Predicting the Temperature-Dependent CMC of Surfactant Mixtures with Graph Neural Networks

Surfactants are key ingredients in foaming and cleansing products across various industries such as personal and home care, industrial cleaning, and more, with the critical micelle concentration (CMC) being of major interest. Predictive models for CMC of pure surfactants have been developed based on recent ML methods, however, in practice surfactant mixtures are typically used due to to performance, environmental, and cost reasons. This requires accounting for synergistic/antagonistic interactions between surfactants; however, predictive ML models for a wide spectrum of mixtures are missing so far. Herein, we develop a graph neural network (GNN) framework for surfactant mixtures to predict the temperature-dependent CMC. We collect data for 108 surfactant binary mixtures, to which we add data for pure species from our previous work [Brozos et al. (2024), J. Chem. Theory Comput.]. We then develop and train GNNs and evaluate their accuracy across different prediction test scenarios for binary mixtures relevant to practical applications. The final GNN models demonstrate very high predictive performance when interpolating between different mixture compositions and for new binary mixtures with known species. Extrapolation to binary surfactant mixtures where either one or both surfactant species are not seen before, yields accurate results for the majority of surfactant systems. We further find superior accuracy of the GNN over a semi-empirical model based on activity coefficients, which has been widely used to date. We then explore if GNN models trained solely on binary mixture and pure species data can also accurately predict the CMCs of ternary mixtures. Finally, we experimentally measure the CMC of 4 commercial surfactants that contain up to four species and industrial relevant mixtures and find a very good agreement between measured and predicted CMC values.