A new approach to micellization parameters using iterative mathematical method

This paper announces the use of an iterative mathematical method for determining the three micellization parameters for ionic surfactants, the micellization constants Kn, the micelle aggregation number n, and the number of counterions per micelle m, according to mass action model of micelle formation. The new approach required only the concentrations of both surfactants ion and counterion over cmc as an input data. The new method has been based upon that hypothetical values of n and m could estimate Kn using the derived equation at various concentrations of surfactant over cmc. The correct values of n and m must give constant values of Kn at these concentrations. Application of the method to the micellization of sodium dodecyl sulfate has been found to be quite successful for obtaining the three parameters with excellent agreement between the calculated and the reported values of surfactant concentrations up to 10 times of cmc. The results indicate that the presented method could confidently determine the degree of counterion binding to micelle (m/n). The validity of the new approach has been confirmed through the application to micellization of lithium 1-perfluoroundecanoate at different temperatures. It has been concluded that presented method is simple, reliable, accurate, relatively less time consuming and required less experimental data with no graphical treatments.