136
4 Vibrational Up-Pumping in Some Molecular Energetic Materials
to differentiate between β-HMX and α-FOX-7. In the former, the doorway modes
tend towards the bottom of the doorway region, while in the latter they tend towards
the top. Thus, while a simple counting method appeared sufficient to describe the
vibrational up-pumping in the vibrationally ‘simple’ azide molecules, it appears
inadequate to treat the more complex vibrational structure here. Thus P
(2) alone
does not appear sufficient.
4.5.3.3 Two-Layer Combination Pathways
As a first step to develop this model further within the 0 K limit, and attempting
to unify previous works, energy transfer is instead explicitly treated as the two-step
process that was described above [61], namely:
1. Excitation of the doorway modes by the first overtone, followed by
2. Up-pumping by combination pathways to a maximum of 3 max
This is done by imposing the populations of the doorway modes that result from
the overtone up-pumping calculations in Sect. 4.5.3 onto g(ω), and subsequently
assessing P((
(2)
) as before. This is demonstrated in Fig. 4.14 for α-FOX-7.
If the model (bottom panel, Fig. 4.14) is constructed, and the up-pumping contributions re-examined, the predicted trend in sensitivities sits in excellent agreement
with experimental results, Fig. 4.15. It is assumed here that excitation of all modes
between max → 3 max (i.e. the entire internal vibrational manifold) should be
considered. The predicted sensitivity ordering follows as HNB > β-HMX > α-FOX7 > NTO > TATB across the −NO 2 based energetics, and ABT > HBT for the N–N
energetic materials. While the model imposed here is slightly more complex than
that required in Chap. 3, it does highlight the need for a more physical basis in
understanding the properties of energetic materials with large quantities of doorway
modes and complex vibrational structure.
Whilst the ordering proposed in Fig. 4.15 shows excellent agreement with
experimental impact sensitivities it has been postulated [61, 62] that for some
materials the main target modes (e.g. bond stretching) are confined to the region
2 max < ω < 3 max . Without a deeper understanding of the dissociation mechanisms of these energetic materials, it is not possible to say explicitly whether the
range max < ω < 3 max or 2 max < ω < 3 max should be considered. However,
it is worth highlighting that if the integration from Fig. 4.15 is restricted to the upper
range, Fig. 4.16 is the result. This leads to truly excellent agreement with experimental impact sensitivity ordering, including the positioning of ABT. Now only
HBT remains as an outlier. Further information as to which bonds require activation
is therefore of great importance in developing this model further.
4 Vibrational Up-Pumping in Some Molecular Energetic Materials
to differentiate between β-HMX and α-FOX-7. In the former, the doorway modes
tend towards the bottom of the doorway region, while in the latter they tend towards
the top. Thus, while a simple counting method appeared sufficient to describe the
vibrational up-pumping in the vibrationally ‘simple’ azide molecules, it appears
inadequate to treat the more complex vibrational structure here. Thus P
(2) alone
does not appear sufficient.
4.5.3.3 Two-Layer Combination Pathways
As a first step to develop this model further within the 0 K limit, and attempting
to unify previous works, energy transfer is instead explicitly treated as the two-step
process that was described above [61], namely:
1. Excitation of the doorway modes by the first overtone, followed by
2. Up-pumping by combination pathways to a maximum of 3 max
This is done by imposing the populations of the doorway modes that result from
the overtone up-pumping calculations in Sect. 4.5.3 onto g(ω), and subsequently
assessing P((
(2)
) as before. This is demonstrated in Fig. 4.14 for α-FOX-7.
If the model (bottom panel, Fig. 4.14) is constructed, and the up-pumping contributions re-examined, the predicted trend in sensitivities sits in excellent agreement
with experimental results, Fig. 4.15. It is assumed here that excitation of all modes
between max → 3 max (i.e. the entire internal vibrational manifold) should be
considered. The predicted sensitivity ordering follows as HNB > β-HMX > α-FOX7 > NTO > TATB across the −NO 2 based energetics, and ABT > HBT for the N–N
energetic materials. While the model imposed here is slightly more complex than
that required in Chap. 3, it does highlight the need for a more physical basis in
understanding the properties of energetic materials with large quantities of doorway
modes and complex vibrational structure.
Whilst the ordering proposed in Fig. 4.15 shows excellent agreement with
experimental impact sensitivities it has been postulated [61, 62] that for some
materials the main target modes (e.g. bond stretching) are confined to the region
2 max < ω < 3 max . Without a deeper understanding of the dissociation mechanisms of these energetic materials, it is not possible to say explicitly whether the
range max < ω < 3 max or 2 max < ω < 3 max should be considered. However,
it is worth highlighting that if the integration from Fig. 4.15 is restricted to the upper
range, Fig. 4.16 is the result. This leads to truly excellent agreement with experimental impact sensitivity ordering, including the positioning of ABT. Now only
HBT remains as an outlier. Further information as to which bonds require activation
is therefore of great importance in developing this model further.