Introduction

1,1-Diamino-2,2-dinitroethylene (FOX-7) is a novel high-energy material with high-thermal stability and low sensitivity to impact and friction. Since first synthesized in 1999 [1, 2], FOX-7 has been considered as an important research field of energetic materials and will be used in insensitive ammunition or solid propellant [3–14]. FOX-7 is a representative “push–pull” nitro-enamine compound, which possesses a highly polarized carbon–carbon double bond with positive and negative charges being stabilized by the amino group and nitro group, respectively, and presents certain acidic properties [15, 16]. So, FOX-7 can react with strong alkalis to prepare some energetic slats, such as potassium salt, rubidium salt, cesium salt, and guanidine salt [8, 17–19]. Other salts and metal complexes of FOX-7 also can be synthesized throng replacement reaction. Garg et al. [20, 21] and Vo et al. [22] have reported Ag(amine)(FOX-7) [amine: ammonia, methylamine and propylamine], Cu(amine)2(FOX-7)2 [amine: ammonia, methylamine, propylamine and dimethylamine, ethylenediamine and 1,3-propane diamine], and other copper (nickel) bipyridyl (phenanthroline) FOX-7 complexes. He et al. [23] also reported two copper complexes containing other anions [[Cu(phen)2FOX-7](phen)NO3·4H2O and [Cu(phen)2FOX-7]Cl·3H2O]. The syntheses, crystal structures, theoretical calculations, and properties of these complexes have been discussed. Despite those studies, the reactivity of FOX-7 is still an unresolved issue. We hope to explore the structure–property relationship through largely synthesizing series of FOX-7 complexes. The synthesis and crystal structure of a new zinc-FOX-7 complex [Zn(NH3)2(FOX-7)2] is just reported by our group [24]. In this article, we will first report the nonisothermal decomposition kinetics, specific-heat capacity, and adiabatic time-to-explosion of Zn(NH3)2(FOX-7)2 to evaluate its thermal stability.

Experimental

Synthesis

K(FOX-7)·H2O was prepared according to Ref. [18].

K(FOX-7)·H2O (0.01 mol) was put into excess ammonia water (15 mL) to clear, and then zinc nitrate (0.005 mol) was added to it. After reaction at room temperature for 20 min, the resulting mixture was stored at room temperature. Then, many yellow crystals of Zn(NH3)2(FOX-7)2 were formed, which were filtered, washed with water, and dried under vacuum, yielding 0.83 g (42 %). Anal. Calcd.(%) for C4H12N10O8Zn: C 12.20, H 3.073, N 35.58; found: C 12.11, H 3.11, N 35.36. IR (KBr): 3407, 3326, 2737, 2505, 1645, 1613, 1508, 1467, 1357, 1232, 1128, 802, 758 cm−1. The powder XRD result and the theoretical result of single-crystal diffraction are shown in Fig. 1. We can see that they are consistent with each other and all have big diffraction peaks at 107, 15.3, 19.4, 21.2, 29.5, and 34.5 degree, respectively. The molecular structure of Zn(NH3)2(FOX-7)2 is shown in Fig. 2. The crystal belongs to monoclinic, space group C2/c with crystal parameters of a = 18.468(2) Å, b = 6.454(1) Å, c = 12.979(2) Å, β = 117.11°, V = 1377.1(3) Å3, Z = 4, μ = 0.185 mm−1, F(000) = 800, D c = 1.898 g cm−3, R 1 = 0.0252, and wR 2 = 0.0594 [24]. The crystal data of Zn(NH3)2(FOX-7)2 have been deposited in the Cambridge Data Center with the number of 873109.

Fig. 1
figure 1

XRD result of Zn(NH3)2(FOX-7)2

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Fig. 2
figure 2

Molecular structure of Zn(NH3)2(FOX-7)2

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Experimental equipments and conditions

The DSC experiments were performed using a DSC200 F3 apparatus (NETZSCH, Germany) under a nitrogen atmosphere at a flow rate of 80 mL min−1. The crucible is a standard aluminum product, and the condition of crucible is open. The heating rates were 5.0, 7.5, 10.0, 12.5, and 15.0 °C min−1 from ambient temperature to 350 °C, respectively.

The TG/DTG experiment was performed using a SDT-Q600 apparatus (TA, USA) under a nitrogen atmosphere at a flow rate of 100 mL min−1. The crucible is a standard aluminum product, and the condition of crucible is open. The heating rate was 10.0 °C min−1 from ambient temperature to 500 °C.

The specific-heat capacity was determined using a Micro-DSCIII apparatus (SETARAM, France). The heating rate used was 0.15 °C min−1 from 10 to 80 °C. The sample cell is a standard sealed cell of apparatus. The sample mass used was 302.59 mg.

Results and discussion

Thermal decomposition behavior

Typical DSC and TG-DTG curves (Figs. 3, 4) indicate that the thermal decomposition of Zn(NH3)2(FOX-7)2 can be divided into two continuous exothermic decomposition processes. The first is an intense exothermic decomposition process which occurs at 180–235 °C with a mass loss of about 37.5 %. The extrapolated onset temperature and peak temperature are 198.1 and 204.4 °C, respectively, at the heating rate of 10.0 °C min−1. The second is a slow exothermic decomposition process with a mass loss of about 28.1 % at the temperature range of 235–330 °C, and the peak temperature is 279.3 °C at a heating rate of 10.0 °C min−1. The decomposition heat of the two continuous processes is 2,072 ± 71 J g−1. The final residue at 500 °C is about 28 %. Comparing with the thermal behavior of similar Cu(NH3)2(FOX-7)2, we can see that they have the same thermal decomposition behavior, but Zn(NH3)2(FOX-7)2 has much higher thermal stability than Cu(NH3)2(FOX-7)2, the extrapolated onset temperature of which and peak temperature of the first decomposition process are 165.1 and 167.3 °C at a heating rate of 10.0 °C min−1, respectively [21, 25, 26].

Fig. 3
figure 3

DSC curve of Zn(NH3)2(FOX-7)2

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Fig. 4
figure 4

TG/DTG curves of Zn(NH3)2(FOX-7)2

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Nonisothermal decomposition kinetics

In order to obtain the kinetic parameters [the apparent activation energy (E) and preexponential constant (A)] of the first exothermic decomposition process, the multiple heating method (Kissinger method [27] and Ozawa method [28]) was employed. The determined values of the beginning temperature (T 0), extrapolated onset temperature (T e) and the peak temperature (T p) at the different heating rates are listed in Table 1. The values of T 00 and T e0 corresponding to β → 0 obtained by Eq. (1) are also listed in Table 1 [29].

$$ T_{{0{\text{i}}\,{\text{or}}\,{\text{ei}}}} = T_{{00{\text{ or e}}0}} + n\beta_{\text{i}} + m\beta_{\text{i,}}\,\,\,\,\,\,\,\,\,{i} = { 1} - 5 , $$
(1)
Table 1 The values of T 0, T e, T p, T 00, and Te0 and the kinetic parameters of the first exothermic decomposition process for Zn(NH3)2(FOX-7)2 determined from the DSC curves
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where n and m are coefficients.

The calculated values of kinetic parameters (E and A) are also listed in Table 1. The apparent activation energy obtained by Kissinger method is consistent with that by Ozawa method. The linear correlation coefficients (r) are all close to 1. So, the results are credible. Moreover, the apparent activation energy of the exothermic decomposition process is low, indicating that Zn(NH3)2(FOX-7)2 easily decompose at temperature above 170 °C.

T versus α (the conversion degree) curves at different heating rates (thermal decomposition data from DSC curves) were shown in Fig. 5. By substituting corresponding data (β i, T i and α i, i = 1, 2, 3,…) into Ozawa equation, the values of E a for any given value of α were obtained and shown in Fig. 6. The values of E steadily distribute from 130 to 138 kJ mol−1 in the α range of 0.15–0.85, and the average value of E is 135.3 kJ mol−1, which is in approximate agreement with that obtained by Kissinger method and Ozawa method from only peak-temperature values. So, the values were used to check the validity of E by other methods.

Fig. 5
figure 5

T versus α curves for the decomposition reaction of Zn(NH3)2(FOX-7)2 at different heat rates

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Fig. 6
figure 6

E a versus α curve for the decomposition reaction by Ozawa method

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Five integral equations (The general integral equation, the universal integral equation, MacCallum–Tanner equation, Šatava–Šesták equation, and Agrawal equation) were cited to obtain the values of E, A, and the most probable kinetic model function [f(α)] from each DSC curve [29, 30]. Forty-one types of kinetic model functions taken from Ref. [29] and experimental data form each DSC curve were put into the above five integral equations for calculating, respectively. The kinetic parameters (E and A), probable kinetic model function and linear correlation coefficient (r), standard mean square deviation (Q), and believable factor [d, where d = (1−r)Q] are listed in Table 2. We can see that the values of E and logA obtained by the five equations agree with each other, and the mean value is much close to that by Kissinger method and Ozawa method and that by equal conversion-degree method. So, the most probable kinetic model function is classified as:

$$ f\left( \alpha \right) = 4(1 - \alpha )[ - \ln (1 - \alpha )]^{{{3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-0pt} 4}}} , $$
(2)

(No. 10, Avrami–Erofeev equation, assumes random nucleation and its subsequent growth, n = 1/4, m = 4),

$$ G\left( \alpha \right) = [ - \ln (1 - \alpha )]^{{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-0pt} 4}}} , $$
(3)

according to the unanimity rule of calculation results from each model equation [29]. The kinetic equation of the first exothermic decomposition process for Zn(NH3)2(FOX-7)2 can be described as:

$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = \frac{{10^{13.99} }}{\beta }4(1 - \alpha )[ - \ln (1 - \alpha )]^{{{3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-0pt} 4}}} { \exp }( - 1.448 \times 10^{5} /RT) $$
(4)
Table 2 Calculated values of kinetic parameters of the decomposition reaction
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Self-accelerating decomposition temperature and critical explosion temperature

The self-accelerating decomposition temperature (T SADT) and critical temperature of thermal explosion (T b) are two important parameters required to ensure safe storage and process operations for energetic materials and then to evaluate the thermal stability. T SADT and T b can be obtained by Eqs. (5) and (6) [29, 31], respectively.

$$ T_{\text{SADT}} = T_{e0} { ,} $$
(5)
$$ T_{\text{b}} = \frac{{E_{\text{O}} - \sqrt {E_{\text{O}}^{ 2} - 4E_{\text{O}} RT_{\text{e0}} } }}{2R}, $$
(6)

where E O is the apparent activation energy obtained by Ozawa method.

T SADT and T b for Zn(NH3)2(FOX-7)2 are 183.2 and 195.8 °C, respectively, which all are much higher than those of analogous Cu(NH3)2(FOX-7)2 as 142.1 and 152.9 °C [26], also indicating Zn(NH3)2(FOX-7)2 has higher thermal stability than Cu(NH3)2(FOX-7)2.

Specific-heat capacity

Figure 7 shows the determination result of Zn(NH3)2(FOX-7)2, using a continuous specific-heat capacity mode of Micro-DSCIII. In determined temperature range, specific-heat capacity presents a good linear relationship with temperature. Specific-heat capacity equation of Zn(NH3)2(FOX-7)2 is:

$$ C_{\text{p}} \left( {{\text{J}}\, {\text{g}}^{ - 1} \,{\text{K}}^{ - 1} } \right) = 0.3727 + 2.6240 \times 10^{ - 3} \,T\left( {285.0 \,{\text{K}} < T < 350.0 \,{\text{K}}} \right) $$
(7)
Fig. 7
figure 7

Determination results of the continuous specific-heat capacity of Zn(NH3)2(FOX-7)2

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The molar-heat capacity of Zn(NH3)2(FOX-7)2 is 454.6 J mol−1 K−1 at 298.15 K.

Estimating of adiabatic time-to-explosion

The adiabatic time-to-explosion is also an important parameter for evaluating the thermal stability of energetic materials and can be calculated by Eqs. (8) and (9) [29, 32–35].

$$ C_{\text{p}} \frac{{{\text{d}}T}}{{{\text{d}}t}} = QA{ \exp }({{ - E} \mathord{\left/ {\vphantom {{ - E} {RT}}} \right. \kern-0pt} {RT}})f(\alpha ), $$
(8)
$$ \alpha = \int\limits_{{T_{0} }}^{T} {\frac{{C_{\text{p}} }}{Q}} {\text{d}}T, $$
(9)

where C p is the specific-heat capacity (J mol−1 K−1), T is the absolute temperature (K), t is the adiabatic time-to-explosion (s), Q is the exothermic values (J mol−1), A is the preexponential factor (s−1), E is the apparent activation energy of the thermal decomposition reaction (J mol−1), R is the gas constant (J mol−1 K−1), f(α) is the most probable kinetic model function, and α is the conversion degree.

After integrating of Eq. (8), the adiabatic time-to-explosion equation can be obtained as:

$$ t = \int\limits_{0}^{t} {{\text{d}}t} = \int\limits_{{T_{0} }}^{T} {\frac{{C_{\text{p}} { \exp }({E \mathord{\left/ {\vphantom {E {RT}}} \right. \kern-0pt} {RT}})}}{QAf(\alpha )}} {\text{ d}}T, $$
(10)

where the limit of temperature integration is from T 00 to T b.

In fact, the conversion degree (α) of energetic materials from the beginning thermal decomposition to thermal explosion in the adiabatic conditions is very small, and it is very difficult to obtain the most probable kinetic model function [f(α)] at the process. So, we separately used Power-low model [Eq. (11)], Reaction-order model [Eq. (12)], Avrami–Erofeev model [Eq. (13)], and the above obtained kinetic model function to estimate the adiabatic time-to-explosion and supposed different rate orders (n) [29, 30]. The calculation results are listed in Table 3.

$$ f(\alpha ) = n\alpha^{{{{(\text{n} - 1)} \mathord{\left/ {\vphantom {{(n - 1)} \text{n}}} \right. \kern-0pt} \text{n}}}} $$
(11)
$$ f(\alpha ) = (1 - \alpha )^{\text{n}} $$
(12)
$$ f(\alpha ) = n(1 - \alpha )[ - \ln \left( {1 - \alpha } \right)]^{{{{(\text{n} - 1)} \mathord{\left/ {\vphantom {{(\text{n} - 1)} \text{n}}} \right. \kern-0pt} \text{n}}}} $$
(13)
Table 3 The calculation results of adiabatic time-to-explosion
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From Table 3, we can see that the calculation results exhibit some deviation and the decomposition model has big influence on the estimating result of adiabatic time-to-explosion. From the whole results, we believe the adiabatic time-to-explosion of Zn(NH3)2(FOX-7)2 should be about 20 s. It is a relatively short time, and the result can be proved credible according to the intense change of DSC curves in the first exothermic decomposition process.

Conclusions

Zn(NH3)2(FOX-7)2 was first synthesized and structurally characterized. The thermal decomposition behavior of Zn(NH3)2(FOX-7)2 presents two continuous exothermic decomposition processes. The nonisothermal kinetic equation of the first decomposition process is obtained. The self-accelerating decomposition temperature (T SADT) and critical temperature of thermal explosion (T b) are 183.2 and 195.8 °C, respectively.

Specific-heat capacity equation of Zn(NH3)2(FOX-7)2 is C p (J g−1 K−1) = 0.3727 + 2.6240 × 10−3 T (283.0 K < T < 353.0 K), and the molar-heat capacity is 454.6 J mol−1 K−1 at 298.15 K. Adiabatic time-to-explosion of Zn(NH3)2(FOX-7)2 was estimated to be about 20 s. The thermal stability of Zn(NH3)2(FOX-7)2 is good and higher than that of analogous Cu(NH3)2(FOX-7)2.