Predicting the Critical Micelle Concentration in a pH-Mediated Ternary-Surfactant Mixture Using the Regular Solution Approximation

Abstract

Theregular solution approximation was used to model the critical micelle concentration (CMC) of a mixed-surfactant system containing dimethylhexadecyl betaine (cetyl betaine) and dimethyltetradecylamine oxide (myristylamine oxide) in the pH range of 4–6. With a pKa of 4.95, myristylamine oxide exists in both the protonated and unprotonated forms while cetyl betaine with a pKa of 1.83 does not have a significant fraction of protonated form under the experimental conditions. Therefore, the result is a ternary-surfactant system with the relative amounts of the amine oxide forms dictated by the pH. Individual- and binary-surfactant CMC values were determined by Wilhemy plate method and the regular solution approximation used to determine the binary β values. When these β values are used, the micellar mole fractions and the component micellar activities were obtained and a priori CMC predictions were made. Predictions agreed well with experimental CMC measurements conducted at various mole fractions of the three components. The regular solution approximation provided accurate results. While data collection is initially time consuming, multiple-surfactant CMC values can be readily predicted once the binary β values have been determined.