Theoretical Studies of Energy Transfer Rates of Secondary Explosives

Theoretical insight into different energetic groups on the performance of energetic materials 2,5,7,9-tetranitro-2,5,7,9-tetraazabicyclo[4,3,0]nonane-8-one

CONTEXT

Energetic materials are a class of materials containing explosive groups or containing oxidants and combustibles. The optimization of energetic materials has a significant impact on the development of industry and national defense. For high-energy density compounds (HEDC) that have not been synthesized or are dangerous to experimental operation, it is of guiding significance to predict its energy level, physicochemical properties, and safety through molecular design and theoretical calculation. Cyclic urea nitramine series compounds are a type of energetic compounds with high density and excellent detonation performance. In this study, 2,5,7,9-tetranitro-2,5,7,9-tetraazabicyclo[4,3,0]nonane-8-one (K-56) was used as the parent structure, and 36 energetic derivatives were designed. The effects of introducing single and multiple substituents on the electronic structure, energy gap, heat of formation, detonation performance, thermal stability, thermodynamic parameters, and surface electrostatic potential of K-56 and its derivatives were discussed in detail. The results exhibit the following: (1) the single substitution of -C(NO₂)₃ (A6) can reduce the detonation velocity of K-56 by 11.9 % and the detonation pressure by 19.8 %, while the double substitution of -C(NO₂)₃ (B6) can increase the density of K-56 by 11.6 %, the detonation velocity by 10.9 %, and the detonation pressure by 31 %. (2) The heat of formation of K-56 (-110.0 kJ mol^-1) increased by 324.18 % and 628.81 %, respectively, proving that -N₃ is an extremely effective group to improve HOF. (3) The thermal stability of the derivatives generated by the monosubstitution of the target group on the six-membered ring is better than that of the parent compound.

METHODS

Gaussian16 and Multiwfn 3.8 packages are the software for calculation. In this study, the parent structure K-56 and its derivatives were optimized at the B3LYP/6-311G (d,p) level to obtain the zero point energy and thermal correction data of all compounds. Then the vibration analysis of the optimized structure is carried out to confirm that its configuration is stable. Then the M06-2X-D3/def2-TZVPP basis set is used to calculate the single point energy.

Are HOMO-LUMO gaps reliable indicators of explosive impact sensitivity?

A high priority in designing and evaluating proposed explosives is to minimize sensitivity, i.e., vulnerability to unintended detonation due to an accidental stimulus, such as impact. In order to establish a capability for predicting impact sensitivity, there have been numerous attempts to correlate it with some molecular or crystal property or properties. One common approach has been to relate impact sensitivity to the difference between the energies of the highest-occupied and lowest-unoccupied molecular orbitals of the explosive molecule, the "HOMO-LUMO gap." In the present study, we tested this approach for a series of twelve explosive nitroaromatics, using four different computational methods. We found that the HOMO-LUMO gap does not appear to be a reliable indicator of relative impact sensitivity. Since detonation initiation involves a series of steps, all of which influence sensitivity; it seems more realistic to try to identify fundamental factors and general trends related to sensitivity ‒ an approach that has already had some success ‒ rather than to seek correlations with one or two specific properties.

3-Phonon Scattering Pathways for Vibrational Energy Transfer in Crystalline RDX

A long-held belief is that shock energy induces initiation of an energetic material through an energy up-pumping mechanism involving phonon scattering through doorway modes. In this paper, a Fermi's golden rule-based 3-phonon theoretical analysis of energy up-pumping in RDX is presented that considers possible doorway pathways through which energy transfer occurs. On average, modes with frequencies up to 102 cm^-1 scatter quickly and transfer over 99% of the vibrational energy to other low-frequency modes up to 102 cm^-1 within 0.16 ps. These low-frequency modes scatter less than 0.5% of the vibrational energy directly to modes with significant nitrogen-nitrogen (NN) activity. The midfrequency modes from 102 to 1331 cm^-1 further up-pump the energy to these modes within 5.6 ps. The highest-frequency modes scatter and redistribute a small fraction of the vibrational energy to all other modes, which last over 2000 ps. The midfrequency modes between 457 and 462 cm^-1 and between 831 and 1331 cm^-1 are the most critical for vibrational heating of the NN modes and phenomena, leading to initiation in energetics. In contrast, modes stimulated by the shock with frequencies up to 102 cm^-1 dominate vibrational cooling of the NN modes.

Predicting the impact sensitivities of energetic materials through zone-center phonon up-pumping

The development of new energetic materials (EMs) is accompanied by significant hazards, prompting interest in their computational design. Before reliable in silico design strategies can be realized, however, approaches to understand and predict EM response to mechanical impact must be developed. We present here a fully ab initio model based on phonon up-pumping that successfully ranks the relative impact sensitivity of a series of organic EMs. The methodology depends only on the crystallographic unit cell and Brillouin zone center vibrational frequencies. We, therefore, expect this approach to become an integral tool in the large-scale screening of potential EMs.

Vibrational energy redistribution in crystalline nitromethane simulated by ab initio molecular dynamics

Ab initio molecular dynamics simulations (AIMD) are systematically performed to study the Vibrational Energy Redistribution (VER) in solid nitromethane (NM) by combining normal mode decomposition and short-time Fourier transform technique. After the selective excitations of all fourteen intramolecular vibrational modes above 400 cm⁻¹, four three-dimensional (3D) excitation and detected vibrational spectra are obtained. The evolution of the kinetic energy proportion of all vibrations are also given and discussed quantitatively. These results show that, as the daughter modes, NO₂ symmetric stretches, CH₃ stretches and bends are usually excited quickly and relatively conspicuously compared with the other vibrations. Interestingly, we found that, although the stretching vibration of the CN bond which is a bridge between the methyl and nitro group can not respond immediately to the selective excitations, it always accumulates the vibrational energy slowly and steadily. Then, the underlying mechanisms are discussed based on the response of vibrational modes in both the time and frequency domain. As a result, we found that anharmonic transfers following symmetry rules which involve the couplings assisted by the overtones and rotations, as well as the transfers among the adjacent modes, play important roles in the VER of solid NM.

Ab initio molecular dynamics simulations (AIMD) are systematically performed to study the Vibrational Energy Redistribution (VER) in solid nitromethane (NM) by combining normal mode decomposition and short-time Fourier transform technique.

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.

Sub-picosecond to Sub-nanosecond Vibrational Energy Transfer Dynamics in Pentaerythritol Tetranitrate

The time scale associated with shock-induced detonation is a key property of energetic materials that remains poorly understood. Herein, we test aspects of one potential mechanism, the phonon up-pumping mechanism, where shock compression excites lattice phonon modes, transferring energy to intramolecular vibrations leading to chemical bond cleavage and reaction. Using ultrafast infrared pump-probe spectroscopy on pentaerythritol tetranitrate (PETN), we reveal sub-picosecond vibrational energy transfer (VET) from the photoexcited band at 1660 cm^-1 into every other infrared-active mode in the probed frequency range 800-1800 cm^-1. Energy transfer processes remain incomplete at 150 ps. Computational predictions from density functional theory are used in tandem to elucidate VET pathways in PETN.

Experimental Charge-Density Study of the Intra- and Intermolecular Bonding in TKX-50

The intra- and intermolecular bonding in the known phase of dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate, TKX-50, has been analyzed on the basis of the experimentally determined charge density distribution from high-resolution X-ray diffraction data obtained at 20 K. This was compared to the charge density obtained from DFT calculations with periodic boundary conditions using both direct calculations and derived structure factors. Results of topological analysis of the electron density corroborate that TKX-50 is best described as a layered structure linked primarily by a number of hydrogen bonds as well as by a variety of other interactions. Additional bonding interactions were identified, including a pair of equivalent 1,5-type intramolecular closed-shell interactions in the dianion. Refinement of anharmonic motion was shown to be essential for obtaining an adequate model, despite the low temperature of the study. Although generally unusual, the implementation of anharmonic refinement provided a significant improvement compared to harmonic refinement of both traditional and split-core multipole models.

Temperature dependence of thermal expansion tensors of energetic materials

Unit-cell values as well as thermal expansion tensors for 13 energetic materials are calculated from variable-temperature X-ray diffraction data. The thermal expansion tensors and their temperature dependence are reported numerically, algebraically and graphically.

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

A physically motivated model is put forward to estimate impact sensitivity of nitro compounds on the basis of the relationship h(50) ∝ k(pr)(-4) between drop weight impact test data h(50) and rate constant k(pr) for the propagation of the decomposition. An approximate expression involving two adjustable parameters is introduced to estimate k(pr) from molecular structure. As a result, using only a hand-held calculator, ln(h(50)) values are estimated with a good reliability (R(2) ≃ 0.8) compared to previous schemes. These results support the underlying assumption that sensitivity primarily depends on the ability of reacting species to propagate the decomposition before the released energy dissipates away.

The great diversity of HMX conformers: probing the potential energy surface using CCSD(T)

The octahydro-1,3,5,7-tetranitro-1,3,5,7-tetraazocine (HMX) molecule is a very commonly studied system, in all 3 phases, because of its importance as an explosive; however, no one has ever attempted a systematic study of what all the major gas-phase conformers are. This is critical to a mechanistic study of the kinetics involved, as well as the viability of various crystalline polymorphs based on the gas-phase conformers. We have used existing knowledge of basic cyclooctane chemistry to survey all possible HMX conformers based on its fundamental ring structure. After studying what geometries are possible after second-order many-body perturbation theory (MBPT(2)) geometry optimization, we calculated the energetics using coupled cluster singles, doubles, and perturbative triples (CCSD(T))/cc-pVTZ. These highly accurate energies allow us to better calculate starting points for future mechanistic studies. Additionally, the plethora of structures are compared to existing experimental data of crystals. It is found that the crystal field effect is sometimes large and sometimes small for HMX.

Toward a physically based quantitative modeling of impact sensitivities

Among the subsequent steps leading from impact to explosive decomposition in nitro compounds, the ability of early exothermic reactions to trigger the decomposition of neighboring molecules before the released energy has dissipated away is assumed to be critical. The rate of this process is roughly estimated using as inputs the energy content and the dissociation energy of the weakest X-NO2 bonds. While the sensitivity index thus obtained was previously shown to exhibit striking correlations with gap test pressures, its correlation with drop weight impact test data is poorer. Nevertheless, considering four different subsets of molecules depending on the environment of the most labile nitro groups, straightforward regressions against this sensitivity index yield a practical method to estimate impact sensitivity, whose combination of fair performance and generality is provided by no alternative approach, except purely empirical models based on extensive parametrization.

Theoretical shock sensitivity index for explosives

On the basis of simple physical arguments, the ratio of the weakest bond dissociation energy of nitro compounds to their decomposition enthalpy per covalent bond is put forward as a practical shock sensitivity index. Without any empirical fitting, it correlates remarkably well (R ≥ 0.95) with shock sensitivity data reported for 16 molecules spanning the most significant families of explosive compounds. This result supports the underlying assumption that this property depends on the ability of decomposition events to propagate into the material. It demonstrates that sensitivity-structure relationships should take the energy content of the material into account. A linear regression against the present sensitivity index yields a predictive method with better performance than previous ones. Its sounder physical bases provide new insight into the molecular determinants of sensitivity and a compelling explanation for the sensitivity values reported for TATB and FOX-7.

Understanding the desensitizing mechanism of olefin in explosives: shear slide of mixed HMX-olefin systems

We simulated the shear slide behavior of typical mixed HMX-olefin systems and the effect of thickness of olefin layers (4-22 Å) on the behavior at a molecular level by considering two cases: bulk shear and interfacial shear. The results show that: (1) the addition of olefin into HMX can reduce greatly the shear sliding barriers relative to the pure HMX in the two cases, suggesting that the desensitizing mechanism of olefin is controlled dominantly by its good lubricating property; (2) the change of interaction energy in both systoles of shear slide is strongly dominated by van der Waals interaction; and (3) the thickness of olefin layers in the mixed explosives can influence its desensitizing efficiency. That is, the excessive thinness of olefin layers in the mixed explosive systems, for example, several angstroms, can lead to very high sliding barriers.

Vibrational energy transfer in shocked molecular crystals

We consider the process of establishing thermal equilibrium behind an ideal shock front in molecular crystals and its possible role in initiating chemical reaction at high shock pressures. A new theory of equilibration via multiphonon energy transfer is developed to treat the scattering of shock-induced phonons into internal molecular vibrations. Simple analytic forms are derived for the change in this energy transfer at different Hugoniot end states following shock compression. The total time required for thermal equilibration is found to be an order of magnitude or faster than proposed in previous work; in materials representative of explosive molecular crystals, equilibration is predicted to occur within a few picoseconds following the passage of an ideal shock wave. Recent molecular dynamics calculations are consistent with these time scales. The possibility of defect-induced temperature localization due purely to nonequilibrium phonon processes is studied by means of a simple model of the strain field around an inhomogeneity. The specific case of immobile straight dislocations is studied, and a region of enhanced energy transfer on the order of 5 nm is found. Due to the rapid establishment of thermal equilibrium, these regions are unrelated to the shock sensitivity of a material but may allow temperature localization at high shock pressures. Results also suggest that if any decomposition due to molecular collisions is occurring within the shock front itself, these collisions are not enhanced by any nonequilibrium thermal state.

Reactive molecular dynamics of hypervelocity collisions of PETN molecules

Born-Oppenheimer direct dynamics classical trajectory simulations of bimolecular collisions of PETN molecules have been performed to investigate the fundamental mechanisms of hypervelocity chemistry relevant to initiating reactions immediately behind the shock wavefront in energetic molecular crystals. The solid-state environment specifies the initial orientations of colliding molecules. The threshold velocities for initiating chemistry for a variety of crystallographic orientations were correlated with available experimental data on anisotropic shock sensitivity of PETN. Collisions normal to the planes (001) and (110) were found to be most sensitive with threshold velocities on the order of characteristic particle velocities in detonating PETN. The production of NO2 is the dominant reaction pathway in most of the reactive cases. The simulations show that the reactive chemistry, driven by dynamics rather than temperature during hypervelocity collisions, can occur at a very short time scale (10(-13) s) under highly nonequilibrium conditions.