Mesoscale Simulations of Hot Spot Ignition in Cyclotetramethylene Tetranitramine Using the Kinetic Monte Carlo Method

Critical temperatures for the ignition of cylindrical hot spots up to 0.5 μm in diameter in the secondary explosive cyclotetramethylene tetranitramine (HMX) have been computed using the kinetic Monte Carlo (kMC) method. By combining the thermal bit transfer model with effective single-step Arrhenius kinetics for the onset of thermal explosion, we are able to observe the homogeneous nucleation and growth of sustained deflagration reactions in HMX at the mesoscale. The kMC simulations capture the stochastic onset of thermal explosion seen in quantum molecular dynamics simulations at the nanometer length scales that are required to adequately resolve the temperature profile across a deflagration front. Deflagration velocities and hot spot critical temperatures have been evaluated for four sets of single-step Arrhenius kinetics for HMX that account for the effects of self-heating on the acceleration of the reaction rate in different ways. It is shown that the single-step Arrhenius kinetics proposed by Manner et al., Burnham and Weese, and Henson et al. give roughly similar hot spot critical temperatures, but a reparametrization of the 2001 Henson-Smilowitz kinetics to include the effects of self-heating on the reaction rate gives rise to significantly different behavior, with hot spot critical temperatures that are about 700 K higher than those from the other models. The origins of this behavior are discussed.