Morphological Characterization of Graphene Flake Networks Using Minkowski Functionals

Abstract

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.

Functional Nanomaterials from Waste and Low‐Value Natural Products: A Technological Approach Level

“…On the other hand, plasma-based technologies are usually more expensive and more complex, requiring more expert personnel and expensive equipment, as compared with the thermochemical techniques. [211,212] Indeed, the structure of both plasma-based and thermal types of materials synthesis systems includes i) the reaction vacuum/gas supply systems which are commonly similar for plasma and thermal systems, ii) reaction chamber which is simple for the thermal system but could be quite complex for the plasma system as it includes additional coils, multiple power supply leads and other specific units and instruments to ignite, sustain, and control the plasma, and iii) power supply system which is also very simple for the thermal reactors needing heating only, and quite complex for the plasma systems which are often powered by radiofrequency current, require matching units and other specific electronic equipment. Apparently, this results in the significant differences in the costs of the equipment.…”

Correlating the Nonlinear Roughening and Optical Properties of Anatase Thin Films—A Fractal Geometric Approach

“…[35][36][37] Specifically, the features of electron-ion beamassisted TiO 2 thin films' 3D surface deposited with varying ion beam energies were scrutinized by Shakoury et al [38] Moreover, distinct works are also reported utilizing Minkowski functionals to characterize the properties of surface topography. [1,[38][39][40] Furthermore, few works have also focused on analyzing microscopy images employing multivariate statistical analysis. [1,41,42] In exaction, due to the ability to reduce the observed dimension without compensating for the loss in information, principal component analysis (PCA) has gained significant attention among various multivariate analyzing tools.…”

Morphological and multifractal properties of Cr thin films deposited onto different substrates

“…Besides, to avoid limitation of characterizing surfaces with monofractal analysis owing to the variation in scaling along the surface, multifractal analysis of film surfaces has been carried out via two‐dimensional multifractal detrended fluctuation analysis (2D‐MFDFA), multifractal moving average analysis (MFDMA) (Habibi et al, 2022; Shakoury et al, 2020; Shidpour & Movahed, 2018). In other works, Minkowski functionals, that is, boundary, volume, and connectivity or Euler‐Poincaré characteristic have provided substantial insights into the surface structure and structure–property relationship in thin films (Korpi et al, 2019; Levchenko et al, 2016; Maity et al, 2021; Pierpaoli et al, 2021; Salerno & Banzato, 2005; Shakoury et al, 2020; Toccafondi et al, 2014). However, despite significant applicability of Chromium thin films and utility of concepts from fractal geometry and Minkowski functionals, to the best of our knowledge no studies have been conducted to understand the surface structure or spatial patterns using of Cr thin films.…”