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

arXiv: https://arxiv.org/abs/2411.02224 · HTML: https://mlsanity.com/paper/2411.02224/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 87 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 18 of 18)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction](https://mlsanity.com/paper/2306.07937/) (2023)
- [Graph Neural Networks for Temperature-Dependent Activity Coefficient Prediction of Solutes in Ionic Liquids](https://mlsanity.com/paper/2206.11776/) (2022)
- [Graph neural networks for the prediction of molecular structure-property relationships](https://mlsanity.com/paper/2208.04852/) (2022)
- [Gibbs-Helmholtz Graph Neural Network: capturing the temperature dependency of activity coefficients at infinite dilution](https://mlsanity.com/paper/2212.01199/) (2022)
- [Thermodynamics-Consistent Graph Neural Networks](https://mlsanity.com/paper/2407.18372/) (2024)
- [Graph Neural Networks for Surfactant Multi-Property Prediction](https://mlsanity.com/paper/2401.01874/) (2024)
- [MolSets: Molecular Graph Deep Sets Learning for Mixture Property Modeling](https://mlsanity.com/paper/2312.16473/) (2023)
- [Predicting the Temperature Dependence of Surfactant CMCs Using Graph Neural Networks](https://mlsanity.com/paper/2403.03767/) (2024)

## Built on by (most cited first, 3 of 3)

- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [DeepEOSNet: Capturing the dependency on thermodynamic state in property prediction tasks](https://mlsanity.com/paper/2509.17018/) (2025)
- [A Systematic Evaluation of Molecular Mixture Behavior Prediction](https://mlsanity.com/paper/2605.29698/) (2026)

## Abstract (arXiv)

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.