Predicting Activity Coefficients at Infinite Dilution for Varying Temperatures by Matrix Completion

Abstract

Activity coefficients describe the nonideality of liquid mixtures and are essential for calculating equilibria. The activity coefficients at infinite dilution in binary mixtures are particularly important as the activity coefficients at finite concentrations can be predicted based on their knowledge not only in binary mixtures but also in multicomponent mixtures. The available experimental data on these activity coefficients at infinite dilution in binary mixtures is readily accessible in databases and can be organized in a matrix with the rows representing the solutes and the columns representing the solvents or vice versa. As experimental data is lacking for many binary mixtures, this matrix is only sparsely populated. Filling its gaps using predictive methods is essential. Recently, matrix completion methods (MCMs) have been applied successfully for this purpose. However, only isothermal data sets have been considered. In the present work, we apply an MCM to predict activity coefficients at infinite dilution at varying temperatures. Furthermore, we show how one can incorporate physical knowledge on the nature of the temperature dependency of the activity coefficients at infinite dilution. The predictions obtained with this new approach outperform those obtained with the best currently available physical prediction method for activity coefficients at infinite dilution, the modified UNIFAC (Dortmund) method.

Graph neural networks for the prediction of infinite dilution activity coefficients

“…A notable exception to this was the application of the matrix completion methodology (MCM) that allows for the predictions to be based only on an incomplete matrix of solvent-solute activity coefficients. 21,40,41 This eliminates the necessity of computing many expensive descriptors. However, the application domain of the MCM method is limited to the systems that dene the matrix.…”

Making thermodynamic models of mixtures predictive by machine learning: matrix completion of pair interactions

“…We have also extended the approach to modeling the dependence of γ ∞ ij on the temperature T , by simply exploiting the fact that this dependence can be well described by γ ∞ ij ( T ) = A ij + B ij / T with system-specific but temperature-independent parameters A ij and B ij in many cases. 20 …”

“…17 We have recently introduced a completely new approach for predicting thermodynamic properties of unstudied binary systems. [18][19][20][21] This approach is based on employing matrix completion methods (MCMs) from machine learning (ML), where the MCMs are prominently associated with recommender systems. 22,23 E.g., for movie recommendations, these methods can implicitly learn and quantify similarities among users and similarities among movies by observing interaction patterns (ratings or clicks) between them, allowing to predict preference scores for unseen pairs of users and movies.…”

“…We have also extended the approach to modeling the dependence of g N ij on the temperature T, by simply exploiting the fact that this dependence can be well described by g N ij (T) ¼ A ij + B ij /T with system-specic but temperature-independent parameters A ij and B ij in many cases. 20 In the present work, we further expand the MCM approach by combining it with the physical modeling of thermodynamic properties of mixtures. We thereby exploit the fact that all physical models of mixtures are based on the idea of pair interactions, described by pair-interaction energies as critical parameters.…”

“…We have recently introduced a completely new approach for predicting thermodynamic properties of unstudied binary systems. 18–21 This approach is based on employing matrix completion methods (MCMs) from machine learning (ML), where the MCMs are prominently associated with recommender systems. 22,23 E.g.…”