Thermodynamics of mixed micellization. Pseudo-phase separation models

The authors present a general model of micellization of binary nonionic and binary ionic surfactant mixtures in dilute solution. For the latter they use the parameter ..beta.. to describe the fraction of counterions bound to the micelle. For the former, ..beta.. = 0. The degree of nonideality of mixing in the micelles is described by a dimensionless excess free energy function w(x) is identical to gEPSILON/(RTx(1 - x)), where x is the mole fraction of component 1 in the mixed micelles. For the strictly regular solution model, w(x) = w/sub 0/, we calculate cmc(s); monomer, micelle, and counterion inventories; micelle compositions; and second cmc and micellar pseudo-phase diagrams when demixing occurs. The condition for ''azeotrope'' micellization, in which the micelle composition matches the overall monomer composition, is exclamationw/sub 0/exclamation greater than or equal to (1 + ..beta..) in (c/sub 2//c/sub 1/), where c/sub 1/ and c/sub 2/ are the pure surfactant cmc's. The condition for micelle demixing is w/sub 0/ greater than or equal to 2. In comparing their model with experimental results, the authors observe that if w/sub 0/ is estimated from measured mixed cmc's it is extremely sensitive to small errors in c and to uncertainties in ..beta... Hence comparison with a wider body of data is needed for precisely determining the nonideality of mixing in the mixed micelles.