Introduction

Nitrogen-rich energetic compounds based on heterocyclic energetic anions, as a prominent family of novel energetic materials, have attracted considerable attention owing to their excellent detonation properties and good stability [1,2,3,4,5]. Heterocyclic energetic anions possess aromatic ring skeletons and large numbers of C–N and N–N bonds which can possess good stability and release more energy. In general, the introduction of nitrogen-rich cations can increase the nitrogen content and performance.

Ammonium 3,3′-dinitrimino-5,5′-bis(1H-1,2,4-triazole) (ADNABT) has been described in the literature previously [1]. The detonation velocity (9407 m s−1) and pressure (34.9 GPa) of ADNABT were similar to that of RDX and HMX and deemed as a promising energetic material. However, the structural characterization by IR spectroscopy, 1H/13C NMR and single-crystal X-ray diffraction was not mentioned, and its thermal safety properties have not been evaluated.

The purpose of this study was to determine the thermal decomposition and kinetic parameters of ADNABT and provide some thermal hazard indicators for production, transportation and storage. First, the thermal decomposition processes of ADNABT was investigated by thermogravimetry–differential thermal analysis (TG–DTA). Next, the heat capacities (Cp) of ADNABT were measured by difference scanning calorimeter (DSC). The non-isothermal decomposition was measured by DTA at different heating rates. The adiabatic decomposition was measured by accelerating rate calorimeter (ARC) in heat-wait-search mode. Then, the kinetic parameters by DTA and ARC tests were simulated by Thermal Safety Software (TSS) [6,7,8,9,10,11,12]. Finally, several thermal hazard indicators such as time to maximum rate (TMR), reaction temperature at which TMR is 24 h (TD24) and time to conversion limit (TCL) and self-accelerating decomposition temperature (SADT) were simulated by TSS on kinetic models [6,7,8,9,10,11,12].

Experimental

Materials

3,3′-dinitrimino-5,5′-bis(1H-1,2,4-triazole) (DNABT) was homemade and purified according to the literature [1, 13]. Sodium hydroxide (0.60 g, 15 mmol) was added to a suspension of DNABT (1.92 g, 7.5 mmol) in water (50 mL) at room temperature. The reaction mixture was heated at reflux for 1 h. Then, a solution of ammonia chloride (0.80 g, 15 mmol) in water (5 mL) was added to the reaction mixture and heated at reflux for 1 h. The resulting precipitate was collected by filtration, washed with ethanol and dried at 50 °C to give ADNABT (0.86 g, 39%) (Scheme 1). ADNABT: IR (KBr pellet cm−1) 3342, 3205, 3036, 1628, 1525, 1445, 1439, 1396, 1351, 1281, 1253, 1119, 1087, 1011, 977, 863, 804, 766, 738; 1H NMR (400 MHz d6-DMSO ppm) 9.55, 7.00; 13C NMR (100 MHz d6-DMSO ppm) 158.08, 153.39.

Scheme 1
scheme 1

The synthesis route of ADNABT

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Suitable crystals of ADNABT for single-crystal X-ray diffraction were obtained by slow evaporation a solution of ADNABT in dimethyl sulfoxide (DMSO). The crystallographic data and crystal structure are shown in Table 1 and Fig. 1, respectively. The results revealed that one molecule of ADNABT was connected to two molecules of DMSO.

Table 1 Crystallographic data of ADNABT
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Fig. 1
figure 1

Crystal structure of ADNABT. Thermal ellipsoids are set to 50% probability. Selected bond lengths/Å: C1–N1 1.345(34), C1–N3 1.343(39), C2–N2 1.314(39), C2–N3 1.358(31), N3···H6B 1.983(347), N1–H1 0.816(387), H1···O3 2.010(360). Selected bond angles/°: N1–C1–N3 107.39(230), N1–C1–N4 133.77(239), N2–C2–N3 113.90(225), C1–N4–N5 116.50(240). Selected torsion angles/°: C2–N3–C1–N4 178.89(250), N3–C1–N4–N5 179.56(240), N2–N1–H1···O3 4.90(7647), N2–C2–N3···H6B 172.61(1782)

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Instruments

A Netzsch difference scanning calorimeter device (DSC200 F3) was used to measure Cp of ADNABT. The sample was heated from 30 to 110 °C with a heating rate of 10 °C min−1 under a nitrogen flow of 50 mL min−1. A Shimadzu DTG-60H simultaneous thermal analyzer was used to record the non-isothermal decomposition of ADNABT. All samples were 1.5 mg and were heated from 50 to 400 °C at different heating rates of 2, 4, 6, 8 °C min−1, respectively. A THT accelerating rate calorimeter (ARC) [14,15,16,17] was used to record the adiabatic test of ADNABT. The sample was 100.3 mg and was heated from 80 to 350 °C in heat-wait-search mode. The heat steps and wait times were 15 °C and 15 min, respectively.

Results and discussion

Thermal decomposition processes by TG–DTA test

TG–DTA curve of ADNABT under a heating rate of 8 °C min−1 is shown in Fig. 2. Obviously, there were two significant peaks, among which, the first endothermic peak ranges from 122.53 to 168.35 °C with a mass loss of 36.0%, and the second exothermic peak ranges from 216.40 to 278.05 °C with a mass loss of 32.2%. The theoretically calculated mass loss of DMSO was 35.0%, and that was similar to the mass loss of first endothermic peak. Hence, the first endothermic peak was a process of lost DMSO.

Fig. 2
figure 2

TG–DTA curve of ADNABT at a heating rate of 8 °C min−1

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Heat capacity by DSC test

The relationship between Cp and T of ADNABT was established by four steps. First, get the values of Cp by DSC. Next, open the ARKS-CK of TSS, and input the needed parameters, such as formula, density, temperature and Cp. Then, press calculator button, the relationship between Cp and T was simulated on the default model (Cp = a0 + a1T + a2T2). Finally, get the calculated results of a0, a1 and a2. Thus, we got the relationship between CP and T, and the simulated Cp is shown in Fig. 3. The Cp of ADNABT at 298.15 K is calculated as 1.277 J g−1 K−1. The relationships between Cp and T were described as follows:

Fig. 3
figure 3

Simulated heat capacity of ADNABT by DSC test

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$$C_{\text{p}} = 1. 5 4 0\times 1 0^{ - 1} - 4. 1 1 9\times 1 0^{ - 3} \times T + 1. 0 7 0\times 1 0^{ - 6} \times T^{2}.$$
(1)

Kinetic simulation by DTA test

DTA curves of ADNABT under different heating rates (β) of 2, 4, 6 and 8 °C min−1 are shown in Fig. 4. The experimental parameters, such as onset temperature (To), peak temperature (Tp), endset temperature (Te) and heat production (Q), are listed in Table 2. The DTA results revealed that the heights and areas of first endothermic and second exothermic peaks were increased when the heating rates were raised.

Fig. 4
figure 4

Thermal decomposition curves of ADNABT by DTA test

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Table 2 Experimental parameters of ADNABT by DTA tests
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Most simulation of kinetic models involves complex multi-stage reactions, which consist of several of independent, parallel and consecutive stages. The simple, nth-order and autocatalytic kinetic models for a single-stage reaction (A → B) were presented in Eqs. (2)–(4), respectively [8, 18,19,20,21].

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k_{0} \exp \left( { - \frac{E}{{{\text{R}}T}}} \right)f\left( \alpha \right)$$
(2)
$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k_{0} \exp \left( { - \frac{E}{{{\text{R}}T}}} \right)\left( { 1- \alpha } \right)^{\text n}$$
(3)
$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k_{0} \exp \left( { - \frac{E}{{{\text{R}}T}}} \right)\left( {1 - \alpha } \right)^{{\text n_{1} }} \left( {\alpha^{{\text n_{2} }} + z} \right)$$
(4)

where α is the degree of conversion; t is the time; k0 is the pre-exponential factor; E is the activation energy; R is ideal gas constant; T is the temperature; n1, n2 and n are the reaction orders of a specific stage; z is autocatalytic constant.

The kinetic models that include two consecutive stages (A → B → C) were described as follows [8, 18,19,20,21]:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k_{ 1} \exp \left( { - \frac{{E_{ 1} }}{{{\text{R}}T}}} \right)\left( { 1- \alpha } \right)^{{\text n_{1} }}$$
(5)
$$\frac{{{\text{d}}\gamma }}{{{\text{d}}t}} = k_{2} \exp \left( { - \frac{{E_{2} }}{{{\text{R}}T}}} \right)\left( {\alpha - \gamma } \right)^{{\text n_{2} }}$$
(6)

where α and γ are the degree of conversion of stage one and two, respectively; k1 and k2 are the pre-exponential factors of stage one and two, respectively; E1 and E2 are the activation energies of stage one and two, respectively; n1 and n2 are the reaction orders of stage one and two, respectively.

The kinetic models for two parallel reactions (A → B; A + B→2B) were described as follows [8, 18,19,20,21]:

$$\begin{aligned} \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} & = r_{1} \left( \alpha \right) + r_{2} \left( \alpha \right) = k_{ 0 1} \exp \left( { - \frac{{E_{ 1} }}{{{\text{R}}T}}} \right)\left( { 1- \alpha } \right)^{{\text n_{11} }} \\ & \quad + \,k_{ 0 2} \exp \left( { - \frac{{E_{ 2} }}{{{\text{R}}T}}} \right)\alpha^{{\text n_{21} }} \left( { 1- \alpha } \right)^{{\text n_{22} }} \\ \end{aligned}$$
(7)

where r1 and r2 are the rates of stage one and two, respectively.

Assuming that n11 = n22 = n1 and n21 = n2, then the kinetic model of full autocatalysis can be described as follows [20, 21]:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k_{0} \exp \left( { - \frac{E}{{{\text{R}}T}}} \right)\left( {1 - \alpha } \right)^{{\text n_{1} }} \left[ {z_{0} \exp \left( { - \frac{{E_{z} }}{{{\text{R}}T}}} \right) + \alpha^{{\text n_{2} }} } \right]$$
(8)

where z0 is the ratio of pre-exponential factor k01/k02; Ez is the difference E1 and E2.

The kinetic parameters of ADNABT by DTA tests were simulated by TSS, and the results are listed in Table 3. The simulated and experimental values of heat production rate and heat production are shown in Fig. 5. The simulated values of heat production rate and heat production were similar to the experimental values. Hence, It could be concluded that the exothermic decomposition of ADNABT under non-isothermal conditions followed a full autocatalysis model.

Table 3 The simulated kinetic parameters of ADNABT by DTA tests
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Fig. 5
figure 5

Simulated and experimental heat product rate and heat production of ADNABT by DTA tests. a Heat production rate versus time, b heat production versus time

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Kinetic simulation by ARC test

The exothermic decomposition of ADNABT by ARC is shown in Fig. 6. The experimental parameters such as onset temperature, final temperature, adiabatic temperature rise, max self-heating rate, max pressure and so on are listed in Table 4. The endothermic decomposition of loss DMSO was between 148.25 and 156.08 °C, and the pressure was increased by 8.64 bar. The exothermic decomposition of ADNABT started at 245.17 °C and ended at 264.28 °C, and the pressure was increased by 6.48 bar.

Fig. 6
figure 6

The exothermic decomposition curve of ADNABT by ARC test

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Table 4 Experimental parameters of ADNABT by ARC test
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The kinetic parameters of ADNABT were evaluated by AC and FK of TSS. The kinetic model of ADNABT by ARC test was described as Eq. (8). The simulated results such as E, ln k0, n, Q are listed in Table 5. The simulated and experimental values of heat production rate, heat production, gas production rate and gas production of ADNABT by ARC test are shown in Fig. 7. The simulated values of heat production rate, heat production, gas production rate and gas production were similar to the experimental values which revealed that the simulated results were credible. From the simulated results by using TSS, It could be concluded that the exothermic decomposition of ADNABT by ARC test also followed a full autocatalysis model.

Table 5 The kinetic parameters of ADNABT by ARC test
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Fig. 7
figure 7

Simulated and experimental heat production rate, heat production, gas production rate and gas production of ADNABT by ARC test. a Heat production rate versus time, b heat production versus time, c gas production rate versus time, d gas production versus time

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TMR is the time instant when reaction reaches its maximal rate under adiabatic conditions which was proposed by Townsend and Tou [22], and their method was only suitable for simple single-stage n-order reactions. In the case of more complex reactions (including autocatalytic reactions), TMR can be properly determined merely by applying a kinetic-based simulation [6, 23,24,25,26,27]. TD24 is the reaction temperature at which TMR is 24 h [6]. The kinetic parameters of ADNABT were got from Table 5. The TMR was estimated by applying a kinetic-based simulation, and the simulated TMR is shown in Fig. 8. The TMR at 150 °C was calculated as 109.38 days, and the TD24 was calculated as 183.37 °C.

Fig. 8
figure 8

Simulated TMR and TCL of ADNABT by ARC test

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Assessment of thermal stability of a substance (stability analysis) lies in evaluating the dependency of time instant (time to conversion limit, TCL) when conversion of a reaction reaches some predefined value-conversion limit, at constant set temperature [6, 23,24,25,26,27]. Thermal stability is essentially characterized by the time of TCL necessary to reach a certain level of conversion at a specific constant temperature. Therefore, for long-term storage, it can be selected as the maximum permissible time during which the conversion of the product does not have any prominent impact on the product quality. The TCL (10% conversion limit) was estimated by applying a kinetic-based simulation, and the simulated TCL is shown in Fig. 8. The TCL (10% conversion limit) at 150 °C was calculated as 25.68 days.

SADT is defined as the lowest ambient air temperature at which self-accelerating decomposition may occur within a substance in the packaging as used in transport and storage. Assuming 50 kg ADNABT was loaded in a steel barrel with heat 40 cm and radius 15 cm. SADT was evaluated by ThermEx of TSS. The SADT50 kg was calculated as 167.00 °C.

Conclusions

In conclusion, the thermal decomposition of ADNABT was performed by TG–DTA and ARC, and these tests data were simulated by TSS. The results were reported in detail.

  1. 1.

    The TG–DTA measurement showed that ADNABT has two decomposition processes, and the first process is an endothermic decomposition of loss DMSO, and the second process is an exothermic decomposition. The kinetic parameters of exothermic decomposition such as E, k0 and f(α) were evaluated by TSS. The exothermic decomposition of ADNABT under non-isothermal conditions followed a full autocatalysis model.

  2. 2.

    The ARC measurement also showed that ADNABT has an endothermic and an exothermic decomposition. The kinetic parameters of exothermic decomposition such as E, k0 and f(α) were also simulated by TSS, and the results indicated that the exothermic decomposition of ADNABT under adiabatic condition also followed a full autocatalysis model. The several thermal hazard indicators such as TMR, TD24, TCL and SADT were also simulated by TSS on kinetic model. The TMR and TCL (10% conversion limit) at 150 °C were calculated as 109.38 and 25.68 days, respectively. The TD24 and SADT50 kg were calculated as 183.37 and 167.00 °C, respectively.