Journal of Thermal Analysis and Calorimetry

, Volume 103, Issue 2, pp 569–575

Thermal behavior and thermal safety on 3,3-dinitroazetidinium salt of perchloric acid

Authors

    • School of Chemical Engineering/Shaanxi Key Laboratory of Physico-Inorganic ChemistryNorthwest University
  • B. Yan
    • School of Chemical Engineering/Shaanxi Key Laboratory of Physico-Inorganic ChemistryNorthwest University
    • School of Chemistry and Chemical EngineeringYulin University
  • Y. H. Ren
    • School of Chemical Engineering/Shaanxi Key Laboratory of Physico-Inorganic ChemistryNorthwest University
  • Y. Hu
    • School of Chemical Engineering/Shaanxi Key Laboratory of Physico-Inorganic ChemistryNorthwest University
  • Y. L. Guan
    • School of Chemical Engineering/Shaanxi Key Laboratory of Physico-Inorganic ChemistryNorthwest University
  • F. Q. Zhao
    • Xi’an Modern Chemistry Research Institute
  • J. R. Song
    • Department of Conservation TechnologyThe Palace Museum
    • School of Chemical Engineering/Shaanxi Key Laboratory of Physico-Inorganic ChemistryNorthwest University
  • R. Z. Hu
    • Xi’an Modern Chemistry Research Institute
Article

DOI: 10.1007/s10973-010-0950-2

Cite this article as:
Ma, H.X., Yan, B., Ren, Y.H. et al. J Therm Anal Calorim (2011) 103: 569. doi:10.1007/s10973-010-0950-2

Abstract

3,3-Dinitroazetidinium (DNAZ) salt of perchloric acid (DNAZ·HClO4) was prepared, it was characterized by the elemental analysis, IR, NMR, and a X-ray diffractometer. The thermal behavior and decomposition reaction kinetics of DNAZ·HClO4 were investigated under a non-isothermal condition by DSC and TG/DTG techniques. The results show that the thermal decomposition process of DNAZ·HClO4 has two mass loss stages. The kinetic model function in differential form, the value of apparent activation energy (Ea) and pre-exponential factor (A) of the exothermic decomposition reaction of DNAZ·HClO4 are f(α) = (1 − α)−1/2, 156.47 kJ mol−1, and 1015.12 s−1, respectively. The critical temperature of thermal explosion is 188.5 °C. The values of ΔS, ΔH, and ΔGof this reaction are 42.26 J mol−1 K−1, 154.44 kJ mol−1, and 135.42 kJ mol−1, respectively. The specific heat capacity of DNAZ·HClO4 was determined with a continuous Cp mode of microcalorimeter. Using the relationship between Cp and T and the thermal decomposition parameters, the time of the thermal decomposition from initiation to thermal explosion (adiabatic time-to-explosion) was evaluated as 14.2 s.

Keywords

3,3-Dinitroazetidine (DNAZ)HClO4Thermal behaviorThermal safety

Introduction

Highly nitrated small-ring heterocycles are good candidates for energetic materials (EMs) because of the increased performance from the additional energy release upon opening of the strained ring system during decomposition [1]. Azetidine-based explosives, such as 1,3,3-trinitroazetidine (TNAZ) [2, 3] demonstrate excellent performance partly because of the high strain associated with the four-membered ring. As one of the important derivates of TNAZ, 3,3-dinitroazetidine (DNAZ, pKb = 6.5) [3, 4] can prepare a variety of solid energetic DNAZ salts with high oxygen-balance [3, 511]. In this study, the energetic salt of DNAZ with perchloric acid (HClO4) was synthesized, its thermal behavior was studied by DSC and TG/DTG techniques, and the non-isothermal kinetics was determined by means of Kissinger method, Ozawa method, the differential method, and the integral method. The specific heat capacity was determined with a continuous Cp mode of microcalorimeter (Micro-DSCIII). The adiabatic time-to-explosion was also estimated for evaluating the safety performance of DNAZ·HClO4.

Experimental

Materials

DNAZ·HClO4 used in this study was prepared according to the following method: an appropriate amount of HClO4 was put into methanol, which was then stirred and the same equimolar of DNAZ was added to the above solution at room temperature, stirred for 2 h. The white precipitate was collected by filtration. Single crystal suitable for X-ray measurement was obtained by slow evaporation in methanol for 15 days. The structure was characterized by elemental analyses, IR spectrometry and nuclear magnetic resonance spectrometry. Anal. Calcd (%): N 16.97, C 14.56, H 2.443, found (%): N 17.21, C 14.23, H 2.456. 1HNMR (CD3OD, TMS) (δ/ppm): 5.108(s, 4H), 3.320 (s, 2H). 13CNMR (CD3OD, TMS) (δ/ppm): 44.979(C-2,4), 97.653(C-3). IR(KBr, cm−1): \( \nu_{\text{NH}}^{s} \) = 3074.75, \( \nu_{{{\text{CH}}_{ 2} }}^{{\alpha {\text{s}}}} \) = 3006.07, \( \nu_{{{\text{NH}}_{ 2}^{ + } }}^{\text{S}} \) = 2657.24–2409.56, \( \nu_{{{\text{NO}}_{ 2} }}^{{\alpha {\text{s}}}} \) = 1588.87, \( \nu_{{{\text{NO}}_{ 2} }}^{\text{s}} \) = 1339.22, \( \nu_{{{\text{ClO}}_{ 4}^{ - } }} \) = 1071.12. The sample was kept in a vacuum desiccator before use.

Experimental equipments and conditions

The elemental analysis was measured on a PE-2400 Elemental Analytical instrument (Perkin-Elmer, USA) and IR on a Nicolet 60 SXR FT-IR (Nicolet, USA) spectrometer in the 4,000–400 cm−1 region using KBr pellets. 1H-NMR and 13C-NMR spectra were recorded on an INOVA-400 NMR (VARIAN, USA) spectrometer using CD3OD as the solvent.

X-ray intensities were recorded at room temperature on Bruker SMART APEX CCD X-ray diffractometer using MoKα radiation (λ = 0.071073 nm) graphite monochromation. In the range of 2.76° < θ < 25.10°, −8 < h < 9, −13 < k < 12, −12 < l < 15, 1492 independent reflections were obtained. The final conventional R1 is 0.1627 and ωR (unit weight) is 0.4199 for 892 observable independent reflections with reflection intensity I > 2σ(I). The structure was solved by the direct methods (SHELXTL-97) and refined by the full-matrix-block least-squares method on F2 with anisotropic thermal parameters for all non-hydrogen atoms. The hydrogen atoms were added according to the theoretical models.

The crystal structure is monoclinic with space group P2(1)/n. Crystal data: a = 0.7779(4) nm, b = 1.0925(6) nm, c = 1.2663(5) nm, β = 127.67(2)°, V = 0.8518(8) nm3, Dc = 1.930 gcm−3, Z = 4, F(000) = 504, μ = 0.486 mm−1. The analytical results indicate that the formula of the molecule is C3N3O4H6+ClO4, which is made up of a cation C3N3O4H6+ (DNAZ+) and an anion ClO4. The molecular structure and atom labeling are shown in Fig. 1.
https://static-content.springer.com/image/art%3A10.1007%2Fs10973-010-0950-2/MediaObjects/10973_2010_950_Fig1_HTML.gif
Fig. 1

Molecular structure of DNAZ·HClO4

Thermal decomposition condition

The DSC and TG-DTG experiments for DNAZ·HClO4 were performed using a model Q600SDT (TA, USA) under a nitrogen atmosphere, at a flow rate of 100 mL min−1 with the sample mass of about 0.935 mg. The heating rates used were 2.5, 5.0, 10.0, and 15.0 °C min−1 from ambient temperature to 500 °C. The temperature and heat were calibrated using pure indium and tin particles. The DSC and TG-DTG curves obtained under the same conditions overlap with each other, indicating that the reproducibility of tests was satisfactory.

The determination of the specific heat capacity

The specific heat capacity of DNAZ·HClO4 was determined by a continuous Cp mode within 283–353 K at a heating rate of 0.15 K min−1 on Micro-DSCIII (Seteram, France) with the sample mass of 320.60 mg. The Micro-calorimeter was calibrated with α-Al2O3 (calcined), its mathematical expression is Cp (Jg−1 K−1) = 0.1839 + 1.9966 × 10−3 T within 283 to 353 K and the standard heat capacity \( C_{\text{p,m}}^{\Uptheta } (\alpha - {\text{Al}}_{ 2} {\text{O}}_{ 3} ) \)at 298.15 K was determined as 79.44 J mol−1 K−1 which is in an excellent agreement with the value reported in the literature [12] (79.02 J mol−1 K−1).

Results and discussion

Thermal behavior and analysis of kinetic data for the exothermic main decomposition reaction of DNAZ·HClO4

Typical DSC and TG-DTG curves for DNAZ·HClO4 are shown in Figs. 2 and 3. The DSC curve indicates that the thermal decomposition of DNAZ·HClO4 is composed of one exothermic process with a peak temperature of 200.84 °C. However, the TG-DTG curves show two stages of mass loss processes. The first stage begins at about 165.81 °C and completes at 233.92 °C with a mass loss of 79.33% and the second stage begins at 233.92 °C and completes at 387.17 °C with a mass loss of 18.59%.
https://static-content.springer.com/image/art%3A10.1007%2Fs10973-010-0950-2/MediaObjects/10973_2010_950_Fig2_HTML.gif
Fig. 2

DSC curve of DNAZ·HClO4 at 10 °C/min

https://static-content.springer.com/image/art%3A10.1007%2Fs10973-010-0950-2/MediaObjects/10973_2010_950_Fig3_HTML.gif
Fig. 3

TG/DTG curves of DNAZ·HClO4 at 10 °C/min

In order to obtain the kinetic parameters [apparent activation energy (Ea) and pre-exponential factor (A)] of the exothermic main decomposition reaction for DNAZ·HClO4, three model-free isoconversional methods (Eqs. 13) were employed. These methods are as follows.

Differential method

Kissinger equation [13]
$$ {\frac{{{\text{dln}}{\frac{\beta }{{T_{\text{p}}^{ 2} }}}}}{{{\text{d}}{\frac{ 1}{{T_{\text{p}} }}}}}} = - {\frac{{E_{\alpha } }}{R}} $$
(1)

Integral method

Flynn–Wall–Ozawa (F–W–O) equation [14]
$$ \lg \beta + {\frac{{ 0. 4 5 6 7E_{\alpha } }}{RT}} = C $$
(2)
integral isoconversional non-linear [NL-INT] equation [15]
$$ \left| {\sum\limits_{i}^{n} {\sum\limits_{j \ne i}^{n} {{\frac{{\beta_{j} I\left( {E_{\alpha } ,T_{\alpha ,i} } \right)}}{{\beta_{i} I\left( {E_{\alpha } ,T_{\alpha ,j} } \right)}}} - n\left( {n - 1} \right)} } } \right| = \min $$
(3)
where α is the conversion degree, T is the absolute temperature, Eα is the apparent activation energy, β is the heating rate, R is the gas constant, Tp is the peak temperature of DSC curve, and A is the pre-exponential factor.
From the original data in Table 1, Eα obtained by the Kissinger [13] method is determined to be 154.44 kJ mol−1. The pre-exponential constant (A) is 1015.12 s−1. The linear correlation coefficient (rk) is 0.9978. The value of Eα obtained by Ozawa’s method [14] is 154.26 kJ mol−1 and the value of ro is 0.9980. The value of Eoe obtained by Tei vs. βi relation is 164.32 kJ mol−1. The value of roe is 0.9991.
Table 1

Values of the kinetic parameters for the exothermic decomposition reaction for DNAZ·HClO4 calculated from the DSC curves at various heating rates and a flowing rate of N2 gas of 100 ml/min

β/°C min−1

Te/°C

Eoe/kJ mol−1

roe

Tp/°C

Ek/kJ mol−1

log(Ak/s−1)

rk

Eo/kJ mol−1

ro

2.5

177.90

164.32

0.9991

185.06

154.44

15.12

0.9978

154.26

0.9980

5.0

185.55

191.75

10.0

192.09

200.84

15.0

196.27

204.58

Mean: Eo = (164.32 + 154.44 + 154.26)/3 = 157.67 kJ mol−1

αβ, heating rate; Te, onset temperature in the DSC curve; Tp, maximum peak temperature; E, apparent activation energy; A, pre-exponential constant; r, linear correlation coefficient; subscript k, data obtained by Kissinger’s method, subscript o, data obtained by Ozawa’s method. Eoe means the activation energy obtained by Te through Ozawa’s method and roe is the corresponding linear correlation coefficient

By substituting the original data, βi, T0i, Ti, αi, and (dα/dT)i, i = 1,2,…,n, tabulated in Table 2 from TG-DTG curves into Eqs. 2 and 3, the values of Eα for any given value of α in Table 2 are obtained. The average value of Eα in the α range of 0.375–0.925 in Fig. 4 is in good agreement with the calculated values obtained by Kissinger’s method and Ozawa’s method. The E values calculated using Eqs. 2 and 3 were used to check the validity of activation energy by other methods.
Table 2

Data of DNAZ·HClO4 determined by TG at different heating rates and apparent activation energies (Ea) of thermal decomposition obtained using isoconversional methods

Data point

\( \alpha \)

T2.5/K

T5/K

T10/K

T15/K

ENL-INT/kJ mol−1

EF–W–O/kJ mol−1

1

1.000

470.44

484.97

507.11

488.20

69.26

73.16

2

0.975

459.13

469.05

482.30

478.66

123.54

124.65

3

0.950

458.83

466.14

475.01

477.66

158.88

158.26

4

0.925

458.72

465.58

474.36

477.30

161.50

160.83

5

0.900

458.59

465.26

474.09

477.03

162.33

161.62

6

0.875

458.46

465.02

473.86

476.80

162.62

162.23

7

0.850

458.31

464.80

473.64

476.58

163.41

162.64

8

0.825

458.15

464.61

473.43

476.38

163.68

162.90

9

0.800

457.97

464.42

473.21

476.18

163.84

163.04

10

0.775

457.79

464.23

472.98

475.98

164.05

163.24

11

0.750

457.60

464.04

472.75

475.77

164.23

163.41

12

0.725

457.40

463.85

472.52

475.55

164.39

163.56

13

0.700

457.19

463.66

472.27

475.33

164.57

163.72

14

0.675

456.97

463.47

472.01

475.10

164.76

163.90

15

0.650

456.75

463.27

471.75

474.86

164.99

164.11

16

0.625

456.53

463.06

471.48

474.62

165.23

164.34

17

0.600

456.3

462.85

471.20

474.37

165.49

164.59

18

0.575

456.06

462.63

470.91

474.10

165.81

164.89

19

0.550

455.82

462.40

470.60

473.82

166.27

165.31

20

0.525

455.57

462.17

470.29

473.51

166.82

165.84

21

0.500

455.32

461.93

469.97

473.20

167.40

166.38

22

0.475

455.05

461.69

469.62

472.89

167.94

166.89

23

0.450

454.78

461.43

469.27

472.56

168.55

167.47

24

0.425

454.5

461.16

468.89

472.19

169.47

168.34

25

0.400

454.21

460.88

468.5

471.77

170.65

169.46

26

0.375

453.91

460.59

468.10

471.35

171.78

170.53

27

0.350

453.60

460.27

467.70

470.90

172.94

171.63

28

0.325

453.26

459.95

467.29

470.38

174.37

172.98

29

0.300

452.91

459.6

466.86

469.82

176.02

174.54

30

0.275

452.54

459.22

466.40

469.31

177.19

175.65

31

0.250

452.14

458.80

465.90

468.78

178.31

176.71

32

0.225

451.70

458.35

465.37

468.20

179.46

177.80

33

0.200

451.22

457.84

464.80

467.58

180.55

178.82

34

0.175

450.67

457.27

464.18

466.90

181.42

179.65

35

0.150

450.06

456.59

463.48

466.12

182.55

180.71

36

0.125

449.32

455.79

462.67

465.19

183.64

181.74

37

0.100

448.42

454.76

461.70

464.08

184.56

182.59

38

0.075

447.25

453.46

460.45

462.63

185.84

183.80

39

0.050

445.57

451.54

458.62

460.52

187.96

185.78

40

0.025

442.73

448.20

455.31

456.75

194.49

191.96

Mean: 0.375–0.925

T with the subscript 2.5, 5.0, 10.0, and 15.0 are the temperature obtained at the heating rates of 2.5, 5.0, 10.0, and 15.0 °C min−1, respectively. E with the subscript F–W–O and NL-INT are the activation energy calculated by NL-INT and F–W–O equations

https://static-content.springer.com/image/art%3A10.1007%2Fs10973-010-0950-2/MediaObjects/10973_2010_950_Fig4_HTML.gif
Fig. 4

Ea vs. α curve of DNAZ·HClO4 by NL-INT and Flynn–Wall–Ozawa’s methods

The integral Eqs. 36 are cited to obtain the values of E, A, and the most probable kinetic model function G(α) from a single non-isothermal TG curve [16].

Mac Callum–Tanner equation
$$ \lg \left[ {G\left( \alpha \right)} \right] = \lg \left( {{\frac{AE}{\beta R}}} \right) - 0.4828E^{0.4357} - {\frac{0.449 + 0.217E}{0.001}}\frac{1}{T} $$
(4)
Satava–Sestak equation
$$ \lg \left[ {G\left( \alpha \right)} \right] = \lg \left( {{\frac{AE}{\beta R}}} \right) - 2.315 - 0.4567\frac{E}{RT} $$
(5)
Agrawal equation
$$ \ln \left[ {{\frac{G(\alpha )}{{T^{2} }}}} \right] = \ln \left\{ {{\frac{AR}{\beta E}}\left[ {{\frac{{1 - 2\left( {\frac{RT}{E}} \right)}}{{1 - 5\left( {\frac{RT}{E}} \right)}}}} \right]} \right\} - \frac{E}{RT} $$
(6)
The Universal Integral equation
$$ \ln \left[ {{\frac{G(\alpha )}{{T - T_{0} }}}} \right] = \ln \left( {{\frac{A}{\beta }}} \right) - \frac{E}{RT} $$
(7)
The General Integral equation
$$ \ln \left[ {{\frac{G\left( \alpha \right)}{{T^{2} \left( {1 - \frac{2RT}{E}} \right)}}}} \right] = \ln \left( {{\frac{AR}{\beta E}}} \right) - \frac{E}{RT} $$
(8)
where G(α) is the integral model function, T is the temperature (K) at time t, α the conversion degree, R the gas constant.
Forty-one types of kinetic model functions in reference [17] and the original data tabulated in Table 2 are put into Eqs. 37 for calculation, respectively. The kinetic parameters and the probable kinetic model function was selected by the logical choice method and satisfying the ordinary range of the thermal decomposition kinetic parameters for energetic materials (E = 80–250 kJ mol−1, log A = 7–30 s−1). These data together with the appropriate values of linear correlation coefficient (r), standard mean square deviation (S), and believable factor (d, where d = (1 − r)S), are presented in Table 3. The values of E are very close to each other. The values of Ea and A obtained from a single non-isothermal DSC curve are in good agreement with the calculated values obtained by Kissinger’s method and Ozawa’s method. Therefore, we conclude that the reaction mechanism of exothermic main decomposition process of the compound is classified as reaction order f(α) = (1 − α)−1/2. Substituting f(α) with (1 − α)−1/2, E with 156.47 kJ mol−1 and A with 1015.12 s−1 to Eq. 9,
$$ {{{\text{d}}\alpha } \mathord{\left/ {\vphantom {{{\text{d}}\alpha } {{\text{d}}T}}} \right. \kern-\nulldelimiterspace} {{\text{d}}T}} = {\frac{A}{\beta }}\,f\left( \alpha \right){\text{e}}^{{ - {E \mathord{\left/ {\vphantom {E {RT}}} \right. \kern-\nulldelimiterspace} {RT}}}} $$
(9)
where f(α) and dα/dT are the differential model function and the rate of conversion, respectively.
Table 3

Calculated values of kinetic parameters of decomposition reaction for DNAZ·HClO4

β/K min−1

Eq.

E/kJ mol−1

log (A/s−1)

r

S

d

2.5

(4)

164.00

16.25

0.9856

2.68 × 10−3

3.86 × 10−5

 

(5)

163.02

16.18

0.9856

2.68 × 10−3

3.86 × 10−5

 

(6)

163.84

16.28

0.9843

1.42 × 10−2

2.24 × 10−4

 

(7)

163.84

16.28

0.9843

1.42 × 10−2

2.24 × 10−4

 

(8)

167.64

15.06

0.9850

1.42 × 10−2

2.24 × 10−4

5.0

(4)

171.48

17.14

0.9767

4.33 × 10−3

1.01 × 10−4

 

(5)

170.09

17.02

0.9767

4.33 × 10−3

1.01 × 10−4

 

(6)

171.16

17.15

0.9746

2.30 × 10−2

5.82 × 10−4

 

(7)

175.01

15.92

0.9757

2.30 × 10−2

5.57 × 10−4

 

(8)

171.16

17.15

0.9746

2.30 × 10−2

5.82 × 10−4

10.0

(4)

137.73

13.24

0.9860

2.62 × 10−3

3.66 × 10−5

 

(5)

138.22

13.34

0.9860

2.62 × 10−3

3.66 × 10−5

 

(6)

137.52

13.28

0.9844

1.39 × 10−2

2.17 × 10−4

 

(7)

141.44

12.14

0.9852

1.39 × 10−2

2.05 × 10−4

 

(8)

137.52

13.28

0.9844

1.39 × 10−2

2.17 × 10−4

15.0

(4)

150.61

14.77

0.9874

2.34 × 10−3

2.94 × 10−5

 

(5)

150.38

14.78

0.9874

2.34 × 10−3

2.94 × 10−5

 

(6)

150.25

14.78

0.9861

1.24 × 10−2

1.73 × 10−4

 

(7)

154.19

13.61

0.9868

1.24 × 10−2

1.64 × 10−4

 

(8)

150.25

14.78

0.9861

1.24 × 10−2

1.73 × 10−4

Mean

 

156.47

15.12

   

Note: S means standard mean square deviation and d means believable factor [d = (1 − r)S]

The kinetic equation of the exothermic decomposition reaction may be described as \( {\text{d}}\alpha /{\text{d}}T = {\frac{{10^{15.12} }}{2\beta }}(1 - \alpha )^{ - 1} \exp ( - 1.88 \times 10^{4} /T) \).

The values (Teo and Tpo) of the onset temperature (Te) and peak temperature (Tp) corresponding to β → 0 obtained by Eq. 10 taken from [16] are 171.17 and 177.09 °C, respectively.
$$ T_{\text{e or p}} \, = \, T_{\text{eo or po}} + a\beta_{i} + b\beta_{i}^{2} \quad i = 1\sim 4 $$
(10)
where a and b are coefficients.
The corresponding critical temperatures of thermal explosion (Tb) obtained from Eq. 11 taken from [18] is 188.5 °C.
$$ T_{b} = {\frac{{E_{\text{o}} - \sqrt {E_{\text{o}}^{2} - 4E_{\text{o}} RT_{\text{ po}} } }}{2R}} $$
(11)
where R is the gas constant (8.314 J mol−1 K−1), Eo is the value of E obtained by Ozawa’s method.
The entropy of activation (ΔS), enthalpy of activation (ΔH), and free energy of activation (ΔG) corresponding to T = Tpdo, Ea = Ek, and A = Ak obtained by Eqs. 12, 13, and 14 are 42.26 J mol−1 K−1, 154.44 kJ mol−1, and 135.42 kJ mol−1, respectively.
$$ A = {\frac{{k_{\text{B}} T}}{h}}\,e^{{\Updelta S^{ \ne } /R}} $$
(12)
$$ A{\text{exp(}} - E_{\text{a}} /RT) = \frac{kT}{h}{ \exp }\left( {{\frac{{\Updelta S^{ \ne } }}{R}}} \right){ \exp }\left( { - {\frac{{\Updelta H^{ \ne } }}{RT}}} \right) $$
(13)
$$ \Updelta G^{ \ne } = \Updelta H^{ \ne } - T\Updelta S^{ \ne } $$
(14)
where kB is the Boltzmann constant and h the Plank constant.

Determination of the specific heat capacity

Figure 5 shows the determination results of DNAZ·HClO4 using a continuous specific heat capacity mode of Micro-DSC apparatus. One can see that specific heat capacity of DNAZ·HClO4 presents a good quadratic relationship with temperature in determining temperature range. Specific heat capacity equation is shown as:
$$ C_{\text{p}} \, \left( {{\text{Jg}}^{ - 1} \;{\text{K}}^{ - 1} } \right) = \, - 1. 3 8 3 8+ 1. 2 4 2 3\times 10^{ - 2} T - 1. 3 6 9 7\times 10^{ - 5} T^{ 2} \, \left( { 2 8 3\;{\text{K}} < T < 3 5 3\;{\text{K}}} \right) $$
(15)
The standard molar specific heat capacity of DNAZ·HClO4 is 272.93 J mol−1 K−1 at 298.15 K.
https://static-content.springer.com/image/art%3A10.1007%2Fs10973-010-0950-2/MediaObjects/10973_2010_950_Fig5_HTML.gif
Fig. 5

Determination results of the continuous specific heat capacity of DNAZ·HClO4

Thermal safety

The adiabatic time-to-explosion (t, s) of energetic materials is the time of energetic material thermal decomposition transiting to explosion under the adiabatic conditions, and is an important parameter for assessing the thermal stability and the safety of energetic materials. The estimation formula of adiabatic time-to-explosion of energetic materials is showed as Eq. 17 taken from [18, 19], and t value obtained by the definite integral equation is 14.2 s, longer than that of TNAZ [20] and NTO DNAZ (3-nitro-1,2,4-triazol-5-one 3,3-dinitroazetidinium) [8], shorter than that of DNAZ 3,5-DNSA (3,3-dinitroazetidinium 3,5-dinitrosalicylate) [5].
$$ C_{\text{p}} {\frac{{{\text{d}}T}}{{{\text{d}}t}}} = QA\exp ({{ - E} \mathord{\left/ {\vphantom {{ - E} {RT}}} \right. \kern-\nulldelimiterspace} {RT}})f(\alpha ) $$
(16)
$$ t = \frac{1}{QA}\int\limits_{{T_{0} }}^{T} {{\frac{{C_{\text{p}} \exp ({E \mathord{\left/ {\vphantom {E {RT}}} \right. \kern-\nulldelimiterspace} {RT}})}}{f(\alpha )}}} {\text{d}}T \, $$
(17)
where Cp as expressed by Eq. 15 in the temperature range of 283–353 K; f(α), differential mechanism function f(α) = (1 − α)−1/2; E is the activation energy, 156.47 kJ mol−1; A is the pre-exponential constant, A = 1015.12 s−1; Q is the decomposition heat, 2938.25 Jg−1; n is the decomposition reaction order, 2; R is the gas constant, 8.314 J mol−1 K−1; α is the conversion degree, and
$$ \alpha = \int\limits_{{T_{0} }}^{T} {{\frac{{C_{\text{p}} }}{Q}}{\text{d}}T} $$
(18)
where the integral upper limit T = Tbp = 461.65 K and the lower limit T0 = Te0 = 438.55 K. In the calculation process of adiabatic time-to-explosion, a little change in the activation energy located in the integral equation with exponential form can make a great difference in the result, and a small increase of the activation energy can induce adiabatic time-to-explosion to rise greatly.

Conclusions

  1. (1)

    The thermal behavior of DNAZ·HClO4 under the non-isothermal condition by DSC, TG/DTG methods was studied. The apparent activation energy and pre-exponential factor of the exothermic decomposition reaction are 156.47 kJ mol−1 and 1015.12 s−1, respectively.

     
  2. (2)

    The specific heat capacity was determined with Micro-DSC method. The specific heat capacity equation is Cp(Jg−1 K−1) = −1.3838 + 1.2423 × 10−2T − 1.3697 × 10−5T2 (283 K < T < 353 K) and the standard molar specific heat capacity is 272.93 J mol−1 K−1 at 298.15 K.

     
  3. (3)

    The adiabatic time-to-explosion was calculated to be 14.2 s.

     

Acknowledgements

This study is supported by the National Natural Science Foundation of China (20603026), the Provincial Natural Foundation of Shaanxi (2009JQ2002) and NWU Graduate Experimental Research Funds (09YSY23).

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2010