Topological vectors as a fingerprinting system for 2D-material flake distributions

The production of 2D material flakes in large quantities is a rapidly evolving field and a cornerstone for their industrial applicability. Although flake production has advanced in a fast pace, its statistical characterization is somewhat slower, with few examples in the literature which may lack either modelling uniformity and/or physical equivalence to actual flake dimensions. The present work brings a methodology for 2D material flake characterization with a threefold target: (i) propose a set of morphological shape parameters that correctly map to actual and relevant flake dimensions; (ii) find a single distribution function that efficiently describes all these parameter distributions; and (iii) suggest a representation system—topological vectors—that uniquely characterizes the statistical flake morphology within a given distribution. The applicability of such methodology is illustrated via the analysis of tens of thousands flakes of graphene/graphite and talc, which were submitted to different production protocols. The richness of information unveiled by this universal methodology may help the development of necessary standardization procedures for the imminent 2D-materials industry.