A theoretical reaction rate model of a chemical exothermic decomposition surface from an external gas

Abstract

In this study, kinetic theory was used to derive an equation of state for an exothermic decomposition surface caused by an external gas. The new model is physical, and its quantities have been physically interpreted. A new concept of interaction probability was used to describe the co-volume. This concept describes the interaction between the decomposition surface and the external gas to derive an expression for the linear reaction rate based on kinetic theory. The interaction probability is associated with the particle density of the gases provided by the Lennard-Jones potential and temperature. The Maxwell–Boltzmann distribution was used to establish the initial decomposition conditions based on the concepts of autoignition and activation energy.

The aim of this study was to investigate when burning is a decomposition reaction in which the decomposing molecule contains oxygen and can be used as input to designing fuel cells, rocket motors, and propellants. Therefore, HMX and PETN were used as empirical data, and the new linear reaction rate model provided a good approximation and predicted the burn rate data. The model was compared with Vieille’s law $v_b=a{P}^n$ for the normal pressure range. However, the model goes beyond the law and provides good predictions of burn rates with high pressures found in diamond anvil experiments.