Introduction

3,3′-Diamino-5,5′-bis(1H-1,2,4-triazole) (DABT) is an important raw material and widely used in the production of bistriazoles energetic materials, such as 3,3′-dinitro-5,5′-bis(1H-1,2,4-triazole) (DNBT) [1, 2], 3,3′-dinitrimino-5,5′-bis(1H-1,2,4-triazole) (DNABT) [1, 3], 3,3′-diazide-5,5′-bis(1H-1,2,4-triazole) (DAzBT) [1], 3,3′-dinitro-5,5′-bis(1H-1,2,4-triazole)-1,1′-diol (DNBTO) [4] and their derivatives [2,3,4], carbonic dihydrazidinium bis[3-(5-nitroimino-1,2,4-triazolate)] (CBNT) [3], dihydroxylammonium 3,3′-dinitro-5,5′-bis-1H-1,2,4-triazole-1,1′-diolate (HBNTO) [3], which were reported as two of most promising ionic salts to possibly replaced 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX).

We investigated the heat of formation and detonation properties of DABT by using density functional theory (DFT-B3LYP) method. Previous studies have shown that the basis set 6-311 + G(2df, 2p) is able to predict the molecular structures and energies of energetic organic compounds [5,6,7]. The heat of formation of DABT (334.77 kJ mol−1) in the gas phase was determined at the B3LYP/6-311 + G(2df, 2p) theory level through isodesmic reaction. The detonation velocity (5.70 km s−1) and detonation pressure (13.79 GPa) were evaluated by Kamlet–Jacob equations. For the process safety of these bistriazoles energetic materials synthesized with DABT, the investigations of thermal decomposition behavior and thermal stability of DABT were very necessary.

In order to acquire the thermal decomposition behavior and thermal stability of DABT under non-isothermal and adiabatic conditions, the thermo gravimetry–derivative thermo gravimetry–differential scanning calorimetry (TG–DTG–DSC), differential thermal analysis (DTA) and accelerating rate calorimetry (ARC) were carried out. The thermo-kinetic parameters of the exothermic decomposition and thermodynamic parameters at the initial decomposition temperature (T p0) under non-isothermal condition were obtained from DTA. The self-heating decomposition parameters, adiabatic decomposition kinetics parameters, time to maximum rate (TMR) and self-accelerating decomposition temperature (T SADT) were obtained from ARC. To the best of our knowledge, up to now, there are no report regarding the thermal decomposition behavior and thermal stability of DABT under non-isothermal and adiabatic conditions.

Experimental

Materials

DABT was home-made and purified according to the literature [1, 2]. The synthesis route of DABT was shown in Scheme 1.

Scheme 1
scheme 1

The synthesis route of DABT

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The compound of DABT was additionally characterized by single-crystal X-ray spectroscopy. The result of single-crystal X-ray spectroscopy indicated that one molecule of DABT was associated with two molecules of DMSO. Crystallographic data and parameters as well as the morphology have been compiled in Table 1. The crystal structure of DABT was shown in Fig. 1.

Table 1 X-ray data and parameters of DABT·2DMSO
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Fig. 1
figure 1

Crystal structure of DABT·2DMSO. Thermal ellipsoids are set to 50% probability. Selected bond lengths/Å: C1–C1′ 1.461(2), C1–N1 1.318(15), C1-N3 1.367(15), C2-N2 1.339(16), C2–N3 1.337(2), C2–N4 1.347(17), N1–N2 1.374(15), N4HB···O1 2.058(91). Selected bond angles/°: C1′–C1–N1 121.61(13), C1–N1–N2 102.09(10), C1–N3–C2 102.52(10), N4–C2–N2 122.59(12), N4–C2–N3 127.31(12). Selected torsion angles/°: C2–N3–C1–C1′ 178.19(120), N2–N1–C1–C1′ − 178.08(116), C1–N3–C2–N4 − 177.36(142), N3–C2–N4–N4HB − 0.028(254), N3–C2–N4–N4HB − 179.97(144), C2–N4–N4HB···O1 167.12(924)

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Instruments

The TG–DTG–DSC measurement was performed with a PerkinElmer STA6000 simultaneous thermal analyzer at a heating rate of 10 °C min−1 under a nitrogen flow of 50 mL min−1. The non-isothermal DTA measurements were performed with a Shimadzu DTG-60H simultaneous thermal analyzer at heating rates of 1, 2, 4, 8 °C min−1 under a nitrogen flow of 50 mL min−1. All samples were 2.0 mg and placed in open alumina crucibles, and they were heated from 50 to 650 °C.

The ARC measurement was performed with a Thermal Hazard Technology accelerating rate calorimeter in the Heat-Wait-Search mode. The experiment conditions were listed in Table 2.

Table 2 Experimental conditions of DABT by ARC
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Results and discussion

Thermal decomposition processes

The TG–DTG–DSC curve at a heating rate of 10 °C min−1 was given in Fig. 2. From the TG and DTG curves, two stages were obviously seen. The first stage was started at 388.23 °C and ended at 462.73 °C, and the mass loss was 49.00%. This was a process of lost DMSO, and the theoretically calculated value of the process was in exact accordance with the experimental value. The second stage was started at 468.23 °C and ended at 535.73 °C, and the mass loss was 21.20%. From the DSC curve, the first stage was an endothermic decomposition, and the peak temperature was determined as 449.23 °C, and the second stage was an exothermic decomposition, and the peak temperature was determined as 495.23 °C.

Fig. 2
figure 2

TG–DTG–DSC curve of DABT at a heating rate of 10 °C min−1

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Non-isothermal decomposition kinetics

The DTA curves at heating rates of 1, 2, 4, 8 °C min−1 were given in Fig. 3. Both an endothermic decomposition of lost DMSO and an exothermic decomposition were observed. Different onset temperatures (429.62, 446.91, 454.33, 465.45 °C) and peak temperatures (447.59, 466.74, 479.09, 494.09 °C) of the exothermic decomposition processes were observed at heating rates of 1, 2, 4, 8 °C min−1, respectively. When the heating rate was high, the onset temperature of the exothermic decomposition was delayed, and the corresponding peak temperature shifted to a higher temperature.

Fig. 3
figure 3

DTA curves of DABT at heating rates of 1, 2, 4, 8 °C min−1

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To determine the non-isothermal decomposition kinetics parameters of energetic materials, Ozawa’s method [8] and Kissinger’s method [9] were employed. The Ozawa Eq. (1) and Kissinger Eq. (2) were given below:

$$\log \beta = - \frac{{0.4567E_{\text{a}} }}{R}\left[ {\frac{1}{{T_{\text{p}} }}} \right] + C$$
(1)
$${ \ln }\left[ {\frac{\beta }{{T_{\text{p}}^{2} }}} \right] = - \frac{{E_{\text{a}} }}{\text{R}}\left[ {\frac{1}{{T_{\text{p}} }}} \right] + \ln \left[ {\frac{{{\text{R}}A}}{{E_{\text{a}} }}} \right]$$
(2)

where β is the heating rate, E a is the apparent activation energy, R is the gas constant, T p is the peak temperature, C is an arbitrary constant and A is the pre-exponential factor. The logβ against 1/T p and ln(β/T 2p ) against 1/T p were two straight lines. According to Eqs. (1) and (2), the slops of two lines were used to calculate the activation energies. According to Eq. (3), the obtained activation energies were used to calculate the logarithm of pre-exponential factor (logA/s−1).

$$A = \beta \frac{{E_{\text{a}} }}{{RT_{\text{p}}^{2} }}\exp \left( {\frac{{E_{\text{a}} }}{{RT_{\text{p}} }}} \right)$$
(3)

The E a, logA/s−1 and corresponding regression coefficient (r) which were obtained by Ozawa’s and Kissinger’s methods were listed in Table 3.

Table 3 Non-isothermal kinetics and thermodynamics parameters of DABT obtained by Ozawa’s and Kissinger’s methods
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Thermodynamics at initial decomposition temperature (T p0)

The value of initial decomposition temperature (T p0) in the exothermic decomposition process corresponding to β → 0 was calculated by Eq. (4) [10, 11]

$$T_{\text{pi}} = T_{\text{p0}} + a\beta_{\text{i}} + b\beta_{\text{i}}^{2} \quad i = 1,\,2,\,3,\,4$$
(4)

where T pi is the peak temperature of a heating rate of β i, a and b are the coefficients.

The free energy of activation (ΔG ≠), activation enthalpy (ΔH ≠) and activation entropy (ΔS ≠) were calculated by Eqs. (5), (6) and (7) [11]:

$$\Delta G^{ \ne } = E_{\text{a}} - RT_{\text{P0}} \ln \left[ {\frac{Ah}{{k_{\text{B}} T_{\text{P0}} }}} \right]$$
(5)
$$\Delta H^{ \ne } = E_{\text{a}} - RT_{\text{p0}}$$
(6)
$$\Delta S^{ \ne } = \frac{{\Delta H^{ \ne } - \Delta G^{ \ne } }}{{T_{\text{p0}} }}$$
(7)

where E a is the apparent activation energy, h is the Planck constant, k B is the Boltzmann constant. The T p0, ΔG ≠, ΔH ≠ and ΔS ≠ were listed in Table 3.

Critical temperature of thermal explosion (T bp0)

The value of critical temperature of thermal explosion (T bp0) was calculated by Eq. (8) [12, 13]:

$$T_{{{\text{bp}}0}} = \frac{{E_{\text{a}} - \sqrt {E_{\text{a}}^{2} - 4E_{\text{a}} RT_{{{\text{P}}0}} } }}{2R}$$
(8)

Self-heating decomposition parameters

Under experiment conditions of ARC, heat from the exothermic reaction of the sample induced the temperature rise of both the sample and the reaction cell, The relationship between the real adiabatic and near adiabatic conditions was described as follows [14,15,16]. The corrected and measured self-heating decomposition parameters of DABT were given in Table 4.

$$\phi = 1 + \frac{{M_{\text{b}} C_{{{\text{v}},{\text{b}}}} }}{{M_{\text{s}} C_{{{\text{v}},{\text{s}}}} }}$$
(9)
$$T_{{{\text{o}},{\text{corr}}}} = \left[ {\frac{1}{{T_{\text{o}} }} + \frac{R}{{E_{\text{a}} }}\ln \phi } \right]^{ - 1}$$
(10)
$$T_{{{\text{f}},{\text{corr}}}} = \phi \Delta T_{\text{ad}} + T_{{{\text{o}},{\text{corr}}}}$$
(11)
$$\Delta T_{{{\text{ad}},{\text{corr}}}} = \phi \Delta T_{\text{ad}}$$
(12)
$$m_{\text{o,corr}} = \phi m_{\text{o}}$$
(13)
$$m_{\text{m,corr}} = \phi m_{\text{m}}$$
(14)
$$T_{\text{m,corr}} = T_{\text{o,corr}} + \phi \left( {T_{\text{m}} - T_{\text{o}} } \right)$$
(15)
$${\text{TMR}}_{\text{corr}} = \frac{\text{TMR}}{\phi }$$
(16)

where φ is the thermal inertia factor, M b is the test cell mass, C v,b is the test cell heat capacity, M s is the sample mass, C v,s is the sample heat capacity. T o,corr and T o are the corrected and measured onset decomposition temperature, respectively; T f,corr and T f are the corrected and measured final decomposition temperature, respectively; ΔT ad,corr and ΔT ad are the corrected and measured adiabatic temperature rise, respectively; m o,corr and m o are the corrected and measured onset temperature rate, respectively; m m,corr and m m are the corrected and measured max self-heating rate, respectively; T m,corr and T m are the corrected and measured temperature at max rate, respectively; TMRcorr and TMR are the corrected and measured time to maximum rate, respectively.

Table 4 Self-heating decomposition parameters of DABT by ARC
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The ARC curves of DABT were given in Fig. 4. As seen from Fig. 4a, an endothermic decomposition and an exothermic decomposition were observed. The endothermic decomposition of lost DMSO started at 395.10 °C and ended at 441.09 °C, and the pressure of the period increased 5.80 bar (Fig. 4b). The exothermic decomposition started at 443.61 °C and ended at 480.91 °C, within the time span of 1397.50 min (Fig. 4c). The max self-heating rate was 0.04 °C min−1 at 463.00 °C (Fig. 4d). From Fig. 4, it could be concluded that when the ambient temperature below 395.10 °C, DABT was not decomposition.

Fig. 4
figure 4

ARC curves of DABT. a Temperature and pressure versus time, b loss of DMSO temperature and pressure versus time, c decomposition temperature and pressure versus time, d decomposition temperature and temperature rate versus time

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Adiabatic decomposition kinetics

For an nth-order single step reaction with a single reaction, the self-heating rate could be expressed as following [14, 16]:

$$m_{\text{T}} = \frac{{{\text{d}}T}}{{{\text{d}}t}} = k\left[ {\frac{{T_{\text{f}} - T}}{{\Delta T_{\text{ad}} }}} \right]^{\text{n}} \Delta T_{\text{ad}} C_{0}^{{\text{n}} - 1}$$
(17)

where m T is the temperature rate at the temperature T, k is the rate constant of the reaction at temperature T, T is the temperature at time t, C 0 is the initial concentration of the reactant.

Rearranging Eq. (17), we had [14, 16]:

$$k^{ * } = kC_{0}^{{\text{n}} - 1} = \frac{{m_{\text{T}} }}{{\left[ {\frac{{T_{\text{f}} - T}}{{\Delta T_{\text{ad}} }}} \right]^{\text{n}} \Delta T_{\text{ad}} }}$$
(18)

where k * is a pseudo zero-order rate constant at the temperature T. According to the Arrhenius equation, one could obtain [14, 16].

$$\ln k^{ * } = \ln C_{0}^{{\text{n}} - 1} A - \frac{{E_{\text{a}} }}{R}\left[ {\frac{1}{T}} \right]$$
(19)

The curves of lnk * versus T −1 for the self-heating decomposition of DABT were illustrated in Fig. 5. The E a and A could be calculated from the plot, and they were listed in Table 5.

Fig. 5
figure 5

Lnk* versus T −1 of DABT

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Table 5 Adiabatic decomposition kinetic parameters of DABT by ARC
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Time to maximum rate (TMR)

According to the literature, the TMR and T have the following relationship [16,17,18].

$$\ln {\text{TMR}} = \frac{{E_{\text{a}} }}{R}\left[ {\frac{1}{T}} \right] - \ln A + \ln \frac{{RT^{2} }}{{C_{0}^{{\text{n}} - 1} \left[ {\frac{{T_{f} - T}}{{\Delta T_{\text{ad}} }}} \right]^{\text{n}} \Delta T_{\text{ad}} E_{\text{a}} }}$$
(20)

From Table 5, n = 2, E a was 345.76 kJ mol−1, logA/s−1 was 19.66. Then, the plot of TMR versus T was given in Fig. 6.

Fig. 6
figure 6

TMR versus T of DABT

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Self-accelerating decomposition temperature (T SADT)

The T 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. The adiabatic decomposition kinetics parameters were used for the estimation of the T SADT for DABT in a 50 kg package. Firstly, Eq. (21) was used to get the time constant (τ), then, the temperature of no return (T NR) would be obtained from the curve of TMR versus T. Lastly, the T SADT was calculated based on Eq. (22) [19, 20].

$$\tau = \frac{{M_{\text{s}} C_{{{\text{v}},{\text{s}}}} }}{Ua}$$
(21)
$$T_{\text{SADT}} = T_{\text{NR}} - \frac{{{\text{R}}T_{\text{NR}}^{2} }}{{E_{\text{a}} }}$$
(22)

where U is the heat transfer coefficient, a is the contact area of the system and environment. Assuming 50 kg DABT is loaded in the cylinder with the height of 60 cm and the diameter of 30 cm, so the contact area of the system and environment was 0.5652 m2. In this study, the heat transfer coefficient U = 5 J m−2 K−1 s−1 had been chosen for prediction of the T SADT. The T SADT of DABT was calculated as 429.54 °C.

Comparison of onset temperatures of DABT with DNABT

The values of onset temperatures of DABT and its derivative DNABT were listed in Table 6.

From Table 6, it could be concluded that the onset temperatures of DABT were determined in the DSC and ARC experiments were found to be higher than that of DNABT. DABT was a stable compound compared with DNABT.

Table 6 Onset temperatures of DABT and DNABT
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Conclusions

The thermal decomposition behavior of DABT were studied by TG–DTG–DSC, DTA and ARC techniques. The results from TG–DTG–DSC, DTA and ARC all suggested that DABT had an endothermic decomposition of lost DMSO and an exothermic decomposition. The TG–DTG–DSC measurement showed that the endothermic decomposition of lost DMSO started at 388.23 °C and ended at 462.73 °C, and the exothermic decomposition started at 468.23 °C and ended at 535.73 °C. The values of non-isothermal decomposition kinetics and thermodynamics parameters that were obtained by the Ozawa’s and Kissinger’s methods for DABT showed good correlation. The critical temperature of thermal explosion (T bp0) obtained by the Ozawa’s and Kissinger’s methods were calculated as 470.46 and 470.73 °C, respectively. The self-heating decomposition parameters, including the T 0, T f, T m, m m, ΔT ad and TMR, were obtained and corrected by φ. The self-accelerating decomposition temperature (T SADT, 50kg) was calculated as 429.54 °C. DABT was a stable compound compared with DNABT.