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.

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

“…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].…”

“…As demonstrated in our previous work [18,19], this approach even outperforms the present state-of-the-art method for predicting activity coefficients, namely the modified UNIFAC (Dortmund) model [10,11], if γ ∞ ij at 298 K are considered. 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]. In the present work, we further expand the MCM approach by combining it with the physical modeling of thermodynamic properties of mixtures.…”

Prediction of Henry's law constants by matrix completion

“…However, these methods can be extended to include the temperature dependence of properties once they are established for the isothermal case. We have shown a possible approach to implement such an extension in a recent work 11 for the prediction of activity coefficients at infinite dilution , where we have modeled the dependence of on the temperature T by exploiting the fact that it can be well described by with system‐specific, but temperature‐independent, parameters A ij and B ij in many cases.…”

“…We have shown a possible approach to implement such an extension in a recent work 11 for the prediction of activity coefficients at infinite dilution γ ∞ ij , where we have modeled the dependence of γ ∞ ij on the temperature T by exploiting the fact that it can be well described by…”

Capturing Molecular Interactions in Graph Neural Networks: A Case Study in Multi-Component Phase Equilibrium

“…Activity coefficients are one of the fundamental properties of a mixture and therefore can lead to the derivation of equilibrium conditions (e.g., phase diagrams), which are important in physical chemistry and engineering for understanding and optimizing chemical separations. 38 Previous studies have developed ML-based methods to predict infinite-dilution activity coefficients for binary mixtures, including matrix completion on the activity coefficient matrix 28,39 and multilayer perceptrons on the system descriptors. 40 However, these methods did not account for molecular structural information directly, and the latter is limited to systems of water in ionic liquids.…”