Extension to Mixed Micelles

Aniansson showed that mixed micellar solutions of binary svuTactant mixtures are characterized by three relaxation processes two fast processes associated with the exchange of the two surfactants between mixed micelles and bvdk phase (Xn and X12) and a slow process associated with the forma-tion/breakdown of the mixed micelles (X2). The basic assumptions and the methods used to derive the expressions of the 

The theoretical aspects of the kinetics of two-component micelles based on the stepwise association model were later extended to high surfactant concentrations. - This model applies to binary mixtures of nonionic surfactants as well as to one ionic surfactant, the surfactant ion and its counterion then being the two components of the system. 

The thermodynamics of irreversible processes was also used to derive very general expressions of the relaxation times for mixed micellar solutions (two surfactants). - Unfortunately, these expressions are not easy to handle. 

The first theoretical treatment of the exchange process was of phenomenological character and assmned a simrdtaneous exchange of several surfactants between micelles and bulk phase. 1 The reported expression of bears much resemblance to Equation 3.9. Sams et al. derived an expression of on the assumption that the rate constants for the associa-tion/dissociation of one surfactant to/from an aggregate Aj are proportional to i. This assumption was later shown to be not valid. Inoue et al. have tried to incorporate the features of Aniansson and Wall treatment and those of Sams et al. in a unified theory of the fast exchange. This treatment suffers from the same shortcomings as that of Sams et al. and 5nelds unrealistic values of the rate constants k+ and k.  

Inoue et al. also derived an expression of %2 by using the stepwise association/dissociation reactions (4), including the counterions and assuming all reaction steps to be fast except an intermediate step that is slow and rate-limiting. 

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We now turn to the kinetic results. Aniansson (29) has recently reported an extension to mixed micelles, made out of two detergents, of his theoretical treatment of the kinetics of simple micellar systems (8,25). The expressions given for and T2 can be used to qualitatively assess the effect of alcohol on these relaxation times, since the alcohol molecules can be considered to form mixed micelles with the detergent. The ratio C /cmc, where is the micelle concentration, appears in the predominant term in Aniansson s equation for 1/Tj. At constant detergent concentration, close to the cmc, an addition of alcohol brings about an increase of C and a decrease of cmc. The ratio C /cmc, and thus l/Tj should increase with the alcohol concentration, as is indeed observed. 

A theory for the stepwise association and dissociation of surfactant micelles was developed a few years ago. Its application to a large quantity of experimental data has provided a consistent interpretation of these data and enabled the extraction of basic kinetic and equilibrium parameters for these systems In the following extension to mixed micelles the concepts and assumptions used are closely analogous to those of the previous treatment to which the reader is referred for more details. For simplicity the treatment is limited to two-component micelles but the extension to larger number of components is quite straightforward. 

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