1 Introduction

Compounds containing nitroxyl group (N—NO₂) are of interest for practical use as energetic materials owing to their high energy density and nitrogen content ^[1-4]. Nitroguanidine (NG) is a simple nitroxyl compound. The effect of electron withdrawing of ni- tro group makes the lower electron density in the single carbon atom, so NG can behave as an active starting material in the reactions with nucleophilic reagents to get a series of NG-based energetic materials ^[5-9]. Because of the excellent property and low cost, NG has become an important moiety to design and synthesize other new high - nitrogen energetic materials ^{[6-8, 10-12]}.

Bis (nitroguanidine) methane (BNGM) was report- ed firstly by Yu et al ^[13]through the reaction of NG and formaldehyde. BNGM was considered as an important intermediate to synthesize other heterocyclic compounds because of the existence of C＝NNO₂ and —NH₂ groups. It is remarkable to note that when BNGM was treated with nitric acid/acetic anhydride, 2, 4 -dinitramino - 1, 5 -dinitro -1, 3, 5 -triazine was obtained^[13-16]. Namely, the deammoniation cyclization and the nitration of cyclized product occurred simultaneously. 2, 4-Dinitramino-1, 5-dinitro-1, 3, 5-triazine is a nitrogen-rich explosive with slight positive oxygen balance. Unfortunately, its stability decreased obviously in comparison to that of BNGM. Containing two explosive groups ( C＝N—NO₂) and possessing good thermal stability will make BNGM serve as an appropriate candidate of energetic materials.

In this paper, we mainly report the thermal behavior, specific heat capacity and adiabatic time-to- explosion of BNGM, further estimating its thermal stability and exploring essential application values as an energetic material. The difference of thermal behavior between the parent material and BNGM is also discussed.

2 Experimental 2.1 Synthesis

The parent materials were purchased from the trade, and formaldehyde was AR grade product. The purity of nitroguanidine was 98% and the concentration of hydrochloric acid was 38%. BNGM was prepared according to Ref [15] and the synthetic route of BNGM was showed in Scheme 1. ¹H NMR (DMSO - d₆, 500 MHz):8.157, 4.597, 3.345. ¹³C NMR (DMSO-d₆, 500 MHz):159.532, 73.329. IR (KBr, ν/cm^-1):3319, 3180, 1586, 1542, 1367, 1252, 983, 719. Anal. calcd for C₃H₈N₈O₄ (%):C 16.36, H 3.64, N 50.91;Found:C 16.45, H 3.74, N 51.17.

2.2 Experimental Measurements

The differential scanning calorimetry (DSC) experiments were performed using a DSC200 F3 (NETZSCH, Germany) apparatus under a nitrogen atmosphere with a flow rate of 80 mL · min^-1. The heating rates were 5.0, 7.5, 10.0, 12.5 ℃ · min^-1 and 15.0 ℃ · min^-1 from ambient temperature to 350 ℃, respectively. The thermogravimetry/differential thermogravimetry (TG/DTG) experiment was determined using a SDT-Q600 apparatus (TA, USA) under a nitrogen atmosphere at the flow rate of 100 mL·min^-1. The heating rate used was 10.0 ℃·min^-1 from ambient temperature to 500 ℃. The specific heat capacity was determined using a Micro-DSCⅢ apparatus (SETARAM, France), and the sample mass was 196.9 mg. The heating rate used was 0.15 ℃ ·min^-1 from 10 ℃ to 80 ℃. Energy of combustion was determined by IKA C5000 oxygenbomb calorimeter (German) adiabatically. The calorimeter was calibrated with the standard substance benzoic acid having a purity of 99.99%, and the sample was tested with 6 times. The impact sensitivity was determined by using a ZBL-B impact sensitivity instrument (Nachcn, China). The mass of drop hammer was 2.0 kg, and the sample mass for test was 30 mg.

3 Results and Discussion 3.1 Thermal Decomposition Behavior

Typical DSC and TG-DTG curves (Fig. 1) indicate that the thermal behavior of BNGM can be divided into two exothermal decomposition processes. The onset temperature, peak temperature and decomposition enthalpy at a heating rate of 10 ℃·min^-1 are 205.7 ℃, 208.1 ℃ and 303.3 J·g^-1 with a mass loss of about 32.2% for the first decomposition process, and 276.4 ℃, 292.5 ℃, 172.0 J · g^-1 with a mass loss of about 31.7% for the second process, respectively. The final residue is about 25.4% at 400 ℃. The DSC curve of NG was also obtained, and there is an endothermic peak as a melting peak at 249.2 ℃. Subsequently, an intense exothermic process occurred at 254.5 ℃ for NG. It can be seen that the DSC curves of NG and BNGM are obviously different. Although BNGM possesses a good thermodynamic stability, it is lower than that of NG and the reason should be the new unstable —NH—CH₂—NH— bond of BNGM molecule.

In order to obtain the kinetic parameters (the apparent activation energy (E) and preexponential constant (A)) of the first exothermic decomposition process, a multiple heating method (Kissinger′s method ^[17] and Ozawa′s method ^[18]) was employed according to the data in Fig. 2. The determined values of the beginning temperature (T₀), extrapolated onset temperature (T_e) and peak temperature (T_p) at different heating rates are listed in Table 1. The values of T₀₀ and T_e0 corresponding to heating rate β →0 obtained by Eq. (1) are 164.1 ℃ and 189.6 ℃^[19].

$ {T_{\left ( {{\rm{ 0}}\;\;{\rm{or}}\;\;{\rm{ e }}} \right) i}} = {T_{\left ( {{\rm{ }}00\;\;{\rm{ or}}\;\;{\rm{ e0 }}} \right) }} + n{\beta _{\rm{i}}} + m\beta _i^2 + p\beta _i^3,\;\;i = {\rm{ }}1{\rm{ }} - {\rm{ }}5 $

(1)

where n, m and p are coefficients.

The calculated values of kinetic parameters (E and A) are listed in Table 1. E obtained by Kissinger′s method is consistent with that by Ozawa ′s method. The linear correlation coefficients (r) are all close to 1. So the results are credible.

The self-accelerating decomposition temperature (T_SADT) and critical temperature of thermal explosion (T_b) are two important parameters required in evaluation of their safe storage and process operations for energetic materials and then to evaluate the thermal stability. T_SADT and T_b for BNGM are calculated as 189.6 ℃ and 190.9 ℃, respectively ^[19-20], indicat- ing that the thermal stability of BNGM is good.

3.2 Specific Heat Capacity

Figure 3 shows the determination result of specific heat capacity (c_p) for BNGM, using a continuous specific heat capacity mode of apparatus. It can be seen that c_p presents a good linear relationship with temperature in determined temperature range. Specific heat capacity equation is shown as:

$ {c_p} = 0.1763 + 3.2461 \times {10^{ - 3}}T\left ( {285.0{\rm{ K}} < T < 350.0{\rm{ K}}} \right) $

(2)

The specific heat capacity and molar heat capacity of BNGM are 1.15 J·g^-1·K^-1 and 251.9 J·mol^-1·K^-1 at 298.15 K, respectively.

3.3 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. (3) and (4) ^{[19, 21-25]}.

$ {c_p}\frac{{{\rm{d}}T}}{{{\rm{d}}t}} = QA{\rm{exp}}\left ( { - E/RT} \right) f (\alpha ) $

(3)

$ \alpha = \int_{{T_0}}^T {\frac{{{c_p}}}{Q}{\rm{d}}T} $

(4)

where c_p is the specific heat capacity, J·mol^-1·K^-1; T is the absolute temperature, K;Q is the exothermic values, J·mol^-1; A is the pre-exponential factor, s^-1; E is the apparent activation energy of the thermal decomposition reaction, J·mol^-1; R is the gas con- stant, J·mol^-1·K^-1; f (α) is the most probable kinetic model function and α is the conversion degree.

After integrating of Eq. (3), the adiabatic time- to-explosion equation can be obtained as:

$ t = \int_0^t {{\rm{d}}t} = \int_{{T_0}}^T {\frac{{{c_p}{\rm{exp}}\left ( {E/RT} \right) }}{{QAf (\alpha ) }}{\rm{d}}T} $

(5)

where the limit of temperature integration is from T₀₀ 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, Reaction-order model, Avrami- Erofeev model and the above obtained kinetic model function to estimate the adiabatic time - to - explosion and supposed different rate orders (n) ^{[19, 26]}. The calculation results are listed in Table 2.

From Table 2, we can see that the calculation results exhibit some deviations and the decomposition model has big influence on the estimate of adiabatic time-to-explosion. From the whole results, we believe the adiabatic time - to - explosion of BNGM should be about 280 s. It is a relatively long time, and the result indicates that BNGM has a good thermal stability.

3.4 Enthalpy of Combustion

The determination results of the energy of constant volume combustion are shown in Table 3, so the constant-volume combustion enthalpy for BNGM is (-10171.4±27.5) J·g^-1.

The standard molar enthalpy of combustion (${\Delta _{\rm{c}}}H_{\rm{m}}^\theta $) was referred to the energy of combustion change of the following idealized reaction formulas (a) and (b) at T = 298.15 K and p_θ = 101.325 kPa. Under the ideal condition of sufficient oxygen, we believe that the oxidation product of nitro group is NO₂ (g) and other N element would be oxidized to N₂ (g).

$ \begin{array}{l} {{\rm{C}}_{\rm{3}}}{{\rm{H}}_{\rm{8}}}{{\rm{N}}_{\rm{8}}}{{\rm{O}}_{\rm{4}}}\left ( {{\rm{ s }}} \right) {\rm{ }} + {\rm{ }}5{{\rm{O}}_2}\left ( {{\rm{ g }}} \right) {\rm{ }} = {\rm{ }}3{\rm{C}}{{\rm{O}}_{\rm{2}}}\left ( {{\rm{ g }}} \right) {\rm{ }} + {\rm{ }}4{{\rm{H}}_{\rm{2}}}O (l) {\rm{ }} + \\ 3{{\rm{N}}_{\rm{2}}}\left ( {{\rm{ g }}} \right) {\rm{ }} + {\rm{ }}2{\rm{N}}{{\rm{O}}_{\rm{2}}}\left ( {{\rm{ g }}} \right) \end{array} $

(a)

$ 2{\rm{N}}{{\rm{O}}_{\rm{2}}}\left ( {{\rm{ g }}} \right) {\rm{ }} + \frac{2}{3}{{\rm{H}}_{\rm{2}}}{\rm{O}} (l) {\rm{ }} = \frac{4}{3}{\rm{HN}}{{\rm{O}}_{\rm{3}}}{\rm{ (}}l) {\rm{ }} + \frac{2}{3}{\rm{NO}}\left ( {{\rm{ g }}} \right) $

(b)

$ {\Delta _{\rm{c}}}H_{\rm{m}}^\theta $ can be derived from the standard molar enthalphy of combustion in accordance with equations (6) and (7).

$ {\Delta _{\rm{c}}}H_{\rm{m}}^\theta = {\Delta _{\rm{c}}}U_{\rm{m}}^\theta + \Delta {n_1}RT + \Delta {n_2}RT $

(6)

$ \Delta n = \sum {n_i} ({\rm{ products}}, {\rm{g }}) {\rm{ }} - \sum {n_i} ({\rm{reactants}}, {\rm{g }}) $

(7)

where ∑n_i is the total molar amount of gases in products or reactants.

The standard molar enthalpy of formation (${\Delta _{\rm{f}}}H_{\rm{m}}^\theta $) can be calculated by Hess′s law ^[27], according to the above thermochemical equations. For BNGM, the standard molar enthalpy of formation is:

$\begin{array}{l} {\Delta _{\rm{f}}}H_{\rm{m}}^\theta ({\rm{BNGM}}, {\rm{s}}) = {\rm{ }}3{\Delta _{\rm{f}}}H_{\rm{m}}^\theta {\rm{ (C}}{{\rm{O}}_{\rm{2}}}, {\rm{g}}) + \frac{{10}}{3}{\Delta _{\rm{f}}}H_{\rm{m}}^\theta ({{\rm{H}}_{\rm{2}}}{\rm{O}}, l) \\ + \frac{2}{3}{\Delta _{\rm{f}}}H_{\rm{m}}^\theta ({\rm{NO}}, {\rm{g}}) + {\rm{ }}\frac{4}{3}{\Delta _{\rm{f}}}H_{\rm{m}}^\theta ({\rm{HN}}{{\rm{O}}_{\rm{3}}}, l) \\ - {\Delta _{\rm{c}}}H_{\rm{m}}^\theta ({\rm{BNGM}}, {\rm{s}}) \end{array} $

(8)

The standard molar enthalpies of formation for CO₂ (g), H₂O (l), HNO₃ (l) and NO (g) are as follows: ${\Delta _{\rm{f}}}H_{\rm{m}}^\theta $ (CO₂, g) =- (393.51±0.13) kJ·mol^-1, ${\Delta _{\rm{f}}}H_{\rm{m}}^\theta $ (H₂O, l) =- (285.83±0.04) kJ · mol^-1, ${\Delta _{\rm{f}}}H_{\rm{m}}^\theta $ (HNO₃, l) =- (174.10±0.8) kJ · mol^-1, ${\Delta _{\rm{f}}}H_{\rm{m}}^\theta $ (NO, g) = (90.25±0.75) kJ·mol^-1[28]

The standard molar enthalpy of combustion (${\Delta _{\rm{c}}}H_{\rm{m}}^\theta $) and the standard molar enthalpy of formation ($ {\Delta _{\rm{f}}}H_{\rm{m}}^\theta $) were calculated as (-2238.53±6.04) kJ·mol^-1 and (-66.73±6.05) kJ · mol^-1 (T =298.15 K and p^θ =101.325 kPa).

3.5 Sensitivity

The test result indicates that impact sensitivity of BNGM is higher than 23.5 J. So, BNGM is relatively less sensitive. The sensitivity is close to that of parent material NG (> 30 J), but much lower than that of RDX (7.4 J) ^[29].

4 Conclusions

(1) The thermal decomposition behavior of BNGM presents two exothermic decomposition processes. The self-accelerating decomposition temperature (T_SADT) and critical temperature of thermal explosion (T_b) are 189.6 ℃ and 190.9 ℃, respectively.

(2) Specific heat capacity equation of BNGM is c_p = 0.1763+3.2461×10^-3T (285.0 K < T < 350.0 K), and the molar heat capacity is 251.9 J· mol^-1 · K^-1 at 298.15 K. Adiabatic time-to-explosion of BNGM is estimated to be about 280 s. The standard molar enthalpy of formation of BNGM is (-66.73±6.05) kJ·mol^-1, and the impact sensitivity of BNGM is higher than 23.5 J. The thermal stability of BNGM is good.