Exploring the thermal decomposition and detonation mechanisms of 2,4-dinitroanisole by TG-FTIR-MS and molecular simulations

Abstract

2,4-dinitroanisole (DNAN), an insensitive explosive, has replaced trinitrotoluene (TNT) in many melt-cast explosives to improve the safety of ammunition and becomes a promising material to desensitize novel explosives of high sensitivity. Here, we combine thermogravimetric-Fourier transform infrared spectrometry-Mass spectrometry (TG-FTIR-MS), density functional theory (DFT), and ReaxFF molecular dynamics (MD) to investigate its thermal decomposition and detonation mechanisms. As revealed by TG-FTIR-MS, the thermal decomposition of DNAN starts at ca. 453 K when highly active NO₂ is produced and quickly converted to NO resulting in the formation of a large amount of Ph(OH)(OH₂)OCH₃⁺. DFT calculations show that the activation energy of DNAN is higher than that of TNT due to the lack of α-H. Further steps in both thermal decomposition and detonation reactions of the DNAN are dominated by bimolecular O-transfers. ReaxFF MD indicates that DNAN has a lower heat of explosion than TNT, in accordance with the observation that the activation energies of polynitroaromatic explosives are inversely proportional to their heat of explosion. The inactive –OCH₃ group and less nitro groups also render DNAN higher thermal stability than TNT.

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1. Introduction

Nitro-aromatic compounds are important energetic materials that are widely used in many military and civilian applications.^1–11 Among them, 2,4-dinitroanisole (DNAN) is an insensitive melt-cast matrix ingredient, which was used to prepare Amatol-40 explosives in WWII.^11,12 Since the 1980s, DNAN has again aroused strong attention and has become a promising energetic material to replace the traditional trinitrotoluene (TNT) in melt-cast explosives to make them less sensitive^13–19 owing to its kinetic inertness and thermal stability. Various DNAN-based melt-pour explosive formulations have been developed^20–32 and put into service.^33–35 However, researchers have identified several drawbacks and challenges related to the physical properties, sensitivity, stability, compatibility, and oxygen balance of DNAN, which could potentially hinder its future applications.³⁶ Therefore, a comprehensive understanding of the characteristics of DNAN is essential to solve various problems caused by its use.

In the past decade, the heat capacity, thermal behavior, and thermal hazards of DNAN have been investigated by many research groups.^37–44 Researchers studied the thermal decomposition behavior of DNAN using accelerated calorimetry (ARC) and differential scanning calorimeter (DSC). The activation energies (E_a) of DNAN calculated from ARC data is 61.91 kcal mol⁻¹,⁴⁰ and that measured by DSC and ARC under adiabatic conditions is 71.19 kcal mol⁻¹.⁴¹ These data indicate that DNAN exhibits greater kinetic inertness and thermal stability compared to TNT and enable researchers to predict the stability and safety of DNAN-based melt-cast explosives. It is unsurprising that the use of DNAN to desensitize novel emerging sensitive high-energy density explosives has become very promising.^27,45–51

On the other hand, the Evans–Polanyi–Semenov (E–P–S) equation^52–56 describes a relationship between activation energies (E) of many radical reactions and their heats of reaction , where B is a constant and can be viewed as a measure of how far a reaction has proceeded along the reaction coordinate when the transition state (TS) is reached. Based on the EPS equation, it was found that for polynitroaromatics, such as TNT and TATB, the activation energy for thermal decomposition is inversely proportional to the heat of detonation.⁵⁷ It can be used to explain the chemical micromechanism governing between thermal decomposition and detonation of DNAN, a kind of polynitroaromatics.

The thermal decomposition mechanism of DNAN cannot be adequately understood without analyzing its thermal decomposition intermediates and products. To gain insight into the detailed thermal decomposition mechanism of energetic materials, researchers have employed a range of analytical techniques, including thermogravimetric analysis (TG), Fourier transform infrared spectrometry (FTIR), and mass spectrometry (MS), to analyze the evolved gaseous intermediates and products.^58–67 In 2014, Maharrey et al.⁶⁷ used simultaneous thermogravimetric modulated beam mass spectrometry to explore the thermal decomposition process of DNAN. The decomposition onset was measured to be 483 K. Their results suggested that the first step is the melting of DNAN, followed by the equilibrium evaporation of liquid DNAN. Later, 2,4-dinitrophenol is formed from DNAN through a rearrangement reaction involving an H transfer from C to O in the –OCH₃ group and the subsequent release of CH₂. In 2015, Liu et al.⁵⁸ proposed a dynamic pressure-measuring thermal analysis (DPTA) techniques to evaluate the thermal stability of energetic materials. They combined DPTA, MS, and density functional theory (DFT) calculations to study the thermal decomposition of three volatile low-melting explosives, i.e. TNT, DNAN, and 3,4-bis(3-nitrofurazan-4-yl)furoxan (DNTF). The results suggested that DNAN has the best thermal stability, while DNTF is the most heat-sensitive. In 2021, Wojtas et al.⁶³ combined DSC with thermally enhanced Fourier-transform infrared spectroscopy to analyze the entire process of thermal decomposition of DNAN. DNAN was stable in the liquid phase up to 423 K, and the fastest thermal decomposition rate was detected at 613 K, and the gas products measured during the thermal decomposition of DNAN were mainly CO, CO₂, N₂O, and CH₃OH.

Despite the efficiency of the aforementioned measurements,^58,63,67 the information they provided was still limited because many reaction intermediates cannot be detected due to their short lifetime and trace amounts. Thus, the results are insufficient to establish a detailed thermal decomposition mechanism and detonation of DNAN convincingly at the molecular level. The combination of TG-FTIR-MS with molecular simulations turns out to be a useful tool for this purpose. In the last decade, reaction force field (ReaxFF) molecular dynamics (MD) simulations^68–85 have been widely used to obtain detailed information for reaction processes at the molecular level beyond measurements.

In the present study, we combine ReaxFF MD and DFT calculations with TG-FTIR-MS analysis to investigate the thermal decomposition and detonation mechanisms of DNAN. TG-FTIR-MS is used to identify the products generated from the initial thermal decomposition of DNAN under mild conditions. Based on the measured data, a thermal decomposition mechanism of DNAN is proposed and further rationalized by our DFT calculations. ReaxFF MD simulations are also performed to investigate the detonation process of DNAN. Based on the experimental and computational results, the major reaction pathways as well as key kinetic parameters of DNAN thermal decomposition and detonation are obtained. Moreover, the relationship between the thermal decomposition and detonation mechanisms of DNAN is analyzed.

2. Methods

2.1 Experiments section

DNAN produced by Alfa Aesar, with a purity above 98%, was dried at 348 K for one day before experiments. TG-FTIR-MS tests were carried out to analyze the species of products in gas phase during the entire thermal decomposition process of DNAN in the temperature range of 308–683 K. These tests consist of the following parts: a TG-DTA instrument (ErkinElmer STA8000), an FTIR spectrometer (ErkinElmer Spectrum 3) and a GC-MS instrument (Clarus SQ 8 GC-MS). The reaction vessel was first heated to 308 K, then approximately 5 mg samples were loaded into an open aluminum pan and heated to 683 K at 5 K min⁻¹ under a nitrogen flow at 20 ml min⁻¹. The spectra of the evolution of gas fragments during the thermal decomposition of DNAN were recorded by an FTIR spectrophotometer in real-time tracking mode with a scan range of 4000 cm⁻¹ to 500 cm⁻¹ at a resolution of 2 cm⁻¹. The m/z for gas-phase fragments evolution during DNAN decomposition was recorded by the mass spectrometer conducting the dynamic scanning in the m/z range from 1 to 400.

2.2 Computational methods

The thermal decomposition processes of DNAN are studied using DFT calculations, while ReaxFF-lg MD calculations simulate its detonation. The temperature is set to 500 K in DFT calculations in accordance with the TG-FTIR-MS analysis. DFT calculations are also performed to compare the potential energy (PE) barrier of key reactions. The NVT ensemble is employed for ReaxFF-lg MD simulations at 2500 K and 3500 K to ensure the detonation of DNAN is complete.

2.2.1 DFT calculations. DFT calculations were carried out to estimate the thermodynamic parameters, i.e. enthalpy and Gibbs free energy changes, for some key reaction pathways. The calculations were performed using the Gaussian09 package⁸⁶ and the M062X-D3 (ref. 87) density functional in conjunction with the 6-311+G(d,p) basis set were used. The vibrational analysis was performed at the same level of theory to reliably characterize the optimized structures either as the local minima or TS. Intrinsic reaction coordinates (IRC) calculations were performed to examine whether the TS under consideration connected the expected reactants and products properly.

2.2.2 ReaxFF-lg MD simulations. In this study, we use the large-scale atomic/molecular massively parallel simulator (LAMMPS) to perform the ReaxFF-lg MD simulations.^69,76–78 The force field parameters of DNAN are obtained from the report by Liu et al.⁷⁶ The crystal structures of DNAN and TNT belong to the monoclinic system with the space group P21/n and orthorhombic system with the space group Pca21, respectively (Fig. 1). Their lattice parameters from the X-ray diffraction are provided in Table S1†.^79,80 The optimized cell parameters and densities of the DNAN and TNT unit cells by the ReaxFF-lg agree well with experimental data within less than 5% deviation (Table S1†). The bond lengths of DNAN and TNT by ReaxFF-lg and DFT agree well with the experimental data^79,80 (Table S2†).

Fig. 1 The unit cell of DNAN (left) and TNT (right). The C, H, O, and N atoms are colored gray, white, red, and blue, respectively.

The following fast-heating protocol is employed to compare the thermal sensitivity of DNAN and TNT. First, an internal pressure relaxation for the crystal unit cells was performed for 10 ps with an isothermal-isobaric (NPT) ensemble at 300 K and 0 Pa. Then, DNAN and TNT unit cells were quickly heated to 2500 K in 2 ps. Afterward, the two systems evolve under the canonical (NVT) ensemble for 100 ps.

A slow-heating protocol is employed to simulate the detonation process of DNAN at 2500 K and 3500 K, respectively, for which a 2 × 4 × 1 supercell of 1.56 g cm⁻³ was used. First, the system was relaxed at 300 K and 0 Pa for 10 ps with the NPT ensemble, after which its equilibrium density slightly decreased to 1.53 g cm⁻³. Then, the system was slowly heated to the set temperature of 50 ps. Finally, the system evolves under the NVT ensemble at the two temperatures for 500 ps and 250 ps, respectively. In MD simulations, the time step was set to 0.1 fs to effectively cover the phase space and allow the collisions and reactions to occur smoothly. Snapshots along the MD trajectories were recorded every 100 fs. These collected data were analyzed using Findmole⁸¹ and in-house programs to extract information about chemical reactions during the process.

2.3 Kinetic analysis

The thermal decomposition process of DNAN is divided into three stages. The initial and intermediate stages are separated at t_max, when the PE reaches the maximum.^61,83,86 For the intermediate stage, the following linear form of the Arrhenius equation is used to describe the reaction kinetics,where k is the rate constant, A is the pre-exponential factor, E_a is the activation energy, R is the universal gas constant, and T is the temperature. The rate constant for reactions in the second stage (k₁) is fitted with an exponentially decaying function,

U_t = U_∞ + (U_max − U_∞)exp[−k₁(t − t_max)], (2)

where U_t is the value of PE at moment t, U_∞ is the asymptotic value of PE, U_max is the maximum PE. The kinetic parameters A and E_a in eqn (2) are determined from the rate constants k's at 2500 and 3500 K.

In the final stage, the reaction slows down compared to the intermediate stage, and the amounts of final products, i.e. H₂O, N₂, CO₂, and H₂, steadily increase. The rate constant for reactions in the final stage (k₂) can be calculated for each product by fitting the following function,

C_t = C_∞{1 − exp[−k₂(t − t_i)]}, (3)

where C_∞ is the asymptotic amount of the ith product, t_i is the moment of its earliest formation.

3. Results and discussion

Here, we first discuss the thermal decomposition of DNAN, followed by its detonation in the condensed phase, and finally compare the key reactions that occurred in them.

3.1 DNAN thermal decomposition

3.1.1 Products from DNAN thermal decomposition. The various fragments produced by DNAN thermal decomposition were simultaneously detected by TG coupled with FTIR. The 3D diagrams of the infrared spectrum for gas-phase fragments evolution are shown in Fig. 2(a). No absorption bands can be distinguished before 459 K, indicating that DNAN does not decompose before 459 K. Then, absorption bands reach the maximum at 510 K, and several noticeable absorption bands can be distinguished.

Fig. 2 3D diagrams of infrared spectrum for gas-phase fragments evolution (a) and FTIR in the 500–4000 cm⁻¹ spectral region of the evolved products at the selected temperatures (b) during the DNAN thermal decomposition.

FTIR spectral region in the 500–3500 cm⁻¹ of the evolved products at the selected temperatures (459 K, 510 K, 546 K) during the thermal decomposition of DNAN are shown in Fig. 2(b). Several noticeable absorption bands are attributed to the gas phase vibrations of NO, NO₂, CH₃OH, and benzene. The peaks at 3095 cm⁻¹, 1020 cm⁻¹, 915 cm⁻¹, 1609 cm⁻¹, and 1494 cm⁻¹ are assigned to C–H stretching, C–H bending, and C=C stretching of benzene, respectively. The absorption peak at 2950 cm⁻¹ signals NO. The vibration of NO₂ produces two absorption bands at 1548 cm⁻¹ (antisymmetric stretching) and 1347 cm⁻¹ (symmetric stretching). The absorption peak at 1143 cm⁻¹ is assigned to CH₃OH. The absorption peak at 2854 cm⁻¹ is assigned to the C–H stretching of the methyl group. The absorption peaks at 1280 cm⁻¹, 834 cm⁻¹, and 1068 cm⁻¹ are assigned to the N–O and C–O stretching of the functional group –C–O–NO₂. Further MS analysis was performed to identify the gas products and volatile compounds from the thermal decomposition of DNAN.

The gas phase products were simultaneously detected by GS-MS followed by TG-FTIR, and the evolutions of the intensity of the main gas products are shown in Fig. 3. As shown in Fig. 3, some remarkable characteristic peaks (m/z = 30, 46, 107, 127, 141 and 142) are visible. Combined with the absorption peaks in the FTIR, the peaks with m/z of 30 and 46 are assigned to NO (m/z = 30) and NO₂ (m/z = 46), respectively. Three heavier compounds containing the benzene moiety (m/z = 107, 127, 141, and 142) are also produced. It can be found from Fig. 3 that NO is not produced before 455 K and reaches its maximal concentration at 601 K. Then, this is accompanied by the appearance of Ph(OH)(OH₂)OCH₃⁺ (m/z = 141/142) at 460 K, with a maximum at 530 K. Clearly, Ph(OH)(OH₂)OCH₃⁺ is the dominant species in the gas products exhibiting the highest intensity. Later at 465 K, another major species in the gas products, Ph(OH)₂–OH₂⁺ (m/z = 127), is produced and peaks their maximum at 530 K. Finally, trace amounts of NO₂ (m/z = 46) and PhOCH₃ (m/z = 107) appear at 510 K and 554 K, respectively. Note that the protons in various species detected by GS-MS are from DNAN molecules under thermal decomposition since we used the traditional electron impact ionization method, which produces no proton.

Fig. 3 Evolutions of the intensity of main gas products: NO (pink), NO₂ (blue), Ph(OH)₂–OH₂⁺ (violet), Ph(OH)(OH₂)OCH₃⁺ (orange), PhOCH₂⁻ or Ph⁻·OCH₃ (green).

3.1.2 Thermal decomposition mechanism of DNAN. Based on the TG-FTIR-MS results, the following reaction schemes are proposed for the initial thermal decomposition of DNAN (Fig. 4). At the beginning, highly active NO₂ is produced, but is not detected since it is quickly converted to NO. This results in the formation of a large amount of Ph(OH)(OH₂)OCH₃⁺ (Fig. 4 and Scheme 1). Most of them were detected, although a small amount further decomposed to CH₂O and Ph(OH)₂OH₂⁺ (Fig. 4 and Scheme 2) in the condensed phase. Subsequently, CH₃O⁺ loses its H successively to decompose to CH₂O and CHO⁺. Scheme 1 is the major reaction and the nitro group is more reactive than the methoxy group. Finally, trace amounts of DNAN decompose to NO₂ and Ph⁻–OCH₃ (Fig. 4 and Scheme 3) at a higher temperature.

Fig. 4 The proposed reaction schemes for the initial thermal decomposition of DNAN based on the TG-FTIR-MS data.

Previous experimental studies and molecular simulations have revealed some basic mechanisms that govern the decomposition of nitroaromatic explosives such as TNT and TATB.^{76–80,86–90} Four major routes were reported as the initiating agents of detonation: (1) C–N bond homolytic cleavage to generate NO₂,^76–80 (2) nitro (–NO₂) isomerization rearrangement to form nitrite (–ONO) followed by the O–NO bond breaking to form NO,^88–92 (3) intra- (α-) and intermolecular H transfer,^{68,87,88,90–93} (4) intermolecular O transfer.⁹³

The major unimolecule reactions, that initiate the thermal decomposition of DNAN, are summarized in Fig. 5(a). Previous studies suggest that the triggering reaction is the homolysis of the ortho-C–NO₂ bond (P1), which is endothermic, and DFT calculations show that ΔH is 68.80 kcal mol⁻¹ at 500 K. The homolysis of the remaining para-C-NO₂ bond requires much more heat (ΔH = 78.21 kcal mol⁻¹). This explains why only a very small amount of Ph–OCH₃ is detected by our TG-FTIR-MS experiment at a higher temperature of ca. 554 K (Fig. 3). Another key unimolecular route is the C–NO₂ rearrangement (P2). The TS (TS2₁) contains a triangular C–N–O ring. The breaking of the C–N bond in TS2₁ leads to the formation of INT2₁. Subsequent O–NO bond homolysis in INT2₁ produces NO and INT2₂. The third unimolecular path, i.e. the homolysis of the C–OCH₃ bond, is more difficult for DNAN (P3) since more heat is required for this reaction (ΔH = 100.35 kcal mol⁻¹). The p–π conjugation between the O atom and the phenyl ring strengthens the C–OCH₃ bond. This path causes the formation of ˙OCH₃ and INT3₁. The ˙OCH₃ radical is further dehydrogenated to form HCHO. Note that the overall enthalpy changes for these three unimolecular reaction paths are all positive and they produce highly active radicals for later reactions.

Fig. 5 (a) Major unimolecular reaction paths (P1 to P3) and (b) bimolecular reaction path (P4) during the decomposition of the DNAN. Numbers in green are enthalpy changes of each step at 500 K (kcal mol⁻¹) calculated from DFT.

In our TG-FTIR-MS experiment, Ph(OH)₂–OH₂⁺ is detected, indicating an O transfer should occur at C_OCH3 of DNAN. DFT calculations suggest that highly active NO₂ can attack the C_OCH3 atom to form TS4₁ (Fig. 5(b), P4). Then, TS4₁ turns to its more unstable tautomer, TS4₂, via INT4₁. The C–OCH3 bond is now effectively activated. Further release of the –OCH₃ group from TS4₂ results in the formation of INT4₂, which decomposes to NO and INT4₃. Thus, in this environment, NO₂ is a highly active radical and reacts quickly with DNAN and other species to be reduced to NO.

We calculated the enthalpy changes (ΔH) of each step (Fig. 5) and the relative Gibbs free energies (Table 1) of the involved species for the initiating reactions at 500 K through DFT. The energy barrier (ΔH = 17.76 kcal mol⁻¹) of P4 is much smaller than those initiating reactions, so P4 is expected to be a route of high frequency, which explains why NO is detected earlier (at ca. 408 K) and in larger quantities than NO₂ in our TG-FTIR-MS analysis (Fig. 3). Moreover, ˙OCH₃ mainly departs from the benzene ring through P4 instead of P3.

Table 1 Major species involved in the initial thermal decomposition paths of DNAN and their Gibbs free energies relative to a DNAN (P1, P2, P3) or NO₂ and DNAN (P4) at 500 K (kcal mol⁻¹).^a

Path	Gibbs free energy
a Note that in DNAN, the –OCH3 and ortho-NO2 adopt opposite orientations (Fig. 1) and are too far away for intramolecular H transfer. In contrast, both intra- and intermolecular H transfers were reported in the thermal decomposition of TNT^80–83 and the former, i.e. the α-H transfer is the triggering reaction.
P1	INT11 + NO2 (45.68), INT12 + 2NO2 (102.11)
P2	TS21 (59.92), INT21 (−7.17), INT22 + NO (−10.13)
P3	INT31 + OCH3 (77.55)
P4	TS41 (46.21), INT41 (38.28), TS42 (59.27) INT42 + OCH3 (28.12), INT43 + NO + OCH3 (31.13)

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3.2 Detonation of DNAN in condensed phase

In the condensed phase, DNAN bimolecular reactions are facilitated by the proximity of neighboring molecules. The phenyl ring of DNAN is positively charged due to the electron-withdrawing substituents. Thus, the nitro oxygen atom can attack the carbon of the phenyl ring leading to nucleophilic substitutions. There are three types of reaction sites for intermolecular O transfer on the phenyl ring, i.e. C2 and C4, C1, and C3, C5 and C6 (Fig. 1).

3.2.1 Detonation of DNAN vs. TNT during fast heating. We compare the thermal sensitivities and detonation properties of DNAN and TNT in the condensed phase using the fast-heating protocol outlined in 3.1. The PE of both systems spikes due to the fast heating as the temperature increases from 300 K to 2500 K (Fig. S1†). Under the same temperature conditions, the PE of TNT reaches the maximum earlier than that of DNAN. Naturally, TNT decomposes before DNAN does. Afterward, a steeper decrease in PE is predicted for TNT than for DNAN, suggesting a more violent decomposition in the TNT crystal. Previous studies⁸⁷ have shown that TNT in the condensed phase mainly undergoes bimolecular H transfer reaction, and analysis of the TNT MD trajectory shows that the number of H transfer reactions is three times greater than that of O transfer reactions (Fig. S2†).

In contrast, the lack of α-H in DNAN hinders its activation, while its contains only two NO₂ causes severe negative O balance and the oxidation of C, H, and N is inadequate in the later stage. Furthermore, in DNAN, the C_ph–O–C bond angle is 120° (Fig. 1), indicating sp² hybridization for the O in the methoxyl group. The p–π conjugation renders –OCH₃ in DNAN higher stability and lower reactivity. Consequently, the bimolecular H transfer reaction is more difficult and suppressed during the thermal decomposition of DNAN. These factors to some extent explain the lower thermal sensitivity of DNAN than that of TNT.

3.2.2 Detonation mechanism of DNAN during slow heating. We further use the slow-heating protocol outlined in 3.1 to simulate the thermal decomposition of DNAN at 2500 K and 3500 K, respectively. The evolution of the PE and the total number of DNAN (n_DNAN) in the supercell are shown in Fig. 6. In the first stage, the PE increases rapidly with the temperature. When the set temperature (2500 K or 3500 K) is reached at 60 ps, the PE is almost at its maximum and the energy absorbed by DNAN is already above the activation energy for its thermal decomposition. Thus, a significant number of DNAN molecules have decomposed. In the second stage, the decomposition continues and a lot of heat is rapidly released. Clearly, the rate of decomposition is faster at 3500 K than at 2500 K and so does the rate of PE drop. In the third stage, the rate of decomposition drastically decreases and the PE curve plateaus, approaching chemical equilibrium. At 3500 K, the higher stable value of PE at the end compared to that at 2500 K is mainly due to the more complete decomposition of DNAN leading to more small fragments and less chemical bonds and larger deformation of product molecules and clusters.

Fig. 6 The evolution of the PE (solid lines) and n_DNAN (dashed lines) during the decomposition of DNAN under the NVT condition at 2500 K (blue) and 3500 K (red). Black lines are the exponential fit of the PE. The arrows indicate the separation of the three decomposition stages.

The numbers of direct bonding between C, H, O, and N atomic pairs during the decomposition of DNAN are summarized in Fig. S3.† Carbon is oxidized because the amount of C–H bonds gradually decreases, while the amount of C–O bonds increases. The amount of O–N bonds gradually decreases and that of N–N bonds increases, indicating that nitrogen is reduced. The amounts of O–H and H–H bonds keep increasing proving that H is partially oxidized. More N₂ is produced at 3500 K than at 2500 K at the end since a higher temperature causes more N atoms to escape from the carbon cluster product. A higher temperature also favors the breaking of C–H bonds, leading to more H˙ radicals and H₂, which can reduce more NOx to N₂.

3.2.2.1 Initial decomposition stage. All reactions involving at least one complete DNAN at the initial decomposition stage are summarized in Table 2. These reactions are classified into three categories. The first category includes three types of unimolecular reactions (P1, P2, P3) as discussed in 4.2.1. The second category includes reactions between two DNAN molecules (referred to as reaction A + A), while the third category contains reactions between a DNAN molecule and another active fragment radical produced from primary reactions (referred to as reaction A + B). Reactions A + B include O transfer and H transfer reactions. The former is similar to O transfer between two DNAN (P5-7), while the latter is similar to H transfer between two DNAN (P8). Note that more than 50% of DNAN molecules undergo A + B reactions in the third category at both temperatures.

Table 2 The initial time and frequency of the initial decomposition paths for condensed phase DNAN under NVT conditions at 2500 K and 3500 K

Reaction	2500 K		3500 K
	tinitial (ps)	Frequency	tinitial (ps)	Frequency
a The frequencies of three types of A + A bimolecular oxygen transfer reactions (P5–7) are 3,2,1 and 2,1,1 at 2500 K and 3500 K, respectively.
Unimolecular	53.4	16	40.0	17
C–NO2 homolysis (P1)	53.4	11	40.0	12
C–NO2 rearrangement (P2)	62.8	2	49.4	1
C–OCH3 homolysis (P3)	60.2	3	47.6	4
Bimolecular (A + A)	56.8	8	43.2	5
O transfer (P5–7)^a	56.8	6	43.2	4
H transfer (P8)	60.2	2	50.6	1
Bimolecular (A + B)	57.2	32	44.2	37
O transfer	57.2	15	44.2	30
H transfer	58.2	17	47.8	7

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In the condensed phase, about 25% of DNAN molecules undergo unimolecular reactions in the early stage. The frequency of unimolecular reactions decreases as: P1 > P3 > P2 (Fig. 5(a)). The remaining 75% of initial reactions are bimolecular. At both temperatures, the number of O transfer reactions is greater than that of H transfer reactions. At higher T, the number of O transfers increases, while that of H transfer decreases, indicating a competition between the two types of reactions and a lower reaction barrier for the latter. At both temperatures, the C–NO₂ homolysis occurs first, followed by the O transfer reaction. The chronological order of bimolecular reactions at 2500 K is shown in Fig. S4.†

The four types of A + A biomolecule reactions (P5–8) are summarized in Fig. 7. The frequencies of O transfer reactions decrease as P5 > P6 ≥ P7. The nitro oxygen prefers to transfer to C_NO2 (P5). The nitro group at C4′ rotates to approach C2, forming INT5₁, whose C–NO₂ bond is effectively activated. Thus, NO₂ is released from INT5₁, and INT5₂ is produced, which further breaks apart into INT5₃, INT5₄, and NO₂. In contrast, the transfer of nitro O to C1 (P6), which is less favorable due to the p–π conjugation between –OCH₃ and the phenyl ring, leads to the formation of INT6₁. Further release of the –OCH₃ group from INT6₁ leads to the formation of INT6₂ and radicle, which is an endothermic process. Then, INT6₃ and INT6₄ can be formed from the dissociation of INT6₂. The third type of oxygen transfer pathway involves the transfer of the nitro O to C3, C5, or C6 (P7), which produces INT7₁. The connection bridge of INT7₁ breaks to yield INT7₂ and INT7₃.

Fig. 7 Major bimolecular reaction paths and intermediate species during the initial thermal decomposition of condensed phase DNAN. P5, P6, and P7 are three bimolecular O transfer reactions, while P8 is a bimolecular H transfer reaction.

As to the bimolecular H transfer (P8), the nitro O at C2 of one DNAN adsorbs the H atom from the –OCH₃ group of the adjacent DNAN to form TS8₁ containing a five-membered C–H–O–N–O ring. Then, TS8₁ relaxes to its more stable tautomer, INT8₁. The newly formed weak C–O bond in the connection bridge of INT8₁ breaks to yield INT8₂ and INT8₃. The breaking of the C1′–OCH₂ bond in INT8₂ and the N–OH bond in INT8₃ leads to the formation of HCHO molecules and OH˙ radicles. Afterwards, OH˙ combines with H˙ to produce H₂O.

In the A + B bimolecular reactions, a DNAN reacts with its various fragments produced from primary reactions, which also include O transfer and H transfer reactions. As the temperature increases from 2500 K to 3500 K, the frequency of A + B bimolecular reactions increases significantly (Table 2) because more fragments and radicals like NO₂ of higher mobility are produced to facilitate the oxidation of remaining DNAN molecules. As shown in Fig. S5,† in the condensed phase, NO₂ generated from primary reactions can make a nucleophilic attack at the phenyl ring to generate NO. Consequently, the frequency of A + B type O transfer reactions increases by 100% (Table 2). In contrast, at 3500 K, the frequency of bimolecular H transfer reactions decreases due to their competition with bimolecular O transfer reactions.

Besides NO_X, CH₂O and H₂O are also produced in the initial decomposition of DNAN. At 2500 K, an H is transferred from the ˙OCH₃ produced from P6 to the nitro of another DNAN to form the first CH₂O at 57.1 ps (Fig. 8(a)). This is followed by the formation of the first H₂O at 58.5 ps (Fig. 8(b)). An intramolecular H transfer first occurs in INT7₂ produced from P7 leading to the formation of the –NO₂H group, which further abstracts an H atom from the –OCH₃ group of another DNAN. The products include H₂O and Ph(NO₂)₂–OCH₂ and then the C_phyl–O bond of the latter is broken to release the second CH₂O.

Fig. 8 The formation of the first CH₂O (a) and H₂O (b) at 57.1 and 58.5 ps, respectively, during the initial decomposition of DNAN in the condensed phase at 2500 K. The C, H, O, and N atoms are colored gray, white, red, and blue, respectively.

3.2.2.2 Intermediate decomposition stage. In the DNAN intermediate decomposition stage in the condensed phase (Fig. 6), the system contains DNAN-dimer and monomer fragments, small molecules, and radicals. The second stage is characterized by reactions among primary products and the subsequent decomposition of benzene rings into carbon clusters. Fast generation of N₂, CO₂, H₂O, and H₂ is visible, accompanied by the depletion of NO₂, CH₂O, and NO (Fig. 9).

Fig. 9 The time evolution of the number of light intermediates from the DNAN decomposition at 2500 K (a) and 3500 K (b).

At 3500 K, CH₂O is almost completely consumed at the end of the second stage (Fig. 9(b)). CO is generated from CH₂O by dehydrogenation and is further oxidized to the more stable CO₂ (Fig. S6(a)†). When substitution groups fall off from DNAN, the remaining phenyl ring can also rupture to generate CO₂ (Fig. S6(b)†). However, the amount of CO₂ produced by the former is much greater than that by the latter. Alternatively, the remaining phenyl ring can also directly polymerize to form carbon clusters (Fig. S7†). The number of N–O bonds further decreases (Fig. S3†), because H˙ radicals reduce NO_X to N₂, which also produces OH˙. The combination of OH˙ with H˙ yields H₂O eventually. At the same time, C–O bonds form promptly due to the oxygen transfer from N to C. The increase in the numbers of N–N, O–H, and C–O bonds is also partially due to the formation of stable N₂, H₂O, and CO₂ molecules, respectively (Fig. S3†).

The DNAN decomposition rate constants in the intermediate stage are estimated by fitting the PE curve (Fig. 6) through eqn (3), and the calculated k₁ at 2500 and 3500 K are 0.013 and 0.059 ps⁻¹, respectively (Table 3). Small molecules, like NO₂, NO, and CH₂O, all vanish much faster at 3500 K than at 2500 K (Fig. 9). Then the pre-exponential factor A and activation energy E_a can be obtained from eqn (2), whose values are 2.59 ps⁻¹ and 26.30 kcal mol⁻¹ (Table 3), respectively, which reasonably agrees with the experimental value (19.15 ± 1.36 kcal mol⁻¹).⁴¹

Table 3 Comparison of the kinetic parameters for DNAN decomposition at 2500 and 3500 K

T/K	k1/ps^−1	A/ps^−1	Ea/kcal mol^−1	k2/ps^−1
				CO2	N2	H2O
2500	0.013	2.59	26.30	0.0066	0.0062	0.0089
3500	0.059			0.011	0.011	0.012

---

3.2.2.3 Final product evolution stage. In our MD simulations, the final products from the thermal decomposition of DNAN at high temperatures include CO₂, N₂, H₂O, H₂, and carbon clusters containing some O, H, and N atoms (Fig. S8†). The amounts of stable gas products decrease in the order: of H₂O > N₂ > CO₂. At higher temperatures, more N₂ is formed since fewer N atoms are trapped in carbon clusters. Moreover, a large amount of H₂ is also generated (Fig. 9 and S8†) due to the severe negative oxygen balance of DNAN. Since the C=O bond energy is greater than the O–H bond energy, the O atom prefers to combine with C to form CO₂. Besides these small molecules, the decomposition of DNAN leads to the formation of the copious amount of large molecular clusters, containing mostly carbon atoms. These carbonaceous clusters start to form in the second stage of the DNAN decomposition and further grow in size afterward. At 3500 K, more heat is available for the ring-opening reactions to form larger carbon clusters with a maximum molar mass up to 3000 g mol⁻¹. These carbon clusters in DNAN capture a significant amount of O and, to a lesser extent, N atoms, suspending the formation of final gas-phase products. When most of the H₂O, CO₂, and N₂ molecules are formed, the energy release slows down. Then, carbon cluster residues begin to release O, H, and N atoms at a slower pace, while their C content gradually increases. A close inspection of the MD trajectories at the end of the decomposition identifies large C₁₅₀H₂₁O₆₄N₁₅ (Fig. S8(b)†) and C₁₇₅H₄₀O₆₃N₁₀ clusters at 2500 K and 3500 K, respectively.

The reaction rate constant k₂ for this stage is estimated by the reaction rate analysis method (Sec. 2.2.2). Effective rate constants for each product creation can be calculated from eqn (3). Simulated results are presented in Fig. 10 and Table 3. There is a good agreement between the simulated and fitted asymptotic amounts of all final gas products, indicating that the simulation reactions have reached equilibrium. As expected, the formation rates of all three final gas products increase with the temperature, and that of H₂O is the highest.

Fig. 10 Time evolution of the number of H₂O, N₂, and CO₂ products from the DNAN decomposition at 2500 K (a) and 3500 K (b). Black lines are the exponential fits.

3.3 Analysis of key reactions

The TG-FTIR-MS analysis reveals that among the various species produced by the initial thermal decomposition of DNAN, the amounts of NO and CH₂O are greater than that of NO₂, while the amount of Ph(OH)₂OCH₃ is greater than that of Ph(OH)₃ and far greater than that of PhOCH₃ (Fig. 3 and 4). The measured data can be rationalized by our MD simulations, which reveal that the initial decomposition stage is dominated by the unimolecular P1 and later by bimolecular P4 (NO₂ attacks the –OCH₃ group of DNAN) reactions (Fig. 5), and the NO₂ produced by P1 is deoxidized to NO by P4. Another source of NO is from P2 (Fig. 5(a)), the C–NO₂ rearrangement of DNAN. Ph(OH)(OH₂)OCH₃⁺ (m/z = 141, 142) can be produced through P2 or P5. Due to its p–π conjugation with the phenyl ring, the reaction of –OCH₃ is more difficult than –NO₂. However, –OCH₃ can be knocked off through P4 or P6. P4 is more prone to occur than P6, as NO₂ is much more reactive than DNAN. The production of Ph(OH)₃ requires the –OCH₃ group and two nitro groups of a DNAN molecule to react away simultaneously, which is of low probability. This explains why the amount of Ph(OH)₂–OH₂⁺ is relatively low in the TG-FTIR-MS analysis. Only a small amount of DNAN undergoes C–NO₂ homolysis in both ortho and para position, especially in the condensed phase, resulting in a low amount of PhOCH₃.

The ortho-NO₂ homolysis process of DNAN and TNT single molecules is further compared using the relaxed scan algorithm via DFT. As shown in Fig. 11(a), both pathways are barrierless, in accordance with the report⁶⁴ by Wang et al. For both molecules, the changes of PE are similar, 75.96 kcal mol⁻¹ for TNT and 77.54 kcal mol⁻¹ for DNAN. In contrast, the reaction barrier of the triggering α-H transfer of TNT is only 47.15 kcal mol⁻¹ as shown in Fig. 11(b) and S9(c).†

Fig. 11 The PE changes due to the release of ortho-NO₂ (a) and the O and H transfer (b) of the DNAN and TNT computed from DFT. The dimer, TS, and product structures of reactions in (b) are provided in Fig. S9.†

The PE changes of bimolecular H or O transfer reactions for DNAN and TNT are computed via DFT and compared in Fig. 11(b). For DNAN bimolecular (A + A) reactions, the energy barriers are relatively high, 78.61 kcal mol⁻¹ and 99.92 kcal mol⁻¹ for inter-molecular H and O transfer, respectively. This explains why the frequencies of these bimolecular (A + A) reactions are low during the DNAN detonation (Table 2). However, after NO₂ radicals are produced from primary reactions, the reactions of DNAN become faster as the activation energy of bimolecular (A + B) O transfer reactions is significantly reduced to 25.52 kcal mol⁻¹. This is particularly favorable for DNAN decomposition in the gas phase since small radicals like NO₂ have greater mobility than those in a condensed phase. This explains the experimental observation in ref. 58 that the thermal decomposition of DNAN happens mostly in the gas phase when it is in vapor–liquid equilibrium.

4. Conclusions

We combine the TG-FTIR-MS analysis, DFT, and RaxFF-lg MD calculations to investigate the thermal decomposition and detonation processes of DNAN. Based on the measured and computed results, the following conclusions are drawn:

(1) Due to the lack of α-H, the thermal decomposition of DNAN is triggered by unimolecular C–NO₂ homolysis at ca. 453 K, which produces active NO₂ radical for secondary reactions. The maximum reaction rate is reached at ca. 513 K, and gas products are NO, NO₂, CH₃OH and fragments containing the benzene moiety. The estimated activation energy from DFT computations is 77.54 kcal mol⁻¹, which is close to the measured one of 71.19 kcal mol⁻¹.

(2) Unlike the –CH₃ group of TNT, the –OCH₃ group of DNAN is significantly less reactive due to its p–π conjugation with the phenyl ring. Instead of C–O homolysis, the –OCH₃ group is mainly reacted by NO₂ attack. This reaction renders the decomposition of DNAN highly favorable especially in the gas phase due to its low energy barrier and high mobility of NO₂ radical.

(3) The detonation of DNAN in the condensed phase is dominated by bimolecular reactions and 37.5% of them are O transfer reactions, while 33.3% of them are H transfer reactions in our ReaxFF MD simulation at 2500 K. At 3500 K, the frequency of O transfer reactions increases, while that of H transfer reactions decrease. This is mainly due to the increase in the number of fragment radicals like NO₂ and their mobility, which is important for condensed-phase reactions.

(4) For the second stage of DNAN detonation, unstable intermediate species, like NO_X and CH₂O, are further converted to stable products, H₂O, CO₂, and N₂, and a large quantity of explosion heat is generated. Due to its poor O balance, C and H in DNAN cannot be fully oxidized. At the end of the reaction, there is a certain amount of H₂ and carbon clusters.

(5) The higher thermal stability and lower explosion heat of DNAN than TNT is attributed to several structural factors, i.e. the lack of α-H, inactive –OCH₃ group, and less nitro groups causing severe negative O balance.

(6) Our results provide explanation for the empirical E–P–S equation of polynitroaromatic explosives, whose activation energy is inversely proportional to the heat of explosion. Due to the higher activation energy of DNAN than TNT, less active radicals are produced during the initiation stage of the former’ detonation. Consequently, the detonation heat of DNAN is lower than that of TNT.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research is funded by the National Natural Science Foundation of China [grant no. 12272184]. We thank Miss Ayesha Hina for proofreading the manuscript.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ra00860j

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