Determining Ion Activity Coefficients in Ion-Exchange Membranes with Machine Learning and Molecular Dynamics Simulations

The activity coefficients of ions in polymeric ion-exchange membranes (IEMs) dictate the equilibrium partitioning coefficient of the ions between the membrane and the liquid. It also affects ion transport processes, such as conductivity, in ion-exchange membranes. Accurately predicting the ion activity coefficient without experimental data has been elusive as most models are empirical or semi-empirical. This work employs an embedding process that maps microscopic and macroscopic properties for modeling of ion activity coefficients in IEMs with molecular dynamics (MD) and machine learning (ML). This strategy is effective for accurately predicting activity coefficients in various IEM materials, including random copolymer and block copolymer systems. ML algorithms are increasingly being used for the analysis of complex systems when limited knowledge is available. The framework uses small experimental activity coefficient datasets in conjunction with polymer structure information and molecular attributes describing the solvation of ions and polymers to predict the ion activity coefficient in IEMs. Two different ML models were developed to estimate the molecular attributes and the ion activity coefficient. The best ML model accurately predicts the solvation descriptors and ion activity coefficient with an average mean absolute error of <7 and 10%, respectively. Adopting the said approach allows for the estimation of ion activity coefficients in IEMs without the need for new time-consuming MD simulation runs and experiments.