A comprehensive mechanism for liquid-phase decomposition of 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (HMX): Thermolysis experiments and detailed kinetic modeling

Combustion and Flame 212 (2020) 67–78

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A comprehensive mechanism for liquid-phase decomposition of 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (HMX): Thermolysis experiments and detailed kinetic modeling Lalit Patidar, Mayank Khichar, Stefan T. Thynell∗ Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, USA

a r t i c l e

i n f o

Article history: Received 9 August 2019 Revised 16 October 2019 Accepted 16 October 2019

Keywords: HMX Reaction mechanism TGA FTIR spectroscopy Thermal decomposition

a b s t r a c t The nitramines 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (HMX), and 1,3,5-trinitro-1,3,5-triazinane (RDX) are energetic materials commonly used in solid propellants and explosives. In order to predict ignition and deflagration of propellants containing these ingredients, their thermal decomposition behaviors must be thoroughly understood. In this study, the thermal decomposition of HMX was investigated using synergetic application of experimental and computational methods. Mole fraction profiles of the gaseous decomposition products evolving from the liquid-phase HMX were obtained using Fourier transform infrared (FTIR) spectroscopy for two types of thermolysis experiments – thermogravimetric analysis (TGA) and confined rapid thermolysis (CRT). Four heating rates (5, 10, 15, and 20 K/min) in TGA experiments and four set temperatures (290, 300, 310 and 320 °C) in CRT experiments were considered. In the TGA and differential scanning calorimetry (DSC) results, steep mass loss and rapid decomposition were observed after the melting of the HMX at 280 °C. CH2 O and N2 O were identified as the major decomposition products. Smaller quantities of H2 O, HCN, NO and NO2 , CO and CO2 were also formed. In the complementary computational study, liquid-phase elementary reactions were investigated using quantum mechanics calculations at B3LYP/6-311++G(d,p) level of theory with the conductor-like polarizable continuum model (CPCM). A zero-dimensional model was developed to simulate the TGA and CRT experiments based on conservation of mass and species in the condensed-phase and the gas-phase control volumes. The predicted mass loss and gas-phase mole fraction profiles of the decomposition products are in good agreements with the corresponding experimental results, indicating that the comprehensive mechanism proposed here captures the important reactions occurring during liquid-phase decomposition of HMX. © 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction The cyclic nitramines HMX and RDX are important energetic ingredients commonly used in many applications, including, among others, explosives and rocket propellants. A quantitative understanding of chemical kinetics during thermal decomposition is necessary for predictive modeling of ignition, combustion and detonation behavior of explosives and solid propellants containing these ingredients. Thus, RDX and HMX have been extensively investigated with a focus on structural characterization [1–6], phase transformation [7–12], thermo-physical properties [13–15], thermal decomposition behavior [16–25], detonation characteristics [26–32], as well as burn-rate and gas-phase flame structure

∗

Corresponding author. E-mail address: [email protected] (S.T. Thynell).

[33–39]. During the past few decades, theoretical studies have also become increasingly important for predictive modeling of the ignition, combustion and detonation behaviors of these energetic materials [40–46]. Brill and Karpowicz [8] used FTIR spectroscopy to obtain Arrhenius parameters for the β -δ phase transition in HMX and proposed that the breakdown of intermolecular forces controls the rate of thermal decomposition. A detailed quantum molecular dynamics study was performed by Ye et al. [12] to explain the structural changes associated with β -HMX to δ -HMX phase transition and the initial unimolecular reaction pathways of these two conformers. Second-harmonic imaging microscopy was used to investigate the β -δ phase transition mechanism [9] and develop a kinetic model [10,11]. Products formed during thermal decomposition of HMX have been identified by rapid-scan/FTIR spectroscopy [16] and triple quadruple mass spectrometry [19]. Temporal evolution profiles of gaseous decomposition products of

https://doi.org/10.1016/j.combustflame.2019.10.025 0010-2180/© 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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various energetic materials have been probed using simultaneous thermogravimetric modulated beam mass spectrometry (STMBMS) [20,21] and confined rapid thermolysis (CRT)/FTIR spectroscopy [22]. The kinetics of phase change, thermal ignition, and decomposition have been investigated using cook-off studies [26,27]. Using the measured gas formation rates from STMBMS experiments of Behrens, kinetic parameters for global decomposition models were obtained and applied to slow cookoff in accident scenarios [23,24]. The times-to-explosion for HMX-based plastic-bonded explosives calculated by Tarver and Tran [29] using a global kinetic model are in reasonable agreement with the experimental results [30–32]. Nonetheless, the times-to-explosion are over-predicted using the global model above the liquefaction temperature of HMX, i.e., 553 K, which may be attributed to the inability of the model to account for faster autocatalytic decomposition in the liquid phase. Recently, Hobbs et al. [25] have successfully modeled the cookoff of HMX-based plastic bonded explosive (PBX 9501) using a melt rate accelerator factor at temperatures above melting point. This approach is reasonable from an engineering perspective, however, for a fundamental understanding at the molecular level, the detailed liquid-phase mechanism is required to explain faster rates at higher temperatures. In addition to cook-off models, various theoretical models, as reviewed by Beckstead et al. [41] have been formulated to study ignition [46] and deflagration [42–44] of HMX. These models analyze the combustion wave structure in three regions (solid phase, melt layer and gas phase) by solving the equations for the conservation for mass, momentum, energy, and species. In the solid phase, β -HMX to δ -HMX phase transition is modeled. Other solid-phase decomposition reactions are assumed not to occur in these combustion models. The melt layer is either ignored or modeled by a three-step global mechanism [47]. A detailed reaction mechanism, originally developed by Melius [48,49], refined by Yetter et al. [50], and further updated by Chakraborty et al. [51] is used in the gas phase. During thermal decomposition of HMX, various gaseous species, including CH2 O, N2 O, HCN, NO, NO2 , CO, CO2 , and H2 O, evolve from the condensed phase. Based on the analysis of these decomposition products, various reaction pathways were proposed. However, due to fast reactions and short-lived intermediates, experimental identification of the reaction products and the elementary reactions is quite challenging. Recently, quantum mechanics calculations have been performed in many theoretical studies to probe solid-phase and gas-phase decomposition of HMX. Truong and coworkers [52–54] performed direct dynamics calculations for the gas-phase decomposition of α -HMX at B3LYP/cc-pVDZ level of theory. Based on the analysis of rate constants calculated using transition state theory, they found that the N–NO2 bond fission is the preferred decomposition pathway. Molt et al. [5,6] used high-level ab initio methods to compute the geometries and energetic ordering of various conformers of RDX and HMX in the gas phase. In a subsequent study [55], they were the first to locate a well-defined transition state for N–NO2 bond homolysis during gas-phase decomposition of RDX. With a barrier of 41.9 kcal/mol, HONO elimination was found to be the dominant initial reaction. The equivalent barrier for N–NO2 homolysis was 53.9 kcal/mol. However, a recent study [56] on rate constants using variable reaction coordinate transition state theory have concluded N–NO2 bond dissociation as the dominant pathway in the gas phase. Decomposition of RDX and HMX from their excited electronic states and related anionic species was investigated by Bernstein and co-workers [57–59]. NO2 and HONO were ruled out as sources for NO formation, which indicates that the decomposition mechanism is different in the excited states as compared to the ground states. Zhang et al. [60] found that H+ and OH− accelerates the decomposition of HMX in the gas phase, however, in the aqueous so-

lution, this is true for OH− only. Kuklja and co-workers [61–64] investigated gas-phase and solid-phase decomposition of β - and δ HMX, and observed that N–NO2 bond fission is the dominant pathway in the gas phase. In the condensed phase, N–NO2 bond fission is also the dominant pathway for β -HMX, however, the exothermic HONO elimination channel is found to be more favorable in δ -HMX. Most of these theoretical studies have investigated the gasphase or solid-phase decomposition of HMX and RDX. A large number of reactive molecular dynamics studies [12,65–70] have also been performed with a focus on detonation characteristics. However, very little attention has been given to liquid-phase decomposition of HMX, even though the melt layer has been observed at the surface of burning propellants [71]. The liquid-phase decomposition in various combustion models is still represented by a global mechanism [42–44], which is inadequate for rigorous combustion modeling. The global mechanisms do not accurately capture the evolution of various decomposition products from the condensed phase into the gas phase above the surface of the burning propellants. This may also lead to inaccuracies in the gasphase combustion mechanisms. Hence, liquid-phase chemical kinetics needs further investigation. In this study, we demonstrate synergetic application of quantum mechanics calculations, chemical kinetic modeling and thermolysis experiments to develop and validate a comprehensive mechanism for liquid-phase decomposition of energetic materials consisting of elementary reactions. HMX is chosen as the representative energetic material but the methodology is applicable to other energetic materials as well. The first objective is to quantify species evolution rates during thermal decomposition of HMX using FTIR spectroscopy for low heating rates using TGA setup and for high heating rates using CRT setup. In our previous work [72,73], quantum mechanics calculations were performed to develop initiation mechanism for the liquid-phase decomposition of RDX and HMX. Thus, the second objective is to further expand and validate the HMX initiation mechanism consisting of elementary reactions. The detailed chemical kinetic mechanism in the liquid phase developed and validated here can then be used in threephase deflagration models along with appropriate solid-phase and gas-phase mechanisms to predict the ignition and combustion behavior of HMX. 2. Experimental details 2.1. Slow thermolysis: TGA-FTIR setup The TGA technique in conjunction with FTIR spectroscopy is used to study thermal decomposition of HMX for low heating rates as shown in Fig. 1. HMX samples of 1 mg mass were placed in aluminum crucibles and decomposed in a Netzsch STA 449 F5 Jupiter TGA/DSC apparatus coupled to a Bruker Vertex 80 FTIR spectrometer. Non-isothermal decomposition of HMX from 30 to 320 °C was investigated for four heating rates: 5, 10, 15, and 20 K/min. The decomposition products were transferred to the TGA-FTIR gas cell via a 2 m long Teflon capillary tube with an internal diameter of 2 mm, maintained at 230 °C. The transfer of species was facilitated by pure nitrogen as the purge gas having a flow rate of 70 ml/min. A temperature of 200 °C was maintained inside the FTIR gas cell. The transmission spectra were recorded with a temporal resolution of 0.144 s and at a spectral resolution of 2 cm−1 within 3750–600 cm−1 spectral range. 2.2. Fast thermolysis: CRT-FTIR setup The thermal decomposition of HMX for high heating rates is investigated experimentally using CRT-FTIR setup described in

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the total pressure. Then, the model iteratively fits the theoretical spectral transmittance to the measured spectral transmittance until the squared error converges to within 0.01%. This gives the relative concentrations of CO, CO2 , HCN, H2 O, N2 O, NO, NO2 and CH2 O in the gas-phase region. By repeating the procedure for all spectra, the variation of mole fractions of species in the gas-phase region with time is obtained. Spectral ranges for the gas-phase species, obtained from the NIST webbook [77], are given in the supplementary information as Table S1. 3. Computational details 3.1. Quantum mechanics calculations

Fig. 1. Schematic of the thermogravimetric cell and the FTIR gas cell.

Fig. 2. Schematic of the CRT setup with condensed- and gas-phase control volumes.

detail by Chowdhury and Thynell [74] and is not repeated here. HMX samples of mass 2 mg are sandwiched between two parallel surfaces with a gap of about 300 μm and rapidly heated to a set temperature using PID-controlled cartridge heaters achieving a heating rate of about 20 0 0 K/s. The liquid-phase decomposition products evolving from the sample mix with the purge gas N2 and the gaseous mixture is sampled by a modulated beam from the Bruker Vertex 80 FTIR spectrometer. The FTIR spectra are recorded in near real-time with a time resolution of 0.144 s and at a spectral resolution of 2 cm−1 within 3750–600 cm−1 spectral range. The decomposition of HMX is investigated above its melting point at four set temperatures: 290, 300, 310, and 320 °C. The schematic of the CRT setup is shown in Fig. 2. 2.3. Data reduction Using the two experimental setups described above, 40 0 0 and 400 spectra were recorded with a corresponding measurement period of about 10 min and 1 min for slow and fast thermolysis, respectively. For each acquired transmittance spectrum, the concentrations of species were determined using a data-reduction model developed by Mallery and Thynell [37]. A brief summary is given here. In the theoretical model, the species concentrations are obtained from the measured spectral transmittance assuming that Beer’s law is applicable. The measured transmittance is given by the convolution of the true transmittance with the instrument line shape, which corrects for the finite resolution of the instrument [75]. The overlapping of the absorption bands and the line intensities of rovibrational transitions of various molecules within the gas-phase region determines the true transmittance. These spectroscopic properties of the gas-phase species including CH2 O, N2 O, CO2 , CO, H2 O, HCN, NO2 , and NO are taken from the HITRAN database [76]. The data reduction model utilizes a nonlinear, least-squares method to determine the concentration of species in the gas-phase region. The input data to the model include the measured spectral transmittances, the path length, the gas-phase temperature, and

In the complementary computational study, elementary reactions in the liquid phase were investigated using quantum mechanics calculations performed in Gaussian 09 [78], Density functional theory (DFT) calculations are used for geometry optimization with B3LYP functional [79] and 6–311++G(d,p) basis set. For liquid-phase calculations, implicit conductor-like solvation model CPCM [80] is used with water as a solvent. A detailed comparsion of various combinations of solvation models and solvents was done in our previous study [72]. The reactants and products connected through the identified transition states are verified using Intrinsic reaction coordinate (IRC) calculations. The open-shell singlet state is used during the optimization of ‡ diradicals. Activation barriers G f obtained from thermochemistry calculations are used to compute the rate constants k(T) using the thermodynamic formulation of conventional transition state theory [81–84] given by equation below,



k = σs

τtun

kB T n−1 h cre f

exp

−G‡f



RT

(1)

where σ s is a symmetry factor [85], τ tun is a tunneling factor [86,87], kB is Boltzmann’s constant, h is Planck’s constant, cref is the standard state concentration, n is the order of the reaction, and G‡f is the free energy barrier and R is the universal gas constant. The initiation mechanism developed in our previous study [73] was further expanded and a comprehensive reaction mechanism was developed. Additional reactions of larger intermediates were added which eventually form simple final products observed experimentally. The comprehensive reaction mechanism includes 109 species and 157 elementary reactions. The coordinates of the species and chemical kinetic parameters of the reactions are provided as Supplementary information. 3.2. Detailed kinetic modeling for validation of the mechanism 3.2.1. Analysis of the liquid-phase region The mass of various species in the decomposing liquid-phase HMX changes due to chemical production and consumption, as well as vaporization. Hence, the conservation of mass of liquidphase species, for i = 1–Nl , leads to a set of equations written as Eq. (2). A detailed derivation of this equation is given in the supplementary information.

dYi,l = dt

Ng  ω˙ i,l MWi − kl−g,iYi,l + Yi,l kl−g, jY j,l ρl j=1

(2)

Here Yi, l is the mass fraction, ω˙ i,l is the net production rate and MWi is the molecular weight of species i in the liquid phase. ρ l is the temperature dependent density and is assumed to be that of the liquid HMX taken from the molecular dynamics study of Smith and Bhardwaj [88,89]. The rate of liquid-to-gas conversion of species i via vaporization is modeled as m˙ i,vaporized = kl−g,i mi,l ,

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where kl−g,i is the corresponding rate constant, which can be modeled via the Arrhenius equation and mi, l is the mass of the species i in the liquid phase. Ng is the number of species evolving from the liquid phase to the gas phase and Nl is the number of species in the liquid phase. The net rate constant knet for an elementary reaction is given by equation below,

1 1 1 = + knet kkin kdi f f

(3)

where kkin is the kinetics-based rate constant given by Eq. (1) and kdiff is the diffusion-based rate constant as described in detail in our previous work [90]. The temperature dependent viscosity of the liquid required for calculating the diffusion-based rate constant is assumed to be the viscosity of liquid HMX obtained from the molecular dynamics study of Smith and Bhardwaj [88]. 3.2.2. Analysis of the gas-phase region The smaller molecular weight species formed during the decomposition of HMX including CH2 O, N2 O, NO2 , NO, HONO, HCN, H2 O, CO2 , and CO desorb from the liquid phase and evolve into the gas phase. These decomposition products mix rapidly with the purge gas N2 and evolve into a relatively cooler region. Hence, they are assumed not to undergo further reactions in the gas phase. The concentration gradient within the gas phase region is also assumed to be negligible. Since the pressure and the temperature in the gasphase control volume remain almost constant, the total number of moles in the gas phase remains conserved. The conservation of mass of species i in the gas-phase control volume based on molar analysis is shown in Eq. (4). The conservation of mass for the purge gas via molar balance is given by Eq. (5). A detailed derivation of these two equations is given in the supplementary information.



dXi,g Ru Tg = dt PgVg



ml kl−g,iYi,l − MWi

Ng  ml kl−g, jY j,l m˙ p + MWp MW j





Xi,g ,

j=1

i = x1, 2, . . . , Ng − 1

 dXp Ru Tg = dt PgVg

m˙ p + ml kl−g,pYi,p − MWp

Fig. 3. Temperature profiles in the CRT setup for a set temperature of 573 K.

(4)



Ng  ml kl−g, j Y j,l m˙ p + MWp MW j

  Xp

(5) Fig. 4. (a) TGA data and (b) DSC data.

j=1

where Xi, g is the mole fraction of species i in the gas phase and Xp is the mole fraction of the purge gas in the gas phase. Ru is the universal gas constant, Tg , Pg , and Vg are the temperature, pressure, and volume of the gas-phase region. For the FTIR gas-cell of the Bruker Vertex 80 spectrometer, the temperature, pressure, and volume are 200 °C, 1 atm and 8.7 × 10−6 m3 , respectively. ml is the mass of the liquid phase, Ng is the number of species in the gas phase, MWp and m˙ p represents the molecular weight and the flow rate of the purge gas.

by first-order differential Eqs. (2), (4) and (5) is numerically integrated using the VODE solver [91]. The mass fraction of HMX in the liquid phase and the mole fraction of the purge gas in the gas phase are taken as unity at the start of the simulation. With these initial conditions, the solution of the initial value problem gives the species mass fraction profiles in the liquid phase and mole fraction profiles in the gas phase. 4. Results and discussions

3.2.3. Temperature profiles of the sample in liquid-phase In the case of TGA experiments, the temperature profile is defined by the heating rate. In the case of CRT experiments, the temperature profile is approximated based on the measurement of heating rates by a 25 μm K-type thermocouple with an inert sample [22] as shown in Fig. 3 for a set temperature of 573 K. The fitted exponential function to reproduce the temperature variation obtained experimentally is given by equation below,

T = Tset − (Tset − Ti ) exp (−25t ).

(6)

where Tset is set temperature, Ti is the initial sample temperature, and t is the time in seconds. Since the temperature profiles for both types of experiments are known, the energy equation is not needed. By employing the comprehensive reaction mechanism, the initial value problem defined

4.1. TGA and DSC results The TGA curves for the four heating rates are given in Fig. 4(a) and the corresponding DSC curves are given in Fig. 4(b). These results are the average of three repeatable experiments with similar sample masses. The β -HMX to δ -HMX phase transformation is observed at around 190 °C as indicated by a slight endothermic peak in the DSC data (given in Supplementary information as Fig. S9). As the temperature is further increased above 260 °C, the mass loss starts very slowly. On further heating, the melting of the sample is observed at 280 °C as revealed by the endothermic peaks in Fig. 4(b). These endothermic peaks shift to a slightly higher temperature at higher heating rates due to heat transfer limitations. Hence,

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at the maximum possible temperature of 230 °C. At 5 K/min, the evolution of species ends with the complete mass loss at around 285 °C since more time is available for the sample to decompose at lower temperatures just after liquefaction. As the heating rate is increased, temperature increases relatively quickly and hence the species evolution continues until a higher temperature is reached as revealed by the stretched profiles at higher heating rates in Fig. 6(b)–(d).

Fig. 5. FTIR spectrum of the evolved gases (a) TGA setup (heating rate = 20 K/min and temperature = 285 °C) and (b) CRT setup (Tset = 300 °C and t = 10.08 s).

280 °C is taken as the approximate melting temperature of HMX. The melting of the sample is immediately followed by rapid mass loss and exothermic decomposition as shown by the TGA and DSC data. At 5 K/min, approximately 20% of the initial sample mass sublimates before the melting temperature of 280 °C. At 10, 15 and 20 K/min, the corresponding values are approximately 8%, 5%, and 3% respectively. At low heating rates, the mass loss starts to occur at a lower temperature because more time is available for the sample to undergo sublimation and possibly solid-phase decomposition. At higher heating rates, the sample temperature reaches the liquefaction temperature of 280 °C relatively quickly before any substantial sublimation and solid-phase decomposition could occur. Exothermicity of the decomposition is observed to increase with the heating rate as revealed in the DSC curves in Fig. 4(b). Hence, these TGA and DSC results suggest that the decomposition of HMX, at the heating rates considered in this study, occurs predominantly in the liquid phase. 4.2. Species evolution Figure 5(a) shows a single transmittance spectrum in the case of TGA experiments for a heating rate of 20 K/min and a sample temperature of 285 °C. For CRT experiments, a single transmittance spectrum is shown in Fig. 5(b) which was obtained for a set temperature of 300 °C at t = 10.08 s. Various decomposition products identified in earlier studies [18,92] including CH2 O, N2 O, NO2 , NO, HCN, H2 O, CO2, and CO can be observed in the spectrum recorded in the present study. Signal intensities of the absorption bands of CO and NO are weak due to small permanent dipole moments. In addition to these species, thermal decomposition products in the gas phase may include other similar molecules. Here, temporal evolution profiles were obtained for only these eight species using the data reduction model previously described. 4.2.1. Effect of heating rate in TGA experiments Species evolution profiles, obtained from FTIR spectroscopy and shown in Fig. 6, reveal that CH2 O and N2 O are major decomposition products followed by H2 O, HCN, NO2 , NO, CO2 and CO in smaller concentrations. The rates of evolution of N2 O and CH2 O are considerably higher compared to other species. The rapid evolution of species is observed only after the temperature reaches 280 °C for all heating rates as shown in Fig. 6(a)–(d). This indicates that the mass loss before melting of the sample mainly consists of sublimating HMX which condenses out in the transfer tube maintained

4.2.2. Effect of set temperature in CRT experiments In the CRT apparatus, the optical path length is not known with certainty. Hence, in the data reduction model, the path length is assumed to be 1 cm, which renders the concentration profiles as relative. Due to these reasons, the trend of relative mole fractions of species is compared unlike the absolute values used in TGA experiments where the path length is known exactly as 12.3 cm. Species evolution profiles for four set temperatures investigated in this study, as obtained from FTIR spectroscopy, are shown in Fig. 7. It is again observed that CH2 O and N2 O are the major decomposition products followed by H2 O, CO2 , NO2 , NO, HCN and CO. Significant fluctuations are observed in the mole fraction profile of H2 O which are attributed to the difficulty in resolving the fine line structure of H2 O. For high heating rate experiments in CRT-FTIR setup, N2 O and CH2 O evolve at a much higher rate compared to other species. On increasing the set temperature, the decomposition rate increases as evident by a shift in the peaks of mole fraction profiles. At higher set temperatures, the relative mole fraction of NO2 is slightly higher indicating a shift towards high-temperature reaction pathways. NO2 is also consumed very quickly which indicates that it participates in secondary reactions. Maximum levels of CO2 and NO occur later in the decomposition process, which reveal that they are formed from secondary reactions. However, CH2 O and N2 O remain the major decomposition products at all set temperatures investigated in the present study. 4.3. Computational results 4.3.1. Liquid-to-gas conversion rates Results from TGA-DSC experiments are frequently used to obtain apparent activation parameters for thermal decomposition of energetic materials using isoconversional methods [93–95]. It is to be emphasized that the meaning of the term ‘activation energy’ in isoconversional methods differs significantly from its original definition and what is generally accepted in chemical kinetics. These isoconversional methods treat a complex multi-step process as a single-step process. Hence, the obtained activation energy may not have any mechanistic significance and should be treated as apparent activation energy only rather than free energy or enthalpic barrier. Since our objective is to develop and validate a detailed mechanism, describing the complex multi-step decomposition process using elementary reactions, isoconversional analysis is not performed to obtain global apparent activation energy. However, the values of the apparent activation parameters obtained in these isoconversional analysis studies can be used to reproduce the mass loss curves. The liquid-to-gas conversion rates for species i, as described in Section 3.2.1, can be represented using m˙ i,vaporized = kl−g,i mi,c , where kl−g,i is the corresponding rate constant, which can be written in Arrhenius form with the activation energy and pre-exponential factor obtained from the isoconversional analysis. Brill et al. [96] have evaluated different Arrhenius parameters published in the literature for thermal decomposition of HMX and observed kinetic compensation effect where a linear relationship exists between activation energy Ea and logarithm of pre-exponential factor, i.e., ln A. Various values of apparent Arrhenius parameters given by Brill et al. [96] are tested for liquid-to-gas

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Fig. 6. Variation of species mole fractions in the gas phase with temperature during HMX decomposition in TGA-FTIR setup (a) 5 K/min, (b) 10 K/min, (c) 15 K/min and (d) 20 K/min.

conversion rates of species in our kinetic model using a methodology as described in the next section. The final values used for all species in the validated mechanism are Ea = 51.3 kcal/mol and ln A/s − 1 = 43.3. The list of species evolving from liquid to gas includes CH2 O, N2 O, NO2 , NO, HONO, HCN, H2 O, CO2 , CO, and N2 . 4.3.2. Mechanism development and validation methodology The comprehensive reaction mechanism developed using the procedure described in Section 3.1 consists of 109 species and 157 elementary reactions. It is used in conjunction with the chemical kinetic model described in Section 3.2 to simulate the TGA and CRT experiments. The liquid-phase reaction mechanism for HMX was developed and validated using the synergetic application of quantum mechanics calculations, kinetic modeling, and TGA and CRT experiments. The development of the reaction mechanism was guided by the experimental results. For example, we see in the ex-

periments that CH2 O and N2 O are the major decomposition products. Hence, we look into our database of thousands of reactions and add the reactions involving CH2 O and N2 O in our mechanism. We then continue the process and add reactions of other species such as NO, NO2 , HCN. The initial version did not have reactions for the formation of CO and CO2 but we see these species as well in the experiments. Hence, we also perform additional quantum mechanics calculations which lead to the formation of CO and CO2 and add those reactions to the mechanism. None of the input parameters required for the computational model are coming from our experimental data. The vaporization parameters are obtained from various Arrhenius parameters compiled by Brill et al. [96] and the kinetic parameters are obtained directly from quantum mechanics calculations. The experimental data are not used in any mathematical function within some optimization routine to obtain or tweak the kinetic parameters. The experimental data are merely

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Fig. 7. Species mole fractions profiles in the gas phase during HMX decomposition in CRT-FTIR setup at a set temperature of (a) 290 °C, (b) 300 °C, (c) 310 °C and (d) 320 °C.

used to guide the development of the mechanism. This is our mechanism development methodology. The experimental results are used only to validate the model. The liquid-to-gas conversion rates and the chemical kinetic parameters were validated by comparing the following results: 1. Mass loss data obtained from the TGA experiments. 2. Species evolution profiles obtained from the TGA experiments. 3. Species evolution profiles obtained from the CRT experiments. A sensitivity analysis provides information about what reactions need to be further refined in order to obtain a better agreement with the experimental data. This is justified because the free energy values in solution are uncertain to a few kcal/mol and changes were made to 6 reactions out of 147; the largest change was 3 kcal/mol, which is within the uncertainty of the calculated free energy barriers. The original and new values are provided as Supplemental Information.

4.3.3. Prediction of mass loss and species evolution profiles The computational results for the mass loss are shown in Fig. 8. The model predictions are in excellent agreement with the experimental mass loss curves for all heating rates considered in this study. Since the computational model is developed for the liquid-phase decomposition of HMX, sublimation is not included. Hence, in the computational results, the mass loss does not occur before the melting temperature of 280 °C. The discrepancies in the mass loss for temperatures lower than 280 °C, especially at low heating rates of 5 K/min and 10 K/min, are attributed to sublimation of HMX. After the melting of the sample above 280 °C, the computational model accurately captures the rate of mass loss for all heating rates. For example, the complete mass loss occurs at a temperature of 285 °C for a heating rate of 5 K/min. The corresponding temperatures for heating rates of 10, 15, and 20 K/min are 290, 295, and 300 °C, respectively. The model also predicts 100% mass loss at these temperatures accurately for different heating rates.

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Fig. 8. Mass loss curve for HMX decomposition at four heating rates.

Fig. 9. HMX decomposition for a heating rate of 15 K/min. Species mole fractions profiles in the gas phase (a) computational and (b) experimental.

The species evolution profiles predicted by the model for a heating rate of 15 K/min are shown in Fig. 9(a) and compared against the corresponding experimental results shown in Fig. 9(b). The model predicts CH2 O and N2 O as the major decomposition products. The peak mole fractions of CH2 O and N2 O in the FTIR gas cell are also in excellent agreement with the experimental peak values. The evolution of H2 O, NO and CO2 are also in good agreement with the experimentally obtained evolution profiles. How-

ever, HCN is formed in slightly larger quantities in the computational model as compared to the experimental results, whereas NO2 is formed in smaller quantities. A large fraction of NO2 is consumed in secondary reactions in our mechanism which explains the low mole fraction of NO2 . Computational results for other heating rates considered in this study are given as Supplementary information (Figs. S1–S3). The computational model predicts the species evolution profiles for

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Fig. 10. HMX decomposition in the liquid phase at 300 °C. Temporal evolution of species relative mole fractions in the gas phase (a) computational and (b) experimental.

other heating rates with good accuracy as well. Variation of mass fraction of HMX and its decomposition products in the liquid phase is also given as supplementary information (Fig. S4). The CRT simulation results for species relative mole fraction profiles at a set temperature of 300 °C are shown in Fig. 10(a) and compared against the corresponding experimental results shown in Fig. 10(b). The model predicts CH2 O and N2 O as the major decomposition products for isothermal decomposition as well. The evolution of NO2 and NO is also captured reasonably well. The computational evolution profile of H2 O lies within the experimental fluctuation range. HCN is produced in larger concentration in the computational model as compared to the experimental results. On the other hand, smaller quantities of CO2 are predicted by the computational model. The computational model for CRT simulations also captures the shift in peaks as the set temperature is changed (not shown here for brevity, computational results for all set temperatures investigated in this study are included in Supplementary information as Figs. S5–S7). Variation of mass fraction of HMX and its decomposition products in the liquid phase during isothermal decomposition at 300 °C is also given as supplementary information (Fig. S8). The computational and experimental results for the species mole fraction profiles are in reasonable agreement with each other for both types of experiments. This indicates that the initiation and subsequent reactions for the liquid-phase decomposition of HMX are reasonably captured by the comprehensive reaction mechanism developed and validated in the present study. 4.4. Sensitivity analysis A sensitivity analysis is performed to identify important reactions in the liquid phase at various time instants during the thermal decomposition of HMX. The sensitivity coefficient Sij was defined as shown in equation below,

Si j =

A j y i , i = 1, 2, . . . , Nspecies ; j = 1, 2, . . . , Nreactions A j y i

(7)

where yi represents the change in the mass fraction yi of ith species in the liquid phase and Aj represents the change in Afactor Aj of jth reaction in the liquid-phase mechanism. Repre-

sentative values of the sensitivity coefficients at a heating rate of 15 K/min and at a temperature of 283 °C are shown in Fig. 11. The liquid phase decomposition of HMX can begin via four unimolecular initiation steps – (1) HONO elimination (2) N–NO2 bond fission, (3) concerted ring fission (4) C–N bond scission of the ring. Early bimolecular reactions include hydrogen abstraction and nitroso formation pathways. A detailed comparison of these pathways with other studies in the literature was presented in our previous studies [72,73]. The analysis of the activation barriers for forward and backward reactions reveals that the decomposition of HMX in liquid phase begins with HONO elimination. This is in agreement with results for the gas-phase decomposition of RDX by Molt et al. [55] and for the solid-phase decomposition of δ -HMX by Sharia et al. [63] who also found HONO elimination channel to be dominant. In most other studies, N–NO2 bond fission has been considered a dominant step for the initiation of HMX decomposition. However, the barrier for the backward radical recombination reaction is negligible. Hence, this reaction is less significant in the liquid phase. Decomposition of HMX begins with HONO elimination. HONO formed from the initiation step subsequently undergoes various self-reactions and forms ONNO2 , NO2 , NO, and H2 O. Autocatalytic hydrogen abstraction pathway from HMX was found to be the most sensitive pathway at all time instants. During the initial stage of the decomposition, reactions of HMX and larger intermediate species such as INT249a (HMX-HONO ) were found to be more sensitive. As the mass fraction of HMX decreases in the liquid phase, reactions of smaller intermediate species such as CH2 NNO2 and CH2 NH becomes more sensitive. The subsequent reactions of HONO formed from HONOelimination and hydrogen abstraction reactions are governed by the cage effect [97,98] in the liquid phase. The first step during the liquid-phase decomposition of HMX is the HONO elimination reaction, which forms INT249a and HONO. However, the diffusion of HONO away from INT249a may be hindered by the cage effect. It reacts back with INT249a and the subsequent decomposition of INT249a occurs via autocatalytic prompt oxidation by HONO addition. As discussed in detail in our previous study [73], these prompt oxidation reactions are highly exothermic and

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Fig. 11. Sensitivity coefficients of forward rate constants on HMX mass fraction in the liquid phase at 15 K/min heating rate and 283 °C during TGA simulations.

summary of important reaction pathways in the liquid-phase HMX is presented in Fig. 12.

5. Conclusions

Fig. 12. Summary of liquid-phase decomposition mechanism of HMX.

they explain the simultaneous formation of CH2 O and N2 O as observed experimentally. Similar prompt oxidation reactions were postulated for simple –NO2 containing energetic molecules [98]. Autocatalytic prompt oxidation of INT249 also occurs via ONNO2 . These prompt oxidation reactions of INT249 produces CH2 NNO2 , CH2 NHCHO, and CH2 NH which subsequently decompose and contribute towards formation of a significant amount of final decomposition products i.e. CH2 O, N2 O, HCN, NO, NO2 , CO, and CO2 . A

Thermal decomposition of HMX was studied using TGA-FTIR setup for different low heating rates and using CRT-FTIR setup for high heating rates to isothermal conditions at different set temperatures. A phase transformation from β -HMX to δ -HMX was observed around 190 °C. DSC data shows the endothermic melting at approximately 280 °C. This was followed by rapid mass loss and exothermic decomposition. For heating rates of 10, 15 and 20 K/min, sublimation of HMX was very small and it decomposed predominately in the liquid phase. During both types of experiments, CH2 O and N2 O were observed to be major decomposition products followed by smaller quantities of H2 O, HCN, NO, NO2 , CO, and CO2 . Using quantum mechanics calculations, an existing detailed liquid-phase reaction mechanism for the decomposition of HMX was further augmented to yield 109 species and 157 reactions. The reaction mechanism was employed in a computational model to simulate TGA and CRT experiments. The mass loss curves predicted by the computational model are in excellent agreement with the TGA data. The species mole fraction profiles predicted by the computational model are also in good agreement with the experimental results obtained from FTIR spectral transmittance data. The computational model accurately predicts CH2 O and N2 O as the major decomposition products for both types of experiments. The evolution of other decomposition products formed in smaller quantities such as NO2 , NO, H2 O, CO, CO2, and HCN were also captured reasonably well. Based on a sensitivity analysis, hydrogen abstraction and prompt oxidation reactions were found to play an important role in the liquid phase. The validated liquid-phase mechanism is being used in a multi-phase combustion model with

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