This work investigates kinetics and thermal decomposition behaviors of pentaerythritol tetranitrate (PETN) and two polymer-bonded explosive (PBX) samples created from PETN (named as PBX-PN-85 and PBX-PP-85) using the vacuum stability test (VST) and thermogravimetry (TG/DTG) techniques. Both model-free (isoconversional) and model-fitting methods were applied to determine the kinetic parameters of the thermal decomposition. It was found that kinetic parameters obtained by the modified Kissinger–Akahira–Sunose method (using non-isothermal TG/DTG data) were close to those obtained by the isoconversional and model-fitting methods that use isothermal VST data. The activation energy values of thermal decomposition reactions were 125.6–137.1, 137.3–144.9, and 143.9–152.4 kJ·mol−1 for PBX-PN-85, PETN, and PBX-PP-85, respectively. The results demonstrate the negative effect of the nitrocellulose-based binder in reducing the thermal stability of single PETN, while the polystyrene-based binder seemingly shows no adverse influence on the thermal decomposition of PETN in our presented PBX compositions.
Pentaerythritol tetranitrate (also called PETN), which is a popular nitrate explosive, is extensively used in civilian and military applications due to its high energy characteristics [
Like all other high-energy materials, the PBX composition is also an unstable thermodynamic system [
In this study, we investigate the thermal decomposition kinetics of two PETN-based PBX samples named as PBX-PN-85 and PBX-PP-85. These results were compared with those of a single PETN to evaluate the influence of binders on the thermal decomposition behaviors of explosives. Thermal analyses were conducted by thermogravimetry (TG/DTG) and vacuum stability test (VST), where the VST method (developed by STABIL, Czech Republic) is commonly used to examine the chemical stability, compatibility, and shelf-life of energetic materials in recent years [
We imported Class-1 PETN with a melting temperature of over 139.0°C from South Korea. Good quality nitrocellulose (NC), that has a nitrogen content of 12.20%, was supplied from the Vietnam factory. Polystyrene (PS), which has an average molecular weight of 80,000
PS and NC were plasticized by DOP (the ratios of DOP/NC and DOP/PS are 3/1 and 2/1, respectively), then dissolved in the suitable solvents (toluene for PS and ethyl acetate for NC), maintaining the polymer/solvent ratio of 1/15 (w/v), and kept for approximately 5 hours to obtain a homogeneous solution. The sample preparation method was carried out by mixing PETN crystals with the binders based on PS and NC. The mixing process took place on the heating device at 70°C for 30 minutes, and the PETN crystals were covered by the binder layers [
The composition of two PBX samples based on PETN.
Composition | Content of materials (wt%) | |||
PETN | DOP | PS | NC | |
PBX-PP | 85.00 | 10.00 | 5.00 | — |
PBX-PN | 85.00 | 11.25 | — | 3.75 |
The thermal decomposition behaviors of PBX samples were determined by employing thermogravimetry (TG/DTG) and vacuum stability test (VST). The experimental conditions are as follows.
TG/DTG analysis was conducted using a NETZSCH STA 409 PC/PG (NETZSCH-Gerätebau GmbH, Selb, Germany). PBX samples (around 5.0 mg) were put in an aluminum oxide crucible and heated at various heating rates of 3, 5, 7, and 10 K·min−1. The sample vial was heated from 30 to 350°C. Experimental heating processes were carried on under a dynamic nitrogen atmosphere with a flow rate of 30 mL·min−1.
The VST test was carried out in a STABIL apparatus (OZM Research, Pardubice, Czech Republic). During this test, PBX samples were heated isothermally at different temperatures of 135, 140, 145, and 150°C under vacuum pressure (at most 0.672 kPa). A pressure sensor and a computer are used to record the relationship of the released gas volume versus heating time. The sample mass was 20.0 mg, and we performed the test from 5 to 10 days (depending on the temperature test), until the end of the thermal decomposition reaction.
The kinetics of thermal decomposition reactions in solids can be expressed as the following equation:
Different reaction models generally applied to describe the thermal decomposition in solids [
Model no. | Reaction model | |||
---|---|---|---|---|
1 | Avarami-Erofe’ev (A2) | [−ln | ||
2 | Avarami-Erofe’ev (A3) | [−ln | ||
3 | Avarami-Erofe’ev (A4) | [−ln | ||
4 | Power law (P2) | 2 | ||
5 | Power law (P3) | 3 | ||
6 | Power law (P4) | 4 | ||
7 | 1-D diffusion (D1) | 1/(2 | ||
8 | 2-D diffusion (D2) | [ | ||
9 | 3-D diffusion-Jander (D3) | [3 | [ | |
10 | First-order (F1) | −ln | ||
11 | Second-order (F2) | |||
12 | Third-order (F3) | |||
13 | Contracting area (R2) | 2 | ||
14 | Contracting volume (R3) | 3 |
For isothermal conditions, equation (
At a linear heating rate
For each extent of conversion
TG/DTG curves of PETN, PBX-PN-85, and PBX-PP-85 at different heating rates (i.e., 3, 5, 7, and 10 K·min−1) were recorded and are shown in Figure
TG/DTG curves of PETN, PBX-PN-85, and PBX-PP-85 at several heating rates.
For comparison, the characteristic parameters of TG/DTG curves of PETN, PBX-PN-85, and PBX-PP-85 are summarized in Table
Kinetic parameters from TG/DTG data of PBX-PN-85, PBX-PP-85, and PETN.
Material | TG/DTG curve | |||||
---|---|---|---|---|---|---|
Mass loss (%) | Residue (%) | |||||
PETN | 3.0 | 165.5 | 130.2 | 186.0 | 98.3 | 1.7 |
5.0 | 169.6 | 132.0 | 191.1 | 97.2 | 2.8 | |
7.0 | 172.7 | 133.2 | 196.0 | 96.3 | 3.7 | |
10.0 | 178.9 | 135.6 | 200.8 | 96.0 | 4.0 | |
PBX-PN-85 | 3.0 | 162.3 | 127.1 | 183.9 | 95.3 | 4.7 |
5.0 | 166.8 | 129.8 | 188.2 | 94.4 | 5.6 | |
7.0 | 169.0 | 130.9 | 194.5 | 94.0 | 6.0 | |
10.0 | 175.3 | 133.5 | 198.8 | 93.1 | 6.9 | |
PBX-PP-85 | 3.0 | 168.6 | 136.2 | 189.4 | 93.7 | 6.3 |
5.0 | 172.5 | 138.0 | 194.2 | 93.1 | 6.9 | |
7.0 | 177.0 | 139.9 | 197.4 | 91.5 | 8.5 | |
10.0 | 183.2 | 142.5 | 203.6 | 91.9 | 8.1 |
It has been shown that only a single decomposition step is related to the thermal decomposition of a single PETN (i.e., one-step reaction model) in all samples. The peak temperatures in DTG curves for the thermal decomposition of PETN, PBX-PN-85, and PBX-PP-85 were observed in a range of 186–201, 183–199, and 189–204°C, respectively. Generally, the decomposition residue of all samples increases with the increasing heating rate, and the residue mass of PBX-PN-85 and PBX-PP-85 may be less than that of PETN because of the presence of inert ingredient (i.e., DOP and PS) in their formulation.
As seen, the thermal decomposition of PETN occurred at a higher temperature than PBX-PN-85 but lower than that of PBX-PP-85. DTG curves in Figure
According to equation (
As recommended by the ICTAC kinetics committee [
Isoconversional plots at selected conversion degree of PETN, PBX-PN-85, and PBX-PP-85 according to the modified KAS method.
The activation energy
Kinetic parameters of PETN and PBXs by the modified KAS method.
PETN | PBX-PN-85 | PBX-PP-85 | |||||||
---|---|---|---|---|---|---|---|---|---|
ln | ln | ln | |||||||
0.1 | 133.8 | 24.7 | 0.9955 | 124.5 | 21.3 | 0.9835 | 139.3 | 27.8 | 0.9880 |
0.2 | 138.3 | 26.3 | 0.9915 | 136.3 | 25.4 | 0.9905 | 150.4 | 32.5 | 0.9950 |
0.3 | 141.3 | 27.2 | 0.9850 | 136.5 | 24.9 | 0.9945 | 152.6 | 33.2 | 0.9915 |
0.4 | 145.2 | 28.4 | 0.9884 | 138.6 | 26.8 | 0.9964 | 152.1 | 32.4 | 0.9835 |
0.5 | 145.3 | 28.6 | 0.9935 | 137.9 | 24.8 | 0.9924 | 155.5 | 34.1 | 0.9980 |
0.6 | 147.1 | 29.9 | 0.9828 | 136.6 | 24.6 | 0.9920 | 153.2 | 32.2 | 0.9909 |
0.7 | 145.8 | 28.9 | 0.9845 | 135.8 | 24.7 | 0.9960 | 148.5 | 31.3 | 0.9945 |
0.8 | 141.4 | 27.5 | 0.9899 | 137.9 | 26.4 | 0.9949 | 147.6 | 29.8 | 0.9952 |
0.9 | 141.8 | 27.7 | 0.9854 | 127.2 | 22.6 | 0.9935 | 146.7 | 27.8 | 0.9960 |
Mean |
The dependence of activation energy on the conversion by the modified KAS method.
The mean activation energy (
To verify these results obtained by the KAS method, the kinetic parameters were recalculated using NETZSCH Thermokinetic software according to the ASTM E698 [
Compared to single PETN, the introduction of NC in PBX-PN-85 formulation leads to the decrease of its activation energy because the thermal stability of the nitrate group in NC is less than that in PETN [
Results of TG/DTG were verified by VST studies, which were conducted at several isothermal temperatures (e.g., 125, 130, 135, and 140°C). From the relationship of the volume of released gas versus heating time in VST tests, the conversion fraction values (
Conversion fractions (
It is obvious from Figure
Next, we utilize VST data to find kinetics parameters of PBX samples. By drawing
Kinetic parameter of PETN and PBXs by the isothermal isoconversional method.
PETN | PBX-PN-85 | PBX-PP-85 | |||||||
---|---|---|---|---|---|---|---|---|---|
ln | ln | ln | |||||||
0.1 | 130.2 | 29.4 | 0.9835 | 123.9 | 24.1 | 0.9966 | 135.6 | 31.1 | 0.9767 |
0.2 | 137.4 | 31.8 | 0.9830 | 127.2 | 26.3 | 0.9921 | 138.4 | 32.5 | 0.9773 |
0.3 | 137.9 | 32.0 | 0.9962 | 128.6 | 27.3 | 0.9938 | 145.6 | 34.9 | 0.9897 |
0.4 | 139.2 | 32.5 | 0.9949 | 132.3 | 28.9 | 0.9939 | 147.3 | 35.7 | 0.9890 |
0.5 | 142.6 | 33.7 | 0.9889 | 132.3 | 29.2 | 0.9924 | 147.9 | 36.2 | 0.9883 |
0.6 | 143.6 | 34.0 | 0.9930 | 135.9 | 30.5 | 0.9967 | 147.5 | 36.4 | 0.9885 |
0.7 | 136.8 | 32.0 | 0.9854 | 137.5 | 31.1 | 0.9858 | 145.5 | 36.1 | 0.9900 |
0.8 | 136.6 | 31.9 | 0.9868 | 128.7 | 28.6 | 0.9885 | 145.3 | 36.5 | 0.9857 |
0.9 | 131.2 | 30.2 | 0.9831 | 121.4 | 26.6 | 0.9941 | 142.0 | 36.2 | 0.9879 |
Mean |
The dependence of activation energy on the conversion using the VST technique.
These
The model-fitting method includes two fits:
Kinetic parameters of PETN and PBXs calculated from the model-fitting method.
Model | PETN | PBX-PN-85 | PBX-PP-85 | ||||||
---|---|---|---|---|---|---|---|---|---|
ln | ln | ln | |||||||
1 | 137.4 | 32.4 | 0.9818 | 122.0 | 27.6 | 0.9828 | 144.4 | 34.6 | 0.9896 |
2 | 138.5 | 32.5 | 0.9815 | 121.6 | 27.2 | 0.9830 | 144.5 | 34.4 | 0.9896 |
3 | 138.3 | 32.3 | 0.9827 | 121.9 | 27.1 | 0.9821 | 144.5 | 34.0 | 0.9892 |
4 | 139.1 | 33.6 | 0.9900 | 123.5 | 28.7 | 0.9846 | 146.4 | 35.8 | 0.9908 |
5 | 138.5 | 33.0 | 0.9890 | 122.8 | 28.2 | 0.9833 | 146.2 | 35.4 | 0.9907 |
6 | 134.1 | 31.4 | 0.9845 | 122.9 | 27.9 | 0.9838 | 146.1 | 35.1 | 0.9904 |
7 | 139.4 | 33.0 | 0.9838 | 123.9 | 28.3 | 0.9853 | 146.9 | 35.3 | 0.9906 |
8 | 139.1 | 32.7 | 0.9935 | 123.9 | 28.1 | 0.9844 | 146.9 | 35.1 | 0.9908 |
9 | 139.4 | 32.3 | 0.9862 | 123.7 | 28.5 | 0.9862 | 147.6 | 35.8 | 0.9905 |
10 | 139.8 | 33.3 | 0.9754 | 119.7 | 27.2 | 0.9855 | 146.7 | 35.2 | 0.9886 |
11 | 140.6 | 32.6 | 0.9860 | 125.6 | 28.0 | 0.9918 | 148.5 | 34.9 | 0.9913 |
12 | 139.7 | 34.4 | 0.9853 | 124.9 | 29.8 | 0.9853 | 148.2 | 36.6 | 0.9914 |
13 | 141.3 | 36.2 | 0.9846 | 124.8 | 31.1 | 0.9846 | 150.6 | 36.9 | 0.9940 |
14 | 142.6 | 38.2 | 0.9834 | 129.6 | 34.2 | 0.9834 | 152.4 | 40.0 | 0.9903 |
From Table
On the other hand, we found that the activation energy values calculated by the isothermal isoconversional method are approximate to those derived from the isothermal model-fitting method using the VST technique. To make a comparison, kinetic parameters obtained by different methods are presented in Table
Kinetic parameters of PETN and PBXs obtained by several methods.
Sample | TG/DTG using KAS method | Vacuum stability test (VST) | ||||
---|---|---|---|---|---|---|
Isoconversional method | Model-fitting method | |||||
PETN | 144.9 | 28.6 | 137.3 | 31.9 | 139.1 | 32.7 |
PBX-PN-85 | 137.1 | 25.2 | 129.7 | 28.0 | 125.6 | 28.0 |
PBX-PP-85 | 152.4 | 32.6 | 143.9 | 35.0 | 150.6 | 36.9 |
The values in Table
The ranges of
According to Brill et al. [
The linear dependence of
It can be observed the linear relationship of
The thermal decomposition behavior and kinetics of PETN, PBX-PN-85 (85% PETN, 15% NC-based binder), and PBX-PP-85 (85% PETN, 15% PS-based binder) were examined by TG/DTG and VST techniques using model-fitting and isoconversional methods. The activation energy values computed by the non-isothermal technique (modified KAS method) were close to those calculated by model-fitting and isothermal isoconversional methods, ranging from 125.6–137.1 kJ·mol−1 for PBX-PN-85, 137.3–144.9 kJ·mol−1 for PETN, and 143.9–152.4 kJ·mol−1 for PBX-PP-85. The results indicate that the NC-based binder accelerates the thermal decomposition of PBX, thus reducing the activation energy of single PETN. One more valuable conclusion of this study is the influence of the PS-based binder. Specifically, the presence of the PS-based binder causes no adverse effect on the thermal stability of the main explosive in PBX composition.
The data used to support the findings of this study are included in the article.
The authors declare that they have no conflicts of interest.
DVT gratefully acknowledges the support of Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant no. 107.02-2018.30.