CMC for Pure Surfactants and Surfactant Mixtures

As the preceding example indicates, micelle formation can be promoted by increasing the length of the surfactant s (straight) hydrocarbon chain or by reducing the repulsion between the head groups. As an illustration of the chain length effect, the measured CMC of sodium alkyl sulfates at 40°C decreases from 140 mM for the Cg compound to 8.6 mM for the C,2 compound to 0.58 mM for the 

For binary surfactant mixtures, one might expect that micelles formed at the CMC of the mixture would be enriched in the less hydrophilic surfactant (i.e., the one with the lower CMC). Analysis based on the phase separation model confirms this expectation. The simplest approach is to assume an ideal mixture in the micellar phase (i.e., activity of each species equal to its mole fraction). With this assumption one obtains the following expression for the ratio x Jx2 of the two surfactants in the micellar phase at the CMC (see Problem 4.3)  

For many binary surfactant mixtures, the ideal solution model discussed above and in Problem 4.3 is inadequate. The most common way of handling these deviations is to apply the regular solution model givrai by Equation 1.80 to the micellar phase  

In contrast, mixtures of hydrocarbon and fluorocarbon surfactants have positive values of p and the CMC-composition curve is above that of an ideal solution. That is, it is energetically unfavorable to mix hydrocarbon and fluorocarbon chains. In some cases, two different types of micelles coexist, one type containing predominantly the hydrocarbon surfactant, the other mainly the fluorocarbon surfactant. Further discussion of surfactant mixtures can be found in the books edited by Holland and Rubingh (1992) and Scamehom (1986), in particular in the chapter by Holland in the former reference. 

---