Predicting impact sensitivities of nitro compounds on the basis of a semi-empirical rate constant

An Integrated Experimental and Modeling Approach for Assessing High-Temperature Decomposition Kinetics of Explosives

We present a new integrated experimental and modeling effort that assesses the intrinsic sensitivity of energetic materials based on their reaction rates. The High Explosive Initiation Time (HEIT) experiment has been developed to provide a rapid assessment of the high-temperature reaction kinetics for the chemical decomposition of explosive materials. This effort is supported theoretically by quantum molecular dynamics (QMD) simulations that depict how different explosives can have vastly different adiabatic induction times at the same temperature. In this work, the ranking of explosive initiation properties between the HEIT experiment and QMD simulations is identical for six different energetic materials, even though they contain a variety of functional groups. We have also determined that the Arrhenius kinetics obtained by QMD simulations for homogeneous explosions connect remarkably well with those obtained from much longer duration one-dimensional time-to-explosion (ODTX) measurements. Kinetic Monte Carlo simulations have been developed to model the coupled heat transport and chemistry of the HEIT experiment to explicitly connect the experimental results with the Arrhenius rates for homogeneous explosions. These results confirm that ignition in the HEIT experiment is heterogeneous, where reactions start at the needle wall and propagate inward at a rate controlled by the thermal diffusivity and energy release. Overall, this work provides the first cohesive experimental and first-principles modeling effort to assess reaction kinetics of explosive chemical decomposition in the subshock regime and will be useful in predictive models needed for safety assessments.

High energy barrier hydroxyl radical dissociation mechanism of a low shock sensitivity dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate (TKX-50) explosive

As a representative of the new generation of high-energy explosives, TKX-50 has attracted widespread attention due to its remarkably low sensitivity toward shock. However, the reported decomposition barriers of TKX-50 (∼37 kcal mol-1) are comparable to those of commonly used explosives. The mechanism of its low shock sensitivity remains unclear. In this study, using an ab initio molecular dynamics method combined with a multiscale shock simulation technique and transition state calculations (at the B2PLYP-D3/Def2TZVP level), we discovered an unconventional reaction pathway of TKX-50 under shock, and its rate-controlling step is the dissociation of the hydroxyl radical (OH) from the anion ring after proton transfer, followed by ring rupture and the production of H2O and N2. The barrier for this OH dissociation reaction is as high as 51.9 kcal mol-1. In contrast, under thermal stimuli, TKX-50 prefers to open rings directly after proton transfer without losing the OH. The corresponding barrier is 35.4 kcal mol-1, which is in good agreement with previous studies. The reason for the unconventional reaction pathway of TKX-50 under shock may be the suppression of anion ring opening in thermal decomposition by steric hindrance upon shock compression. In addition, the dominant N2 generation pathway under shock releases less energy than pyrolysis which further explains the low shock sensitivity of TKX-50. This study comprehensively elucidates the different reaction mechanisms of TKX-50 under thermal and shock conditions and proposes a crucial reaction pathway leading to its low shock sensitivity. These findings will contribute to the understanding and application of tetrazole anionic energetic salts.

Exploring an accurate machine learning model to quickly estimate stability of diverse energetic materials

High energy and low sensitivity have been the focus of developing new energetic materials (EMs). However, there has been a lack of a quick and accurate method for evaluating the stability of diverse EMs. Here, we develop a machine learning prediction model with high accuracy for bond dissociation energy (BDE) of EMs. A reliable and representative BDE dataset of EMs is constructed by collecting 778 experimental energetic compounds and quantum mechanics calculation. To sufficiently characterize the BDE of EMs, a hybrid feature representation is proposed by coupling the local target bond into the global structure characteristics. To alleviate the limitation of the low dataset, pairwise difference regression is utilized as a data augmentation with the advantage of reducing systematic errors and improving diversity. Benefiting from these improvements, the XGBoost model achieves the best prediction accuracy with R2 of 0.98 and MAE of 8.8 kJ mol-1, significantly outperforming competitive models.

Probing into the theory of impact sensitivity: propelling the understanding of phonon-vibron coupling coefficients

The determination of impact sensitivity of energetic materials traditionally relies on expensive and safety-challenged experimental means. This has instigated a shift towards scientific computations to gain insights into and predict the impact response of energetic materials. In this study, we refine the phonon-vibron coupling coefficients ζ in energetic materials subjected to impact loading, building upon the foundation of the phonon up-pumping model. Considering the full range of interactions between high-order phonon overtones and molecular vibrational frequencies, this is a pivotal element for accurately determining phonon-vibron coupling coefficients ζ. This new coupling coefficient ζ relies exclusively on phonon and molecular vibrational frequencies within the range of 0-700 cm-1. Following a regression analysis involving ζ and impact sensitivity (H50) of 45 molecular nitroexplosives, we reassessed the numerical values of damping factors, establishing a = 2.5 and b = 35. This coefficient is found to be a secondary factor in determining sensitivity, secondary to the rate of decomposition propagation and thermodynamic factor (heat of explosion). Furthermore, the relationship between phonon-vibron coupling coefficients ζ and impact sensitivity was studied in 16 energetic crystalline materials and eight nitrogen-rich energetic salts. It was observed that as the phonon-vibron coupling coefficient increases, the tendency for reduced impact sensitivity H50 still exists.

Halogenated PETN derivatives: interplay between physical and chemical factors in explosive sensitivity

Determining the factors that influence and can help predict energetic material sensitivity has long been a challenge in the explosives community. Decades of literature reports identify a multitude of factors both chemical and physical that influence explosive sensitivity; however no unifying theory has been observed. Recent work by our team has demonstrated that the kinetics of "trigger linkages" (i.e., the weakest bonds in the energetic material) showed strong correlations with experimental drop hammer impact sensitivity. These correlations suggest that the simple kinetics of the first bonds to break are good indicators for the reactivity observed in simple handling sensitivity tests. Herein we report the synthesis of derivatives of the explosive pentaerythritol tetranitrate (PETN) in which one, two or three of the nitrate ester functional groups are substituted with an inert group. Experimental and computational studies show that explosive sensitivity correlates well with Q (heat of explosion), due to the change in the number of trigger linkages removed from the starting material. In addition, this correlation appears more significant than other observed chemical or physical effects imparted on the material by different inert functional groups, such as heat of formation, heat of explosion, heat capacity, oxygen balance, and the crystal structure of the material.

Which molecular properties determine the impact sensitivity of an explosive? A machine learning quantitative investigation of nitroaromatic explosives

We decomposed density functional theory charge densities of 53 nitroaromatic molecules into atom-centered electric multipoles using the distributed multipole analysis that provides a detailed picture of the molecular electronic structure. Three electric multipoles, (the charge of the nitro groups), (the total dipole, i.e., polarization, of the nitro groups), (the total electron delocalization of the C ring atoms), and the number of explosophore groups (#NO₂) were selected as features for a comprehensive machine learning (ML) investigation. The target property was the impact sensitivity h₅₀ (cm) values quantified by drop-weight measurements, with a large h₅₀ (e.g., 150 cm) indicating that an explosive is insensitive and vice versa. After a preliminary screening of 42 ML algorithms, four were selected based on the lowest root mean square errors: Extra Trees, Random Forests, Gradient Boosting, and AdaBoost. Compared to experimental data, the predicted h₅₀ values of molecules having very different sensitivities for the four algorithms have differences in the range 19-28%. The most important properties for predicting h₅₀ are the electron delocalization in the ring atoms and the polarization of the nitro groups with averaged weights of 39% and 35%, followed by the charge (16%) and number (10%) of nitro groups. A significant result is how the contribution of these properties to h₅₀ depends on their actual sensitivities: for the most sensitive explosives (h₅₀ up to ∼50 cm), the four properties contribute to reducing h₅₀, and for intermediate ones (∼50 cm ≲ h₅₀ ≲ 100 cm) #NO₂ and contribute to increasing it and the other two properties to reducing it. For highly insensitive explosives (h₅₀ ≳ 200 cm), all four properties essentially contribute to increasing it. These results furnish a consistent molecular basis of the sensitivities of known explosives that also can be used for developing safer new ones.

Understanding Explosive Sensitivity with Effective Trigger Linkage Kinetics

We present a simple linear model for ranking the drop weight impact sensitivity of organic explosives that is based explicitly on chemical kinetics. The model is parameterized to specific heats of explosion, Q, and Arrhenius kinetics for the onset of chemical reactions that are obtained from gas-phase Born-Oppenheimer molecular dynamics simulations for a chemically diverse set of 24 molecules. Reactive molecular dynamics simulations sample all possible decomposition pathways of the molecules with the appropriate probabilities to provide an effective reaction barrier. In addition, the calculations of effective trigger linkage kinetics can be accomplished without prior physical intuition of the most likely decomposition pathways. We found that the specific heat of explosion tends to reduce the effective barrier for decomposition in accordance with the Bell-Evans-Polanyi principle, which accounts naturally for the well-known correlations between explosive performance and sensitivity. Our model indicates that sensitive explosives derive their properties from a combination of weak trigger linkages that react at relatively low temperatures and large specific heats of explosion that further reduce the effective activation energy.

Decomposition mechanism on different surfaces of copper azide

Copper azide, a potential primary explosives that may replace traditional primers such as lead azide, mercury fulminate and silver azide, has received widespread attention, but its decomposition mechanism remains unclear. Here, based on first-principles calculations, (010)_N3, (100)_N3and (001) facets with a copper/nitrogen atom ratio of 1/6 are found to be the most stable surfaces of copper azide crystal. Through transition state (TS) calculations, we find that during the decomposition process on the surface, there is a synergy effect between two Cu-N1-N2-N3 chains, where the terminal N2-N3 bonds on two chains break simultaneously, and the dissociated N3 atom bonds with another N3' atom of adjacent chain to form a N₂ molecule. Next, the Cu-N bond will rupture, and two more N₂molecules (N1-N2, N1'-N2') desorb from the surface. The overall reaction releases above 4 eV energy at a barrier of 1.23 eV on (001) surface. Electronic structure calculations reveal that the TS of N2-N3 rupture is more stabilized than that of N1-N2. According to the above results, we propose a new decomposition mechanism based on simulations of N-N bond breaking on different surfaces of copper azide. The results underscore the surface effect in decomposition of energetic materials.

Quantifying bond strengths via a Coulombic force model: application to the impact sensitivity of nitrobenzene, nitrogen-rich nitroazole, and non-aromatic nitramine molecules

The quantification of bond strengths is a useful and general concept in chemistry. In this work, a Coulombic force model based on atomic electric charges computed using the accurate distributed multipole analysis (DMA) partition of the molecular charge density was employed to quantify the weakest N-NO₂ and C-NO₂ bond strengths of 19 nitrobenzene, 11 nitroazole, and 10 nitramine molecules. These bonds are known as trigger linkages because they are usually related to the initiation of an explosive. The three families of explosives combine different types of molecular properties and structures ranging from essentially aromatic molecules (nitrobenzenes) to others with moderate aromaticity (nitroazoles) and non-aromatic molecules with cyclic and acyclic skeletons (nitramines). We used the results to investigate the impact sensitivity of the corresponding explosives employing the trigger linkage concept. For this purpose, the computed Coulombic bond strength of the trigger linkages was used to build four sensitivity models that lead to an overall good agreement between the predicted values and available experimental sensitivity values even when the model included the three chemical families simultaneously. We discussed the role of the trigger linkages for determining the sensitivity of the explosives and rationalized eventual discrepancies in the models by examining alternative decomposition mechanisms and features of the molecular structures.

Radical pair formation due to compression-induced electron transfer in crystals of energetic salts

An interesting effect was observed when studying explosive and non-explosive crystalline ionic materials at high pressures. A wide benchmark set of 76 crystals of different families was studied using the state-of-the-art methods at ambient pressure and in extremes (at 20, 50 and 100 GPa). It was found that hydrostatic compression leads to an electron transfer from the anion to the cation, which was carried out with different efficiencies for explosive and non-explosive salts. The measure of this electron transfer is reflected in the Hirshfeld charges (q) on cations, which decreased with the rise of pressure. Non-explosive materials are generally resistant to this effect, while explosives are much more susceptible. Thus, at 100 GPa, all the studied energetic salts demonstrate qcat < +0.1e, while for the non-explosive salts qcat > +0.1e. This value can be considered as a conditional boundary between explosive and non-explosive salts. The observed effect is in accord with the Szigeti's dielectric theory as well as with the electrophilicity/electronegativity equalization principle. In the present paper, we develop a mechanism of the explosive decomposition based on the assumption about formation of a radical pair as a result of the following reaction: . The study of such radicals revealed their intrinsic instability, which generally reflects either in a dissociative structure or in the presence of strongly weakened trigger bonds.

Review of the molecular and crystal correlations on sensitivities of energetic materials

Highly efficient design on the levels of molecule and crystal, as well as formulation, is highly desired for accelerating the development of energetic materials (EMs). Sensitivity is one of the most important characteristics of EMs and should be compulsorily considered in the design. However, owing to multiple factors responsible for the sensitivity, it usually undergoes a low predictability. Thus, it becomes urgent to clarify which factors govern the sensitivity and what is the importance of these factors. The present article focuses upon the progress of the molecular and crystal correlations on the sensitivity, and the molecule-based numerical models for sensitivity prediction in the past decades. On the molecular level, composition, geometric structure, electronic structure, energy and reactivity can be correlated with the sensitivity; while the sensitivity can be also related with molecular packing pattern, intermolecular interaction, crystal morphology, crystal size and distribution, crystal surface/interface and crystal defect on the crystal level. And most of these factors, in particle on the crystal level, have been employed as variables in numerical models for predicting sensitivity of categorized EMs. Besides, we stress that more attention should be paid to the sensitivity correlations on the inherent structures of EMs, molecule and crystal packing, because they can be readily dealt by molecular simulations nowadays, facilitating to reveal the physical nature of sensitivity.

Models for predicting impact sensitivity of energetic materials based on the trigger linkage hypothesis and Arrhenius kinetics

In order to predict the impact sensitivity of high explosives, we designed and evaluated several models based on the trigger linkage hypothesis and the Arrhenius equation. To this effect, we calculated the heat of detonation, temperature of detonation, and bond dissociation energy for 70 energetic molecules. The bond dissociation energy divided by the temperature of detonation proved to be a good predictor of the impact sensitivity of nitroaromatics, with a coefficient of determination (R²) of 0.81. A separate Bayesian analysis gave similar results, taking model complexity into account. For nitramines, there was no relationship between the impact sensitivity and the bond dissociation energy. None of the models studied gave good predictions for the impact sensitivity of liquid nitrate esters. For solid nitrate esters, the bond dissociation energy divided by the temperature of detonation showed promising results (R² = 0.85), but since this regression was based on only a few data points, it was discredited when model complexity was accounted for by our Bayesian analysis. Since the temperature of detonation correlated with the impact sensitivity for nitroaromatics, nitramines, and nitrate esters, we consider it to be one of the leading predictive factors of impact sensitivity for energetic materials.

Correlation between molecular charge densities and sensitivity of nitrogen-rich heterocyclic nitroazole derivative explosives

Nitroazole derivatives are nitrogen-rich heterocyclic ring molecules with potential application as energetic materials. Thirty-three of them-nitroimidazoles, nitrotriazoles, and nitropyrazoles-were investigated. Computed density functional theory molecular charge densities were partitioned employing the accurate distributed multipole analysis (DMA) method. Based on the magnitude of the DMA atom-centered electric multipoles (monopole, dipole, and quadrupole values), mathematical models were developed to compute the impact sensitivity of the explosives composed of these molecules. Charge localization and delocalization of the ring nitrogen atoms as well as charges of the atoms of the nitro group affect the sensitivity of explosives composed of nitroazole derivatives. The sensitivity is strongly dependent on the ring position of the nitrogen atoms and the bonding site of the substituent groups. The N/C ratio and the repulsion of the non-bonding electron pairs of the vicinal nitrogen atoms of the ring also play an important role in the stability of nitroazoles. The influence of the withdrawing group (NO₂) and the electron injector groups (NH₂ and CH₃) including their bonding position on the ring could be quantified.

Vibrationally induced metallisation of the energetic azide α-NaN3

As initiation of an energetic material requires rupture of a covalent bond, and therefore population of antibonding electronic states, consideration of the electronic band gap has dominated initiation mechanisms for solid state materials. Most prominent are models based on metallisation, where static mechanical perturbation leads to closing of the electronic band gap. This work explores an alternative mechanism for the dynamic metallisation of a model energetic material, where vibrational excitation resulting from mechanical impact is found to induce transient metallisation of α-NaN3. The normal coordinates associated with bending the azido anion close the electronic band gap, facilitating the formation of highly reactive species important for initiation of energetic materials. The DFT simulated vibrational spectrum of α-NaN3 exhibits excellent reproduction of the experimental low-temperature inelastic neutron scattering spectrum (INS).

Structural Rearrangement of Energetic Materials under an External Electric Field: A Case Study of Nitromethane

As a significant stimulus, the external electric field (EEF) can change the decomposition mechanism and energy release of energetic materials (EMs). Hence, understanding the response of EMs to an EEF is greatly meaningful for their safe usage. Herein, the structural arrangement, a crucial factor in the impact sensitivity and detonation performance of EMs, under the EEF ranging from 0.0 to 0.5 V/Å was investigated via molecular dynamics simulation. Nitromethane (NM) was taken as a case study due to the simple structure. The simulation results show that there exists a critical EEF strength between 0.2 and 0.3 V/Å, which can induce the transition of NM molecules from relatively disordered distribution to solidlike ordered and compacted arrangement with a large density. In this ordered structure, NM dipoles are aligned in a head-to-tail pattern parallel to the EEF direction because of the favored dipole-dipole interactions and weak C-H···O hydrogen bonds. As the EEF strength is enhanced, the potential energy and cohesive energy density of the NM system gradually decrease and increase, respectively, indicative of high thermodynamics stability of ordered arrangement. The results reported here also shed light on the potential of the EEF to induce the nucleation and crystallization to explore new polymorphs of EMs.

Trigger bond analysis of nitroaromatic energetic materials using wiberg bond indices

The identification of trigger bonds, bonds that break to initiate explosive decomposition, using computational methods could help direct the development of novel, "green" and efficient high energy density materials (HEDMs). Comparing bond densities in energetic materials to reference molecules using Wiberg bond indices (WBIs) provides a relative scale for bond activation (%ΔWBIs) to assign trigger bonds in a set of 63 nitroaromatic conventional energetic molecules. Intramolecular hydrogen bonding interactions enhance contributions of resonance structures that strengthen, or deactivate, the CNO₂ trigger bonds and reduce the sensitivity of nitroaniline-based HEDMs. In contrast, unidirectional hydrogen bonding in nitrophenols strengthens the bond to the hydrogen bond acceptor, but the phenol lone pairs repel and activate an adjacent nitro group. Steric effects, electron withdrawing groups and greater nitro dihedral angles also activate the CNO₂ trigger bonds. %ΔWBIs indicate that nitro groups within an energetic molecule are not all necessarily equally activated to contribute to initiation. %ΔWBIs generally correlate well with impact sensitivity, especially for HEDMs with intramolecular hydrogen bonding, and are a better measure of trigger bond strength than bond dissociation energies (BDEs). However, the method is less effective for HEDMs with significant secondary effects in the solid state. Assignment of trigger bonds using %ΔWBIs could contribute to understanding the effect of intramolecular interactions on energetic properties. © 2018 Wiley Periodicals, Inc.

Computational study of the structure and properties of bicyclo[3.1.1]heptane derivatives for new high-energy density compounds with low impact sensitivity

To design new high-energy density compounds (HEDCs), a series of new bicyclo[2.2.1]heptane derivatives containing an aza nitrogen atom and nitro substituent were designed and studied theoretically. The density, heat of sublimation and impact sensitivity were estimated by electrostatic potential analysis of the molecular surface. Based on the designed isodesmic reaction, and the reliable heat of formation (HOF) of the reference compounds, HOFs were calculated and compared at B3LYP/6-311G(d,p) and B3P86/6-311G(d,p), respectively. The detonation performances, bond dissociation energies (BDE) and impact sensitivity were calculated to evaluate the designed compounds. The calculated results show that the number of aza nitrogen atoms and NO₂ groups are two important factors for improving HOF, density and detonation properties. Thermal stability generally decreases with increasing nitro groups. And the N-NO₂ bond is the trigger bond for all designed compounds except B8, whose trigger bond is C-NO₂. Importantly, the BDE values are between 86.95 and 179.71 kJ mol^-1 and meet the requirement for HEDCs. Detonation velocity and detonation pressure were found to be 5.77-9.65 km s^-1 and 12.30-43.64 GPa, respectively. After comprehensive consideration of thermal stability, impact sensitivity and detonation properties, A7, A8, B8, C8, D7, E7, F7 and G6 may be considered as potential HEDCs. Especially, A8, B8, C8, and D7 have better detonation properties than the famous caged nitramine CL-20 (D = 9.40 km/s, P = 42.00GPa). Besides, all the designed potential HEDCs have reasonable impact sensitivity. Graphical abstract New high-energy density compounds (HEDCs) with low impact sensitivity (A8, B8, C8 and D7 have better detonation properties than CL-20).

Molecular Theory of Detonation Initiation: Insight from First Principles Modeling of the Decomposition Mechanisms of Organic Nitro Energetic Materials

This review presents a concept, which assumes that thermal decomposition processes play a major role in defining the sensitivity of organic energetic materials to detonation initiation. As a science and engineering community we are still far away from having a comprehensive molecular detonation initiation theory in a widely agreed upon form. However, recent advances in experimental and theoretical methods allow for a constructive and rigorous approach to design and test the theory or at least some of its fundamental building blocks. In this review, we analyzed a set of select experimental and theoretical articles, which were augmented by our own first principles modeling and simulations, to reveal new trends in energetic materials and to refine known existing correlations between their structures, properties, and functions. Our consideration is intentionally limited to the processes of thermally stimulated chemical reactions at the earliest stage of decomposition of molecules and materials containing defects.

Significance of Theoretical Decomposition Enthalpies for Predicting Thermal Hazards

Much effort is currently put into the development of models for predicting decomposition enthalpies measured using differential scanning calorimetry (DSC). As an alternative to the purely empirical schemes reported so far, this work relies on theoretical values obtained on the basis of simple assumptions. For nitroaromatic compounds (NACs) studied in sealed sample cells, our approach proves clearly superior to previous ones. In contrast, it correlates poorly with data measured in pin-hole sample cells. Progress might be obtained through a combination of the present approach with the usual Quantitative Structure-Property Relationships (QSPR) methodologies. This work emphasizes the significance of the theoretical decomposition enthalpy as a fundamental descriptor for the prediction of DSC values. In fact, the theoretical value provides a valuable criterion to characterize thermal hazards, as a complement to experimental decomposition temperatures.