Micelles nonideality

Of the possible types of measurements, heats of micellar mixing obtained from the mixing of pure surfactant solutions are perhaps of the greatest interest. Also of interest is the titration (dilution) of mixed micellar solutions to obtain mixed erne s. While calorimetric measurements have been applied in studies of pure surfactants (6,7) and their interaction with polymers ( ), to our knowledge, applications of calorimetry to problems of nonideal mixed micellization have not been previously reported in the literature. 

Among the purposes of this paper is to report the results of calorimetric measurements of the heats of micellar mixing in some nonideal surfactant systems. Here, attention is focused on interactions of alkyl ethoxylate nonionics with alkyl sulfate and alkyl ethoxylate sulfate surfactants. The use of calorimetry as an alternative technique for the determination of the cmc s of mixed surfactant systems is also demonstrated. Besides providing a direct measurement of the effect of the surfactant structure on the heats of micellar mixing, calorimetric results can also be compared with nonideal mixing theory. This allows the appropriateness of the regular solution approximation used in models of mixed micellization to be assessed. 

The derivation of a pseudo-phase separation model for treating nonideal mixed micellization is given in detail in reference 3. This leads to the generalized result... 

Titration results for the mixed erne s of the SDS/CgE4 and C12E2S/C8E4 systems as a function of their relative mole fraction in solution are shown in Figures 2 and 3, respectively. Here, the experimentally determined points are compared with calculated results from the nonideal mixed micelle model (solid line) and the ideal mixed micelle model (dashed line). Good agreement with the nonideal model is seen in each case. 

Figure 2. Cmc s of mixtures of SDS and CgE4 in distilled water (at 25°C). The plotted points are experimental data, the solid line is the result for the nonideal mixed micelle model with B = -3.3, and the dashed line is the result for ideal mixing.

The finding that the assumptions of the regular solution approximation do not hold for the mixed micellar systems investigated here suggests a re-examination of how the thermodynamics of mixing enter the nonideal mixed micelle model. 

Calorimetric measurements can be used to obtain heats of mixing between different surfactant components in nonideal mixed micelles and assess the effects of surfactant structure on the thermodynamics of mixed micellization. Calorimetry can also be successfully applied in measuring the erne s of nonideal mixed surfactant systems. The results of such measurements show that alkyl ethoxylate sulfate surfactants exhibit smaller deviations from ideality and interact significantly less strongly with alkyl ethoxylate nonionics than alkyl sulfates. 

The mixed cmc behavior of these (and many other) mixed surfactant systems can be adequately described by a nonideal mixed micelle model based on the psuedo-phase separation approach and a regular solution approximation with a single net interaction parameter B. However, the heats of micellar mixing measured by calorimetry show that the assumptions of the regular solution approximation do not hold for the systems investigated in this paper. This suggests that in these cases the net interaction parameter in the nonideal mixed micelle model should be interpreted as an excess free energy parameter. 

In order to illustrate the eFFect oF micellar nonidealities oF mixing on total surFactant monomer concentrations and micelle compositions in a system at the CHC, consider a hypothetical binary surFactant pair, A and B. Assume CMCa = 1 mli and CMCb = 2 mil. For a equimolar mixture oF A and B as monomer, the values oF Cn and micelle compositions are tabulated in Table I at various values oF W/RT. 

As also seen in Table I, the micellar composition can be a-f-fected substantially by nonideality. In -fact, azeotropic behavior in the monomer—micelle equilibrium is possible -for these nonideal systems i.e., as the monomer composition varies -from pure A to pure B, the micelle can vary -from Xn > y to Xn = y (azeotrope) to Xa < yA. This azeotrope -formation is illustrated -for the cationic/nonionic system in Figure 2, where an azeotrope -forms at Xa = yA = 0.3. The minimum CMC -for a mixture corresponds to the azeotropic composition i-f an azeotrope is present (32.37). For an ideal system, azeotropic behavior is not observed. 

Equations 3 and 4 are derived from Equation 5 (31) which has been Found to be invalid For the systems oF interest. However, Equations 3 and 4 have been shown to accurately describe mixture CMC values and monomer-micelle equilibrium. The resolution is that Equations 3 and 4 should be considered as valuable empirical equations to describe these nonideal systems. The Fact that they were originally derived From regular solution theory is a historical coincidence. 

Only one model to describe nonideal micelle Formation was described here. Regular solution theory in a diFFerent Form than that used here has been applied to these systems ( ). Alternative models have been proposed based on statistical mechanics (37.50). the... 

Counterion Binding. The fractional counterion binding on charged mixed micelles is of fundamental interest because it gives an indication of surface charge density which is related to the mechanism of mixing nonidealities in ionic/nonionic micelles. It is also a necessary... 

The same effect is seen when a non—aromatic cationic surfactant/nonionic surfactant system is used. Since the nonideality of mixed micelle formation in this case is due almost entirely to the electrostatic effects and not to any specific interactions between the dissimilar hydrophilic groups, the geometrical effect just discussed will cause the EO groups to be less compactly structured... 

---