24
1 Introduction
Fig. 1.17 Relative rate of energy up-conversion to the doorway region for a series of energetic
materials. Note the exponential trend. Figure reprinted with permission from Ref. [121], https://
doi.org/10.1021/jp961771l. Copyright 1997 American Chemical Society
Koshi [122] was subsequently first to employ an approach based on ab initio
quantum mechanical calculations, and on a rate equation proposed by Dlott [36],
κ =
j
τ 1 (0)θ e
(1.10)
Here, j is the number of doorway modes with frequency and 0 K lifetime τ 1 . θ e
describes a temperature equivalence term, which describes the temperature at which
the rate of transfer into a doorway mode is the same as the low temperature rate at
which it transfers out of this same doorway mode by two-phonon emission
n /2 (θ e ) − n (θ e ) = 1
(1.11)
Noting that /θ e is constant, and noting that τ 1 (0) is approximately constant for
organic EMs (ca. 2–6 ps) [40], Koshi argued that the rate of energy transfer therefore
depends only on the number of doorway modes. Noting the discrepancy in the upper
limit of the doorway region in earlier studies, the doorway region was varied with
2 max set at 500, 600 and 700 cm
−1 and the number of doorway modes counted
in each material. The gas-phase frequencies were calculated, and the number of
doorway modes correlated well with experimental impact sensitivities Fig. 1.18.
1 Introduction
Fig. 1.17 Relative rate of energy up-conversion to the doorway region for a series of energetic
materials. Note the exponential trend. Figure reprinted with permission from Ref. [121], https://
doi.org/10.1021/jp961771l. Copyright 1997 American Chemical Society
Koshi [122] was subsequently first to employ an approach based on ab initio
quantum mechanical calculations, and on a rate equation proposed by Dlott [36],
κ =
j
τ 1 (0)θ e
(1.10)
Here, j is the number of doorway modes with frequency and 0 K lifetime τ 1 . θ e
describes a temperature equivalence term, which describes the temperature at which
the rate of transfer into a doorway mode is the same as the low temperature rate at
which it transfers out of this same doorway mode by two-phonon emission
n /2 (θ e ) − n (θ e ) = 1
(1.11)
Noting that /θ e is constant, and noting that τ 1 (0) is approximately constant for
organic EMs (ca. 2–6 ps) [40], Koshi argued that the rate of energy transfer therefore
depends only on the number of doorway modes. Noting the discrepancy in the upper
limit of the doorway region in earlier studies, the doorway region was varied with
2 max set at 500, 600 and 700 cm
−1 and the number of doorway modes counted
in each material. The gas-phase frequencies were calculated, and the number of
doorway modes correlated well with experimental impact sensitivities Fig. 1.18.