Introduction

4,10-Dinitro-2,5,8,12-tetraoxa-4,10-diazotetracyclo[5.5.0.05,903,11]dodecane (TEX) is caged polynitramine. Its structure (Fig. 1) is similar to that of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazatetracyclo[5.5.0.05,903,11]dodecane (CL-20)—one of the strongest explosive materials. TEX is characterized with high density (ρ = 1.985 g cm−3) [1].

Fig. 1
figure 1

The structure of TEX (a) and CL-20 (b)

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TEX is the representative of low-sensitive explosive materials class. TEX sensitivity to impact and friction is similar to those of 3-nitro-1,2,4-triazol-5-one (NTO) and 1,1-diamino-2,2-dinitroethene (FOX-7). The friction sensitivity for TEX, NTO and FOX-7 is more than 350 N [2–4]. The impact sensitivity in BAM fall-hammer test for TEX equals 24 J [2] and for FOX-7 25.2–31.8 J [5]. The impact sensitivity in ABL test for TEX (200 μ) equals 33 cm and for NTO (250 μ) 26 cm [1]. TEX sensitivity to the electric spark is lower in comparison with those of FOX-7 and NTO (TEX—13.1 J [2], NTO—8.98 J [3], FOX-7 4.5 J [5]). TEX is widely used in insensitive munition (IM) [6]. Several examples were found in the literature about its use in, e.g., castable high explosive compositions, pressable or extrudable explosives formulations, plastic bonded explosives (PBX) [7–12]. Lin et al. determined the detonation parameters of TEX based on density functional theory (DFT). The detonation parameters of TEX were slightly lower than for Cl-20. The parameters for TEX calculated were based on Kamlet–Jacobs equation: detonation velocity V det = 9.28 km s−1 (ρ = 2.01 g cm−3), detonation pressure p CJ = 40.72 GPa and detonation energy Q det = 5.65 kJ g−1 [3, 13]. In the work [14], the authors determined experimentally detonation velocity of PBX containing TEX—the detonation velocity equaled V det = 7.45 km s−1 (ρ = 1.87 g cm−3). The detonation velocity and impact sensitivity of PBX containing mixture of TEX and 1,3,5-trinitroperhydro-1,3,5-triazine (hexogen, RDX) were also studied and compared with PBX containing RDX. The addition of 40 % TEX caused a significant decrease in impact sensitivity, and the detonation velocity was at the same level.

TEX is thermostable compound, and its stability is comparable with that of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) [15]. TEX undergoes decomposition above 260 °C with heat effect Q = 1.5 kJ g−1. TEX evolves small amount of gases (0.05 mL of gases after 48 h at 100 °C) in vacuum thermal stability test [1]. The properties of TEX were also studied using differential scanning calorimetry (DSC) and thermogravimetric analysis (TG) [16, 17]. DSC studies were performed on 2–3 mg samples in closed hermetic aluminum pans with the heating rate β = 2 °C min−1. Single exothermic peak corresponding to decomposition at 297 °C was observable on the DSC curve. TG studies were performed on 5 mg samples in open aluminum pans with the different heating rate (β = 2.5–20 °C min−1). The results indicated that TEX sublimates at temperature above 240 °C. Single peak at 284 °C was visible on the DTG curve. The activation energy (E a) was calculated using model-free isoconversional methods and equals E a = 133 ± 2 kJ mol−1 in the conversion range 0.12 ≤ α ≤ 0.96. In works [18, 19], activation energy using Soviet manometric method (SMM) was also notified. The TEX decomposition was analyzed in the temperature range 210–225 °C. Kinetic parameters equal: E a = 196.8 kJ mol−1 and logA = 15.4. Xiao et al. [20] studied the thermal decomposition of TEX using microcalorimeter C-500 type Calvet (SETARAM, France) in 10-mL vessels. The study was done for very low heating rates β = 0.2–0.6 °C min−1. Single exothermic transition was visible on the DSC curve. This transition was shifted from 265.7 to 282.2 °C with the increasing heating rate. Obtained kinetic parameters equal: E a = 156.65 kJ mol−1 and logA = 11.54. Kinetic parameters of TEX decomposition described in the literature are divergent. Activation energy varied in the range of 133.0–196.8 kJ mol−1, logA 11.5–15.4. The difference in obtained values is associated with different measurement conditions.

The influence of measurement conditions on obtained values of kinetic parameters was also observed for another compound [21–25]. Authors of publication [21] observed constant activation energy (isothermal condition) of decomposition process for poly(vinyl chloride) (PVC). The dependence of apparent activation energy on conversion of PVC was obtained for non-isothermal condition [22, 23]. The effect of measurement conditions in higher temperature on processes was also observed for 1,3,3-trinitroazetidine (TNAZ). The authors determined the activation energy of TNAZ decomposition for large sample mass using microcalorimeter [24]. The processes of sublimation and evaporation were observed for this compound for low sample mass using DSC and TG–DTA technics. They also determined the kinetic parameters of these processes [25]. The thermal decomposition study should be performed to minimize the influence of physical processes (polymorphic transitions, melting, sublimation, evaporation) on analyzed decomposition process.

The uncontrolled decomposition of high-energetic materials might run to the thermal explosion [26]. This situation may take place for low conversion degrees [27]. For this reason, it is important to know the kinetic parameters of decomposition reaction for initial decomposition stage.

The aim of work was to study the thermal decomposition process of TEX in different conditions. Kinetic parameters of decomposition reaction and sublimation of TEX were calculated. The influence of measurement condition on the decomposition process was analyzed. Obtained kinetic parameters for initial decomposition stage are important for users for the estimation of TEX use and storage safety.

Experimental

Materials

TEX was synthesized in the Department of High-Energetic Materials of the Warsaw University of Technology [28]. The purity of compound was determined using high-performance liquid chromatography (HPLC) and equals 99.5 %.

Instrumental analysis

DSC analysis was carried out using Thermal Analysis (TA) Instruments Q2000 calorimeter. The measurements were done in hermetic aluminum pans (TA 900786.901, 900779.901) with nitrogen flow rate equal to 50 mL min−1. The thermogravimetric analysis was carried out using TA Instruments SDT Q600 thermogravimeter. The measurements were done in open aluminum pans (TA 901684.901) with the nitrogen rate of 100 mL min−1. DSC and TG analyses were performed using six different heating rates in the range: β = 0.5–16.0 °C min−1. The measurements for extreme heating rate were repeated three times in accordance with International Confederation for Thermal Analysis and Calorimetry (ICTAC) [29]. The partial decomposition of TEX was done at the heating rate β = 2 °C min−1 using TG method.

The Fourier transform infrared spectroscopy (FTIR) analysis was carried out using Thermo Scientific NICOLET 6700 spectrometer. The disk for analysis was prepared by triturating and pressing 1 mg of TEX sample and 200 mg potassium bromide. The spectrum was recorded in the wave number range: 4000–400 cm−1. The bands were separated using PeakFit program of SeaSolve Software Inc. company.

Kinetic analysis

Kinetic parameters of decomposition reaction were calculated using Thermokinetics 3.1 program of NETZSCH company. Many parallel and sequent reactions take place during TEX decomposition. Obtained kinetic parameters were the resultant of all reactions. For this reason, the calculated activation energy in the next part of this manuscript was called apparent activation energy (a E a) [20, 28]. The apparent activation energy and logarithm of pre-exponential factor were calculated using Friedman’s isoconversional method according to the ICTAC recommendation [29]. The first-order kinetic model was assumed in order to determine pre-exponential factor.

Results and discussion

Thermogravimetric analysis (TG) of TEX decomposition performed in open pan

TG–DSC measurements were performed in open pans for TEX sample mass of 3.8 ± 0.2 mg. Typical TG–DSC curve for heating rate β = 16 °C min−1 is presented in the Fig. 2.

Fig. 2
figure 2

Typical TG and DSC curves for TEX sample mass of m = 3.8 ± 0.2 mg for heating rate β = 16 °C min−1

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The mass loss of the sample begins at 200 °C. This is a one-step process. One endothermic process was observed on the DSC curve (the temperature of process was T peak = 304.0 °C, and the enthalpy was ΔH = 315 J g−1). This process was associated primarily with the sublimation of sample. The series of TG–DSC measurements with different heating rates were performed for samples of 3.8 ± 0.2 mg. The mass loss for all samples was associated with endothermic processes. TG curves are presented in Fig. 3.

Fig. 3
figure 3

TG curves for TEX samples of 3.8 ± 0.2 mg for different heating rates (β = 0.5, 1, 2, 4, 8, 16 °C min−1)

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As expected, with increasing the heating rate, the mass loss process occurred at higher temperature. The termination of mass loss process shifts in temperature from 244 to 306 °C. Kinetic parameters were determined using TG curves. The dependence of apparent activation energy and logarithm of pre-exponential factor on conversion degree is presented in Fig. 4. The values of apparent activation energy and the logarithm of pre-exponential factor are presented in Table S1 (Supplementary Material).

Fig. 4
figure 4

The dependence of apparent activation energy (a E a) and the logarithm of pre-exponential factor (logA) on conversion degree (α) for TEX decomposition reaction for the samples of 3.8 ± 0.2 mg in open pans determined with TG method

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The apparent activation energy was constant up to α = 0.6 and equaled a E a = 128 ± 3 kJ mol−1. For conversion degrees higher than α = 0.6, the apparent activation energy increased to value a E a = 136 ± 8 kJ mol−1 for α = 0.95. The results corresponded well to the published literature where the activation energy equals E a = 133 ± 2 kJ mol−1 [16, 17]. The logarithm of pre-exponential factor increased with increasing conversion degree and ranges from 9.95 for α = 0.02 to 11.51 for α = 0.95. The characteristics of logA changed with a pattern similar to the apparent activation energy. In order to examine the influence of sample mass on the mass loss process, TG–DSC measurements for samples of 4, 10 and 20 mg were performed. DSC curves are shown in Fig. 5.

Fig. 5
figure 5

DSC curves for TEX samples of 3.8 ± 0.2, 10.2 ± 0.2 and 20 mg. The measurements were performed in open pans in which heating rate equals β = 16 °C min−1

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The mass loss (TG–DSC measurement) for sample mass of 4 mg was associated with endothermic process. For the sample of 10 mg, the exothermic process overlapped with the endothermic transition. The decomposition for the sample of 20 mg was uncontrolled because strong exothermic effect on the graph was visible, which took place in the end of mass loss process. The series of TG–DSC measurements with the different heating rates were performed for samples of 10.2 ± 0.2 mg to determine the influence of sample mass on kinetic parameters. Kinetic parameters were determined using TG curves. The apparent activation energy and the logarithm of pre-exponential factor for different conversion degrees are shown in Fig. 6. The values of apparent activation energy and the logarithm of pre-exponential factor are presented in Table S2 (Supplementary Material).

Fig. 6
figure 6

The dependence of apparent activation energy (a E a) and the logarithm of pre-exponential factor (logA) on conversion degree (α) for TEX sample mass of 10.2 ± 0.2 mg achieved in TG measurements

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The apparent activation energy is constant up to α = 0.55 and equals a E a = 132 ± 3 kJ mol−1. For conversion degrees higher than α = 0.55, the apparent activation energy increases to the value of a E a = 186 ± 20 kJ mol−1 for α = 0.80. The apparent activation energy equals a E a = 154 ± 9 kJ mol−1 for conversion degree α = 0.95. The characteristics of logA changed with a pattern similar to the apparent activation energy. LogA equals 10.23 for α = 0.02. For α = 0.81, the logarithm of pre-exponential factor achieves maximum and is equal to 15.62. In the end of decomposition, logA (for α = 0.95) equals 13.04. The results (from α = 0.02 to α = 0.55) correspond well to the published literature where the activation energy is E a = 133 ± 2 kJ mol−1 [7, 17]. The kinetic parameters achieved for α = 0.80 correspond well to Soviet manometric method (SMM) where E a = 196.8 kJ mol−1 and logA = 15.4. The results achieved during TG–DSC measurement performed in open pans indicated that the mass loss was associated with sublimation process. With increasing the mass sample, the mass loss was associated with greater participation of the TEX decomposition process. The apparent activation energy of sublimation process equals about 130 kJ mol−1.

The FTIR analysis of TEX decomposition performed in open pans

The series of TG measurements of TEX were performed with the heating rate β = 2 °C min−1. The measurements were interrupted in different conversion degrees (from α = 0.10 to α = 0.96). The comparison of FTIR spectrum obtained for partially decomposed sample and for output sample was made to determine whether the decomposition of TEX in solid phase took place during the sublimation. FTIR spectrum of output TEX in KBr is presented in Fig. 7. FTIR spectra of output TEX and partially decomposed TEX (conversion degree α = 0.96) with wave number assigned are presented in Figs. S1 and S2, respectively (Supplementary Material). This spectrum corresponds well to the spectra found in the literature [2, 26]. The absorption bands and the modes of vibration assigned to them are summarized in Table 1.

Fig. 7
figure 7

The FTIR spectrum of TEX in KBr disk

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Table 1 The wave number and modes of vibration for TEX sample
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The comparison of three spectra, output sample of TEX and two sample of partially decomposed TEX (conversion degrees α = 0.50 and α = 0.96), are presented in Fig. 8. All spectra were normalized relative to the v = 1174 cm−1 band.

Fig. 8
figure 8

The comparison of three FTIR spectra of TEX samples obtained for conversion degrees: α = 0.00, 0.50 and 0.96 and for the range of wave number 2000–400 cm−1

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The FTIR spectrum of TEX output sample (α = 0.00) and that for sample with less mass loss are similar. Ratios of separated peaks heights for the spectrum of TEX samples with higher mass loss are changed. It was very good visible for conversion degree α = 0.96. The differences in heights were visible for peaks, e.g., 1596, 1330, 1174, 1116, 1055, 874 cm−1. The ratio of peak height to peak height at v = 1174 cm−1 was determined in order to define the changes in band intensity for different conversion degrees (Fig. 9).

Fig. 9
figure 9

The ratios of peak heights at 873, 903, 1100 and 1136 cm−1 in accordance with 1174 cm−1 for TEX sample achieved in partial decomposition with TG method

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The ratios of selected waves varied small in the conversion degree range of α = 0.00–0.76. The changes in selected waves for larger conversion degrees are visible. The ratios of waves 873, 903 and 1136 cm−1 to 1174 cm−1 increased with increasing conversion degree, but for 1100 cm−1, the ratio decreased. FTIR studies have confirmed that for TEX sublimation is the main process and the decomposition in solid phase starts for the conversion degree above α = 0.76.

Differential scanning calorimetry (DSC) analysis of TEX decomposition performed in hermetic pans

The series of DSC measurements of TEX thermal decomposition were carried out in hermetic pans with the different heating rates. The measurements were done for the sample mass of 0.095 ± 0.005 mg. Obtained DSC curves are illustrated in Fig. 10.

Fig. 10
figure 10

The DSC curves of TEX decomposition made in hermetic pans for sample mass of 0.095 ± 0.005 mg with different heating rates (β = 0.5, 1, 2, 4, 8, 16 °C min−1)

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TEX decomposition shifts toward higher temperature with the increasing heating rate, which was expected. There were two stages of TEX decomposition for higher heating rates (β = 4–16 °C min−1). Two stages of decomposition process of caged polynitramines were described in the literature [30, 31]. Kinetic parameters were calculated for TEX decomposition reaction. The dependence of apparent activation energy and the logarithm of pre-exponential factor on the conversion degree is presented in Fig. 11. The values of apparent activation energy and the logarithm of pre-exponential factor are presented in Table S3 (Supplementary Material).

Fig. 11
figure 11

The dependence of apparent activation energy and the logarithm of pre-exponential factor on the conversion degree for TEX decomposition reaction for sample mass of 0.095 ± 0.005 mg in hermetic pans

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The apparent activation energy at the initial stage (α = 0.02) is equal to a E a = 328 ± 19 kJ mol−1 and it decreases with increasing conversion degree to α = 0.93 gaining value a E a = 36 ± 25 kJ mol−1. The minimum apparent activation energy corresponds to 0.09 mg of TEX conversion. The apparent activation energy at the terminal stage (α = 0.95) is equal to a E a = 39 ± 20 kJ mol−1. The logarithm of pre-exponential factor also decreases with increasing conversion degree, logA amounted from 28.53 (α = 0.02) to 1.80 (α = 0.95). The major changes in kinetic parameters indicated that TEX decomposition in hermetic pans was a complex process. The fulfillment of pans could influence the decomposition process due to the possibility of partial TEX sublimation. For this reason, measurements for higher fulfillment were made for the heating rates of β = 0.5 and 16 °C min−1 for the samples of 0.35 ± 0.05 mg. This was a limit mass for which total decomposition in hermetic pans without pans leakage could be done. In Fig. 12, the comparison of DSC curves of decomposition process for the samples of 0.35 ± 0.05 and 0.095 ± 0.005 mg was illustrated.

Fig. 12
figure 12

DSC curves of TEX decomposition for samples of 0.095 ± 0.005 and 0.36 ± 0.05 mg in hermetic pans (heating rates β = 0.5 and 16 °C min−1)

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The large influence of mass on the DSC curves of TEX decomposition reaction is visible on the graph. The shape of peak is changed and also the temperature shift is observable. It was not expected that the larger mass of the sample caused a shift toward higher temperature—about 11 °C for the heating rate β = 0.5 °C min−1 and about 8 °C for β = 16 °C min−1. For sample mass of 0.35 ± 0.05 mg, new exothermic process at high temperature appeared. The series of DSC measurements of TEX thermal decomposition were carried out for sample mass of 0.35 ± 0.05 mg in hermetic pans for the different heating rates. Obtained DSC curves are illustrated in Fig. 13.

Fig. 13
figure 13

DSC curves of TEX decomposition made in hermetic pans for sample mass of 0.35 ± 0.05 mg with different heating rates (β = 0.5, 1, 2, 4, 8, 16 °C min−1)

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Multistage decomposition of TEX samples is visible on DSC curves. The inflexion is observable at the falling edge of peak for heating rates β = 4–16 °C min−1. For all heating rates, exothermic processes at high temperature characterized by a small value of enthalpy are visible. TEX decomposition shifts toward higher temperature with the increasing heating rate, which was expected. The values of shift are different for first and second stages. The first stage shifted toward higher temperature about 5.6 ± 1.0 °C with double increased heating rate, and the second stage about 2.2 ± 1.0 °C with the same change in heating rate. This indicated that the value of activation energy differs significantly for first and second stages of TEX decomposition. Kinetic parameters were calculated for TEX decomposition reaction for the samples of 0.35 ± 0.05 mg. Figure 14 presents the dependence of apparent activation energy and the logarithm of pre-exponential factor on the conversion degree. The values of apparent activation energy and the logarithm of pre-exponential factor are presented in Table S4 (Supplementary Material).

Fig. 14
figure 14

The dependence of apparent activation energy and the logarithm of pre-exponential factor on the conversion degree of TEX decomposition reaction for the samples of 0.35 ± 0.05 mg in hermetic pans

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Significant changes in the apparent activation energy with the conversion degree of TEX are visible on the graph. The apparent activation energy at the initial stage of decomposition (α = 0.02) is equal to a E a = 355 ± 29 kJ mol−1. Three extremes of function are observable in the next part of curve: two local minima a E a = 290 ± 6 kJ mol−1 (α = 0.27) and a E a = 328 ± 19 kJ mol−1 (α = 0.78) and one local maximum a E a = 362 ± 14 kJ mol−1 (α = 0.42). The apparent activation energy at the end of decomposition (α = 0.95) equals a E a = 403 ± 90 kJ mol−1. LogA at the initial stage of decomposition (α = 0.02) equals 30.64 and also significantly changes with the conversion degree of TEX. The pattern of these changes is similar to the changes in the apparent activation energy. The first decrease in the apparent activation energy with local minimum for conversion degree α = 0.27 corresponds to 0.09 mg of TEX reacted. It was observed that first decrease in the apparent activation energy in two series of measurement (0.095 ± 0.005 and 0.35 ± 0.05 mg) was for the same amount of TEX reacted. In order to confirm the influence of pans fulfillment on the TEX decomposition process, another series of DSC measurements for the sample mass of 0.195 ± 0.005 mg in hermetic pans for different heating rates were made. Kinetic parameters were calculated for TEX decomposition reaction, which was illustrated in Fig. 15. The values of apparent activation energy and the logarithm of pre-exponential factor are presented in Table S5 (Supplementary Material).

Fig. 15
figure 15

The dependence of apparent activation energy and the logarithm of pre-exponential factor on the conversion degree for TEX decomposition reaction for the samples of 0.195 ± 0.005 mg in hermetic pans

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The apparent activation energy at the initial stage of TEX decomposition (α = 0.02) is equal to a E a = 331 ± 18 kJ mol−1, and three extremes of function were observable in the next part of the curve: two local minima a E a = 279 ± 10 kJ mol−1 (α = 0.43) and a E a = 234 ± 28 kJ mol−1 (α = 0.78) and one local maximum a E a = 297 ± 10 kJ mol−1 (α = 0.56). The apparent activation energy at the end of decomposition (α = 0.95) equals a E a = 334 ± 111 kJ mol−1. The logarithm of pre-exponential factor also significantly changes with the conversion degree of TEX. The pattern of these changes is similar to the changes in the apparent activation energy with conversion degree. The first decrease in the apparent activation energy with local minimum for conversion degree α = 0.43 corresponds to 0.08 mg TEX reacted and it corresponds well to the measurements for the samples of 0.095 ± 0.005 and 0.35 ± 0.05 mg. The obtained results indicated that the first decrease in the apparent activation energy was connected with the sublimation of the sample. For three series of measurements for the sample mass of 0.095 ± 0.005, 0.195 ± 0.005 and 0.35 ± 0.05 mg, the initial value of apparent activation energy is equal to, respectively, a E a = 328 ± 19, 331 ± 18 and 355 ± 29 kJ mol−1 and logarithm of pre-exponential factor equals, respectively, logA = 28.53, 28.55 and 30.64.

Conclusions

The processes observed during thermal analysis depended on measurement conditions, the sample mass and the pan filling degree. Sublimation of the sample was the main process, whereas the thermal decomposition was the secondary process during the heating of TEX in open pans. When the sample mass was increased, the participation of thermal decomposition of TEX increased. Thermal decomposition was the main process observed during heating the sample of TEX in hermetic pans. Sublimation of the sample was the marginal process in hermetic pans. This effect decreased with the increase in sample mass. The apparent activation energy for sublimation was about 130 kJ mol−1 and about 340 kJ mol−1 for thermal decomposition.

The studies have shown large influence of measurement conditions on kinetic parameters of TEX decomposition process. The decomposition process of TEX could be measured in hermetic pans with high degree of filling. The low values of apparent activation energy in the literature were associated with overlapping the sublimation process with the decomposition process of TEX. Kinetic parameters determined for the initial decomposition stage of TEX in hermetic pans should be used for the security evaluation of TEX use (because decomposition is the main observed process).