ARTICLE pubs.acs.org/JPCA
On the Shock Sensitivity of Explosive Compounds with Small-Scale Gap Test Bisheng Tan,*,†,‡ Xinping Long,*,‡,§ Rufang Peng,† Hongbo Li,† Bo Jin,† and Shijin Chu† †
State Key Laboratory Cultivation Base for Nonmetal Composites and Functional Materials, Southwest University of Science and Technology, Mianyang, People's Republic of China 621010 ‡ School of Mechano-Electronic Engineering, Beijing Institute of Technology, Beijing, People's Republic of China 100081 § China Academy of Engineering Physics, Mianyang, People's Republic of China 621900 ABSTRACT: In this work an improved set of small-scale gap tests was applied to measure the shock sensitivity of 13 explosive compounds, and a MnCu manometer was also employed to measure the output pressures of shock waves passed through aluminum gaps with different thicknesses to draw a standard curve. The critical initiation thicknesses of aluminum gaps of different explosive compounds (244 shots in total) were treated according to statistical method, and the Mulliken charges of nitro groups, bond dissociation energies of X-NO2 (X = C, N), resonance energies, and ring strain energies of these explosive compounds were calculated with the means of DFT/BLYP/DNP calculations and homodesmotic reactions designs. Genetic function approximation was used to construct a relationship between the critical initiation thicknesses of aluminum gaps of different explosive compounds and their forementioned molecule structural parameters.
1. INTRODUCTION Shock sensitivity is a more stable and reliable index of safety usage of explosives than impact sensitivity.1 Compared with impact, shock is a kind of mechanical force with shorter time of duration (90% TMD will lead to an imperfect pillar because it is too brittle to connect). After purification and compression of 13 explosive compounds as acceptors, including RDX, TNAZ, TATB, NTO, BTF, 2,4-DNI, HMX, TNT, NQ, MeNQ, ketoRDX, FOX-7, and LLM-105 (the names are shown in the Glossary), 300 or so pillars of acceptor explosives and 600 pillars of RDX acceptor explosives were manufactured. We measured the thickness (x) of aluminum gaps with the calibrated set in terms of “go” or “no go” for the tested explosive pillars, and the measurement of shock sensitivities of 13 explosive compounds was finished and shown in Tables 2 and 3. The thickness (x) values of aluminum gaps were treated according to eq 1 ts μ ¼ x̅ ( pffiffiffi n
ð1Þ
where x, t, s, and n denote average thickness of aluminum gap, confidence level, standard deviation, and test number, respectively. μ50% and μ95% (Tables 2 and 3) denote the 10611
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Table 2. Detonation (Go or No Go) Results under Different Thickness of Aluminum Gaps and the Statistical Analysis of These Data (Part 1) n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 x μ50% μ95%
K6 √ 13.55√ 14.75√ 15.08 16.06 √ 15.58 15.90 √ 15.73√ 15.92√ 15.92 16.27 15.91√ 13.68/√ 13.74/√ 13.72/√ 13.91/√ 13.96/ 13.75/ √ 12.81/√ 13.36/√ 13.75/ 13.83/ 13.39/ — — — — — — — 14.57 14.57 ( 0.16 14.57 ( 0.50
2,4-DNI √ 2.10√ 4.16√ 6.27√ 8.27 12.38 10.80 √ 9.47 10.39 9.62 9.37 9.12 √ 9.03 9.26 — — — — — — — — — — — — — — — — 8.48 8.48 ( 0.54 8.48 ( 1.72
Fox-7 √ 8.40√ 8.86√ 8.97√ 9.31 12.37 10.80 9.98 9.69 √ 9.44√ 9.71 9.76 √ 9.20 9.77√ 8.47/√ 8.54/√ 8.54/√ 8.57/√ 8.90/ 8.55/ 8.61/ 9.06/ 9.47/ √ 8.53/√ 5.32/√ 7.50/ 8.88/ √ 7.87/√ 8.50/ — 8.98 8.98 ( 0.15 8.98 ( 0.44
TNAZ √ 13.10√ 13.38√ 14.78 16.05 15.04 √ 14.95√ 15.10√ 14.92√ 15.09 15.71 √ 15.22 15.52 √ 14.97 √ 12.96/√ 13.21/√ 13.41/√ 13.47/√ 13.91/√ 13.96/ 14.13/ 14.83/ 13.70/ √ 13.06/ 13.30/ 13.06/ 12.76/ — — — 14.22 14.22 ( 0.13 14.22 ( 0.38
LLM-105 √ 7.80 8.03 √ 7.77 8.00 7.62 √ 7.50√ 7.96√ 8.1 8.42 8.57 8.00/ √ 8.02/ 8.18/ √ 8.21/ 8.29/ 8.30/ 8.39/ 8.53/ √ 5.30/√ 7.51/ 8.43/ 8.06/ √ 7.71/ — — — — — — 7.95 7.95 ( 0.10 7.95 ( 0.28
NTO √ 2.17√ 1.95√ 1.83√ 2.46√ 2.40√ 2.28 2.99 √ 2.28 3.00 2.88 √ 2.94 √ 2.13/√ 2.13/√ 2.26/√ 2.38/√ 2.38/ 2.42/√ 2.51// 2.54/ 5.33/ 2.13/ √ 0.96/√ 1.44/√ 1.81/ — — — — — 2.40 2.40 ( 0.11 2.40 ( 0.31
BTF √ 9.29√ 9.64 √ 10.40√ 11.93√ 12.44√ 9.61 √ 10.23√ 11.05 14.18 √ 12.93 13.57 √ 9.57/√ 9.76/√ 9.96/ √ 10.16/√ 10.67/ 11.28/ 13.47/ 10.96/ 9.79/ √ 8.04/√ 9.26/ 9.66/ — — — — — — 10.78 10.78 ( 0.23 10.78 ( 0.70
Table 3. Detonation (Go or No Go) Results under Different Thicknesses of Aluminum Gaps and the Statistical Analysis of These Data (Part 2) n 1
HMX 14.91/ √
2
11.69/
3
13.25/
4
12.56/
5 6 7 8 9
11.62/ √
11.12/
√ 11.62/ 12.19/
14
11.89/ √ 11.68/ √ 11.82/ √ 11.82/ √ 12.17/ √ 12.23/
15 16
12.35/ 12.45/
10 11 12 13
NQ √ 0.5/ 1.5/ √ 1.0 √ 1.0 1.5/ √ 1.0
TNT
RDX √ 10.50
8.36/ √
7.43/
12.88
7.78/ √ 7.91/ √ 8.49/ √ 8.90/ √ 9.03/ 9.32/
11.99 √ 11.17 √ 11.47
1.5/ 1.5/ √ 1.41/
9.32/
1.82/
9.50/
11.84
MeNQ √ 0.42/ √ 0.95/ 1.0/
5.15
1.29/
4.65 √ 4.21
—
— — —
—
12.27
4.34 4.40 √ 4.25 √ 4.72 √ 4.66
—
—
5.36
—
—
—
4.61
—
—
—
—
—
— —
— —
— —
— —
2.08/
11.62 √ 11.33 √ 11.60 √ 11.77
TATB √ 0.94 √ 2.13 √ 4.09
— — —
x
12.21
1.35
8.60
11.68
4.12
0.92
μ50%
12.21 ( 0.15
1.35 ( 0.10
8.60 ( 0.16
11.68 ( 0.13
4.12 ( 0.24
0.92 ( 0.14
μ95%
12.21 ( 0.48
1.35 ( 0.30
8.60 ( 0.52
11.68 ( 0.41
4.12 ( 0.76
0.92 ( 0.58
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BTF is a kind of explosive compound without a nitro group, but there are three furazan rings in its molecular structure, and its strain energy can be solved in terms of homodesmotic reactions 7 and 8.
Figure 4. The critical thickness estimation of aluminum gaps of different explosives under 95% confidence level.
estimators according to the 50% and 95% confidence levels, respectively. The thickness estimators of aluminum gap under 95% confidence level are shown in Figure 4.
4. CONSTRUCTING A RELATIONSHIP BETWEEN THE SHOCK-INITIATED MODEL AND THE MOLECULAR STRUCTURES OF EXPLOSIVE COMPOUNDS All of the electronic structure calculations were performed using the DMol318,19 numerical-based density-functional computer software implemented in the Materials Studio Modeling 3.0 package20 distributed by Accelrys, Inc. Geometrical optimizations were obtained by using the BLYP21,22 general-gradient potential approximation in conjunction with the double-numerical plus polarization basis set, which was denoted as DNP. There are resonance structures in TNT, TATB, LLM105, 2,4DNI, and BTF;, the strain energies2328 were calculated in terms of homodesmotic reactions 3,6. NTO is also an experimentally studied explosive compound in this work; there is originally no resonance structure (I), but it can tautomerize with II or III. The tautomerizm phenomenon was shown in Figure 5, II is the advantageous structure, its strain energy can be calculated according to homodesmotic reaction 2.
The homodesmotic reactions 2,8 include both strain energies and resonance energies, because the double bonds (CdC or CdN) are separated and resonance structures are destroyed. It is not surprising that the strain energies of NTO, TNT, TATB, and LLM105 are positive; resonance energies play positive major roles in strain energies; on the contrary, resonance energies play a secondary role in 2,4-DNI and BTF. There are no resonance structures in TNAZ, RDX, K6, and HMX, and their string strain energies can be computed via the designs of homodesmotic reactions 912
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negative, resonance energies are positive for the ring-shaped explosive compounds which were included in ring strain energies, and zero for the aliphatic series explosive compounds, such as NQ, MeNQ, and Fox-7, because there are neither ring strain nor resonance structures (Figure 6). BTF is not considered in the calculation because there is no nitro group in its molecule structure. The relevant parameters are shown in Table 4. Genetic function was originally created by Holland.29 Under the enlightenment of Darwinian Theory, the natural evolution process “Heredity f Variation f Survival of the fittest” was computationally simulated to search the optimum solution, that is, a series of parameters to be optimized are arranged in proper sequence and regarded as a chromosome, and each parameter is a genetic gene of the chromosome. The propagation is controlled by various genetic manipulations, the best chromosome is eventually gained through eliminating the poor ones and retaining the good ones, and it means a global optimum is achieved. The relative parameters being regarded as genetic genes of the chromosome; genetic manipulations were performed according to default values of the “Statistics” module of the executable program Materials Studio 3.0. The calculated and experimental values were shown in Table 5. In table 5, xexp and xcal denote average thickness of aluminum gap and the calculated value in terms of genetic function approximation, respectively, and Figure 7 shows their relations. According to Figure 7, except NQ and RDX, the relation of the calculated values in terms of genetic function approximation and the experimental values are approximately linear; this indicates genetic function approximation is powerful in prediction, and the expression is shown in eq 13.
Formulas qNO2 = qN + qO1 + qO2 and ED = E(•NO2) + E(•X) E(XNO2) were employed to calculate Mulliken charges of nitro groups and bond dissociation energies of X-NO2 (X = C, N) of the above explosive compounds, respectively. Genetic function approximation was applied to construct a relationship between the shock sensitivities (in Tables 2 and 3) and ring strain energies, (average) Mulliken charges of nitro groups, and bond dissociation energies of X-NO2 (X = C, N) of the above explosive compounds, where the values of the ring strain energies are
Figure 5. Molecular tautomerism structures schematic diagram of NTO.
^ ðX3 þ 193:364389917Þ x̅ cal ¼ 0:127377470 R ^ ð 0:270732694-X1 Þ þ 52:773070186 R ^ ð1:584948219 X3 Þ 7:078289705 R ^ ð0:371743279 X3 Þ þ 7:029009676 R þ 34:973159436
Figure 6. The structures of Fox-7, NQ, and MeNQ.
ð13Þ
Table 4. Mulliken Charges of Nitro Groups qNO2,max(e), Average Mulliken Charges of Nitro Groups qNO2(e), Bond Dissociation Energies of X-NO2 (X = C, N) ED, Ring Strain EnergiesES of the Tested Explosive Compounds qNO2,max(e)
ED (kJ/mol)
qNO2(e)
ES (kJ/mol)
TNT
0.281
0.285
260.9
22.2
TNAZ
0.131
0.161
178.0
152.6
TATB RDX
0.465 0.105
0.465 0.142
356.7 170.1
124.5 109.6 155.1
HMX
0.098
0.134
171.6
Fox-7
0.370
0.370
304.0
0
NTO
0.304
0.304
290.8
86 38.2
LLM-105
0.340
0.340
277.1
NQ
0.265
0.265
243.9
0
MeNQ
0.295
0.295
266.9
0
2,4-DNI keto-RDX
0.318 0.029
0.318 0.040
291.3 151.2
Figure 7. Curve fitting of calculated critical thickness of aluminum gaps and experimental ones of the tested explosive compounds, correlation coefficient R = 0.966.
52.7 240.2
Table 5. Comparison of Calculated Critical Thickness of Aluminum Gaps and Experimental Ones of the Tested Explosive Compounds MeNQ
NQ
NTO
TATB
LLM-105
TNT
2,4-DNI
Fox-7
HMX
RDX
TNAZ
keto-RDX
xexp (mm)
0.92
1.35
2.40
4.12
7.95
8.60
8.48
8.98
12.21
11.68
14.22
14.57
xcal(mm)
3.01
1.74
1.14
4.74
9.13
8.06
8.35
6.98
13.85
10.30
13.65
14.53
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The Journal of Physical Chemistry A Where X1 = qNO2,max(e), X3 denotes ring strain energies. X2, a parameter relating to average Mulliken charges of nitro groups, and X3, bond dissociation energies of X-NO2 (X = C, N), were eliminated in the course of the genetic manipulation approxima^ is an operator, namely, ramp function.30 When the natural tion. R evolution process “Heredity f Variation f Survival of the fittest” was finished, q NO 2,max(e) and ring strain energy were filtered to be good genetic genes of the explosives. The genetic function approximation calculations indicated that Mulliken charges of nitro groups and ring strain energy may play important roles in the determination of shock sensitivies of explosive compounds. Qualitatively, the more negative the Mulliken charges of nitro groups is and the fewer the value of ring strain energy, the lower the shock sensitivity of an explosive compound exhibits.
5. CONCLUSIONS Shock-initiated aluminum gap critical thickness values of 13 explosive compounds were measured with the improved smallscale gap test set, and the explosive pillars were counted up to 224. According to the experimental results, the proper order of the shock sensitivity is: MeNQ < NQ < NTO < TATB < LLM105
