4.6 Conclusions
151
Consideration of the combination pathways by means of the two-phonon density
of states leads to rather poor correlation with experimental sensitivities. However,
this can be largely rectified by implementing a two-layered model. That is, if explicit
consideration is given for the initial excitation of the doorway modes by the first
overtone, and the combination pathways considered subsequently, then the overall
correlation with experiment becomes promising. However, clear deficiencies remain.
As a final step, it is found that the distribution of doorway modes (i.e. clustered at the
upper or lower end of the doorway region) requires some consideration for the relative
contribution of each doorway mode to up-pumping. This was treated by the addition
of a temperature term, populating vibrational states by the Bose-Einstein populations.
If this term is considered, the predicted trend in impact sensitivities matches very
well with experimental values. Hence, the work in this chapter has developed a fully
ab initio approach to ranking the impact sensitivity of EMs based on a vibrational
up-pumping model. In doing so, the work in this chapter has successfully unified and
expanded on competing models that have been reported in the literature.
Reproducing the models based on zone-centre frequency calculations leads to the
same conclusions. This is presumably due to the low wave vector dispersion that
is exhibited for these materials. Hence, the zone centre frequencies provide a good
representation of the total vibrational structure. This opens the door to implementing
this model to large molecular materials, such as TATP, for which the task of obtaining
complete phonon dispersion curves is simply too large.
It is remarkable to find that this simple mechanism of up-pumping appears to
provide a means to predict the relative impact sensitivity of a wide range of structural types. The minor discrepancies that remain are likely due to the intricacies
that surround the differences in phonon scattering rates (i.e. anharmonic coupling
strengths) rates of phonon propagation in these materials, as well as the dissociation
energies of the different molecules.
4.7 Suggestions for Further Work
The method presented here has been a first approach at understanding the up-pumping
structure in EMs. Foremost, the work presented here includes only seven molecular
EMs, and therefore a larger number of systems is a clear direction for additional
work. On this subset of organic EMs, the model has proved promising, despite the
numerous simplifications and assumptions that have been made. Enhancing this
model by reducing the significance of these assumptions is also a clear direction for
further work, namely:
• It is clear that these methods perform well at ordering materials with structurally
similar explosophoric moieties. However, better understanding of the electronic
structure and decomposition pathways is required to compare across different
structure types.
151
Consideration of the combination pathways by means of the two-phonon density
of states leads to rather poor correlation with experimental sensitivities. However,
this can be largely rectified by implementing a two-layered model. That is, if explicit
consideration is given for the initial excitation of the doorway modes by the first
overtone, and the combination pathways considered subsequently, then the overall
correlation with experiment becomes promising. However, clear deficiencies remain.
As a final step, it is found that the distribution of doorway modes (i.e. clustered at the
upper or lower end of the doorway region) requires some consideration for the relative
contribution of each doorway mode to up-pumping. This was treated by the addition
of a temperature term, populating vibrational states by the Bose-Einstein populations.
If this term is considered, the predicted trend in impact sensitivities matches very
well with experimental values. Hence, the work in this chapter has developed a fully
ab initio approach to ranking the impact sensitivity of EMs based on a vibrational
up-pumping model. In doing so, the work in this chapter has successfully unified and
expanded on competing models that have been reported in the literature.
Reproducing the models based on zone-centre frequency calculations leads to the
same conclusions. This is presumably due to the low wave vector dispersion that
is exhibited for these materials. Hence, the zone centre frequencies provide a good
representation of the total vibrational structure. This opens the door to implementing
this model to large molecular materials, such as TATP, for which the task of obtaining
complete phonon dispersion curves is simply too large.
It is remarkable to find that this simple mechanism of up-pumping appears to
provide a means to predict the relative impact sensitivity of a wide range of structural types. The minor discrepancies that remain are likely due to the intricacies
that surround the differences in phonon scattering rates (i.e. anharmonic coupling
strengths) rates of phonon propagation in these materials, as well as the dissociation
energies of the different molecules.
4.7 Suggestions for Further Work
The method presented here has been a first approach at understanding the up-pumping
structure in EMs. Foremost, the work presented here includes only seven molecular
EMs, and therefore a larger number of systems is a clear direction for additional
work. On this subset of organic EMs, the model has proved promising, despite the
numerous simplifications and assumptions that have been made. Enhancing this
model by reducing the significance of these assumptions is also a clear direction for
further work, namely:
• It is clear that these methods perform well at ordering materials with structurally
similar explosophoric moieties. However, better understanding of the electronic
structure and decomposition pathways is required to compare across different
structure types.