Unraveling the morphological complexity of two-dimensional macromolecules

2D macromolecules, such as graphene and graphene oxide, possess a rich spectrum of conformational phases. However, their morphological classification has only been discussed by visual inspection, where the physics of deformation and surface contact cannot be resolved. We employ machine learning methods to address this problem by exploring samples generated by molecular simulations. Features such as metric changes, curvature, conformational anisotropy and surface contact are extracted. Unsupervised learning classifies the morphologies into the quasi-flat, folded, crumpled phases and interphases using geometrical and topological labels or the principal features of the 2D energy map. The results are fed into subsequent supervised learning for phase characterization. The performance of data-driven models is improved notably by integrating the physics of geometrical deformation and topological contact. The classification and feature extraction characterize the microstructures of their condensed phases and the molecular processes of adsorption and transport, comprehending the processing-microstructures-performance relation in applications.