10
1 Introduction
the intermolecular potential is more anharmonic than the intramolecular potential,
coupling processes that include higher numbers of external modes (q) are dominant
over processes that contain higher numbers of internal modes (Q). Calculations on
naphthalene [39] suggested the coupling to decrease by an order of magnitude with
inclusion of Q terms, hence q 1 q 2 q 3 > Q 1 q 2 q 3 > Q 1 Q 2 q 3 . It follows that upon
mechanical perturbation, the phonon bath becomes excited, and equilibrates quickly
(in the order of ps) [36]. This leads to the formation of a vibrationally ‘hot’ phonon
bath and a vibrationally ‘cold’ internal molecular manifold. This state of quasiequilibrium evolves, with energy flowing upwards at rates in the order of 10 s of ps.
Hence, this model suggests an ability for energy transfer and localisation immediately
behind a shock front [40], and is consistent with prevailing theories of deflagration
and detonation. These theories require primary decomposition reactions to occur on
the time scale of ps [41].
In the initial model proposed by Coffey and Toton [35], a direct phonon upconversion mechanism was proposed for RDX. Using a complete quantum mechanical model, the rate of energy transfer from a shock-excited phonon bath into a select
vibrational mode in RDX was calculated. It was demonstrated that the localisation
of energy due to up-pumping was sufficient to overcome the bond dissociation limit
from a mild shock. This result was a crucial step in understanding localisation of
shock energy and hot-spot formation.
The subsequent models proposed by Dlott [36, 37, 39, 40] and colleagues instead
suggested an indirect phonon up-pumping mechanism. Using heat flow models, they
calculated the rate of energy up-pumping into the internal vibrational region. The
initial model of Dlott and Fayer [36] considered only the excitation of so-called
doorway modes (i.e. modes with frequencies less than twice the highest phonon
frequency). However, subsequent models later included the effects of doorway mode
up-pumping [39]. In these models, it was found that up-pumping occurs in three
stages: (1) equilibration of phonon modes within a time period of <2 ps, (2) excitation
of doorway modes, and (3) up-pumping of doorway modes only a few ps later. Hence,
while the rate-limiting step is indeed excitation of the doorway modes, additional uppumping occurs almost immediately afterwards. Additional work by Toton [42] and
Bardo [43] also discussed the addition of shock pressure in models of nitromethane,
where the pressure response of the vibrational density of states led to changes in
reaction rates according to the up-pumping model.
Both Coffey [35] and Dlott [36, 40] noted a particularly intriguing feature of
this model. Defect sites within the crystalline lattice introduce points of extreme
vibrational anharmonicity. Hence, the strength of anharmonic coupling in the vicinity
of a defect is larger and the corresponding rate of up-pumping to these sites is greater,
Fig. 1.7. This offered a mechanism for the localisation of energy near defect sites,
and thus the role of internal defects in generating hot-spots [25, 26]. However, the
exact anharmonic enhancement introduced by defect sites remains unknown.
Hence, with these early fundamental developments, vibrational up-pumping
appeared to offer a complete mechanism for the introduction, propagation and localisation of energy, capable of describing initiation of EMs. The phenomenon has
1 Introduction
the intermolecular potential is more anharmonic than the intramolecular potential,
coupling processes that include higher numbers of external modes (q) are dominant
over processes that contain higher numbers of internal modes (Q). Calculations on
naphthalene [39] suggested the coupling to decrease by an order of magnitude with
inclusion of Q terms, hence q 1 q 2 q 3 > Q 1 q 2 q 3 > Q 1 Q 2 q 3 . It follows that upon
mechanical perturbation, the phonon bath becomes excited, and equilibrates quickly
(in the order of ps) [36]. This leads to the formation of a vibrationally ‘hot’ phonon
bath and a vibrationally ‘cold’ internal molecular manifold. This state of quasiequilibrium evolves, with energy flowing upwards at rates in the order of 10 s of ps.
Hence, this model suggests an ability for energy transfer and localisation immediately
behind a shock front [40], and is consistent with prevailing theories of deflagration
and detonation. These theories require primary decomposition reactions to occur on
the time scale of ps [41].
In the initial model proposed by Coffey and Toton [35], a direct phonon upconversion mechanism was proposed for RDX. Using a complete quantum mechanical model, the rate of energy transfer from a shock-excited phonon bath into a select
vibrational mode in RDX was calculated. It was demonstrated that the localisation
of energy due to up-pumping was sufficient to overcome the bond dissociation limit
from a mild shock. This result was a crucial step in understanding localisation of
shock energy and hot-spot formation.
The subsequent models proposed by Dlott [36, 37, 39, 40] and colleagues instead
suggested an indirect phonon up-pumping mechanism. Using heat flow models, they
calculated the rate of energy up-pumping into the internal vibrational region. The
initial model of Dlott and Fayer [36] considered only the excitation of so-called
doorway modes (i.e. modes with frequencies less than twice the highest phonon
frequency). However, subsequent models later included the effects of doorway mode
up-pumping [39]. In these models, it was found that up-pumping occurs in three
stages: (1) equilibration of phonon modes within a time period of <2 ps, (2) excitation
of doorway modes, and (3) up-pumping of doorway modes only a few ps later. Hence,
while the rate-limiting step is indeed excitation of the doorway modes, additional uppumping occurs almost immediately afterwards. Additional work by Toton [42] and
Bardo [43] also discussed the addition of shock pressure in models of nitromethane,
where the pressure response of the vibrational density of states led to changes in
reaction rates according to the up-pumping model.
Both Coffey [35] and Dlott [36, 40] noted a particularly intriguing feature of
this model. Defect sites within the crystalline lattice introduce points of extreme
vibrational anharmonicity. Hence, the strength of anharmonic coupling in the vicinity
of a defect is larger and the corresponding rate of up-pumping to these sites is greater,
Fig. 1.7. This offered a mechanism for the localisation of energy near defect sites,
and thus the role of internal defects in generating hot-spots [25, 26]. However, the
exact anharmonic enhancement introduced by defect sites remains unknown.
Hence, with these early fundamental developments, vibrational up-pumping
appeared to offer a complete mechanism for the introduction, propagation and localisation of energy, capable of describing initiation of EMs. The phenomenon has