Application of Time Series Analysis on Kinetic Monte Carlo Simulations of Hyperthermal Oxidation of Graphite

The oxidation of carbon fiber ablators for thermal protection systems has been extensively studied for atmospheric reentry missions. We investigate this oxidation process at the atomic scale using atomistic kinetic Monte Carlo (A-KMC) simulations, focusing on the influence of two pathways of oxygen adsorption on carbon oxidation: adsorption of oxygen on the basal plane as epoxy groups and adsorption of oxygen directly on the edges of defects. We find that the majority of CO formation results from oxygen adsorbed on the basal plane, which subsequently diffuses toward defect edges. This is due to the greater availability of basal sites relative to defect edges throughout most of the simulation, and the rapid diffusion of epoxy groups toward defect edges at the studied temperatures (1700-2200 K). In this study, we exploit the temporal data from these A-KMC simulations to investigate the dynamics between the adsorption and CO formation reactions as they evolve with time. From KMC, we obtain time series that represent the time evolution of the frequency of occurrence of these reactions in the model. Pearson’s correlation coefficient is used as a metric to identify correlated relationships between time series. By comparing adsorption and CO formation time series using this metric, we find that the contribution of each adsorption reaction toward CO formation varies with time due to the evolving oxidized graphite structure. Specifically, as the ratio of basal plane sites (n_basal) to defect edge sites (n_edge) decreases during the simulation, the contribution of basal plane adsorption relative to direct edge adsorption toward CO formation also decreases. We also address several challenges associated with conducting time series analysis in KMC due to the stochastic nature of the method.