Two Minkowski functionals were tested in the capacity of morphological descriptors to quantitatively
compare the arrays of vertically-aligned graphene flakes grown on smooth and nanoporous
alumina and silica surfaces. Specifically, the Euler-Poincaré characteristic and fractal dimension
graphs were used to characterize the degree of connectivity and order in the systems, i.e. in the
graphene flake patterns of petal-like and tree-like morphologies on solid substrates, and meshlike
patterns (networks) grown on nanoporous alumina treated in low-temperature inductivelycoupled
plasma. It was found that the Minkowski functionals return higher connectivity and fractal
dimension numbers for the graphene flakepatterns with more complex morphologies, and indeed
can be used as morphological descriptors to differentiate among various configurations of
vertically-aligned graphene flakes grown on surfaces.
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