J. Phys. Chem. B 2006, 110, 18515-18520
18515
Theoretical Studies of Energy Transfer Rates of Secondary Explosives Shuji Ye and Mitsuo Koshi* Department of Chemical System Engineering, UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ReceiVed: May 8, 2006; In Final Form: July 13, 2006
Understanding the mechanism of shock-induced chemical reaction in secondary explosives is necessary to pursue the development and the safe use of new explosives having high performance and low sensitivity. In an effort to understand the mechanism, the energy transfer rates of such secondary explosives as PETN(I), PETN(II), δ-HMX, R-HMX, β-HMX, RDX, ANTA, DMN, and NM have been evaluated based on the formula derived by Fried and Ruggiero [Fried, L. E.; Ruggiero, A. J. J. Phys. Chem. 1994, 98, 9786]. The energy transfer rates were determined in terms of the density of vibrational states and the unharmonic vibron-phonon coupling term, which were calculated by using a flexible potential containing both intra- and intermolecular terms. For the secondary explosives, a good correlation was found between the energy transfer rates and the impact sensitivity. The energy transfer rates are several times faster for the explosives with higher sensitivity such as PETN, HMX, and RDX than those with lower sensitivity such as ANTA, DMN, and NM. The calculations presented suggest the energy transfer rate in secondary explosive crystals is a significant factor in their sensitivity and introduction of double bond, or hydrogen bonds, or caged structure into secondary explosives is expected to decrease the sensitivity.
I. Introduction Shock or impact initiation of explosives is a quite complicated process. When a mechanical excitation is imposed on an explosive crystal, the excess mechanical energy is eventually dissipated into a bath consisting of the low energy mode of lattice vibrations (phonons). Before the onset of detonation, chemical bonds of molecules in the crystal must be broken to initiate chemical reactions. Therefore, the initial energy transferred to phonons must be deposited to molecular vibrations. Most of the secondary explosives are molecular solids consisting of large organic molecules. Because secondary explosives are stable molecules with large energy barriers to chemical reaction, a sizable amount of energy must be transferred from phonons to the molecules’ internal vibrations. In general, phonon modes lie in the vibrational energy range of less than 200 cm-1, while molecular vibration modes relevant to bond breaking are in the energy range of greater than 1000 cm-1. It is clear that phonon energy must be converted to higher vibrations by multiphonon up pumping.1-5 To understand the multiphonon up pumping mechanism, we have measured the line widths of Raman spectra in such explosives as RDX (1,3,5-trinitro-1,3,5triazacycrohexane), β-HMX (1,3,5,7-tetranitro-1,3,5,7-tetraazacycrooctane), and Tetryl (2,4,6-trinitrophenylnitramine) as a function of temperature ranging from T ) 3.6 to 300.0 K.6,7 As pointed out by Schettino,8 the deconvolution of the experimental line shapes can be used to extract a constant inhomogeneous contribution to the line broadening, probably due to crystal defects, over the whole temperature range. On the basis of temperature dependence of the Raman line width due to pure Lorentzian contribution, it is confirmed that the dominant mechanisms for the relaxation processes of phonons and vibrons are three-phonon and dephasing processes.6,7 The Raman line * Address correspondence to this author. Phone: (+81)-3-5841-7295, Fax: (+81)-3-5841-7488. E-mail:
[email protected].
width due to three-phonon and dephasing processes can be written as,9
γ3d ) B3d(ni + nj + 1)
(1)
γ3u ) B3u(ni - nj)
(2)
γdeph ) Bdephni(ni + 1)
(3)
where the B3d, B3u, and Bdeph coefficients are the usual threephonon down, three-phonon up, and dephasing anharmonic terms of the crystal Hamiltonian, respectively. ni is the occupation number of the phonon or the vibron with energy ωi,
ni )
1 exp(pωi/kBT) - 1
(4)
where kB is Boltzman’s constant. For example, a possible relaxation process of the vibron mode at 365.5 cm-1 in β-HMX crystal can be described as γ(T) ) γ3d(T) + γdeph(T), where γ(T) is the Raman line width due to the homogeneous contribution; parameters for three phonon down process are B3d ) 1.05 cm-1, ω1 ) 84.0 cm-1, and ω2 ) 281.0 cm-1 and those for the dephasing process are Bdeph ) 0.2 cm-1, ω ) 72.0 cm-1. The temperature dependence of the line width is shown in Figure 1. Recently McGrane et al.10,11 studied anharmonic vibrational properties of explosives such as PETN (pentaerythritol tetranitrate), HMX, TATB (1,3,5-triamino-2,4,6-trinitrobenzene), and the inert naphthalene from temperature-dependent Raman spectra and their data suggest that hindered vibrational energy transfer in the molecular crystals is a significant factor in shock sensitivity. Dlott and Fayer3 have studied multiphonon up-conversion processes associated with chemical reactions induced by very strong shock. They derived a simple expression for the phononvibron energy transfer rates. Fried and Ruggiero12 have also
10.1021/jp062815l CCC: $33.50 © 2006 American Chemical Society Published on Web 08/29/2006
18516 J. Phys. Chem. B, Vol. 110, No. 37, 2006
Ye and Koshi to-state energy up-conversion rates κ for the fusion of two phonons or vibrons of energies ωl and ωm into phonon or vibron of energy ωc is,
κ(ωl,ωm,ωc) )
2π |〈...(nl - 1)(nm - 1)(nc p 1)|H1|nlnmnc...〉|2δ(Ec - El - Em) (5)
where H1 is the cubic term in the Hamitonian and ni is the occupation number of phonon or vibron with energy of ωi given by eq 4. On the basis of the three-phonon up-conversion, for a given band ωc, the energy transfer rate per volume of crystal is given as follows Figure 1. The temperature dependence of line width of the vibron at 365.5 cm-1 in β-HMX crystal: open cycle, experimental data; solid lines, theoretical fitting. 3d ) three-phonon down process; deph ) pure dephasing process; 3d + deph ) sum of the contributions of 3d and deph processes.
derived a simple formula for the total energy transfer rates from phonons into a given vibron band in terms of the density of vibrational states and the unharmonic vibron-phonon coupling term. They estimated the phonon up-conversion rates in the energy range of 0 to 600 cm-1 for several explosives such as TATB, RDX, and HMX. The density of vibratonal states they used was derived from inelastic neutron scattering experiments. Fried and Ruggiero12 found that the energy transfer rates of sensitive explosives were several times greater than that of insensitive explosives. They also showed that the energy transfer rates at the vibrational energy of ω ) 425 cm-1 linearly correlated to the impact sensitivities derived from drop hammer tests. Though the density of vibrational states can be determined by inelastic neutron scattering technique, data of density of vibrational states are not available for many sensitive explosives. Computer simulation has been widely used and was proved to be a very effective means to calculate the density of vibrational states. However, the potential functions that include intermolecular potentials are not enough to calculate the precise density of vibrational states and further developments of flexible potential are necessary to describe the intramolecular motion, molecular deformations, and the energy flow inside these crystals. For this purpose, flexible potentials including intraand intermolecular terms were fitted to calculate the lattice properties of secondary explosives.13 The flexible potentials have been very successful in their ability to predict the lattice properties of many secondary explosive crystals. In the present paper, we used the flexible potentials and calculated the density of vibrational states and anharmonic coupling constants of crystalline explosives such as PETN(I), PETN(II), δ-HMX, R-HMX, RDX, β-HMX, ANTA (3-amino5-nitro-1,2,4-triazole), DMN (N,N-dimethylnitramine), and NM (nitromethane). NM is a liquid at room temperature. We performed the calculation of NM using its low-temperature crystalline structure. We evaluated energy transfer rates and twophonon/vibron densities of states as a function of vibrational energy and compared the energy transfer rates with impact sensitivities. II. Theory In the theory of Fried and Ruggiero,12 they fixed the energy of the final (phonon or vibron) states ωc and sum over all phonons or vibrons (ωl,ωm) such that ωl + ωm ) ωc. The state-
κ(ωc,T) )
9|B|2 4π2F0p2
∫dω n(ω) n(ωc - ω) F(ω) F(ωc - ω) (6)
where F0 is the density of the sample, B is the cubic anharmonic coupling coefficient, and F(ω) is the density of vibrational states, given by
F(ω) )
∑s ∫dk
δ(ω - ωs(k)) 8π3
(7)
where k is the crystal momentum. The cubic anharmonic potential is given by9
V(3) )
1
∑
|
∂3V({Ψ})
6 Ψ ∂Ψ1∂Ψ2∂Ψ3
(Ψ1 - Ψ10)(Ψ2 -
{Ψ}0
Ψ20)(Ψ3 - Ψ30) (8) where V({ψ}) is the potential energy for the molecular crystal with a set of normal coordinates {ψ}, and the partial derivative is evaluated at the equilibrium position {ψ}0. The cubic anharmonic coupling coefficient is given by
B)
1
∑
∂3V({Ψ})
|
6 Ψ ∂Ψ1∂Ψ2∂Ψ3
(9)
{Ψ}0
To compare the density of vibrational states for different molecules or different polymorphs, it is necessary to determine a normalization factor. The simplest way is to take the integral of F(ω) over all vibrational energy to be equal to 3NZ/Vc, where N is the number of atoms per molecule, Z is the number of molecules per unit cell, and Vc is the volume of the unit cell.12 We extract 3NZ/Vc from F(ω) and let the integral of F(ω) over all vibrational energies to be equal to 1. Then eq 6 becomes
κ(ωc,T) )
81 |B|2 N2Z2 4π2p2 F0 Vc2
∫dω n(ω) n(ωc ω) F(ω) F(ωc - ω) (10)
III. Calculation Method The calculations of density of vibrational states were performed by using the software package of the general utility lattice program (GULP).14,15 For a crystal with Z molecules per unit cell (N atoms per molecule) at arbitrary positions, these degrees of freedom are determined by the 3NZ positions of the atoms in the unit cell as well as the dimensions and angles of the unit cell. The flexible potential presented in GULP not only
Energy Transfer Rates of Secondary Explosives
J. Phys. Chem. B, Vol. 110, No. 37, 2006 18517
V(R) ) Aij exp(-BijR) V(R) )
Dij R
12
Cij
(11)
R6
Eij
-
(12)
R6
where R is the interatomic separation, and Aij, Bij, Cij, Dij, and Eij are constants characteristic of the type of atom pair.23 For the intermolecular potential described by eq 11, Dlott et al.4 have used a simple method to estimate the ratio of B(V1)/B(V0), where V1 is the volume of the unit cell at pressure of P and V0 is the volume of the unit cell at P ) 0 GPa. For eq 11, recalling that {∂V(R)/∂R}|R)R0 ) 0, the cubic anharmonic potentials averaged over atom-atom pair can be written as Figure 2. The calculated energy transfer rates of RDX at 298 K: (a) in terms of calculated density of vibrational states and (b) in terms of inelastic neutron scattering data taken from ref 12.
contains many kinds of intermolecular potential functions such as Buckingham (eq 11) and Lennard-Jones potentials (eq 12), but also contains a variety of two-, three-, and four-body potentials for intramolecular potential. Thus it is suitable for the treatment of both inorganic and organic systems with fully flexible molecules.14,15 In the present calculations, we locate molecules based on covalent radii and retain all Coulomb interaction within the molecule, and then exclude the intramolecular Coulomb potentials. The minimized configurations at ambient pressure have been verified by phonon calculations that the first three vibrational frequencies are equal to zero and all of the other frequencies have positive values, indicating the existence of a local minimum. The flexible potentials, including both intra- and intermolecular potentials, have been given in our previous work.13 The intramolecular part of the potentials contains bond stretching, angle bending, out-of-plane bending, and torsional and nonbonded motion terms. The force constants of these terms were parametrized based on the ab initio or experimental vibrational frequencies of the molecules.13,16-22 The Buckingham exp-6 functions with Coulombic interactions were used for the intermolecular potentials of PETN, HMX, RDX, DMN, and NM, whereas the Lennard-Jones 6-12 potentials and hydrogen bonding potential with Coulombic interactions were applied for the intermolecular interactions in ANTA. IV. Results and Discussion On the basis of eq 10, the energy transfer rates can be evaluated by knowing the density of vibrational states and the cubic anharmonic coupling coefficient B. We compared the energy transfer rates of RDX in the present study and the results calculated in terms of inelastic neutron scattering data by Fried and Ruggiero.12 It is found that the shapes for these two rates are similar, as shown in Figure 2. A. Cubic Anharmonic Coupling Coefficient B. At ambient pressure, Fried and Ruggiero12 assumed that the anharmonic coupling per molecular volume is the same for all the compounds, this is equivalent to taking B ) VcB0/Z, where B0 is a constant. In the present study, B and B0 are calculated by using intermolecular potentials for each explosive. At high pressure, the cubic anharmonic coupling B increases with compression due to the decrease in intermolecular separation.4 For molecular crystals, the intermolecular potential is often approximated by following functions
∂3V(R) ∂R3
|
(R - R0)3 )
R)R0
AijBij exp(-BijR0)
(
)
56 - Bij2 (R - R0)3 (13) R02
An expression for the relative increase in cubic anharmonic coupling can be derived from the assumption of BijR0 ≈ 13 as follows4
〈V(3)(V1)〉 〈V (V0)〉 (3)
)
[ ( )][
R1 R1 exp 13 1 R0 R0
( )]
1 - 1.5 1 -
R1 R0
(14)
In the present study, we calculated the anharmonic coupling using eq 15. Here, we assumed that the value of {∂R3/ ∂Ψ1∂Ψ2∂Ψ3}|R0,{Ψ}0 is proportional to the averaged atom volume of Vc/NZ.
B)
1
∑
|
∂3V({Ψ})
6 Ψ ∂Ψ1∂Ψ2∂Ψ3
) {Ψ}0
1
∑ 6
∂3V(R)
∂R3
∂R3 ∂Ψ1∂Ψ2∂Ψ3
|
(15)
R0,{Ψ}0
For potentials in eqs 11 and 12, ∂3V(R)/∂R3 is given in eqs 16 and 17, respectively.
∂3V(R) 3
∂R
|
)
336Cij R0
R)R0
|
∂3V(R) ∂R
3
9
) R)R0
- AijBij3 exp(-BijR0)
336Eij R0
9
-
2184Dij R015
(16)
(17)
The calculated lattice energies and anharmonic coupling coefficients B and B0 at ambient pressure are given in Table 1. Because the anhamonic coupling coefficients are determined by the characteristic constants of Aij, Bij, Cij, Dij, and Eij, they are expected to be very sensitive to the potentials used. For different kind of potentials, the anhamonic coupling coefficients for the same molecule will be different. In our study, except for ANTA, Buckingham exp-6 functions with Coulombic interactions are used for the intermolecular potentials. As indicated by Table 1, the anharmonic coupling constants (B) are larger for the materials with higher lattice energy than those with lower lattice energy. The value of anharmonic coupling per molecular volume (B0) is -28.61, -22.85, -30.26, -25.35, -26.12, -23.70, -21.72, -20.91, and -23.24 kJ mol-1 Å-6
18518 J. Phys. Chem. B, Vol. 110, No. 37, 2006
Ye and Koshi
TABLE 1: Lattice Energies and Anharmonic Coupling Coefficients at Ambient Pressurea explosive
V(0)(R0)exp
V(0)(R0)cal
B
B0
NM DMN ANTA β-HMX RDX R-HMX δ-HMX PETN(I) PETN(II)
-52.3b -74.83c
-52.31 -74.14 -124.60 -180.29 -134.91 -179.30 -169.16 -157.08 -157.66
-1990.85 -2444.36 -3599.09 -6547.54 -5412.81 -6334.14 -6012.97 -6514.04 -7195.08
-28.61 -22.85 -30.26 -25.35 -26.12 -23.70 -21.72 -20.91 -23.24
-180.16d -135.06d -166.86e -156.95f
a Experimental and calculated lattice energies per molecule of V(0)(R0)exp and V(0)(R0)cal are in kJ/mol. Anharmonic coupling coefficients of B are in kJ mol-1 Å-3. B0 is in kJ mol-1 Å-6. b Data from ref 24. c Data from ref 25. d Data from ref 26. e Data from ref 27. f Data from ref 28.
Figure 4. The calculated two-phonon/vibron densities of states as a function of vibrational energy at 298 K: (a) NM; (b) DMN; (c) ANTA; (d) β-HMX; (e) RDX; (f) R-HMX; (g) δ-HMX; (h) PETN(II); (i) PETN(I).
Figure 3. The calculated density of vibrational states at 298 K, here ∫dωF(ω) ) 1 over all vibrational energy: (a) NM; (b) DMN; (c) ANTA; (d) β-HMX; (e) RDX; (f) R-HMX; (g) δ-HMX; (h) PETN(II); (i) PETN(I).
for NM, DMN, ANTA, β-HMX, RDX, R-HMX, δ-HMX, PETN(I), and PETN(II), respectively. B0 varies from -21 to 30 kJ mol-1 Å-6 for different materials. Beyond such small variation, B0 values can be roughly assumed to be the same. Our calculations are in agreement with Fried and Ruggiero’s
calculation, where they assumed that the anharmonic coupling per molecular volume is the same for all the compounds.12 Therefore the materials with smaller molecular volume will have weaker anharomic coupling (B). B. Energy Transfer Rates and Impact Sensitivity. The calculated density of vibrational states of the explosives studied is shown in Figure 3. The number of phonon and virbon modes at low vibrational energy of PETN, HMX, RDX, and ANTA is larger than that of DMN and NM, which implied that HMX, RDX, PETN, and ANTA should up-convert phonon energy much faster than DMN and NM. In addition, we also calculated two-phonon/vibron densities of states (F2(ωc)) using eq 19 for these explosives,
F2(ωc) )
9N2Z2 Vc2
∫dω F(ω) F(ωc - ω)
(19)
where the integral of F(ω) over all vibrational energies is equal to 1. Two-phonon/vibron densities of states (F2(ωc)) are shown in Figure 4. F2(ωc) for DMN and NM has many gaps. The
Energy Transfer Rates of Secondary Explosives
J. Phys. Chem. B, Vol. 110, No. 37, 2006 18519
Figure 6. Impact sensitivity plotted against the sum of energy transfer rates at 298 K.
Figure 5. The energy transfer rates as a function of vibrational energy at 298 K: (a) NM; (b) DMN; (c) ANTA; (d) β-HMX; (e) RDX; (f) R-HMX; (g) δ-HMX; (h) PETN(II); (i) PETN(I).
existence of gaps should be unfavorable to the energy transferring from phonons to vibrons, as pointed out by Fried and Ruggiero.12 Fried and Ruggiero12 suggested that the energy transfer rates were more closely related to sensitivity than the density of states alone. We evaluated the energy transfer rates by eq 10. This equation indicates that the energy transfer rates are determined not only by the density of vibrational states, but also by the density of explosives, the atom number per unit cell volume, the occupation number of phonons and vibrons, and the anharmonic coupling coefficients. Resulting energy transfer rates are shown in Figure 5. Energy transfer rates decrease quickly with increasing vibrational energy, which is due to the occupation number of the phonon or the vibron in eq 4 decreasing sharply with increasing energy of ω. Many gaps also exist in the energy transfer rates of DMN and NM. We calculated the sum of the energy transfer rates and found that the order of the sum is PETN(II) ≈ δ-HMX > R-HMX ≈ PETN(I) > RDX > β-HMX . ANTA > NM > DMN. The energy transfer rates in the HMX polymorph are in the order of δ-HMX > R-HMX > β-HMX. The order is in agreement with the experimental stability found by McCrone.29 The energy transfer rates of
PETN(I), PETN(II), δ-HMX, R-HMX, RDX, and β-HMX are several times faster than that of ANTA, DMN, and NM. It has been shown that the impact sensitivities correlated with energy transfer rates between phonons and vibrons.12,30,31 We plotted the sum of energy transfer rates over all frequencies against the impact sensitivity in Figure 6. The impact sensitivity is defined as (H50)-1, where H50 is the 50% explosion height. The values of H50, taken from ref 32, were measured at LANL and/or NSWC with the Bruceton method.32 Impact sensitivity data of liquid NM were roughly used for the crystalline NM. It appears that a good correlation exists between energy transfer rates and impact sensitivities, which suggests the energy transfer rate in secondary explosive crystals is a significant factor in their sensitivity. The correction between vibrational energy transfer and sensitivities has been pointed out in previous publications,12,30,31 but the reason for this correlation is still unknown. Usually, the sensitivity is strongly affected by the way they are processed and method used for the measurements. Nevertheless, the drop hammer sensitivity can be representative of the essential sensitivity of the secondary explosive molecules. To design a new explosive, high performance (having high detonation velocity) coupled with low sensitivity must be considered. For a given performance, the lower the sensitivity is, the better the explosive is. The present study indicates that a lower sensitivity can be obtained by decreasing the energy transfer rates. An approach to decreasing the energy transfer rates is to increase the vibrational frequencies resulting in a large gap between phonons and vibrational frequencies. Usually, the vibrational frequencies are given by ν ) 1/2πxk/m, where k is the force constant, therefore increasing the force constant by introducing a double bond or hydrogen bonds into the molecules can increase the vibrational frequencies and further decrease the sensitivity. Another method to decrease the energy transfer rates is to increase the density of explosives by designing cagedstructure molecules. The caged-structure compound of 4,10dinitro-2,6,8,12-teroaxo-4,10-diazatetracyclo[5.5.0.0 5,9.03,11]dodecane reported by Boyer et al.33 has been investigated as an insensitive energetic material. Its surprisingly high density of 1.99 g/cm2 is attributed to the caged structure.34-36 V. Conclusions We have performed the calculations of the energy transfer rates in energetic materials of PETN(I), PETN(II), δ-HMX, R-HMX, RDX, β-HMX, ANTA, DMN, and NM using intraand intermolecular potential energy surfaces. The energy transfer rates as a function of vibrational energy are evaluated in terms of the density of vibrational states and anharmonic coupling.
18520 J. Phys. Chem. B, Vol. 110, No. 37, 2006 The results suggest that energy transfer rates have a good correlation with the impact sensitivity of explosives and the energy transfer rates are several times faster for PETN(I), PETN(II), HMX(R, β, δ), and RDX than ANTA, DMN, and NM. The order of the energy transfer rates in HMX polymorphs is δ-HMX > R-HMX > β-HMX and it is in agreement with the experimental stability found by McCrone.29 Our results suggest the energy transfer rate in secondary explosive crystals is a significant factor in their sensitivity, and introduction of a double bond, or hydrogen bonds, or a caged structure into secondary explosives is expected to decrease the sensitivity. Acknowledgment. This work was supported by Special Coordination Funds for Promoting Science and Technology (Research and Development program for Resolving Critical Issues; Development of integration system of detection and treatment of explosives for antiterrorism act) from the Japan Ministry of Education, Culture, Sports, Science and Technology. References and Notes (1) Coffey, C. S.; Toton, E. T. J. Chem. Phys. 1982, 76, 949. (2) Walker, F. E. J. Appl. Phys. 1988, 63, 5548. (3) Dlott, D. D.; Fayer, M. D. J. Chem. Phys. 1990, 92, 3798. (4) Tokmakoff, A.; Fayer, M. D.; Dlott, D. D. J. Phys. Chem. 1993, 97, 1901. (5) Tarver, C. M. J. Phys. Chem. A 1997, 101, 4845. (6) Ye, S.; Tonokura, K.; Koshi, M. J. Jpn. Explos. Soc. 2002, 63, 49. (7) Ye, S.; Tonokura, K.; Koshi, M. Chem. Phys., 2003, 293, 1. (8) Panero, C.; Bini, R.; Schettino, V. J. Chem. Phys. 1994, 100, 7938. (9) Califano, S.; Schettino, V.; Neto, N. Lattice dynamics of molecular crystals; Berthier, G., et al. Eds.; Springer Series on Lecture Notes in Chemistry 26; Springer: Berlin, Germany, 1981. (10) McGrane, S. D.; Shreve, A.P. J. Chem. Phys. 2003, 119, 5834. (11) McGrane, S. D.; Barber, J.; Quenneville, J. J. Phys. Chem. A 2005, 109, 9919.
Ye and Koshi (12) Fried, L. E.; Ruggiero, A. J. J. Phys. Chem. 1994, 98, 9786. (13) Ye, S.; Tonokura, K.; Koshi, M. J. Jpn. Explos. Soc. 2002, 63, 104. (14) Gale, J. D. J. Chem. Soc., Faraday Trans. 1997, 93, 629. (15) Gale, J. D. Philos. Mag. B 1996, 73, 3. (16) Weiner, S. J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A. J. Comput. Chem. 1986, 7, 230. (17) Smith, G. D.; Bharadwaj, R. K. J. Phys. Chem. B 1999, 103, 3570. (18) Chambers, C. C.; Thompson, D. L. J. Phys. Chem. 1995, 99, 15881. (19) Wallis, E. P.; Thompson, D. L. J. Chem. Phys. 1993, 99, 2661. (20) Sorescu, D. C.; Bennett, C. M.; Thompson, D. L. J. Phys. Chem. A 1998, 102, 10348. (21) Kohno, Y.; Ueda, K.; Imamura, A. J. Phys. Chem. 1996, 100, 4701. (22) Sorescu, D. C.; Rice, B. M.; Thompson, D. L. J. Phys. Chem. B 2000, 104, 8406. (23) Kitaigorodsky, A. I. Molecular Crystal and molecules; Academic Press: New York, 1973. (24) Chickos, J. S. In molecular Structure and Energetics; Liebman, J. F., Greenberg, A., Eds.; VCH Publishers Inc.: New York, 1987; Vol. 2. (25) Bradley, R. S.; Cotson, S.; Cox, E. G. J. Chem. Soc. 1952, 740. (26) Rosen, J. M.; Dickinson, C. J. J. Chem. Eng. Data 1969, 14, 120. (27) Tayor, J. W.; Crookes, R. J. J. Chem. Soc., Faraday Trans. 1 1976, 72, 723. (28) Olinger, B.; Halleck, P. M.; Cady, H. H. J. Chem. Phys. 1975, 62, 4480. (29) McCrone, W. C. In Physics and Chemistry of the Organic Solid State; Fox, D., Labes, M. M., Wessberger, A., Eds.; Wiley: New York, 1965; Vol. II, pp 726-766. (30) McNesby, K. L.; Coffey, C. S. J. Phys. Chem. B 1997, 101, 3097. (31) Ye, S.; Tonokura, K.; Koshi, M. Combust. Flame 2003, 132, 240. (32) Storm, C. B.; Stine, J. R.; Kramer, J. F. Chemistry and Physics of Energetic Materials; Bulusa, S. N., Ed.; Kluwer Academic: Boston, MA, 1990; pp 606-639. (33) Vayalakkavoor, R. T.; Vedachalam, M.; Boyer, J. H. Heterocycles 1990, 31, 479. (34) Agrawal, J. P. Prog. Energy Combust. Sci. 1998, 24, 1. (35) Fried, L. E.; Manaa, M. R.; Pagoria, P. F.; Simpson, R. L. Annu. ReV. Mater. Res. 2001, 31, 291. (36) Pagoria, P. F.; Lee, G. S.; Mitchell, A. R.; Schmidt, R. D. Thermochim. Acta 2002, 384, 187.
