Graph Theory Applied to Plasma Chemical Reaction Engineering

Abstract

This work explores the following applications of graph theory to plasma chemical reaction engineering: assembly of a weighted directional graph with the key addition of reaction nodes, from a published set of reaction data for air; graph visualisation for probing the reaction network for potentially useful or problematic reaction pathways; running Dijkstra’s algorithm between all species nodes; further analysis of the graph for useful engineering information such as which conditions, reactions, or species could be enhanced or supressed to favour particular outcomes, e.g. targeted chemical formation. The use of reaction-nodes combined with derived parameters allowed large amounts of key information regarding the plasma chemical reaction network to be assessed simultaneously using a leading open source graph visualisation software (Gephi). A connectivity matrix of Dijkstra’s algorithm between each two species gave a measure of the relative potential of species to be created and destroyed under specific conditions. Further investigation into using the graph for key reaction engineering information led to the development of a graph analysis algorithm to quantify demand for conditions for targeted chemical formation: Optimal Condition Approaching via Reaction-In-Network Analysis (OCARINA). Predictions given by running OCARINA display significant similarities to a well-known electric field strength regime for optimal ozone production in air. Time dependent 0D simulations also showed preferential formation for O· and O3 using the respective conditions generated by the algorithm. These applications of graph theory to plasma chemical reaction engineering show potential in identifying promising simulations and experiments to devote resources.

Radiolysis‐Driven Evolution of Gold Nanostructures – Model Verification by Scale Bridging In Situ Liquid‐Phase Transmission Electron Microscopy and X‐Ray Diffraction

“…It consists of 42 chemical species distributed over 184 reactions (see Supporting Information for details, [21,37,38,[52][53][54][55][56][57][58][59][60][61][62][63][64][65][66] including an enlarged and annotated version of the plot depicted in Figure 1d (Figure S3, Supporting Information)). Figure S4 (Supporting Information) depicts the set based on graph theory, [67,68] revealing that the simulated steady-state concentrations of the species do not necessarily coincide with their importance within the reaction set (c.f. Figure S5, Supporting Information).…”

Modeling study on temporal nonlinear behaviors in CO2 dielectric barrier discharges under Martian pressure

“…The CO 2 plasma has a wide variety of particles and complex chemical reactions, to accurately investigate the underpinning physics of the nonlinear behaviors in CO 2 discharges under Martian conditions, the species and chemical reactions in CO 2 discharges are carefully selected according to the graph theory developed by Holmes et al [47] and Murakami and Sakai [48] (CO e , CO v , CO v , CO v , CO v , CO v , CO v ,…”

“…The $${\text{CO}}_{2}$$ plasma has a wide variety of particles and complex chemical reactions, to accurately investigate the underpinning physics of the nonlinear behaviors in $${\text{CO}}_{2}$$ discharges under Martian conditions, the species and chemical reactions in $${\text{CO}}_{2}$$ discharges are carefully selected according to the graph theory developed by Holmes et al [ 47 ] and Murakami and Sakai [ 48 ] , and a $${\text{CO}}_{2}$$ reaction model including 26 species and 278 reactions is obtained. Besides the background species $${\text{CO}}_{2}$$, five neutral particles (O, CO, $${{\rm{O}}}_{2},{{\rm{O}}}_{3}$$, and C), seven charged particles ( e , $${{\rm{O}}}^{-},{{\rm{O}}}_{2}^{-},{\text{CO}}_{3}^{-},{\text{CO}}_{4}^{-},{\text{CO}}_{2}^{+}$$, and $${{\rm{O}}}_{2}^{+}$$), and 13 excited states of $${\text{CO}}_{2}$$ (…”

Enumerate the Number of Vertices Labeled Connected Graph of Order Seven Containing No Parallel Edges

“…The relationship and uni cation of graph theory and physicalchemical measures (such as boiling and melting point, covalent and ionic potentials, and electronic density) make molecular topology can describe molecular structure comprehensively. A weighted directed graph, connectivity matrix, and Dijkstra's algorithm were used by Holmes et al (2021) in plasma chemical reaction engineering. The basic structure of a directed graph is mostly used for the visualization of the reactions.…”