Micellisation constant

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

The alternative approach is to treat micellisation as a simple phase separation of surfactant in an associated form, with the unassociated surfactant concentration remaining practically constant above the... 

Since the equilibrium constant, 07C, in equation (4.23) and the standard free energy change, AG°, for the micellisation of 1 mole of surfactant are related by... 

We have already seen in Chapter 9 that the aggregation of particles can be discussed in terms of a sequence of addition reactions, shown in equation (9.7). Exactly the same arguments can he applied to the case of micellisation, but we have to discuss the problem in a little more detail since, unlike floes, micelles do not grow to a macroscopic size. In particular we have to take account of the fact that the successive equilibrium constants K(i, i + 1) [equation (9.8) depend on i. 

The theoretical line in Figure 3.70 reflects the variations in the ionic product of R and R in the solution, it says however nothing about any surface interactions of R R with either Na R or R Br , because inorgcinic ion adsorption is negligible at the chosen low total concentration. At higher total concentrations, the increase in [Pg.267]

Let us suppose that K i and ni are constant. Then, using the material balance condition (5.19) and the degree of micellisation in the form ai = n CM/Cioti we obtain [12]... 

It was already mentioned above that the condition of monodispersity of micelles means that only one kind of aggregates with a fixed aggregation number nj is formed. From the point of view of chemical kinetics the reaction (5.39) is a reaction of ni order. Because typical micelles consist of some tens or hundreds molecules the probability of this elementary step is zero. Therefore, Eq. (5.39) presents only the final result of nj-l stepwise reactions of first order. The corresponding equilibrium constant is then a product of n -l constants for each step of the micellisation process. In our simplest case we can consider that all these constants are the same and we get [ 12]... 

Primarily, this approach was based on the formal analogy between a first order phase transition and the micellisation. When a new phase of a pure substance is formed the chemical potential of this substance and its concentration in the initial phase do not change with the total content of this substance in the system. A similar situation is observed above the CMC, where the adsorption and the surface tension become approximately constant. In reality variations of these properties are relatively small to be observed by conventional experimental methods. The application of the Gibbs adsorption equation shows that the constancy of the surfactant activity above the CMC follows from the constancy of the surfactant adsorption T2 [13]... 

Beyond the CMC the addition of surfactant leads mainly to the increase of the number of micelles and the total monomer concentration is practically constant. Furthermore, the first forming micelles will have a composition close to the optimum value yA because the free energy of micellisation has a minimum at this composition. As it follows from Eq. (5.110) the mole fraction of these micelles x i at yA is finite and becomes small only when xi expfgm/kuT). Further approximation of the CMC at this concentration and application of Eq. (5.124) for the optimum composition yA allows us to get finally the relation for the CMC of the mixture as... 

Eq. (5.223) coincides with the monomer diffusion equation proposed by Evans et al. [149] if the rate constant Rb in [149] is replaced by c°[rc ,(c + a c, )]. However, the obtained result is not restricted to the interpretation of the coefficients only, which have been used before. Eq. (5.224) does not coincide with the corresponding diffusion equation in [149] even if we replace Rb by this expression. Unlike the equations derived in the preceding works, the system (5.223) and (5.224) takes into account the polydispersity of micelles and the two-step nature of the micellisation. Actually, the release or incorporation of monomers in the second step of disintegration or formation of micelles is determined not only by their transition from the micellar to the premicellar region and their subsequent disintegration (as characterised by the parameter J) but also by the alteration of the size distribution of micelles. The latter change... 

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