Chemical reaction initiation and hot-spot formation in shocked energetic molecular materials

A theoretical model is developed to describe the nature of molecular energy transfer and chemical reactivity in shocked energetic materials. The intent is to develop a fundamental understanding of the sensitivity of secondary explosives, which are solids consisting of large organic molecules. Because secondary explosives are stable molecules with large barriers to chemical reaction, before reactions can occur, a sizable amount of energy must be transferred from the shock produced phonons to the molecules' internal vibrations by multiphonon up-pumping. The dominant mechanism for up-pumping is anharmonic coupling of excited phonon modes with low frequency molecular vibrations, termed doorway modes. Quantitative calculations are presented which show the extent and rate of multiphonon up-pumping caused by shock excitation. A simple expression is derived to describe how the rate of up-pumping increases with shock pressure. It is shown that up-pumping is complete, and Arrhenius kinetics become valid, within ∼30 ps or 100-170 nm behind the shock front. The time dependence of chemical reactivity behind the front is calculated using reaction rate laws for the decomposition of nitramine explosives. The sensitivity of explosives is examined under the conditions of greatest interest: the regime of relatively weak shock waves (p = 1-10 GPa) characteristic of accidents. A mechanism for hot spot formation, based on defect induced local increases in anharmonic coupling, is discussed, and the conditions for ignition and spreading of reactions from hot spots are evaluated.