Role of gas- and condensed-phase kinetics in burning rate control of energetic solids

A simplified two-step kinetics model for the combustion of energetic solids has been used to investigate the effect of gas-phase activation energy on flame structure and burning rate and the role of gas- versus condensed-phase kinetics in determining burning rate. The following assumptions are made: a single-step, unimolecular, high activation energy decomposition process which is overall relatively energetically neutral, is followed by a highly exothermic single-step, bimolecular, gas-phase reaction with arbitrary activation energy, E? _g. The results show that at extremely low (<10⁴ Pa) or high (>10¹² Pa) pressures the burning rate is controlled by the condensed-phase reaction kinetics for any E?_g. At intermediate pressures (10⁵-10¹⁰ Pa) gas reaction kinetics contribute strongly to the burning rate. In this pressure range the value of E?_g plays an important function in determining the role of gas- and condensed-phase reactions: for high E?_g a gas-phase kinetically controlled regime exists; for low E?_g both condensed and gas-phase kinetics are important. The limiting behaviour of asymptotically large E?_g (gas kinetically controlled burning rate) occurs at about E?_g=20 kcal mol^?1 for parameters representative of HMX, while the vanishingly small E?_g behaviour occurs near E?_g. Previous comparison with burning rate and temperature profile data has suggested that the small-E?_g limit is the more accurate of the two extremes. This may imply that the important (burning rate influencing) primary gas reaction zone near the surface has more the character of a chain reaction mechanism than the classical high activation energy thermal decomposition mechanism. To the degree that the low-E?_g chain reaction model is a better approximation than the high-E?_g thermal decomposition model, the possibility exists that the chemistry of either reaction zone, including the molecular structure of the material, might be exploited for favourable tailoring of burning rate. The low-E?_g model also provides a rational mechanistic explanation of observed trends in burning rate temperature sensitivity with pressure and temperature for materials like HMX in terms of a gradual transition from mixed gas- and condensed-phase kinetic control to condensed-phase only kinetic control as the pressure decreases.