Introduction

High nitrogen heterocyclic compounds are one of the developing fields in energetic material research because of their positive enthalpy of formation, high thermal stability and low sensitivity to impact and friction. Moreover, the high nitrogen content is able to increase the density and to easily obtain an oxygen balance; the main combustion (decomposition) product is nitrogen. So, high nitrogen heterocyclic compounds are being considered as green energetic materials, which are used in solid propellants, explosives and civil combustible-gas generators [1–6].

Tetrazole has the highest nitrogen content in single heterocyclic compounds. Tetrazole is also the precursor to synthesize other high nitrogen heterocyclic compounds, such as 5-aminotetrazole, azotetrazole and N, N′-bis[1(2)H-tetrazol-5-yl]-amine (BTA). Tetrazole of BTA bears acidity, its isoelectronic character and symmetry (to a degree) of the anion, and by analogy, one might expect interaction of the tetrazolate anion with base containing nitrogen, such as ammonium salt and hydrazium salt. Dihydrazidinium bis(tetrazolyl)amine (DHBTA) has been prepared, and the structure of DHBTA is shown in Scheme 1. It is shown that DHBTA has high heat of formation, large gas production, good thermal stability and high reaction heat, and it has possible application as gas generant, low signature propellants, low-smoke or non-smoke pyrotechnics and high performance explosives [7–11].

Scheme 1
scheme 1

Structure of DHBTA

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In the present study, thermochemical properties of its solution have been studied for the first time. The aim of this work is to study the dissolution properties of DHBTA in water and N-methyl pyrrolidone (NMP). The kinetic equations of the two dissolution processes are obtained, respectively, which provide valuable information for its applications in the future.

Experimental

Materials

DHBTA used in the experiments was prepared and purified by Beijing Institute of Technology, and had a purity of more than 99.4 %. The sample was conserved under vacuum. NMP (ρ = 1.029 − 1.035 g cm−3) used as solvent was of analysis reagent grade, and their purities were higher than 99.5 %. The water used in the experiments was deionized with an electrical conductivity of 0.8 × 10−4 − 1.2 × 10−4 S m−1 and obtained by purification two times via a sub-boiling distillation device.

Equipment and conditions

A RD496-2000 Calvet Microcalorimeter (China Academy of Engineering Physics Mianyang CEAP Thermal Analysis Instrument Company) was used to measure the dissolution heat. The standard molar enthalpy of the dissolution of KCl (spectrum purity) in distilled water measured by a RD496-2000 Calvet microcalorimeter at 298.15 K was (17.234 ± 0.041) kJ mol−1, and the relative error was less than 0.04 % compared with the literature value (17.241 ± 0.018) kJ mol−1 [12]. This showed that the device for measuring the enthalpy used in this work was reliable. The enthalpies of dissolution were measured at (298.15 ± 0.005) K.

Results and discussion

Thermochemical behaviors of the dissolution of DHBTA in water and NMP

The proper molar sample of DHBTA was, respectively, dissolved in water and NMP at 298.15 K in order to form solution. The molar enthalpy of the dissolution (Δdiss H) was detected on a RD496-2000 Calvet microcalorimeter [13, 14]. Each process was repeated three times to ensure the precision of the data [15–17]. The dissolution of DHBTA in water and NMP was all endothermic processes. The thermochemical data obtained, Δdiss H, b (the molality of DHBTA), Δdiss H partial (the relative partial molar enthalpy of dissolution) and Δdiss H apparent (the relative apparent molar enthalpy of dissolution), are listed in Tables 1 and 2.

Table 1 Enthalpies of dissolution of DHBTA in water
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Table 2 Enthalpies of dissolution of DHBTA in NMP
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With the help of the values of b and Δdiss H in Table 1, the empirical formula of enthalpy for the dissolution processes of DHBTA in water describing the b versus Δdiss H relation is obtained as:

$$ \Delta_{\text{diss}} H = - 126.675 - 1348.48b + 819.754b^{1/2} $$
(1)

The empirical formulae of relative apparent molar enthalpy (Δdiss H apparent), relative partial molar enthalpy (Δdiss H partial) and differential molar enthalpy (Δdif H 1,2) calculated by Eq. 1 are, respectively.

$$ \Delta_{\text{diss}} H_{\text{apparent}} = \, \Delta_{\text{diss}} H\left( {b = b} \right) \, {-} \, \Delta_{\text{diss}} H\left( {b = 0} \right) \, = - 1348.48b + 819.754b^{1/2} $$
(2)
$$ \Delta_{\text{diss}} H_{\text{partial}} = b\left( {\frac{{\partial \Delta_{\text{diss}} H}}{\partial b}} \right) + \Delta_{\text{diss}} H_{\text{apparent}} = - 2696.96b + \, 1229.63b^{1/2} $$
(3)
$$ \Delta_{\text{dif}} H_{1,2} = \Delta_{\text{diss}} H\left( {b = b_{2} } \right) \, \Delta_{diss} H\left( {b = b_{1} } \right) \, = - 1348.48(b_{2} - b_{1} ) + \, 819.75 \, (b_{2}^{1/2} - b_{1}^{1/2} ) $$
(4)

According to the values of b and Δdiss H in Table 2, the empirical formula of enthalpy for the dissolution processes of DHBTA in NMP describing the b versus Δdiss H relation is also obtained as:

$$ \Delta_{\text{diss}} H = - 33.68 - 1021.38b + \, 340.88b^{1/2} $$
(5)

The empirical formulae of relative apparent molar enthalpy (Δdiss H apparent), relative partial molar enthalpy (Δdiss H partial) and differential molar enthalpy (Δdif H 1,2) calculated by Eq. 5 are, respectively.

$$ \Delta_{\text{diss}} H_{\text{apparent}} = \, \Delta_{\text{diss}} H\left( {b = b} \right) - \Delta_{\text{diss}} H\left( {b = 0} \right) \, = - 1021.38b + \, 340.88b^{1/2} $$
(6)
$$ \Delta_{\text{diss}} H_{\text{partial}} = b\left( {\frac{{\partial \Delta_{\text{diss}} H}}{\partial b}} \right) + \Delta_{\text{diss}} H_{\text{apparent}} = - 2042.75b + 511.31b^{1/2} $$
(7)
$$ \Delta_{\text{dif}} H_{1,2} = \Delta_{\text{diss}} H\left( {b = b_{2} } \right) \, {-} \, \Delta_{\text{diss}} H\left( {b = b_{1} } \right) \, = - 1021.38(b_{2} - b_{1} ) + \, 340.88(b_{2}^{1/2} - b_{1}^{1/2} ) $$
(8)

From Tables 1 and 2, we can see that the molality of the solution b can affect the values of Δdiss H, the calculated Δdiss H apparent and Δdiss H partial. In Table 1, the values of Δdiss H decrease with values of b increasing during the dissolution processes of DHBTA in water. One can also find that the relationships between Δdiss H and b 1/2 for the dissolution processes of DHBTA in water is linear equation from Fig. 1, and at the same time, the relationship between Δdiss H and b 1/2 for the dissolution processes of DHBTA in NMP is quadratic equation from Fig. 2.

Fig. 1
figure 1

Relationship between Δdiss H and b 1/2 of DHBTA in water

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Fig. 2
figure 2

Relationship between Δdiss H and b 1/2 of DHBTA in NMP

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The kinetics of dissolution process of DHBTA in water or NMP

Equations 9 and 10 are chosen as the model function describing the dissolution of DHBTA in water or NMP [18–20].

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = kf(\alpha ) $$
(9)
$$ \ln \left[ {\frac{1}{{H_{0} }}\left( {\frac{{{\text{d}}H}}{{{\text{d}}t}}} \right)_{\text {i}} } \right] = \ln k + n\ln \left[ {1 - \left( {\frac{H}{{H_{0} }}} \right)_{\text {i}} } \right]\quad \text{i} = 1,2, \ldots ,L $$
(10)

By putting the original data in Tables 3 and 4, −(dH/dt)i, (H/H 0)i, H ∞, i = 1, 2, …, L, into Eq. 10, the values of n and ln k are obtained and listed in Table 5, where n is the reaction order and k the reaction rate constant.

Table 3 Original data of the dissolution process of DHBTA in water at 298.15 K
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Table 4 Original data of the dissolution process of DHBTA in NMP at 298.15 K
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Table 5 Values of n, lnk and correlative coefficient r for the dissolution process at 298.15 K
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Substituting the values of n and k in Table 5 into Eq. 9, we can get

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 2.70} (1 - \alpha )^{0.82} $$
(11)

for dissolution process of DHBTA in water, and

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = 10^{ - 2.47} (1 - \alpha )^{0.66} $$
(12)

for dissolution process of DHBTA in NMP.

Conclusions

The dissolution processes of DHBTA in water and NMP were investigated by RD496-2000 Calvet microcalorimeter at 298.15 K, respectively. The relationship between Δdiss H and b 1/2 of DHBTA dissolved in water is linear equation, and the relationship between Δdiss H and b 1/2 of DHBTA dissolved in NMP is quadratic equation.

The expressions describing values of Δdiss H, Δdiss H apparent, Δdiss H partial and Δdif H 1, 2 versus the molality (b) for DHBTA dissolved in water are Δdiss H = −126.68 − 1,348.48b + 819.75b 1/2, Δdiss H apparent = − 1,348.48b + 819.75b 1/2, Δdiss H partial = −2,696.96b + 1,229.63b 1/2, Δdif H 1,2 = − 1,348.48(b 2 − b 1) + 819.75 (b 1/22  − b 1/21 ). The expressions describing values of Δdiss H, Δdiss H apparent, Δdiss H partial and Δdif H 1,2 versus the molality (b) of DHBTA in NMP are Δdiss H = − 33.69 − 1,021.38b + 340.88b 1/2, Δdiss H apparent = − 1,021.38b + 340.88b 1/2, Δdiss H partial = − 2,042.75b + 511.31b 1/2, Δdif H 1,2 = − 1,021.38 (b 2 − b 1) + 340.88 (b 1/22  − b 1/21 ).

The kinetics equations of dissolution processes for DHBTA are dα/dt = 10−2.70(1 − α)0.82 in water, and dα/dt = 10−2.47(1 − α)0.66 in NMP.