Vibrational Energy Transfer in Shocked Molecular Crystals

We consider the process of establishing thermal equilibrium behind an ideal shock front in molecular crystals and its possible role in initiating chemical reaction at high shock pressures. A new theory of equilibration via multiphonon energy transfer is developed to treat the scattering of shock-induced phonons into internal molecular vibrations. Simple analytic forms are derived for the change in this energy transfer at different Hugoniot end states following shock compression. The total time required for thermal equilibration is found to be an order of magnitude or faster than proposed in previous work; in materials representative of explosive molecular crystals, equilibration is predicted to occur within a few picoseconds following the passage of an ideal shock wave. Recent molecular dynamics calculations are consistent with these time scales. The possibility of defect-induced temperature localization due purely to nonequilibrium phonon processes is studied by means of a simple model of the strain field around an inhomogeneity. The specific case of immobile straight dislocations is studied, and a region of enhanced energy transfer on the order of 5 nm is found. Due to the rapid establishment of thermal equilibrium, these regions are unrelated to the shock sensitivity of a material but may allow temperature localization at high shock pressures. Results also suggest that if any decomposition due to molecular collisions is occurring within the shock front itself, these collisions are not enhanced by any nonequilibrium thermal state.