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

On the physical processes of mechanochemically induced transformations in molecular solids

Initiating or sustaining physical and chemical transformations with mechanical force - mechanochemistry - provides an opportunity for more sustainable chemical processes, and access to new chemical reactivity. These transformations, however, do not always adhere to 'conventional' chemical wisdom, making them difficult to design and rationalise. This challenge is exacerbated by the fact that not all mechanochemical transformations are equal, with mechanical force playing a different role in different types of processes. In this review we discuss some of the different roles mechanical force can play in mechanochemical transformations, set primarily against the author's own research. We classify mechanochemical reactions broadly as those (1) where mechanical energy is for mixing, (2) where mechanical energy alters the stability of the reagent, and (3) where mechanical energy directly excites the solid. Finally, we demonstrate how - while useful - these classifications have fuzzy boundaries and concepts from across them are needed to understand many mechanochemical reactions.

Revealing the Ultrafast Energy Transfer Pathways in Energetic Materials: Time-Dependent and Quantum State-Resolved

Intramolecular vibrational energy transfer is gaining tremendous attention as a regulator of condensed-phase behavior and reactions. In polyatomic molecules, this transfer is an ultrafast process involving multiple modes with numerous quantum states. The inherent complexity and rapid evolution of these processes pose significant challenges to experimental observation, and the high computational costs make full quantum mechanical calculations impractical with current technology. In the intramolecular energy transfer process, whether the doorway modes are intermediaries for transferring energy from lattice phonons to high-frequency intramolecular vibrational modes has been a controversial issue. However, the broad range of doorway modes complicates the experimental identification of a specific doorway in the transfer process corresponding to a specific end point. Here, for the first time, we utilize a combination of vibrational projection, statistical analysis, and the local quantum vibrational embedding (LQVE) method to elucidate the ultrafast energy transfer pathways that upconvert energy from lattice phonons to intramolecular modes in the typical energetic material β-HMX. This approach enables us to resolve the coupled vibrational mode groups, identify the most probable energy transfer pathways corresponding to the different final modes, and clearly confirm that the doorway region is a mandatory pathway for energy transfer. The LQVE method's time-dependent and quantum state-resolved advantages are leveraged to reveal the microscopic mechanism of the energy transfer process. The time scale of these processes is determined at about 1 ps, and the first theoretical two-dimensional infrared spectroscopy evidence is provided, which is confirmed by the experimental results. These findings deliver important insights into the fundamental mechanisms of ultrafast energy transfer in energetic materials, providing theoretical support for controlling explosive behavior and designing new explosives. The methodologies developed in this work can be extended to other condensed phase materials and used to evaluate the coupling between multiple vibrational modes.

Temperature-dependent Raman spectroscopy and thermodynamic behaviors of energetic NTO crystal

The vibrational and thermodynamic properties of energetic materials (EMs) are critical to understand their structure responses at finite temperature. In this work, the zero-point energy and temperature effects are incorporated into dispersion-corrected density functional theory to improve the calculated accuracy for vibrational responses and thermodynamic behaviors of 3-nitro-1,2,4-triazole-5-one (NTO). Based on temperature-dependent Raman spectroscopy, the emergence and disappearance of new peaks as well as discontinuous Raman shifts indicate the distinct changes of molecular configuration and intermolecular interactions within the temperature of 250-350 K. From Hirshfeld surface and structure analysis, the subtle changes of intermolecular hydrogen bonds (HBs) related with the shrinkage of thermal expansion coefficient, are treated as an essential step of a potential structural transformation of NTO. Moreover, the calculated heat capacity, entropy and bulk moduli could reflect the softening behavior of NTO and further enrich the thermodynamic data set of EMs. These results demonstrate the evolution of NTO molecules controlled by non-covalent interactions and provide vital insights into the thermodynamic behaviors at finite temperature.

Theoretical Investigation into Polymorphic Transformation between β-HMX and δ-HMX by Finite Temperature String

Polymorphic transformation is important in chemical industries, in particular, in those involving explosive molecular crystals. However, due to simulating challenges in the rare event method and collective variables, understanding the transformation mechanism of molecular crystals with a complex structure at the molecular level is poor. In this work, with the constructed order parameters (OPs) and K-means clustering algorithm, the potential of mean force (PMF) along the minimum free-energy path connecting β-HMX and δ-HMX was calculated by the finite temperature string method in the collective variables (SMCV), the free-energy profile and nucleation kinetics were obtained by Markovian milestoning with Voronoi tessellations, and the temperature effect on nucleation was also clarified. The barriers of transformation were affected by the finite-size effects. The configuration with the lower potential barrier in the PMF corresponded to the critical nucleus. The time and free-energy barrier of the polymorphic transformation were reduced as the temperature increased, which was explained by the pre-exponential factor and nucleation rate. Thus, the polymorphic transformation of HMX could be controlled by the temperatures, as is consistent with previous experimental results. Finally, the HMX polymorph dependency of the impact sensitivity was discussed. This work provides an effective way to reveal the polymorphic transformation of the molecular crystal with a cyclic molecular structure, and further to prepare the desired explosive by controlling the transformation temperature.

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.

Tuning energetic properties through co-crystallisation - a high-pressure experimental and computational study of nitrotriazolone: 4,4'-bipyridine

We report the preparation of a co-crystal formed between the energetic molecule 3-nitro-1,2,4-triazol-5-one (NTO) and 4,4'-bipyridine (BIPY), that has been structurally characterised by high-pressure single crystal and neutron powder diffraction data up to 5.93 GPa. No phase transitions or proton transfer were observed up to this pressure. At higher pressures the crystal quality degraded and the X-ray diffraction patterns showed severe twinning, with the appearance of multiple crystalline domains. Computational modelling indicates that the colour changes observed on application of pressure can be attributed to compression of the unit cell that cause heightened band dispersion and band gap narrowing that coincides with a shortening of the BIPY π⋯π stacking distance. Modelling also suggests that the application of pressure induces proton migration along an N-H⋯N intermolecular hydrogen bond. Impact-sensitivity measurements show that the co-crystal is less sensitive to initiation than NTO, whereas computational modelling suggests that the impact sensitivities of NTO and the co-crystal are broadly similar.

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.

Ultrafast vibrational energy redistribution in cyclotrimethylene trinitramine (RDX)

The microscopic mechanism of the energy transfer in cyclotrimethylene trinitramine (RDX) is of particular importance for the study of the energy release process in high-energy materials. In this work, an effective vibrational Hamiltonian based on normal modes (NMs) has been introduced to study the energy transfer process of RDX. The results suggest that the energy redistribution in RDX can be characterized as an ultrafast process with a time scale of 25 fs, during which the energy can be rapidly localized to the -NNO2 twisting mode (vNNO2), the N-N stretching mode (vN-N), and the C-H stretching mode (vC-H). Here, the vNNO2 and vN-N modes are directly related to the cleavage and dissociation of the N-N bond in RDX and, therefore, can be referred to as "active modes." More importantly, we found that the energy can be rapidly transferred from the vC-H mode to the vNNO2 mode due to their strong coupling. From this perspective, the vC-H mode can be regarded as an "energy collector" that plays a pivotal role in supplying energy to the "active modes." In addition, the bond order analysis shows that the dissociation of the N-N bonds of RDX follows a combined twisting and stretching path along the N-N bond. This could be an illustration of the further exothermic decomposition triggered by the accumulation of vibrational energy. The present study reveals the microscopic mechanism for the vibrational energy redistribution process of RDX, which is important for further investigation of the energy transfer process in high-energy materials.

High-pressure structural studies and pressure-induced sensitisation of 3,4,5-trinitro-1H-pyrazole

Herein we report the first high-pressure study of the energetic material 3,4,5-trinitro-1H-pyrazole (3,4,5-TNP) using neutron powder diffraction and single-crystal X-ray diffraction. A new high-pressure phase, termed Form II, was first identified through a substantial change in the neutron powder diffraction patterns recorded over the range 4.6-5.3 GPa, and was characterised further by compression of a single crystal to 5.3 GPa in a diamond-anvil cell using X-ray diffraction. 3,4,5-TNP was found to be sensitive to initiation under pressure, as demonstrated by its unexpected and violent decomposition at elevated pressures in successive powder diffraction experiments. Initiation coincided with the sluggish phase transition from Form I to Form II. Using a vibrational up-pumping model, its increased sensitivity under pressure can be explained by pressure-induced mode hardening. These findings have potential implications for the safe handling of 3,4,5-TNP, on the basis that shock- or pressure-loading may lead to significantly increased sensitivity to initiation.

The mechanochemical excitation of crystalline LiN3

Mechanochemical reactions are driven by the direct absorption of mechanical energy by a solid (often crystalline) material. Understanding how this energy is absorbed and ultimately causes a chemical transformation is essential for understanding the elementary stages of mechanochemical transformations. Using as a model system the energetic material LiN₃ we here consider how vibrational energy flows through the crystal structure. By considering the compression response of the crystalline material we identify the partitioning of energy into an initial vibrational excitation. Subsequent energy flow is based on concepts of phonon-phonon scattering, which we calculate within a quasi-equilibrium model facilitated by phonon scattering data obtained from Density Functional Theory (DFT). Using this model we demonstrate how the moments (picoseconds) immediately following mechanical impact lead to significant thermal excitation of crystalline LiN₃, sufficient to drive marked changes in its electronic structure and hence chemical reactivity. This work paves the way towards an ab initio approach to studying elementary processes in mechanochemical reactions involving crystalline solids.

Spiers Memorial Lecture: Mechanochemistry, tribochemistry, mechanical alloying - retrospect, achievements and challenges

The paper presents a view on the achievements, challenges and prospects of mechanochemistry. The extensive reference list can serve as a good entry point to a plethora of mechanochemical literature.

Can a shock-induced phonon up-pumping model relate to impact sensitivity of molecular crystals, polymorphs and cocrystals?

Impact sensitivity engineering of high-energy molecular crystals requires accurate predictive models. For this purpose, the promising multi-phonon based approach is selected, assessing a bit more its strengths and weaknesses. Presently used with high-quality phonon calculations of 22 molecular crystals, using a physics-based criterion to determine the phonon bath extent, the resulting intrinsic shock sensitivity index (SSI) is compared to the most common marker of impact sensitivity, h 50, as determined from drop-weight impact tests. Selecting a data subset from experiments performed under very similar conditions (2.5 kg hammer with grit and 30-40 mg samples), the model can predict h 50 values for mono-molecular crystals with very good accuracy, including the ability to discriminate the polymorphs of HMX and CL20. This very good agreement validates an initial indirect up-pumping mechanism occurring under these conditions, where the doorway modes also interact with the phonon bath. However, the phonon bath criterion for mono-molecular crystals does not transfer well to cocrystals. Owing to the vibrational coupling of the co-molecules, it seems a broader phonon bath should be considered. Additionally recalling experimental uncertainty and various experimental factors affecting h 50 values for a given compounds, we recommend that the density of the sample, granularity and morphology be systematically considered and reported along with measurements, which will in turn allow for more systematic data and predictive capabilities for sensitivity models.

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.

Low-frequency lattice vibrations from atomic displacement parameters of α-FOX-7, a high energy density material

Highly anharmonic thermal vibrations may serve as a source of structural instabilities resulting in phase transitions, chemical reactions and even the mechanical disintegration of a material. Ab initio calculations model thermal motion within a harmonic or sometimes quasi-harmonic approximation and must be complimented by experimental data on temperature-dependent vibrational frequencies. Here multi-temperature atomic displacement parameters (ADPs), derived from a single-crystal synchrotron diffraction experiment, are used to characterize low-frequency lattice vibrations in the α-FOX-7 layered structure. It is shown that despite the limited quality of the data, the extracted frequencies are reasonably close to those derived from inelastic scattering, Raman measurements and density functional theory (DFT) calculations. Vibrational anharmonicity is parameterized by the Grüneisen parameters, which are found to be very different for in-layer and out-of-layer vibrations.

Time-Resolved In Situ Monitoring of Mechanochemical Reactions

Mechanochemical transformations offer environmentally benign synthesis routes, whilst enhancing both the speed and selectivity of reactions. In this regard, mechanochemistry promises to transform the way in which chemistry is done in both academia and industry but is greatly hindered by a current lack of mechanistic understanding. The continued development and use of time-resolved in situ (TRIS) approaches to monitor mechanochemical reactions provides a new dimension to elucidate these fascinating transformations. We here discuss recent trends in method development that have pushed the boundaries of mechanochemical research. New features of mechanochemical reactions obtained by TRIS techniques are subsequently discussed, which sheds light on how different TRIS approaches have been used. Emphasis is placed on the strength of combining complementary techniques. Finally, we outline our views on the potential of TRIS methods in mechanochemical research, towards establishing a new, environmentally benign paradigm in the chemical sciences.

Predicting the impact sensitivity of a polymorphic high explosive: the curious case of FOX-7

The impact sensitivity (IS) of FOX-7 polymorphs is predicted by phonon up-pumping to decrease as layers of FOX-7 molecules flatten. Experimental validation proved anomalous owing to a phase transition during testing, raising questions regarding impact sensitivity measurement and highlighting the need for models to predict IS of polymorphic energetic materials.

Mode-Selective Vibrational Energy Transfer Dynamics in 1,3,5-Trinitroperhydro-1,3,5-triazine (RDX) Thin Films

The coupling of inter- and intramolecular vibrations plays a critical role in initiating chemistry during the shock-to-detonation transition in energetic materials. Herein, we report on the subpicosecond to subnanosecond vibrational energy transfer (VET) dynamics of the solid energetic material 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) by using broadband, ultrafast infrared transient absorption spectroscopy. Experiments reveal VET occurring on three distinct time scales: subpicosecond, 5 ps, and 200 ps. The ultrafast appearance of signal at all probed modes in the mid-infrared suggests strong anharmonic coupling of all vibrations in the solid, whereas the long-lived evolution demonstrates that VET is incomplete, and thus thermal equilibrium is not attained, even on the 100 ps time scale. Density functional theory and classical molecular dynamics simulations provide valuable insights into the experimental observations, revealing compression-insensitive time scales for the initial VET dynamics of high-frequency vibrations and drastically extended relaxation times for low-frequency phonon modes under lattice compression. Mode selectivity of the longest dynamics suggests coupling of the N-N and axial NO₂ stretching modes with the long-lived, excited phonon bath.

Towards Computational Screening for New Energetic Molecules: Calculation of Heat of Formation and Determination of Bond Strengths by Local Mode Analysis

The reliable determination of gas-phase and solid-state heats of formation are important considerations in energetic materials research. Herein, the ability of PM7 to calculate the gas-phase heats of formation for CNHO-only and inorganic compounds has been critically evaluated, and for the former, comparisons drawn with isodesmic equations and atom equivalence methods. Routes to obtain solid-state heats of formation for a range of single-component molecular solids, salts, and co-crystals were also evaluated. Finally, local vibrational mode analysis has been used to calculate bond length/force constant curves for seven different chemical bonds occurring in CHNO-containing molecules, which allow for rapid identification of the weakest bond, opening up great potential to rationalise decomposition pathways. Both metrics are important tools in rationalising the design of new energetic materials through computational screening processes.

Tribochemistry, Mechanical Alloying, Mechanochemistry: What is in a Name?

Over the decades, the application of mechanical force to influence chemical reactions has been called by various names: mechanochemistry, tribochemistry, mechanical alloying, to name but a few. The evolution of these terms has largely mirrored the understanding of the field. But what is meant by these terms, why have they evolved, and does it really matter how a process is called? Which parameters should be defined to describe unambiguously the experimental conditions such that others can reproduce the results, or to allow a meaningful comparison between processes explored under different conditions? Can the information on the process be encoded in a clear, concise, and self-explanatory way? We address these questions in this Opinion contribution, which we hope will spark timely and constructive discussion across the international mechanochemical community.