Controlling the Morphology of Nanoflakes Obtained by Liquid-Phase Exfoliation: Implications for the Mass Production of 2D Materials

The heterogeneous nature of mass-produced 2D material's nanoflakes requires analysis of size and shape parameters: their distributions around the desired values are essential for production and characterization. In this work, we obtain analytical expressions and behaviors of statistical distributions of experimentally extracted size and shape parameters of nanoflakes obtained by liquid-phase exfoliation. The collected data are open and can be mathematically handled to be analyzed through different associations in different scales, such as the logarithm of the length/thickness (r) and length/width (r(L)) aspect ratios. We find that In(r), a shape parameter, follows nearly Gaussian distributions, being an efficient fingerprint to characterize the material type and processing. On the other hand, the logarithms of thickness and volume follow asymmetric distributions with specific asymptotic behaviors, called exponential-power-Gaussian functions, but centrifugation turns both nearly Gaussian-distributed. Finally, the logarithm of the length/width aspect ratio, In(r(L)) an in-plane shape parameter, was found to follow the single-parameter probability density distribution xe(-lambda x2). The method detected that centrifugation enhances, by up to threefold, the percentage of flakes with large length/width ratios. This statistical methodology can be incorporated into the quality control of mass production of 2D nanoflakes, whose target applications can be found across the fast-growing nanomaterials' industry.