Surfactant Mixtures with a Net Interaction

The superscript m indicates that the values are inside the micelle. If Xi and X2 are the solution composition, then. 

This illustrates the role of contaminants in surface activity, e.g. dodecyl alcohol in sodium dodecyl sulphate (SDS). 

With many industrial formulations, surfactants of different kinds are mixed together, for example anionics and nonionics. Nonionic surfactant molecules shield the repulsion between the negative head groups in the micelle and hence there will be a net interaction between the two types of molecules. Another example is the case when anionic and cationic surfactants are mixed, whereby very strong interaction occurs between the oppositely charged surfactant molecules. To account for this interaction, Eq. (2.31) has to be modified by introducing activity coefficients of the surfactants, ff and in the micelle (Eq. 2.34). 

An expression for the activity coefficients can be obtained using the regular solutions theory, 

Both the predicted c.m.c. and micellar composition depend on the ratio of the c.m.c.s as well as on fi. When the c.m.c.s of the single surfactants are similar, the predicted c.m.c. is very sensitive to small variations in fi. Conversely, when the ratio of the c.m.c.s is large, the predicted value of the mixed c.m.c. and the micellar composition are insensitive to variations of p. For mixtures of nonionic and ionic surfactants, p decreases with increasing electrolyte concentration. This is due to the screening of the electrostatic repulsion on the addition of electrolyte. With 

---