The Shape of Data in Chemistry – Insights Gleaned from Complex Solutions and Their Interfaces*

Highly non-ideal solutions are ever-present within chemistry, physics, and materials science – and are characterized by many-body effects across length and timescale. Understanding, and predicting, many-body correlations in the condensed phase is a grand challenge for the modeling and simulation community. Yet within the data science community, a large suite of tools exist for elucidating complex, correlating, relationships amongst variables. Molecular modeling and simulation data is in fact well-suited for study by methods that include the topology of graphs, point cloud data, and recent advances in applied mathematics methods that investigate surfaces like sublevel set persistent homology and geometric measure theory. We adapt, develop, and apply these tools to study highly non-ideal solutions and their interfaces, with examples drawn from separations science. The new physical insight derived from these methods is paving the way for bespoke liquid/liquid interfaces that optimize transport characteristics for purification and synthesis.