A distributed activation energy model of thermodynamically inhibited nucleation and growth reactions and its application to the β-δ phase transition of HMX

Detailed and global models are presented for thermodynamically inhibited nucleation-growth reactions and applied to the beta-delta phase transition of HMX (nitramine octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). The detailed model contains separate kinetic parameters for the nucleation process, including an activation energy distribution resulting from a distribution of defect energies, and for movement of the resulting reaction interface within a single particle. A thermodynamic inhibition term is added to both processes so that the rates go to zero at the transition temperature. The global model adds the thermodynamic inhibition term to the extended Prout-Tompkins nucleation-growth formalism for single particles or powders. Model parameters are calibrated from differential scanning calorimetry data. The activation energy for nucleation (333 kJ/mol) is substantially higher than that for growth (29.3 kJ/mol). Use of a small activation energy distribution (similar to400 J/mol) for the defects improves the fit to a powered sample for both the early and late stages of the transition. The effective overall activation energy for the global model (208.8 kJ/mol) is between that of nucleation and growth. Comparison of the two models with experiment indicates the thermodynamic inhibition term is more important than the energy distribution feature for this transition. On the basis of the applicability of the Prout-Tompkins kinetics approach to a wide range of organic and inorganic materials, both models should have equally broad applicability for thermodynamically constrained reactions.