Machine learning prediction on the fractional free volume of polymer membranes

Fractional free volume (FFV) characterizes the microstructural level features of polymers and affects their properties including thermal, mechanical, and separation performance. Experimental measurements and theoretical analyses have been used to quantify the FFV of polymers, but challenges remain because of their limitations. Experimental measurements are laborious and based on semi-empirical equations, while Bondi's group contribution theory involves ambiguities like the determination of van der Waals volume and the choice of factor values in the theoretical equation. To efficiently evaluate the FFV of polymers, this study utilizes high-throughput molecular dynamics (MD) simulations to build a large dataset regarding polymer's FFV. Based on this large dataset, we further build machine learning (ML) models to establish the composition-structure relation. Inspired by group contribution theory which correlates polymer's functional groups to FFV, our ML models correlate polymer's sub-structures or physico-chemical indexes to FFV. Our study first benchmarks the MD simulation protocol to obtain reliable FFV of polymers and then carries out high-throughput MD simulations for more than 6500 homopolymers and 1400 polyamides. Such a large and diverse dataset makes the well-trained ML models more generalizable, compared with the group contribution theory. The efficiency of a feed-forward neural network model is further demonstrated by applying it to a hypothetical polyimide dataset of more than 8 million chemical structures. The predicted FFVs of hypothetical polyimides are further validated by MD simulations. The obtained FFVs of the 8 million polymers, plus their previously reported gas separation performances, demonstrate the promising capability of ML virtual screening for the discovery of polymer membranes with exceptional permeability/selectivity.