A classification-based methodology for the estimation of binary surfactant critical micelle concentrations

Abstract

The commercial formulation development for multicomponent complex fluids is time-intensive and data-intensive. There is a need for tools to expedite this process. This work develops an experimental and analytical high-throughput methodology to quantify binary surfactant mixture micellization in a 96-well plate. The novelty of this work lies in (1) employing model-driven design of experiments for efficient experimentation and (2) using physics-informed classification to quantify the mixture critical micelle concentration. This work employs a novel classification-based approach to map the binary critical micelle concentration as a function of the surfactant mixture ratio. Regular solution theory is used as the physics basis for modeling the binary interactions between surfactants (quantifying the β interaction parameter). Other, more complex surfactant interaction models exist; however, this simple model is used to demonstrate the efficacy of this methodology as a high-throughput screening tool for binary surfactant mixtures. Using regular solution theory as a guide to map the critical micelle concentration against the surfactant ratio, the SDS-C₈E₄ surfactant system was determined to have a β = −3.6 ± 0.5, a 14.9% difference from the literature reference of β = −3.1. We demonstrate the utility of the method on the SDS-C₈E₄ system in 0.5 M NaCl which was determined to have a β = −3.1 ± 0.4, which is a 17.5% difference from a similar literature system of SDS-C₁₂E₈ in 0.5 M NaCl with β = −2.6. These two systems support the efficacy and generalizability of this high-throughput methodology to any binary surfactant mixture and future work involves extending this methodology to ternary surfactant mixtures.