Understanding molecular adsorption through the lens of persistent homology

Topological descriptors associated with amphiphile adsorption at liquid/liquid interfaces have been developed. These are based upon sublevel set persistent homology analysis of images of the adsorbate density projected onto a plane. For example, tributyl phosphate (TBP) is considered adsorbed to the electrolyte/hexane interface as a function of the ionic strength of the aqueous phase, which tunes the adsorbate interfacial concentration. TBP is known to form organized dimeric assemblies, and the topology is compared to analogous adsorption surfaces representing stochastic distribution. We demonstrate that persistent homology descriptors like Persistent entropy (PE), Persistent Lifetime, Non-ideality index, Betti curves, etc., are good descriptors for characterizing topological heterogeneity within the adsorption surfaces. This work lays the foundation for further quantification of the PH-based descriptors to understand the fundamental chemistry at chemical and biological interfaces.