Structural Analysis of Nanoscale Network Materials Using Graph Theory

Abstract

Many materials with remarkable properties are structured as percolating nanoscale networks (PNNs). The design of this rapidly expanding family of composites and nanoporous materials requires a unifying approach for their structural description. However, their complex aperiodic architectures are difficult to describe using traditional methods that are tailored for crystals. Another problem is the lack of computational tools that enable one to capture and enumerate the patterns of stochastically branching fibrils that are typical for these composites. Here, we describe a computational package, StructuralGT, to automatically produce a graph theoretical (GT) description of PNNs from various micrographs that addresses both challenges. Using nanoscale networks formed by aramid nanofibers as examples, we demonstrate rapid structural analysis of PNNs with 13 GT parameters. Unlike qualitative assessments of physical features employed previously, StructuralGT allows researchers to quantitatively describe the complex structural attributes of percolating networks enumerating the network's morphology, connectivity, and transfer patterns. The accurate conversion and analysis of micrographs was obtained for various levels of noise, contrast, focus, and magnification, while a graphical user interface provides accessibility. In perspective, the calculated GT parameters can be correlated to specific material properties of PNNs (e.g., ion transport, conductivity, stiffness) and utilized by machine learning tools for effectual materials design.

Spanning Network Gels from Nanoparticles and Graph Theoretical Analysis of Their Structure and Properties

“…Using the Python package StructuralGT , digital micrographs of PbTe NP networks were mapped by utilizing a combination of computer vision and GT methods. [ 27 ] GT analysis is performed by converting the structural networks into mathematical models by taking each instance that fiber branches or multiple fibers intersect to be a node and the fibers that connect these nodes to be edges. The resulting topological model is referred to as a graph, which mathematically is denoted as G(n, e) .…”

“…Explanation of the calculation of each GT parameter is described in the StructuralGT publication and on its Github page: https://github.com/drewvecchio/StructuralGT. [ 27 ] 50 STEM images were analyzed for each gel condition to provide sufficient statistics. The STEM images were not enhanced or altered by other image processing software.…”

“…In this approach, each NP fiber is described as an edge ( e ) and each point of intersection between two or more fibers is described as a node ( n ) . [ 27 ] The influence of gel architecture enumerated by GT parameters upon the mechanical and charge transport properties of PbTe gels is demonstrated.…”

Hydrogen Bonding in 1‐Propanol‐Ethanol Binary Mixture: Experimental and Modeling Approaches

“…The physical properties of the liquids such as density, surface tension, dielectric constant, and excess enthalpy of the ethanol-water mixture were studied using MD simulation by A. Ghoufi et al [37] Of late, there has been a growing interest in the application of graph theoretic models to analyze networks formed among molecular structures. [38][39][40][41] These techniques provide concise and clear information regarding the connectivity among the various moieties present in the system. It can also be integrated seamlessly with many modern, advanced programming workflows.…”

Structure and Performance Attributes Optimization and Ranking of Gamma Irradiated Polymer Hybrids for Industrial Application

“…Although the application of graph theory for the subject matter of interest is simple and straightforward only a few attempts can be found in the literature. For example, Vecchio et al [ 27 ] have explored its potential while quantitatively assessing the structure of aramid nanofibers. They have utilized SEM micrographs and accurately converted the complex structure of aramid nanofibers into graphs, which were then used for structure analysis with 13 graph-theoretical parameters.…”