Introduction

Currently, explosives with superior detonation characteristics and/or decreased sensitivity to exterior stimuli [1–12] are of great concern. 4,10-dinitro-2,6,8,12-tetraoxa-4,10-diazaisowutrzitane, also called as TEX (Fig. 1), is a promising insensitive explosive [13–17] with high detonation velocity similar to RDX and HMX with excellent insensitivities toward mechanical and thermal stimuli comparable to NTO (see Table 1).

Fig. 1
figure 1

Molecular structure of TEX

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Table 1 Detonation properties of TEX in comparison with other commonly used high-energy explosives
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Though the thermal behavior and safety of TEX [14, 22] have been studied by both theoretically and experimentally, the explosion hazard of TEX is desired to be focused on the investigation of its thermal hazardous, especially under adiabatic conditions, which helps developing a thorough understanding of the potential thermal hazards relating to their safe manufacturing, handling and storage.

In this paper, the thermal explosion hazard and adiabatic decomposition progress of TEX were investigated by accelerating rate calorimeter (ARC) to acquire thermodynamic parameters for self-heat reactions. In addition, the self-accelerating decomposition temperature, the adiabatic decomposition temperature rise and the adiabatic time to explosion were also obtained as well, which would provide helpful information for its manufacturing and applications.

Experimental

Materials

The sample (TEX) investigated was purchased from Gansu Yinguang Chemical Industry Group Co., LTD., purity 99.70 %. Element analysis: C% 27.66 (27.49 % calculated), N% 20.78 % (21.37 % calculated), O% 49.21 % (48.83 % calculated), H% 2.35 (2.31 % calculated).

Apparatus and test conditions

Elemental analyses are determined on a Vario EL cube elemental analyzer. ARC has been used widely for estimating the explosion characteristics of explosives [23–27]. In this study, a NETZSCH Co., Ltd accelerating rate calorimeter (ARC) using a 1/4-in. Hastelloy bomb with a thermocouple clip located on the bottom of the bomb was used.

Generally, when measuring one ARC test, the sample is placed in a Hastelloy bomb, sealed with air atmosphere, initially heated to 70 °C, and then equilibrated for 30 min, followed by a 10-min seek for an exothermic signal, which can be detected if the self-heat rate (SHR) is over 0.02 °C min−1. Then, the temperature will be increased by 5 °C with the subsequent repetition of the heat–wait–seek (H–W–S) periods until the exothermic signal is detected.

Data of sample and bomb in the experiment are listed in Table 2. To ascertain the accuracy of measurement, the instrument was calibrated and then verified using 20 mass% di-tertiary-butyl peroxide (DTBP, >98 %) 80 mass% toluene solution before the experiments.

Table 2 Data of samples and sample bomb
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Results and discussion

The specific heat capacity of TEX

Figure 2 showed the specific heat capacity of TEX as a function of temperature using differential scanning calorimetry (DSC). The sample mass was 25.6 mg, and the heating rate was 10 °C min−1 from 5 to 35 °C. In determined temperature range, specific heat capacity of TEX presented a good linear relationship with temperature, and the linear correlation coefficient is 0.9986. The equation describing the relationship can be written as C p = 0.81806 + 0.00341 × T, 5.0 °C ≤ T ≤ 35 °C. The resulted molar specific heat capacity of TEX is therefore calculated as 0.9038 J g−1 K−1 at 298.15 K.

Fig. 2
figure 2

Specific heat capacity of TEX as a function of temperature

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Data analysis

The measured data and curves of test for TEX are given in Figs. 3–5 and Table 3. Figure 3 shows temperature and pressure versus time for TEX in the heat–wait search operational logic of the ARC test, revealing that after five H–W–S periods, the self-decomposition reaction of DNTF started to take place at 215.8 °C and lasted for 984.2 min, during which the temperature and pressure in the reaction system increased abruptly at the rate approximately 274.6 min−1 and 5748 kPa min−1, respectively. This indicated that the decomposition reaction released enormous energy and could cause a disaster when occurred uncontrolled in a closed vessel.

Fig. 3
figure 3

Temperature and pressure versus time (left) and self-heat rate versus temperature (right)

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Fig. 4
figure 4

Pressure versus temperature (left) and temperature conversion rate versus time

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Fig. 5
figure 5

Time to reach maximum temperature rise rate (TMR) versus temperature

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Table 3 Thermal decomposition parameters of TEX by ARC
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As shown in Fig. 3, the self-heat rate (SHR) of TEX decomposition raised slowly when the reaction temperature was below 267 °C, while a runway reaction was found when the reaction temperature exceeded 267 °C along with the significant SHR increase from 5.28 °C min−1 to the maximum value 255.10 °C min−1 (at 274.9 °C).

In Fig. 4, both the pressure and pressure change rate as function of time indicated that the pressure of reaction system had two different stages and the turning point occurred at 240 °C. At the first stage where the temperature was below 240 °C, the pressure rise rate increased slowly due to the presence of small amount of gaseous products produced by the slow decomposition of TEX. At the second stage when the temperature exceeded 240 °C, the pressure rise rate increased suddenly because the rapid decomposition of DNTF occurred and yielded large amount of gaseous products such as NO2, CO2, N2O, CO, NO, HCN, HCHO, and HNCO [28]. Figure 5 demonstrates that longer time was needed to reach the maximum temperature rise rate at lower initial heating temperature in the thermal decomposition reaction of TEX under adiabatic condition.

Data correction

Under experimental conditions of ARC, heat from the exothermic reaction of the sample induced the temperature rise of both sample and reaction bomb. The relationship between the real adiabatic and near adiabatic condition was described as following.

$$M_{\text{s}} C_{\text{v,s}} m_{\text{T}} = \left[ {(M_{\text{s}} C_{\text{v,s}} + M_{\text{b}} C_{\text{v,b}} )} \right]m_{\text{T}}$$
(1)

where M s is the mass of the reactive sample, C v,s is the heat capacity of reaction sample, M b is the mass of the reaction bomb, C v,b is the heat capacity of reaction bomb, and m T is the self-heat rate of the reaction system including the reactive sample and the reaction bomb.

Hence, in order to obtain the data of the sample itself under the absolute adiabatic condition, it is necessary to correct the tested temperature parameters such as the adiabatic temperature rise, temperature rise rate, and the time of maximum temperature rise rate using the thermal inertia factor (Φ) to exclude the effect from reaction bomb, which was defined as following [20]:

$$\varPhi = 1 + \frac{{M_{\text{b}} C_{\text{v,b}} }}{{M_{\text{s}} C_{\text{v,s}} }}$$
(2)
$$T_{{0,{\text{s}}}} = \left[ {\frac{1}{{T_{0} }} + \frac{R}{{E_{\text{a}} }}\ln \varPhi } \right]^{ - 1}$$
(3)
$$T_{\text{f}} = \varPhi \Delta T_{\text{ad}} + T_{{0,{\text{s}}}}$$
(4)
$$\Delta T_{\text{ad}} = \varPhi \Delta T_{{{\text{ad}},{\text{s}}}}$$
(5)
$$m_{{0,{\text{s}}}} = \varPhi m_{0}$$
(6)
$$m_{\text{m,s}} = \varPhi m_{\text{m}}$$
(7)
$$T_{\text{m,s}} = T_{{0,{\text{s}}}} + \varPhi (T_{\text{m}} - T_{0} )$$
(8)
$$\theta_{\text{m,s}} = \frac{{\theta_{\text{m}} }}{\varPhi }$$
(9)

where T 0,s is the corrected initial decomposition temperature; T f is the corrected final decomposition temperature; T ad is the corrected adiabatic temperature rise; m o is the corrected initial temperature rise; m m is the corrected maximum temperature rise; T m is the corrected temperature of maximum temperature rise rate; and θ m is the corrected time of maximum temperature rise rate.

Kinetic parameters calculation

For an nth-order reaction with a single reaction, the SHR of adiabatic system could be expressed as the following:

$$k^{*} = C_{0}^{{\text{n}} - 1} k = \frac{{m_{\text{T}} }}{{\Delta T_{\text{ad}} \left[ {\frac{{T_{\text{f}} - T}}{{\Delta T_{\text{ad}} }}} \right]^{\text{n}} }}$$
(10)

where m T is the SHR at arbitrary temperature T of adiabatic system; \(\Delta T_{\text{ad}}\) is the measured adiabatic temperature rise; T f is the measured final decomposition temperature; and \(k^*\) is a pseudo-zero-order rate constant at temperature T. According to the Arrhenius equation k = A exp (−E a/RT), one can obtain:

$$\ln k^{*} = \ln C_{0}^{{\text{n}} - 1} A - \frac{{E_{\text{a}} }}{R}\left[ {\frac{1}{T}} \right]$$
(11)

The plot of lnk * versus 1/T is, therefore, expected to be a straight line providing that the order of reaction was correctly chosen. The regarding linear coefficient R 2, pre-exponential factor A, and the apparent activated energy E a are listed in Table 4, and the curves between lnk and 1/T for the decomposition of TEX are illustrated in Fig. 6.

Table 4 Kinetic parameters of TEX adiabatic decomposition
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Fig. 6
figure 6

Curve of lnk to 1/T for the decomposition of TEX

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5-Second delay exploding point calculation

According to the literature [29], time to maximum temperature, E a, and A have the relationship as follows:

$$\ln \theta = \frac{E}{R} \times \frac{1}{T} - \ln A$$
(12)

From Table 3, E and A were given as 306.67 kJ mol−1 and 2.47 × 1026 s−1, respectively. Then, the 5-s delay exploding point could be calculated by above equation to be 318.15 °C, which is lower than the data (343 °C) [30] obtained by the traditional Wood’s alloy bathy method.

Conclusions

The thermal decomposition behaviors and the thermal hazard assessment of TEX were first time exploited by using ARC. The results suggested that the standard molar specific heat capacity of TEX is 0.9038 J g−1 K−1 at 298.15 K, and the equation describing values of the capacity versus temperature was obtained to be C p = 0.81806 + 0.00341 × T, 5.0 °C ≤ T ≤ 35 °C. Moreover, from the ARC data, it is suggested that the initial exothermic temperature was 215.8 °C under the adiabatic condition. In addition, the E a, A, and 5-s delay exploding point of TEX were also given.