1 Introduction

Molecules containing nitro groups are high-energy materials (HEMs). HEMs with optimum detonation performances combined with good thermal stabilities and insensitivity to shock and friction are being developed as rocket fuels. Benchmark secondary HEMs such as 1,3,5-trinitroperhydro-1,3,5-triazine (RDX; Research Department Explosives), trinitrotoluene, high-melting explosives (HMX) (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine), and pentaerythritol tetranitrate have different decomposition mechanisms, which involve breaking N–N bonds and concerted rings, followed by release of thermal energy and other nitrogen oxides [1, 2]. At least a few kilograms of a new HEM in propellant form are required for testing the quality of a new HEM as a rocket fuel. These propellants are prepared by mixing secondary HEM powders with other components such as stabilizers, curing agents, and burn rate modifiers with suitable binders in different proportions [3]. The laboratory production of large quantities of HEMs is still a challenging task. Consequently, there is a need to develop new analytical pyro- and laser-based spectroscopic techniques for testing the thermal stabilities and efficiencies of new HEMs in small quantities.

RDX is one of the most powerful explosives and is widely used in military and industrial applications. Several groups have developed theoretical models for understanding the molecular dynamics of RDX and clarified the multistep bond-breaking mechanism [2, 4–6]. In all cases, NO2 was found to be one of the principal by-product gases. However, these bond-breaking mechanisms are predicted to occur at very high temperatures, i.e., above 1200 °C. Some experimental reports on the thermal decomposition mechanisms of RDX, CL-20, and other explosives have described the release of NO2 at just above their melting points, i.e., above 200 °C. The results of thermal decomposition studies of other classes of HEMs such as imidazoles, pyrazoles, triazoles, and tetrazoles with high contents of nitrogen based on detonation velocity and pressure have motivated our group to perform similar laboratory studies on some new HEMs such as 4,6-dinitro-5-(4-nitro-1H-imidazol-1-yl)-1H-benzo[d] [1–3] triazole and 5-chloro-1-(4-nitrophenyl)-1H-tetrazole [7]. Their chemical structures are shown in Fig. 1a, and synthesis details are provided in the Electronic supplementary material.

Fig. 1
figure 1

a Chemical structures of HEM samples, b Some of the calculated eigenmodes of the PA cavity

Full size image

Picric acid [2,4,6-triNitrophenol (TNP)] is one of the most acidic phenols and is classified as a secondary explosive. It is one of the most frequently used compounds in munitions manufacturing. Picric acid improves the staining of acid dyes and is therefore used in the preparation of histology specimens [8], but it can also lead to hydrolysis of DNA present in samples. Nitroaromatic compounds, which are widely used as dyes, pesticides, and explosives, are common environmental pollutants. They can be analyzed using various analytical techniques such as thermogravimetric analysis–differential thermal analysis (TGA–DTA), Fourier transform infrared (FTIR) spectroscopy, and bomb calorimetry.

However, the techniques used to study the thermal decomposition mechanisms of secondary HEMs have some technical limitations. TGA–DTA and differential scanning calorimetry coupled with FTIR spectroscopy and mass spectrometry provide thermal and spectroscopic signals. However, in all these techniques, the samples need to be heated to above their decomposition temperatures. These techniques are therefore unable to provide significant information on the initiation mechanisms of the thermal decomposition of HEMs sample, which probably occurs below their melting points [9–14].

Photoacoustic (PA) spectroscopy has the advantages of high sensitivity, selectivity, a compact setup, and fast responses. It is widely used for trace gas analysis at parts per million to parts per billion levels [15–24]. Several groups, including ours, have reported PA studies of NO2 using the second harmonic of a pulsed Nd:YAG laser. However, these studies are restricted to pure NO2 gas [25–29].

In this study, we used an improved version of an existing PA spectroscopic technique to study the thermal decomposition mechanisms of RDX, picric acid, and two new nitrogen-rich secondary explosives during controlled pyrolysis between 25 and 350 °C. The high sensitivity of the PA technique enabled determination of the NO2 released by HEM molecules just above room temperature. Its selectivity enabled the selection of suitable data acquisition times for recording fingerprint PA spectra of HEM vapor produced by NO2 molecules via non-radiative transitions. The fast response time enabled us to record the multiple steps of the bond-breaking thermal decomposition mechanisms of HEMs. The obtained results were verified using TGA–DTA.

2 Theoretical

Figure 1b shows the calculated eigenmodes of the PA cavity. They were obtained using the inhomogeneous wave equation of sound pressure (P) in a loss-less cylindrical resonator:

$$\frac{{d^{2} P(r,t)}}{{{\text{d}}t^{2} }} - c^{2} \nabla^{2} P(r,t) = (\gamma - 1)\frac{{{\text{d}}H(r,t)}}{{{\text{d}}t}}$$
(1)

where c, γ, and H are the sound velocity, adiabatic coefficient of the gas, and heat density deposited in the gas by absorption of light, respectively. The solution of Eq. (1) gives the eigenfunction and eigenmodes of the PA cavity. The frequency of the acoustic resonance modes generated within the cylindrical cells can be determined using Eq. (2):

$$F_{mnq} = \frac{c}{2}\left( {\left( {\frac{{\alpha_{mn} }}{R}} \right)^{2} + \left( {\frac{q}{L}} \right)^{2} } \right)^{{\frac{1}{2}}}$$
(2)

where c is the sound velocity, α mn is the nth zero of the derivative of the mth Bessel function at r = R, and R and L are the radius and length of the cylinder, respectively. The normal modes are separated into longitudinal (q), radial (n), and azimuthal (m) modes [17, 19].

3 Experimental

Figure 2a shows a schematic diagram of the layout of the PA experiment. We used frequency-doubled 532 nm pulses of duration 7 ns at a 10 Hz repetition rate, obtained using a Q-switched Nd:YAG laser (Model Spit, Coherent Inc., Germany). A specially designed stainless-steel PA cell of length 75 mm and radius 7.5 mm was used to excite a vapor of the explosive. A prepolarized microphone of responsivity 50 mV/Pa (BSWA, China) was placed at the center of the cell to record the PA signal. A round-bottomed flask made of borosilicate glass, housed in a temperature-controlled oven, was used to produce HEM vapors at 25–350 °C. The entire system was connected to a vacuum pump, and a needle valve was used to control the vapor flow rate through the inlet. The output signal from the microphone was fed to a preamplifier, which was coupled to 200 MHz oscilloscope (Tektronix, USA) through a boxcar averager/integrator system (Stanford Instruments Inc., USA). The oscilloscope output was fed to a data acquisition program (LabView software) for signal processing.

Fig. 2
figure 2

a Schematic layout of photoacoustic experiment. PA spectra of b sample 01, c sample 02, d sample 03, and e sample 04

Full size image

Controlled pyrolysis was performed by heating a few grains (~1 mg) of solid HEM in a flask in an oven. The oven temperature was controlled using a laboratory-designed temperature controller and measured using a thermocouple-based sensor. The flask and PA cell were evacuated to 10−3 torr using a vacuum pump. The fresh sample vapor was supplied to the PA cell in a controlled manner using a specially designed gas-handling system coupled with needle valves. The system was connected to a pressure gauge for monitoring the pressure of the PA system. Thermal PA signals were recorded in the same way, using fresh sample vapor.

TGA–DTA of the explosives was performed using a Q600 DT instrument. The solid sample (1.2 mg) was placed in an alumina crucible and heated at 25–350 °C in a nitrogen atmosphere at 760 torr (flow rate 100 cm3/min). An empty alumina crucible was used as a reference for calibration. Non-isothermal TGA runs were conducted at 25–350 °C; the heating rate was 10 °C/min [30–33].

4 Results and discussion

4.1 PA spectra of explosive samples

For a given PA cell, the second-order longitudinal modes of all the HEM samples were observed at 4.8 kHz. The values of the other frequency modes differed slightly from their calculated values; this is attributed to temperature variations. These excited eigenmodes vary from sample to sample and can be treated as a signature of the explosive molecules.

The inset in Fig. 2b shows the time-domain PA signal of 4,6-dinitro-5-(4-nitro-1H-imidazol-1-yl)-1H-benzo[d] [1–3] triazole (sample No. 1) at data acquisition time t = 2.5 ms; this covers the acoustic frequency range up to 50 kHz. The PA strength is between −2 and +2 mV. The fast Fourier transform (FFT) of the corresponding time-domain signal provided a frequency-domain spectrum of sample No. 1. This confirms excitation of low-intensity modes at 12.4, 12.9, 14.3, 15.7, and 26 kHz.

The inset in Fig. 2c shows the time-domain PA signal of 5-chloro-1-(4-nitrophenyl)-1H-tetrazole (sample No. 2) at data acquisition time t = 2.5 ms. The PA strength is between −0.8 and +0.8 mV. The FFT of the corresponding time-domain signal shows the presence of some distinct high-intensity acoustic modes at 12.45, 14.33, 15.75, and 17.5 kHz.

The inset in Fig. 2d shows the time-domain PA signal of RDX (sample No. 3) at data acquisition time t = 2.5 ms. The PA signal strength is between −4 and +4 mV. The FFT of the corresponding time-domain signal shows the presence of a combination of two equally high- and low-intensity modes located at 12.4, 25.9, 15.5, 17.5, and 36.5 kHz.

The inset in Fig. 2e shows the time-domain PA signal of picric acid (sample No. 4) at data acquisition time t = 0.02 ms. The PA signal strength is between −0.6 and +0.6 mV. The FFT of the corresponding time-domain signal provided a frequency-domain spectrum of sample No. 4. The PA spectrum of sample No. 4 has two equal intensity modes located at 5 kHz. Another pair of modes is present near 12 kHz.

These results confirm that the resonance frequencies differ from sample to sample; this is probably because the vapor densities of the explosives are different. It mainly depends on the chemical composition and bond-breaking mechanism of the explosive sample. In addition, the time-domain signals shown in the insets in Fig. 2c, d are affected by digital noise from an unknown source, but the data acquisition program has inbuilt noise filters that can remove undesirable noise from the signal to provide high-quality frequency-domain spectra. The intensity of each peak in the PA spectrum varies significantly with changes in physical parameters such as pressure, temperature, and laser energy. The spectrum can therefore be treated as an acoustic fingerprint of the explosive. The clear distinctions among the intensity profiles of the PA spectra of HEMs also show their relative efficiencies in releasing energy. The peaks of the PA spectrum of RDX are highly resolved and more intense than those of picric acid.

In this study, we showed that the PA signal increases with increasing temperature; this is directly related to an increase in the number of free NO2 molecules. The NO2 molecule has strong coupling between the high vibrational levels of the X2A1 ground state and 2B2 or 2B1. Consequently, all the absorbed optical energy contributes to heating of the sample. The NO2 molecule is excited to the 2B2 level as a result of absorption at 532 nm and transfers its excitation energy to the PA signal by V–T and V–V relaxations through collisions with air molecules.

4.2 Thermal decomposition study

4.2.1 4,6-Dinitro-5-(4-nitro-1H-imidazol-1-yl)-1H-benzo[d] [1–3] triazole (sample No. 1)

Figure 3a shows the temperature dependence of the PA spectrum of sample No. 1. There is a small variation in the strength of the PA signal between 48 and 98 °C, followed by an exothermic decomposition peak of maximum intensity at 194 °C. There are two additional exothermic peaks, at 284 and 327 °C. The high-intensity second exothermic peak represents the final decomposition point (T d). The overall decomposition process takes place in two steps. In the first step, which gives rise to the PA signal at 194 °C, N–NO2 bond breakage occurs, which releases the first batch of NO2 molecules. The second step produces another strong peak, at 284 °C, which is regarded as a critical temperature, and is the starting point for ring breaking or total thermal decomposition. The nitrogen gas released from the broken rings reacts with the oxygen present in the air and produces a new batch of NO2 molecules. Freshly generated NO2 produces a strong PA signal. The different types of chemical reactions involved in the bond-breaking process are shown below [34, 35]:

$$\text{NO}_{2} \to \text{NO} + {\text{O}}$$
(3)
$$3{\text{NO}} \to {\text{N}}_{2} {\text{O}} + {\text{NO}}_{2}$$
(4)
$${\text{N}}_{2} {\text{O}} + {\text{NO}} \to {\text{N}}_{2} + {\text{NO}}_{2}$$
(5)
$${\text{N}}_{2} {\text{O}} \to {\text{N}}_{2} + {\text{O}}$$
(6)
Fig. 3
figure 3

a Temperature effect on PA signal and b TGA–DTA curves of sample 01. c Temperature effect on PA signal and d TGA–DTA curves of sample 02

Full size image

The TGA curve in Fig. 3b provides significant information about the exothermic reactions and corresponding mass losses occurring between 150 and 280 °C. In addition, it shows that 20 % of the initial mass remains unconverted. The DTA curve shows zones with different types of thermal phase transition and highlights the endothermic and exothermic behaviors of the sample. Small endothermic valleys are also present, at 77 and 164 °C. These valleys represent solid–solid phase-transition points. The second thermal zone of interest in the curve lies between 150 and 280 °C. This zone provides information on the initial and final points of the thermal decomposition reaction in terms of rapid phase transition. The exothermic peak at 321 °C represents oxidation of nitrogen released by ring-breaking reactions.

4.2.2 5-Chloro-1-(4-nitrophenyl)-1H-tetrazole (sample No. 2)

Figure 3c shows the thermal PA spectrum of sample No. 2. A flat acoustic peak between 40 and 82 °C is followed by a peak of moderate intensity at 154 °C. The presence of additional peaks from NO2 indicates completion the multistep defragmentation process. Above 250 °C, the reaction path is similar to that for sample No. 1. However, the strength of the generated PA signal is lower than that for sample No. 1. The overall thermal decomposition process shows that the energy-releasing efficiency of sample No. 1 is higher than that of sample No. 2, and it can produce larger amounts of free NO2 and nitrogen compared with sample No. 2.

Figure 3d shows the TGA–DTA thermographs for sample No. 2. The TGA curve shows that mass loss occurs between 150 and 250 °C and confirms that 18 % of the initial mass remains unconverted. The DTA curve shows the phase transition and thermal decomposition behaviors of the sample. The first solid–solid phase transition occurs at 91 °C, and there is a pair of exothermic peaks at 180 °C. These peaks are attributed to thermal decomposition, and the small exothermic peak at 262 °C indicates oxidation.

4.2.3 RDX (Sample No. 3)

Figure 4a shows the temperature-dependent PA spectrum of sample No. 3. The first signature peak of RDX appears at 53 °C, followed by a highly thermally stable zone up to 183 °C. The compound then starts multistep release of NO2. The presence of intense PA signals at 244 and 312 °C confirms decomposition. The experimental temperature was restricted to 350 °C for safety reasons. However, the PA spectrum shows that there is rapid growth of a signal at higher temperature, which represents concerted ring breaking and oxidation of RDX, similar to the processes observed for samples No. 1 and 2.

Fig. 4
figure 4

a Temperature effect on PA signal and b TGA–DTA curves of sample 03. c Temperature effect on PA signal and d TGA–DTA curves of sample 04

Full size image

Figure 4b shows the TGA–DTA thermographs for RDX. The DTA curve shows a small thermal valley at 53.8 °C, whereas the TGA curve shows no change until it reaches the melting point, i.e., 202.5 °C, at which an endothermic valley appears, followed by a decomposition point at 239.3 °C. The presence of an exothermic peak in the DTA curve and the PA signal at 225 °C confirms thermal decomposition.

4.2.4 Picric acid (sample No. 4)

Figure 4c shows the thermal PA spectrum of picric acid. The first PA signal appears above room temperature. In addition, there are three distinct PA peaks, at 52, 150, and 190 °C. The intensity of the first peak is almost half that of the second peak, and the intensity of the second peak is slightly higher than that of the third peak. The PA spectrum therefore indicates multistep thermal decomposition, which is responsible for the release of fresh NO2 from the sample. However, the PA signal of picric acid gradual decays and reaches ground level above 190 °C. This shows that free NO2 is unavailable above this temperature. This can be easily be verified from the structure of picric acid, which contains no nitrogen in the ring.

Figure 4d shows the TGA–DTA thermographs of sample No. 4. The TGA curve shows that mass loss occurs via an exothermic reaction between 150 and 250 °C. The TGA curve also shows a significant amount of residual mass, around 52 % of the initial mass of the sample. The DTA curve shows small endothermic valleys, at 43 and 86 °C. This valley represents the solid–solid phase-transition point. This is followed by a strong exothermic peak at 186 °C, which can also be regarded as the thermal decomposition point of picric acid. Unlike the previous samples, no exothermic peak appears after completion of decomposition. Picric acid has no nitrogen in its ring structure, whereas samples No. 1–3 have more than one nitrogen in their ring structures. These results further corroborate our contention that the nitrogen released from samples No. 1–3 reacts with oxygen to produce fresh NO2, which gives rise to an exothermic peak in the DTA curve. In the case of picric acid, which contains no nitrogen in the ring structure, this exothermic peak is absent from the DTA curve.

4.3 Dependence of PA signal on incident laser energy

The PA signal shows two distinct features with respect to the incident laser energy. When the laser energy is low, the strength of the PA signal is proportional to the gas density, (t/t c)2 (where t and t c are the total de-excitation lifetime and collisional lifetime) and varies linearly with the laser beam intensity (I 0). However, when the laser energy is high, the PA signal varies with respect to I −10 and provides significant information on the saturation behavior [36, 37].

Figure 5b, d shows the effects of the incident laser energy on the PA signals of samples No. 2 and 4; saturation is observed at 10.9 and 11.5 mJ, respectively.

Fig. 5
figure 5

Energy study of a sample 01, b sample 02, c sample 03, and d sample 04

Full size image

However, for samples No. 1 and 3, as shown in Fig. 5a, c, the strength of the PA signal initially increases with increasing incident laser energy and maintains linear growth up to 18 mJ for sample No. 1 and 8 mJ for sample No. 3. Beyond this point, the PA signal shows saturation behavior. However, sample No. 3 shows linear growth even at energies higher than 14 mJ and needs additional energy to reach the saturation limit.

4.4 Scaling of fuel efficiency

The results obtained using the PA technique are in excellent agreement with those using TGA–DTA and open a new channel of research for scaling the efficiency of a HEM as a suitable rocket fuel [38]. The bar diagrams in Fig. 6 show a direct relationship between the strengths of the PA signals and the residual amounts of HEM samples at their respective thermal decomposition temperatures. It is easy to infer that the sample with the lowest residual mass and highest intensity PA signal is a highly efficient fuel, whereas the samples with large residual masses and low-intensity PA signals are low-efficiency fuels. We showed experimentally that sample No. 3, i.e., RDX, has the highest fuel efficiency, with a negligible amount of residual mass, and picric acid has the lowest fuel efficiency, with the highest residual mass. This approach can help us to test the potential performances of new HEMs, which are available in small quantities, in the laboratory. The inset in Fig. 6 is a magnified version of the bar diagram, and it shows the small percentage mass losses and corresponding PA signals for samples No. 1, 2, and 4.

Fig. 6
figure 6

PA signal at E = 10 mJ and residual amounts of samples 01–04

Full size image

4.5 Comparative study of minimum limits of detection

The noise signal of the cavity in the presence of air was recorded at 23 °C. The maximum intensity of the noise signal was of the order of 9.5 µV. We selected an appropriate resonance frequency, at which the incident laser energy and applied pressure are kept in the linear range, i.e., below the saturation limit. Moreover, the laser beam diameter was reduced to 3 mm to control noise fluctuations of the PA signal caused by changes in temperature and pressure. The observed variation in the signal noise level was of the order of ±3 µV.

For example, in case of sample No. 1, the strength of the PA signal was 33 mV at an explosive vapor (which mainly contains NO2) concentration of 2200 ppm buffered in air at a total pressure of 450 torr. The estimated signal/noise ratio (SNR) ratio was of the order of 3.48 × 103, giving a minimum detection limit S min of 632 ppbv. The lowest limits of detection for all the samples are presented in Table 1. It should be noted that all the experiments were based on detection of thermally released NO2 from HEMs. The thermally released NO2 is not pure, because it contains small quantities of other gases such as NO, N2O, H2O, CO, and HCN, which can also be detected by the Q-factor of the PA cell. In the case of pure NO2, the Q-factor of the PA system is higher than that for impure NO2. The minimum detection limits therefore vary from sample to sample. They are much higher than the reported values for pure NO2 [25, 27, 37].

Table 1 Q-factor, SNR, and low limit of detection of samples
Full size table

5 Conclusions

We successfully recorded the time-resolved temperature-dependent PA spectra of RDX, picric acid, 5-chloro-1-(4-nitrophenyl)-1H-tetrazole, and 4,6-dinitro-5-(4-nitro-1H-imidazol-1-yl)-1H-benzo[d] [1–3] triazole for the first time. This technique is based on the detection of free NO2 molecules released by these solid samples during controlled thermal decomposition between 25 and 350 °C. The high sensitivity and selectivity of the technique enabled us to record the acoustic fingerprint spectra of all the samples just above room temperature. The results provided significant information on the thermal decomposition mechanisms, which start well below the melting points and cannot be identified by any other means. In addition, the thermal decomposition data obtained using PA and TGA–DTA techniques helped us to develop a new low-quantity-based tool for scaling HEM efficiencies as fuels for the first time. Our experimental findings confirm the presence of a small thermal peak (from NO2) slightly above room temperature. Moreover, the obtained results also confirm that the thermal decomposition mechanisms of all the selected HEM samples involve a multistep decomposition process and release of free NO2. It was also noted that the generation of NO2 groups at higher temperatures arises from oxidation reactions and is observed for samples that contain nitrogen in their ring structures. The minimum detection levels for the four target explosives were in the range from 38 ppmv to 69 ppbv.