Uncertainty quantification in stochastic simulations of nitrogen–carbon gas–surface interactions

Abstract

This study investigates how uncertainty in the reaction rate parameters of an atomistic kinetic Monte Carlo (KMC) model propagates to model outputs, such as the defect growth rate in carbon materials used for thermal protection systems. A KMC model consisting of key processes between carbon and nitrogen is used to model defect growth caused by nitridation in graphene. Uncertainties in rate parameters of nitrogen adsorption, surface diffusion, and CN formation reactions were identified from density functional theory or other model calculations. These uncertainties result from variations in the model parameters of these methods and, thus, constitute epistemic uncertainties in the KMC model. The KMC model, along with the identified uncertainties, was used to perform a sensitivity analysis to quantify and study the influence of these uncertainties on the resulting defect growth rate uncertainty. The analysis revealed that the activation energy of CN formation contributed significantly higher uncertainties to the defect growth rate than other reaction rate parameters. This result is attributed to the strong limiting effect of CN formation on defect growth, as well as the greater propagation of uncertainty through activation energies rather than prefactor terms. In addition, uncertainty propagation was studied across temperature from 1700 to 2100 K. Results further demonstrated that a reaction’s uncertainty contribution strongly depends on its limiting effect, which varies with temperature. Together, these results highlight the factors influencing uncertainty propagation from key processes in carbon nitridation.