Micellar activity coefficients

In the second group the variation of the CMC of the pure ionic surfactant with the micellar composition was taken into account. However, other effects, such as changes in the micellar electrical potential, are included in the micellar activity coefficients in a manner similar to the first group of theories [45, 46]. 

On the other hand, micelle formation has sometimes been considered to be a phase separation of the surfactant-rich phase from the dilute aqueous solution of surfactant. The micellar phase and the monomer in solution are regarded to be in phase equilibrium and cmc can be considered to be the solubility of the surfactant. When the activity coefficient of the monomer is assumed to be unity, the free energy of micelle formation, Ag, is calculated by an equation... 

One interesting feature of the functional form derived here is the direct relationship of the activity coefficients and composition between the micellar and surface psuedo-phases. This allows a comparison of nonideal interactions in the micelle and monolayer as modeled by their respective net interaction parameters. In principle, this form may also allow extension to more complicated situations such as the treatment of contact angles in nonideal mixed surfactant systems. Here, the functional form derived above depends on differences in surface pressures and these may be directly obtained from experimentally measured parameters under the proper conditions (30). 

Via use of the SED technique, it is possible to determine solute solubilization equilibrium constants (activity coefficients of micellar bound solutes) as well as the surfactant concentration on both sides of the dialysis membrane among other parameters (458-460). 

It seems likely that the cationic CPC micelles, which have a large positive charge at or near the micellar surface, interact attractively with the n-molecular orbital system of benzene, and that this interaction contributes to the fact that the solubilization constant for benzene in CPC is approximately twice as large as that in SDS micelles. A preferential interaction between cationic surfactants and aromatic solutes has been reported by several groups of investigators (25-27), and recent work in our laboratory shows that 1-hexadecyltrimethylammonium bromide micelles also solubilize benzene more effectively than do the anionic alkylsulfate surfactant micelles (28). Thus, the tendency of benzene molecules to solubilize near the surface of the cationic micelles, at low XB values, may lead to a partial saturation of surface "sites" by benzene, diminishing the ability of additional benzene molecules to bind near the surface. Such an effect could be responsible for the initial increase in activity coefficient that occurs, particularly in the CPC solutions, as Xg increases. 

Hr by 1-4 units and Hq by 0-3 unit in 0 10 M HCl (Bunton and Robinson, 1969d). The significance of these results is, of course, that indicator measurements do not allow unambiguous determinations of the proton-donating ability or acidity of micellar media since the influence of micelles on the activity coefficient ratio of the two forms of the indicator cannot be neglected. 

Knowing these mole fractions, the distribution constant K, for the partitioning of MMA between the micellar and aqueous environments can be determined from the ratio of X to X, assuming that all activity coefficients are unity. Then,mthe standard free energy of transfer of MMA from the aqueous to micellar phase can be calculated from... 

The activity coefficient is defined as the relative volatility of the solute in the micelle, compared to the volatility of the solute in an ideal solution at the same mole fraction, i.e., pjp% where p, is the partial pressnre above the micellar solntion and p° the partial pressure above the pure solute. 

Much less is known about micellar charge and counterion binding in the case of bile salts. Based on the result of ionic self-diffusion measurements [20,163,173], conductance studies [17,18,187], Na, and Ca activity coefficients [16,19,144,188,189] and NMR studies with Na, Rb and Cs [190], a number of generalities can be made. Below the operational CMC, all bile salts behave as fully dissociated 1 1 electrolytes, yet interionic effects between cations and bile salt anions decrease the equivalent conductance of very dilute solutions [17,18,187]. With the onset of micelle formation, counterions become bound to a small degree values at this concentration are about < 0.07-0.13 and are not greatly influenced by the species of monovalent alkali cations [163,190]. At concentrations above the CMC, values remain relatively constant to 100 mM in the case of C and this... 

The third important property of ionic micellar solutions is the activity coefficient, which is closely related to the ionic strength. The mean activity coefficient of a non-micellar solution is usually defined as... 

It is noteworthy that the fn in Eq. (5.36) correspond to the real concentrations of ions CtotiVi(l-ai), whereas the experimental values are referred usually to the stoichiometric concentrations CtotiVi. This results in an increase of each activity coefficient by a factor of 1- aj. Then, neglecting the contribution of micelles in Eq. (5,36), the experimental mean activity coefficient of the surfactant ions in micellar solution can be written as... 

Table 2. Micellar composition (x ), interaction parameter (P ), and activity coefficients ( //", ) of binary mixtures of drug IMP and TX-00 at different mole fractions of IMP (fli).

Here and (pi are the activity coefficients for the quencher ion in the aqueous phase and the micellar potential at any given ionic strength The value of the ionic strength can... 

By using vapour pressure measurements (14), the activity of the solute, a = yXmiceiie can be determined as the ratio between the partial pressure above the micellar solution and the partial pressure above the pure solute. In this case, the standard state refers to the pure liquid solute or to solute in a supercooled liquid state. The activity coefficient which gives the deviations from ideality is a way of measuring the interaction between solute and surfactant in the aggregates. Once the activity is determined, the standard Gibb s energy of solubilization could be obtained, as follows ... 

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