Correlation between normal mode vibrations and impact sensitivities of some secondary explosives

Because secondary explosives are stable molecules with large energy barriers to chemical reaction, in shock or impact initiation, a sizable amount of phonon energy must be converted to the molecular internal higher vibrations by multiphonon up pumping. To investigate the relationship between impact sensitivities and energy transfer rate, the number of doorway modes of explosives is estimated by a simple theory in which the rate is proportional to the number of normal mode vibrations. We evaluated frequencies of normal mode vibrations of 2,4,6-trinitro-m-cresol (C7H5N3O7), picric acid, TNB, TNAP, TNT, TNA, TBN, DATB, and TATB by means of density functional theory (DFT) at the b3p86/6-31g (d,p) level. The number of doorway modes in the regions of 200-700 cm−1 was evaluated by the direct counting method. It is found that the number of doorway modes shows a linearly correlation to the impact sensitivities derived from drop hammer tests. This result is in agreement with several previous works. Besides, it is also noted in our study that in those secondary explosives with similar molecular structure and similar molecular weight, the correlation between the impact sensitivity and the number of doorway modes is very high.