group interactions are noncooperative. This allows the formulation of the system in the form of ion-exchange rates that will depend only on the number of ions in a given aggregate and the concentrations of free ions in the external solution. Thus, we may write n = 1, 2, ..., m where Xf and Yf are the concentrations of free X- and Y-
0022-3654/79/2083-1844$01.00/0O 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 14, 1979
Ion Exchange in Micellar Solutions
ion and MY,Xj represents a micelle with i bound Y- and j bound X- ions. (3) The degrees of ionization a of the individual micellar species MYiXj_arethe same and related to m by the expression m = N(l - a ) . Thus, m is the average number of ions associated with any micelle present in the system. (4) Ion-ion exchange rates are rapid relative to the lifetime of the micelle.11J2 (5) The activities of the various micellar and free ionic species present are treatable in terms of their analytical concentrations. With these assumptions both the mass action and the statistical models lead to a binomial di~tributionl~ of micellar species MYiX, and to eq 2 for the selectivity coefficient in the micellar solution. The considerations outlined above refer to any one given set of conditions and do not necessarily mean that KXIyas defined by eq 2 will always remain constant as the conditions are varied. Indeed, K,jy may prove to be dependent on the relative concentrations of exchangeable ions, the total concentrations of these ions, the nature of the ions, and the total detergent ~0ncentration.l~
Applications of the Concept of Ion Exchange in Micellar Solutions In this section, we shall develop a series of general expressions, based on the concept of ion exchange. These expressions, which contain only parameters that are potentially subjectable to independent experimental verification, encompass the most commonly encountered reactivity types in micellar solutions, thus, in order of increasing complexity, we treat (I) the binding of a reactive ion to the micelle in the absence and presence of added salt and presence and absence of buffer; (11)the observed rate constant for a first-order reaction of an ionic substrate; (111) the observed rate constant for a second-order reaction under pseudo-first-order conditions; (IV) apparent pK change of a weakly acidic species; (V) the observed rate constant for a second-order reaction involving the conjugate base of a weakly acidic species. In the model calculations presented with each of these applications, we have assumed that K, , a, and cmc are unaffected by variations in the total detergent concentration (CT). The constancy of K.1, has been referred to above. The free detergent monomer concentration should be relatively constant in the presence of buffer or other added electrolyte, including the salt of a reactive ion, and roughly equal to the critical micelle concentration (cmc).16 Although the relative constancy of a, the degree of ionization of the micelle, is not a recent concept,18it has gained wide,lbvcthough perhaps not universal, acceptance since the cogent analysis by Romsted of the literature data up to 1975.19 Before proceeding further, we should point out that the effective intermicellar concentration X i of a free ion differs from its analytical concentration Xf according to xf‘= xf/(l- CDVex) Nevertheless, as others have noted,lbr6the fraction of the total solution volume excluded by the micellar phase ( C D ~ ~should ,) be relatively small (CDV,,
