Decomposition and Reaction of Polyvinyl Nitrate Under Shock and Thermal Loading: a Reaxff Reactive Molecular Dynamics Study Md Mahbubul Islam and Alejandro Strachan*

Article

pubs.acs.org/JPCC

Decomposition and Reaction of Polyvinyl Nitrate under Shock and Thermal Loading: A ReaxFF Reactive Molecular Dynamics Study Md Mahbubul Islam and Alejandro Strachan*

School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States

*S Supporting Information

ABSTRACT: We use molecular dynamics (MD) simulations with the reactive force field ReaxFF to investigate the response of polyvinyl nitrate (PVN), a high-energy polymer, to shock loading using the Hugoniostat technique. We compare predictions from three widely used ReaxFF versions, and in all cases, we observe shock-induced, volume- increasing exothermic reactions following a short induction time for strong enough insults. The three models predict NO2 dissociation to be the first chemical, and relatively similar final product populations; however, we find significant differences in intermediate populations indicating different reaction mechanisms due to discrepancies in the relative stability of various intermediate fragments. A time-resolved spectral analysis of the reactive MD trajectories enables the first direct comparison of shock-induced chemistry between atomistic simulations and experiments; specifically, ultrafast spectroscopy on laser shocked samples. The results from one of the ReaxFF versions are in excellent agreement with the experiments both in terms of threshold shock strength required for the disappearance of NO2 peaks and in the time scale associated with the process. Such direct comparison between physical observables is an important step toward a definite determination of detailed chemistry for high-energy density materials.

I. INTRODUCTION interactions with molecular monolayers.11 The experiment on 12 Shock-induced chemistry of high-energy (HE) materials and PVN revealed that 18 GPa shocks resulted in chemical the shock to detonation transition involve complex and inter- reactions within approximately 150 ps indicated by the disappearance of a peak associated with NO2. Despite such related physical and chemical processes through which the fi energy in the shockwave is transferred to chemical bonds with signi cant accomplishments, these experimental techniques are characteristic lengths of Ångstroms and vibrational periods of not without limitations. For example, experiments do not enable a direct characterization of chemical mechanisms nor the few femtoseconds. In many cases the microstructure of the fi material plays a key role in localizing the energy in the shock in identi cation of all intermediates and products. Current space, and these hotspots1,2 initiate chemical reactions, spatiotemporal and analytical resolution preclude in situ fl evaluation of the detailed behavior of molecules behind a de agration and eventually detonation. At the same time, 8 inter- and intramolecular relaxation processes transfer energy detonation front. On the simulation side, ab initio and from long wavelength, low-frequency modes of the shock to quantum-based molecular dynamics (MD) simulations have high-frequency bond vibrations, a process called up-pump- been used to identify initiation mechanisms, reaction barriers, 3−5 and rates associated with the decomposition of various energy ing. To complicate matters, these processes occur under 13−20 extreme conditions of temperature, pressure and strain rate and materials. However, the computationally intensity of these involve short time scales. It is, thus, not surprising that despite simulations limits the spatial and temporal scales achievable. fi 21−23 significant efforts in experiments and simulations a definite a Reactive force elds, like ReaxFF, provide a less molecular-level description of shock-induced chemistry is still computationally intensive alternative and enable multimillion atom simulations and capturing the role of microstructure and lacking even in relatively simple materials like nitromethane, a 24,25 liquid at room temperature, or polyvinyl nitrate (PVN), an defects with scales approaching those in experiments. ff amorphous polymer. Recent e orts provide an atomic picture of the shock to fl 24 Recent experimental efforts are yielding insight and de agration transition. While these simulations provide quantitative information about the molecular level processes unparalleled resolution in space and time, they involve 6−10 ff responsible for shock-induced chemistry. For example, approximations whose e ect on predictions remain poorly ultrafast spectroscopy study of laser shocked PVN enabled the detection of chemical reactive events under shock loading,7 Received: June 23, 2017 broadband multiplex vibrational sum-frequency generation Revised: September 5, 2017 (SFG) technique allows real-time observation of shock-front Published: September 6, 2017

© XXXX American Chemical Society A DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article understood. To different degrees, ab initio, tight-binding, and uses the concept of partial BOs between pairs of atoms to reactive potentials approximate atomic interactions and forces; describe covalent interactions including 2-, 3-, and 4-body in addition, the use of classical ionic dynamics is also an bonded interactions. BOs are a continuous, many body, and approximation. functions of the atomic coordinates. The nonbonded van der We note that shock-induced chemistry is an extremely Waals and Coulomb interactions are calculated between every challenging problem for an atomistic model as it needs to pair of atoms, within the respective cutoffs, regardless of capture two interdependent and complex processes: (i) The covalent interactions.33,34 In the nonbonded energy expres- first is the thermo-mechanics of shock loading, the amount of sions, shielding parameters are introduced to circumvent energy the shock deposits into the system and how this energy excessive repulsion at short distances, and a seventh order is distributed among different degrees of freedom via variety of taper function is used to eliminate any energy discontinuity.35,36 relaxation processes: volumetric compression and heating as The electronegativity equalization method (EEM)37 is utilized well as plasticity, fracture, phase transformations, void collapse to obtained environment dependent partial atomic charges that and interfacial sliding that can lead to energy localization and are updated at every step during the MD simulations. For a the formation of hot spots. (ii) The model should also capture more detailed description of the ReaxFF method, see refs the thermodynamics and kinetics of chemical decomposition at 21−23, 38, and 39. various conditions of pressure and temperature; including uni- Over the past decade, a number of ReaxFF parameter sets and multimolecular processes. Given the complexity of the have been developed to describe high-energy density materials. problem, a definite understanding of shock-induced chemistry The accurate prediction of the complex chemistry of these will likely require a synergistic combination of experimental and materials at extreme conditions of pressure and temperature as theoretical investigations26 where the experiments validate the well as the description of physical, thermodynamic, and simulations and simulations help interpret the experimental spectroscopic properties are challenging. Therefore, several results. versions are currently available, each emphasizing different In this paper, we use MD simulations with three different properties. Importantly, the uncertainties associated with versions of the ReaxFF15,27,28 force field to establish the initial different versions have not been characterized, and comparisons decomposition of PVN following shock loading. We build on across different force fields are not common. Therefore, it is an the successful use of ReaxFF in a family of high-energy evident necessity to systematically evaluate the performance of molecular crystals RDX, HMX, PETN, and NM14,17,19,27,29,30 the available force fields in terms of their predictions of and apply it to an energetic polymer. This is motivated by the mechanical, chemical and spectroscopic properties. In this existence of spectroscopic data on shocked PVN which enables study, we used three widely used ReaxFF C/H/N/O force the first direct comparison of ReaxFF predictions of shock- fields to formulate a detailed chemical and mechanical induced chemistry against experiments. Importantly, the description of the PVN polymer. The original C/H/N/O amorphous nature of PVN simplifies the comparison between ReaxFF force field was developed and applied for RDX20,40 and experiments and simulations due to the lack of grain boundaries since then several updates have been proposed. The standard and other crystal defects that can significantly affect shock ReaxFF C/H/N/O force field resulted in a less than ideal response. In addition, PVN is of interest as a binder in explosive description of lattice parameters and equations of states due to and propellant formulations and understanding its physics and the inadequate description of the London dispersion. Rom et chemistry can contribute to their safe operation. A high energy al.27 incorporated additional inner-core repulsions for the van density binder provides not just adhesion but also contributes der Waals interactions to improve the description of lattice to the total energy release.6 Despite the interest of the PVN parameters and updated the previous C/H/N/O force field.40 polymer in explosive applications, only a limited number of We will denote this force field as ReaxFF-IW (inner-wall). The experiments have been performed to investigate the mecha- additional inner core repulsion has the following form nistic details of its response to shock loading. Moreover, no Eccrc=−exp( (1 / )) atomistic simulation studies on PVN chemical dissociation vdw() IW 1 2 ij 3 mechanisms under shock and thermal loading conditions are fi Here c1, c2, and c3 are force eld parameters, and rij is the available in literature. As such the detailed chemistry of PVN interatomic distance between atom i and j. remains unknown. Therefore, we aim to provide a detailed To improve the bulk properties of the energetic materials characterization of the mechanical, chemical, and spectroscopic while, at the same time, maintaining the description of the properties of the PVN polymer. We compute shock Hugoniots chemical reactions of the unmodified ReaxFF− in the ReaxFF- and investigate how shock and thermal loading dictates the fi fi lg force eld, a low gradient (lg) attractive term was chemical reaction pathways. We nd that PVN chemical incorporated to account for the long-range London dispersion dissociation initiates via the formation of NO2 and the using following expression28 activation energy decreases with the increased system densities. N For the first time, our simulations enabled a one-on-one Clg,ij Elg =−∑ comparison of the reaction initiation time scales with the rdR66+ ultrafast shock experiments via time-resolved spectra. In ij, i< j ij eij addition, each of the force fields predicted results are compared Here rij and Reij are the distance and equilibrium vdW radius with the available literature to establish their performance in between atoms i and j, respectively, and Clg,ij is the dispersion predicting the mechanistic details of the PVN polymer. energy correction parameter. It has been shown that the addition of the lg-parameters on II. SIMULATION METHODOLOGY the ReaxFF-IW force field substantially improves the equation II.A. ReaxFF and Force Field Description. ReaxFF is a of states of energetic materials.28 We note that the difference bond order (BO)31,32 empirical reactive force field which allows between ReaxFF-IW and ReaxFF-lg force fields are only the the description of chemical reactions during MD simulations. It low-gradient parameters. More recently, Wood et al.15

B DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article developed an updated version of the C/H/N/O force field specifically to improve the spectroscopic properties and the postdetonation combustion chemistry (denoted here as ReaxFF-2014). II.B. Structure Preparation. Amorphous PVN (molecular − − − formula ( CH( ONO2)CH2 )n) structures were prepared using the Polymer Modeler tool available at nanoHUB.41 In order to investigate the effect of chain molecular weight (MW) on the polymer density, four different structures were constructed. The systems contain 135 chains each 8 monomers long (MW = 714 g/mol), 22 50-monomer chains (MW = 4452 Figure 1. (a) Snapshot of the simulation cell with 200 monomers; g/mol), 11 100-monomer chains (MW = 8902 g/mol), and 5 insert highlights a section of the polymer chain (color code: oxygen, 200-monomer chains (MW = 17 800 g/mol). All systems are red; carbon, gray; nitrogen, blue; and hydrogen, white). (b) Calculated densities as a function of molecular weight of the PVN polymer chains. built using a continuous configurational-bias Monte Carlo 41 ReaxFF-2014, ReaxFF-IW, and ReaxFF-lg are red, green, and blue, method as implemented in Polymer Modeler at an initial respectively. density of 0.5 g/cm3. The structures are relaxed via energy 42 fi minimization using the DREIDING nonreactive force eld, equations of motion for the atoms which are not participating followed by thermalization at temperatures between 300 and in the shock chemistry. Alternatively, equilibrium MD 800 K via isobaric, isothermal MD (NPT ensemble) using a simulations have been proposed to simulate the final state of time step of 1 fs. The annealing simulation steps are comprised the system after the passage of shock, such as Hugoniostat43 of (i) heating the system from 300 to 800 K in 500 ps, (ii) and MSST.44 The Hugoniostat MD simulation technique, holding at 800 K for 2 ns, and (iii) cooling down to 300 K in compresses (uniaxially) and heats up the system to a state 500 ps. Next, the system was further equilibrated at 300 K and corresponding to the desired shock by satisfying the Hugoniot atmospheric pressure for additional 10 ns using NPT MD to jump conditions. These simulations are less intensive computa- ensure molecular relaxation and to obtain the equilibrium fi tionally as the actual shock wave propagation through the density at ambient condition. A nonreactive force eld was used samples is circumvented. Thus, smaller system sizes can be to generate well-relaxed amorphous polymer structures for two simulated and longer time-scale simulations are possible with main reasons. First, large forces due to bad contacts are moderate computational resources, resulting in better statistics common in the structures resulting from Monte Carlo builds, of the chemical decomposition reactions. The jump conditions polymer modeler uses a series of relaxations with scaled van der imposed by the Hugoniostat are Waals parameters to mitigate the effect of bad contacts and the fi use of a reactive force eld during these initial relaxation steps mass:ρρouuussp=− ( ) could result in unwanted chemical reactions. Second, non- momentum: PPuu=+ρ reactive reactive force fields are computationally less intensive zz o o sp than reactive ones, enabling longer relaxation procedures. 1 The 300 K DRIEDING equilibrated structures were used as energy: EEHo−=()() PPVV zzoo + − 2 starting configurations for ReaxFF simulations. We re- equilibrated the structures using all three ReaxFF force fields PP− u = zz o V with NPT simulation at room temperature and pressure for 300 s VV− o ps, enough for the density to achieve steady state. Finally, we o carried out isochoric, isothermal MD (NVT ensemble) at 300 K uPPVV=−−()() for 100 ps to prepare the initial configurations for the shock and pzzoo isothermal decomposition simulations. We used a time step of Here subscript 0 refers to the unshocked initial properties, us 0.2 fs in the ReaxFF relaxation simulations, the time step is and up are shock and particle velocities, respectively. Pzz is the reduced to 0.1 fs in all shock and thermal decomposition normal component of the stress tensor in the shock direction simulations. A snapshot of the simulation cell with 200 and ρ =1/V. Given the desired shock pressure, the monomers and the densities predicted by the ReaxFF-2014, Hugoniostat technique uses a thermostat and a barostat to ReaxFF-IW, and ReaxFF-lg for all the polymer structures satisfy the jump conditions. considered are shown in Figure 1. One can see that the We performed Hugoniot shock simulations in the pressure densities are converged with respect to molecular weight for range of 4 to 36 GPa. In order to investigate the influence of values larger than 4450 g/mol. The densities predicted by initial densities of the systems, we carried out two sets of ReaxFF-2014 and ReaxFF-IW compare well with the simulations with the densities predicted by the respective force − experimental value12 of 1.34 g cm 3 measured by gas fields at ambient conditions (denoted “FF density”) and the pychonometry, while ReaxFF-lg overestimates the density. In experimental density (denoted “experimental density”). We this study, the bulk PVN geometry consisting of 200-monomer note that for the case of ReaxFF-2014 force field both the chains are used for all the shock and isothermal decomposition densities are identical. simulations. II.D. Isothermal Decomposition Simulations. The 300 II.C. Hugoniostat Simulations. Nonequilibrium MD K NVT equilibrated structures with MW = 17800 g/mol were simulations are often used for shock simulations; however, used as starting configurations for studying the homogeneous large system sizes (typically millions of atoms) are required for isothermal decomposition of PVN at three different temper- these simulations due to the fast propagation velocity of shock atures: 2400, 2800, and 3200 K. Three different densities were − ρ ρ ρ waves and the need to achieve steady shock front. Therefore, considered experimental density ( o), 1.2 o, and 1.4 o. The significant computational resources are spent in solving the simulation cell with the experimental density was used to

C DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article

Figure 2. Pressure, volume, and temperature evolution during shock loading of PVN samples starting at the experimental density systems using ReaxFF-2014, ReaxFF-IW, and ReaxFF-lg force fields. generate the volumetrically compressed systems by adjusting sampled at every 2.5 fs to resolve the high-frequency modes volumes to the target densities using deformation simulations. accurately. The time-resolved spectra calculations were carried The compressed systems were further relaxed using 300 K NVT out at 10 ps interval, and each case was averaged over 4000 simulations for 10 ps. Next, the target temperatures were frames. reached by rescaling the atomic velocities at a heating rate of The chemical bonds and molecular species were detected 1000 K/ps using NVT ensemble. The Nose−Hoover thermo- using a conservative bond order cutoff of 0.30 for all the stat was used with a coupling constant of 20 fs. The rapid simulations. The accuracy of on-the-fly species recognition was heating rate is comparable to the time scales of shock loading. improved by sampling bond order values at every 0.50 fs and Once the target temperatures were reached, the systems were averaged over 10 samples. This approach instead of using held at the temperature with an NVT ensemble in the range of instantaneous bond orders also abate identification of spurious 300−800 ps. The lower temperature cases required longer bonds in high-density systems, typical for shocked compression. simulation time to attain steady-state. The isothermal The molecular fractions represented in this study are simulations allowed us to extract Arrhenius parameters to normalized by the total number of monomers. study reaction kinetics of the PVN polymer. The characteristics time for the reaction rate calculations is considered as the time III. SHOCK STATES AND EXOTHERMIC REACTIONS required to reach the half of the total exothermicity in each case. III.A. Evolution of Pressure, Volume, and Temper- II.E. Analysis of MD Simulations. The MD simulation ature. The pressure, volume and temperature evolution of trajectories were postprocessed to obtain power spectra using shocked PVN polymer starting at the experimental density are the following formula:15 shown in Figure 2. The evolution of all the thermodynamic 3N N−1 properties of the ambient pressure simulations is presented in βτ −Δint22πω Figure S1 of the Supporting Information.Duringthe P()ω =|Δ|mvnt ( )e ∑∑j j Hugoniostat shock simulations, system pressure, volume, and N == j 1 n 0 temperature equilibrate to their shocked state within 1 ps time β fi fi where vj(t) are the atomic velocities at time t, is de ned as scale for all three force elds. The high deformation rate is −1 τ (kBT) , T is the temperature, is the sampling period, mj is the typical for shock conditions. This initial fast response is driven mass of atom j, Δt is the sampling rate, and N is the number of by the uniaxial compression in response to the loading. frames to be analyzed. We used fast Fourier transform to Interestingly, for strong enough shocks the systems exhibit a evaluate the power spectra. The atomic trajectories were sudden increase in volume and temperature following the initial

D DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article

Figure 3. Pressure vs density plots using three different ReaxFF force fields for PVN samples shocked starting from (a) experimental density and (b) force field densities. The nonreactive densities are not shown for the cases where volume-increasing reactions have occurred. Color code: red, ReaxFF-2014; green, ReaxFF-IW; blue, ReaxFF-lg.

Figure 4. Temperature vs density plots using three different ReaxFF force fields: (a) experimental density and (b) force field densities. The nonreactive temperatures are not shown for the cases where volume increasing reactions have occurred. Color code: red, ReaxFF-2014; green, ReaxFF-IW; and blue, ReaxFF-lg.

− ff fi Figure 5. us up plots for the PVN at various shock pressures using three di erent ReaxFF force elds and comparison with the experimental data: (a) Experimental density; (b) FF densities. Color code: red, ReaxFF-2014; green, ReaxFF-IW; blue, ReaxFF-lg; and black, experimental data. compression and an induction time. This is due to the reactive Hugoniot as reactions occur. In order to show the exothermic, volume-increasing reactions induced by a combi- transition from nonreactive to reactive Hugoniot we included a nation of temperature and density increase due to the shock. sample case in Figure S2.Wefind that ReaxFF-2014 predicts During this phase, small molecules are produced (expansion rapid chemistry for shocks of 18 GPa and higher pressures. The stage). The simulations show a decrease in the induction time reaction involves a reduction in density of approximately 10% and reaction-induced volume expansion with increasing shock and an increase in temperature of approximately 2000 K. The strength (and pressure). Interestingly, as can be seen in Figure induction time required for exothermic reactions at 18 GPa is S1, ReaxFF-lg force field does not exhibit exothermic reactions ∼180 ps, see Figure 2. The critical shock strength and reaction when shocked from its ambient pressure density for the shock time scales predicted by ReaxFF-2014 are in excellent strengths up to 36 GPa, and time scales of 300 ps. agreement with experimental results of McGrane et al.12 The shock pressure−density data extracted from the shock Their ultrafast spectroscopy experiments show no reactions for simulations for the three force fields and two types of initial shock pressures lower than 17 GPa and reactions within 150 ps conditions are presented in Figure 3; Figure 4 shows the for a shock strength of 17 GPa. ReaxFF-IW and ReaxFF-lg are corresponding temperature-density plots. The shock states slightly less reactive and require 24 GPa shocks to exhibit achieved from the experimental densities, Figures 3a and 4a, reaction within a time scale of 300 ps. It is evident from Figures exhibit two branches: the shock states follow the unreactive 3a and 4a that the nonreactive P-ρ Hugoniots and T−ρ Hugoniot for relatively weak loading and transition to the obtained starting from the experimental density are very similar

E DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article

Figure 6. Molecular population distribution of PVN polymer at shock pressures of 18 and 22 GPa using ReaxFF-2014 force field. Molecular fractions are normalized by the total number of monomers. fi ff − for all the force elds. Interestingly, the more sensitive ReaxFF- the di erences in the us up plots at the reactive zone is due to 2014 exhibits a higher exothermicity than the other two force the fact that ReaxFF-2014 predict chemical reactions at 18 GPa fields. in contrast to 24 GPa for the other two force fields. However, at − Shock simulations starting from the ambient pressure the pressure of 24 GPa or higher, us up values from all the force conditions for each force field exhibit larger discrepancies fields are in close agreement. The ReaxFF-2014 predicts the among each other; see Figures 3b and 4b. The ReaxFF-2014 transition to fast chemical decomposition at up = 2.2 km/s and fi and -IW force elds predicted volume-increasing reactions and us = 6.5 km/s, while in ReaxFF-IW and -lg simulations it occurs fi pressures of 18 and 30 GPa respectively, while no signi cant at approximately up = 2.7 km/s and us = 6.8 km/s. The sound reactions occurred in the ReaxFF-lg simulations for shocks up speed (value of us at up = 0) predicted by the ReaxFF-2014, to a pressure of 36 GPa. The lower reactivity in these ReaxFF-IW, and ReaxFF-lg force fields starting from the simulations can be attributed to the smaller amount of experimental densities are 1.75 ± 0.05, 1.55 ± 0.05, and 1.05 ± mechanical (PV) work done on the system during shock 0.15 km/s, respectively. These values are smaller compared compression. The equations of state in Figure 3b show a with the experimental data10 of 3.2 ± 0.3 km/s. However, the significant difference in density for low pressures among the FF density simulations predict a relatively higher sound speed three force fields, but this difference reduces with compression. values, that is, 2.16 ± 0.02 and 3.14 ± 0.04 km/s for ReaxFF- Thus, the overestimation of density in the ReaxFF-IW and -lg IW and ReaxFF-lg, respectively. force fields resulted in a smaller amount of PV work and The effect of initial systems densities is evident in the results heating of the system as compared with the ReaxFF-2014 presented in Figure 5b. In the FF density simulations, different simulations. As such the first rapid chemistry observed in the force fields exhibit a wider variation. The computed shock- ReaxFF-IW force field simulations is at a higher pressure of 30 particle velocities follow the trend of densities predicted by GPa compared to the 18 GPa in the case of ReaxFF-2014 force each of the force fields. The higher density resulted in a field. stronger shock velocities. Therefore, the highest shock III.B. Shock Velocity−Particle Velocity Hugoniots. The velocities are predicted by the ReaxFF-lg force field, consistent shock and particle velocity was calculated using Hugoniot with the highest density predicted by this force field. The two − relations (section II.C). The shock-vs-particle velocity data for regimes in the us up plots have been observed for ReaxFF-2014 the experimental density simulations are shown in Figure 5a and ReaxFF-IW force fields. The ReaxFF-IW force field together with the nonreactive experimental curve from ref 10. simulations, the volume-increasing reactions occurred at up = − The exothermic reactions lead to a second branch of the us up 3.0 km/s and us = 7.5 km/s. Since there is no experimental or plots and a sudden increase in the shock velocities. However, computational data available for the reactive regimes of the − the slope of the reactive us up curve is lower, and upon increase shocked PVN polymer, we cannot make any comparison. in shock pressure, the reactive and extrapolation of the III.C. Shock-Induced Chemical Decomposition. The − unreactive us up curves approach each other. This behavior processes of shock-induced decomposition of PVN can be was observed in nitromethane shock experiments.7 The categorized into three steps: (i) initial nonreactive compression − predicted us up curves slightly underestimate the experimental and heating when energy transfers from the shock wave to the results, but overall they exhibit reasonable agreement. The shift material and (ii) a shock-induced onset of chemical reactions − in the us up plots is indicative to the chemical reactions. While (iii) followed by rapid exothermic reactions. Therefore, − fi the nonreactive us up data are analogous for all the force elds, investigation of chemical decomposition mechanisms is

F DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article

Figure 7. Molecular population distribution of PVN polymer at shock pressures of 24, and 32 GPa using ReaxFF-IW force ﬁeld (experimental density).

Figure 8. Molecular population distribution of PVN polymer at shock pressures of 24 and 32 GPa using ReaxFF-lg force field (experimental density). required to elucidate the coupling between mechanical loading migration. These paths have been observed as the initiation of and chemistry. The decomposition pathways are contingent reactions in related compounds such as RDX,24,25 HMX,30 CL- upon the nature of the applied load, such as temperature and 20,46 and PETN.29 During the initial compression stage of 1−2 pressure conditions. With increasing shock strength, a larger ps, all systems were unreacted. As reaction initiates, the amount of energy will be transferred to vibrational degrees of homolytic cleavage of the O-NO2 bond was observed as the freedom of the molecules. If this results in sufficiently high first reactive event for all three force fields. The time evolution temperature, chemical reactions will be induced within short of the major intermediates and stable species are shown in time scales.45 In this study, we are primarily interested in Figures 6, 7, and 8 as determined using ReaxFF-2014, ReaxFF- probing the initial chemical reactions and subsequent pathways IW, and ReaxFF-lg force fields, respectively. For clarity, only toward stable species formation. species with populations greater than 2% of the total number of fi Possible reaction initiation mechanisms of PVN are NO2 monomers are shown. For each force eld, we show results for fission, HONO elimination, C−C bond breaking, and hydrogen the weakest shock at which we observe chemistry and a

G DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article stronger shock to highlight how pressure affects chemical decomposition. The rapid exothermic chemistry leads to the fi generation of nal stable gaseous products, most notably H2O, fi CO2,N2, and NH3 for all the force elds. As expected, ReaxFF-IW and ReaxFF-lg that only differ in their description of van der Waals interactions result in very similar chemical reactions. The final population of products is similar in all three force fields; the main difference being the higher population of CO2 in ReaxFF-2014. In addition, we fi observe a signi cant amount of H2 formation in the ReaxFF-IW and -lg simulations. H2O was found as the most abundant species irrespective of simulation conditions and force field Figure 9. Formation energies of key intermediate and stable species as used. Unfortunately, we are not aware of any experimental data ff fi fi calculated using three di erent ReaxFF force elds and comparison on the distribution of nal products of shocked PVN available with the experimental data48. In these calculations, reference states are for the comparison. considered as follows: (i) atomic energies are used for the formation The evolution of intermediate populations can shed light on energies of N2,O2, and H2, and (ii) N2,H2,O2, and graphite are used the reaction mechanisms and also explain differences in the as references for all other cases. relative amount of final products predicted by each of the force fields. We observe that the primary intermediate molecules distribution of the final products shows that ∼20% of C reach a maximum and then react away to form final, exothermic atoms in ReaxFF-2014 are contained in small product products. The reaction initiation yields a significant amount of molecules; this number if only 5% in the ReaxFF-lg and NO2 and creates radical sites, followed by the generation of ReaxFF-IW force fields. This indicates that a significant amount other intermediates. In ReaxFF-2014, at 18 GPa shock pressure, of carbon remains as intermediate species or other final the NO population increases steadily up to ∼180 ps, then products. We further investigated the other carbon containing suddenly drops at the onset of rapid exothermic chemistry. The species, and they can be presented under the general formulas − − − − population of the most dominant intermediate, HCO2, of HCxOy (x =1 4, y =2 5), H2CxOy (x =1 4, y =2 6), − − increases to 25% of the total number of monomers. CH2Ois and H3CxOyN(x =1 2, y =2 3). A list of these representative generated at a relatively later stage. However, the decline of the species are included in the Table S1. We note that in our both HCO2 and CH2O occurs concurrently at the transition-to- simulations we have not observed any carbon cluster formation. fast exothermic reactions. ONH radicals are observed at time One can also see that the distribution of both intermediates scales similar to CH2O, but in a lower quantity. The formation and stable species indicates that the reaction initiation of the radicals proceeded via breaking of the backbone C−C mechanisms are relatively insensitive to the magnitude of the bond of the PVN polymer. The rapid chemistry leads to the applied shock. Overall, the kinetics of the exothermic reactions generation of CNOH, and N2O2 intermediates and stable gases are relatively slower, and the exothermic heat release is lower in are formed at a pronounced rate. At the onset point of rapid ReaxFF-IW and -lg simulations compared to ReaxFF-2014. chemistry, ∼80% of the total C−C bonds of the PVN chains III.D. Spectral Changes During Shock Simulations. are dissociated. In contrast to ReaxFF-2014, a large quantity of Although detailed reaction mechanisms are inaccessible in HNO3, and HONO are produced in the ReaxFF-IW and -lg shock experiments, ultrafast spectroscopy provides important simulations. HONO elimination has been observed in the insight into some of the reactions under shock loading. previous experiment,47 QM,16,17 and ReaxFF18,30,40 studies on Importantly, spectroscopy information can be extracted directly energetic materials. from MD simulations as discussed in section II.E and this can To better understand the population of products and provide a direct comparison between simulation results and intermediate evolution for the three descriptions, we computed experimental measurements. We aim to compare reactive MD their formation energy using the three force fields and simulations with published and ongoing spectral analysis for a compared them to experiments in Figure 9. ReaxFF-2014 direct validation to our simulations and, at the same time, to over stabilizes HCO2, CH2O, and CNOH radicals, compared to help interpret spectral data to detect various reaction pathways the other two force fields and experimental data. This and associated time scales. Thus, we performed spectral analysis stabilization leads to the production of these species in larger using atomistic velocities at various shock conditions and for quantities, while they are almost absent in other two versions. the three force fields. The predicted per element spectra of a Similarly, the high stability of HNO3 predicted by ReaxFF-IW single polymer chain using ReaxFF-2014 is shown in the and -lg force fields causes it to be one of the most dominant Supporting Information, Figure S3a. This enables the assign- intermediate species (see Figures 7 and 8). The formation of ment of peaks to vibrational modes. In order to compare with HONO is endothermic in ReaxFF-2014: as such, this pathway the laser shock experiments by McGrane et al.,12 we considered has rarely been observed in ReaxFF-2014 simulations. Thus, changes in the N−O stretching modes as a measure of chemical our simulations show that the stability of intermediates and reactions in the system. The ReaxFF-2014 predicts NO2 reaction paths have a direct effect on the final products, at least symmetric and asymmetric stretching modes are at 800 and during the initial hundreds of picoseconds during decom- 1900 cm−1, respectively. These values are shifted from the position. The major difference in the population of final experimental values of 1270 and 1624 cm−1.12 However, the fi products across various force elds is the amount of CO2 and discrepancy between experimental and our calculated vibra- fi fl NH3. ReaxFF-2014 correctly stabilizes CO2 with respect to the tional modes does not signi cantly in uence our comparison fi other force elds. The higher preponderance of CO2 with experimental observations regarding the time scale or production in ReaxFF-2014 simulations can also be attributed character of reaction initiation. The C−H stretching mode is in to the dissociation of the HCO2 radical pathway. The good agreement with literature data.

H DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article

Figure 10. (a) ReaxFF-2014 predicted time-resolved full spectra at 18 GPa shock simulation. (b) Expanded view of the disappearance of NO2 vibrational mode at a time scale of ∼150 ps. (c) Time-dependent spectra as computed from a ReaxFF-lg 24 GPa experimental density shock simulation.

Figure 11. (a) Arrhenius plot for PVN dissociation at isothermal conditions (solid line, experimental density (ρο); dashed line, 1.2ρο; and dotted line, 1.4 ρο). (b) Overall activation energies associated with decomposition at diﬀerent densities and for the three force ﬁelds.

During shock simulations, time-resolved spectral data modes due to the formation of stable gaseous molecules. The provides evidence of dissociation of various chemical groups, spectra of a single PVN chain also calculated using ReaxFF-lg hence time scales of the initiation of related reactions pathways. force field as shown in the Figure S3b. It can be seen that the fi In our 18 GPa shock simulation, using ReaxFF-2014, the ReaxFF-lg predicted NO2 stretching mode is signi cantly blue- ν ∼ −1 as(NO2) peak disappeared at a time scale of 150 ps, the point shifted to ∼2400 cm . During a 24 GPa shock simulation at at which rapid chemistry initiates, Figure 10a,b. The calculated the experimental density using ReaxFF-lg, the time evolution of time scale of the NO2 peak disappearance is in excellent the spectra as shown in Figure 10c indicates the disappearance 12 ∼ agreement with the experimental data of McGrane et al. The of the NO2 vibrational mode at a time scale of 100 ps. calculated spectra also elucidate other reaction pathways. For However, the evolution of the key peaks is not as pronounced example, the distribution of the intermediate species at 18 GPa as in the case of ReaxFF-2014 simulations. in Figure 6 depicts the production of a significant amount of ∼ NO starting at 50 ps, which reaches a maximum and IV. THERMAL-INDUCED CHEMICAL DECOMPOSITION completely disappeared at ∼200 ps. The peak appeared in our calculated spectra at ∼1600 cm−1 nicely captures the entire NO As mentioned above, shocked-induced chemical reactions evolution history. The time scale of the presence of the peak depend both on the thermo-mechanics involved in shock matches that of NO production. Thus, our simulation predicted loading and the decomposition at the shock temperature and spectra enabled elucidation of various reaction pathways, at the pressure. To decouple these two effects and compare the same time, the time scale of the reactions. The rapid chemistry description of the chemistry of the three force fields, we causes the disappearance of the major peaks, as the final performed additional simulations where PVN reaction and gaseous products are produced. As a result, low-frequency decomposition is studied under isothermal, isochoric con- modes denoting diffusive processes start to build up. The broad ditions. nature of the peaks with frequencies near 3000 cm−1 stems IV.A. Decomposition Reaction Rate Constants. The from the combination of O−H, N−H, and C−H stretching isothermal decomposition simulations are performed following

I DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article the methodology as described in section II.C and II.D. The time evolution of potential energies at two different densities ρ ρ ( o and 1.4 o) are shown in Figure S4 for all the three force fields. The first step in the analysis of the reaction rate constants is finding the characteristic time scales of reactions. We define it as the time required for the potential energy to reach half of the total exothermicity at a particular temperature and density. The inverse of the characteristic times, the reaction rates, are shown in Figure 11a as a function of temperature in an Arrhenius plot for all the densities and force fields. We observe that both temperature and compression of the structure plays a major role in the reaction rates. The increase in both temperature and density increases the reaction rates. For example, the reaction rate increases by factors of 60, 81, and 79 for the experimental density when system temperature is increased from 2400 to 3200 K, using ReaxFF-2014, ReaxFF- IW, and ReaxFF-lg, respectively. The effect of compression of the bulk structure was also very pronounced. For example, at 2400 K, compressing to 1.4ρο leads to 32-, 49-, and 51-fold increases in the reaction rates with ReaxFF-2014, ReaxFF-IW, and ReaxFF-lg, respectively. The slopes of the exponential regression analysis of Figure Figure 12. Species evolution during isothermal decomposition 11a can be associated with an overall activation energy for ff fi decomposition at isochoric conditions; see Figure 11b. A simulations at 3200 K using three di erent force elds at experimental density. The molecular fractions are normalized by the total monomer similar approach has been used in previous studies to calculate units. activation energies.13,27,40 Consistent with the shock results, we find ReaxFF-2014 exhibits lower activation energy than the other two force fields. The increased reaction rates with the trace of HONO. In contrast, in ReaxFF-IW and -lg simulations, fi volumetric compression are also evident from the decrease in a signi cant amount of HNO3 and HONO has been observed. activation energies as shown in Figure 11b. The ReaxFF-2014 The secondary dissociation reactions of the intermediate force field calculated global activation energies are 16.0, 15.9, radicals lead to the formation of CO ,HO, N ,NH,H, ρ ρ ρ 2 2 2 3 2 and 15.5 kcal/mol for experimental ( ο), 1.2 ο, and 1.4 ο, and CO. The major secondary reactions that produce CO2 and respectively. The ReaxFF-2014 predicted activation energies of H O are given in Tables S2 and S3. The CO formation 49 2 2 the PVN are significantly lower than the Wood et al. reported pathways tracked from the ReaxFF-2014 simulations exhibit data for NM, HMX, and PETN. This indicates a higher that about 50% of the CO2 are evolved from the HCO2. The reactivity of the PVN compared to these high-energy materials. dissociation of the larger population of the HCO2 causes CO2 In contrast to ReaxFF-2014, ReaxFF-IW force field predicts to be the most abundant species. However, we have not around 40% higher activation energies for all the cases. We note observed this CO2 reaction pathway in the ReaxFF-lg and that ReaxFF-lg calculated activation energies are slightly lower ReaxFF-IW force field simulations. Across the temperature and than the ReaxFF-IW at all the densities. pressure range considered in this study, H2O is the most IV.B. Detailed Mechanism of Dissociation Chemistry. dominant species in the case of ReaxFF-IW and -lg force fields. Thermal decomposition of the PVN polymer at the early stages We observe differences in the proportion of reaction results in the formation of a large variety of radical initiation pathways in between shock and isothermal simu- intermediates. Subsequently, the radicals undergo chain-like lations. The concentration of the NO2 produced (Figure 12)in secondary reactions to generate stable final products. The isothermal simulations is much higher than the shock evolution of the species of experimental density samples at simulations. To further illustrate the variation in the NO2 3200 K is presented in Figure 12. The results from the 2400 K production with the simulation conditions, we calculated the ρ − ff experimental density and 2400 K and 3200 K 1.4 ο density O NO2 bond breaking barrier at two di erent densities of the simulations are included in Figures S5−S7.Theresults PVN. ReaxFF-2014 force field predicts the barriers as 43 and 60 presented in Figure 12 reveal that a major initiation pathway kcal/mol for densities of 1.40 and 2.40 g cm−3, respectively. We − 51−53 is the production of NO2 via the dissociation of the O NO2 used a bond-restraint method to calculate the minimum bond linked to the (−C−C−) backbone of the polymer; this is energy pathway to dissociate the O−N bond. Thus, with similar to the shock-induced decomposition. The NO2 peak increasing density, the N−O bond breaking barrier increases reaches a maximum value at the very early stage of that result in a smaller amount of NO2 production in shock decomposition and then rapidly dwindles as the secondary simulations. The higher density caused by the shock loading reaction pathways consume this species. NO2 was found as a reduces the distances among the neighboring monomer units, predominant initial reaction product in the thermal decom- as such NO2 scission become less favorable. This observation is position of other nitramines such as RDX,50 HMX,30 and CL- consistent with the reports on the decomposition of various 46 20. The NO2 evolution mechanisms are similar for all the nitroaminos explosives under shock and thermal load- fi 13,27,46,54 force elds. However, the production of other intermediates ing. The reduction of NO2 scission due to the higher varies significantly with the force fields. The ReaxFF-2014 shock velocity or pressure has been observed in CL-20,46 20 54 generates a larger quantity of CH2O and HCO2 along with RDX, and HMX. Moreover, a FTIR study on the thermal other radical intermediates such as NO, ONH, CNOH, and a decomposition of RDX and HMX also corroborate our

J DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article observation on the effect of pressure. It was found that an versions required stronger shocks for initiation. The combina- 50 increase in system pressure reduces NO2 scission. To further tion of reactive MD simulations and ultrafast spectroscopy understand the effect of shock vs thermal loading, we opens the possibility of both the validation of ReaxFF at performed isothermal simulations at equivalent thermodynam- extreme conditions and can contribute to the interpretation of ics conditions such as temperature, and density of the final state the experimental data relating changes in spectral features to of the shocked material. The comparison of the species atomic processes. Unfortunately, the narrow spectral region of evolution in the cases of equivalent shock and thermal loading existing experiments only enables a partial validation of the conditions are shown in Figures S8−S10 and a summary of the predictions. Broad spectral analysis of laser-shocks, currently distribution of the final gaseous products are presented in under development, will enable a more complete validation of Figure S11. The details of the thermodynamic conditions are atomistic simulations and a detailed understanding of chemical given in the captions of Figures S8−S10. From these figures, it decomposition paths. is evident that the nature of the loading has a significant Our investigation of the reaction initiation pathways reveals a fl fi in uence on the evolution of the intermediate species, as such signi cant dependency on the loading type. NO2 formation is reaction pathways. We observe a pronounced effect of predominantly found as a reaction initiation step, however, the mechano-chemistry due to the shock loading on the initial relative amount of the species is contingent on the nature of the reaction pathways. The shock loading resulted in a decrease in applied load. The shock and volumetric compression results in  the amount of the intermediates those are evolved in a the reduction of NO2 production, consistent with observations reasonable quantitycompared to the thermal loading for all in other high energy explosives. The final product populations the force fields. This implies that the PVN dissociates into predicted by the three force fields are similar, the main ff many smaller fragments, the individual quantities of the di erence being a higher population of CO2 in ReaxFF-2014. fragments were small thus we ignored them in the population This can be attributed to the, correct, relative stability of this analysis. However, despite the variation in the amount of the molecule, see Figure 9, but also by the overstabilization of the fi intermediates, the distribution of nal gaseous products is HCO2 intermediate by ReaxFF-2014. While the comparison almost identical for both the simulation cases (see Figure S11). experimental spectroscopic studies with the MD simulations We observe that higher compression and temperature alters indicates that ReaxFF-2014 provides a more accurate the reaction pathways and final products distribution in the description of threshold for chemical initiation and its time isothermal simulations. The increase in density reduces the scales, the lack of broadband data does not enable a fi amount of NO2 production for all the cases. In ReaxFF-2014 comprehensive validation of the three force elds and the simulations, the amount of CHNO radicals produced increases detailed chemistry they predict. We expect such comparisons to with the system pressure. At 3200 K simulations, ReaxFF-2014 be possible in the near future. resulted in a reduction of CH2O and HCO2 and a substantial increase in NO and H2O population. At 2400 K, irrespective of ■ ASSOCIATED CONTENT the system densities, the amount of CO2 produced is notably *S Supporting Information higher than the other stable products; however, with the ρ The Supporting Information is available free of charge on the increasing temperature and density such as at 3200 K and 1.4 o ACS Publications website at DOI: 10.1021/acs.jpcc.7b06154. (see Figure S6), this dominance dwindles, and CO2 and H2O are generated in a comparable quantity. This is due to the Further details of the temporal evolution of thermodynamics quantities during FF density shock simulations, reduction of CO2 and an increase of H2Oathigher temperatures. In contrary, higher temperature decreases the per element spectra of a single polymer chain, evolution of potential energies, and species in isothermal H2O population in both ReaxFF-IW and -lg simulations; however, the effect is less discernible at higher densities. At decompositions (PDF) experimental density ReaxFF-IW and -lg simulations, CO2, H2O, and H2 reach at similar asymptotic quantities at 3200 K as ■ AUTHOR INFORMATION a result of the reduced amount of H2O population. The Corresponding Author quantity of the H2 production exhibits an increasing trend with *(A.S.) E-mail: [email protected]. the increasing system temperature. We note that H2 formation pathways are absent in ReaxFF-2014 force field simulations. ORCID Md Mahbubul Islam: 0000-0003-4584-2204 One can also observe that the amount of N2 produced is insensitive to the change in temperature and densities. Notes The authors declare no competing financial interest. V. CONCLUSIONS In conclusion, the first atomistic study of the chemical ■ ACKNOWLEDGMENTS decomposition of PVN polymer under shock and thermal This work was support by the US Office of Naval Research, loading conditions provides a detailed description of mechan- Multidisciplinary University Research Initiatives (MURI) ical, chemical, and spectroscopic properties. The predicted Program, Contract N00014-16-1-2557. Program managers: shock vs particle velocity Hugoniots using ReaxFF are in Clifford Bedford and Kenny Lipkowitz. reasonable agreement with available experimental data. More importantly, this study enabled the first direct comparison ■ REFERENCES between reactive MD simulations and experiments for the (1) Tarver, C. M.; Chidester, S. K.; Nichols, A. L. Critical Conditions decomposition of a material under shock loading. We found for Impact- and Shock-Induced Hot Spots in Solid Explosives. J. Phys. that ReaxFF-2014 predicts the onset of chemical reactions and Chem. 1996, 100, 5794−5799. the time scale associated with the formation of NO2 in excellent (2) McGuire, R. R.; Tarver, C. M. Chemical-Decomposition Models for agreement with shock experiments. The ReaxFF-IW and -lg the Thermal Explosion of Confined Hmx, Tatb, Rdx, and Tnt Explosives;

K DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article

UCRL-84986; CONF-810602-15; Lawrence Livermore National Lab.: H. M.; et al. The ReaxFF Reactive Force-Field: Development, Livermore, CA, 1981. Applications and Future Directions. Npj Comput. Mater. 2016, 2, (3) Dlott, D. D.; Fayer, M. D. Shocked Molecular Solids: Vibrational 15011. up Pumping, Defect Hot Spot Formation, and the Onset of Chemistry. (24) Wood, M. A.; Cherukara, M. J.; Kober, E. M.; Strachan, A. J. Chem. Phys. 1990, 92, 3798−3812. Ultrafast Chemistry under Nonequilibrium Conditions and the Shock (4) Wen, X.; Tolbert, W. A.; Dlott, D. D. Multiphonon up-Pumping to Deflagration Transition at the Nanoscale. J. Phys. Chem. C 2015, and Molecular Hot Spots in Superheated Polymers Studied by 119, 22008−22015. Ultrafast Optical Calorimetry. Chem. Phys. Lett. 1992, 192, 315−320. (25) Nomura, K.; Kalia, R. K.; Nakano, A.; Vashishta, P.; van Duin, A. (5) Kim, H.; Dlott, D. D. Theory of Ultrahot Molecular Solids: C. T.; Goddard, W. A. Dynamic Transition in the Structure of an Vibrational Cooling and Shock-induced Multiphonon up Pumping in Energetic Crystal during Chemical Reactions at Shock Front Prior to Crystalline Naphthalene. J. Chem. Phys. 1990, 93, 1695−1709. Detonation. Phys. Rev. Lett. 2007, 99, 148303. (6) Moore, D. S.; McGrane, S. D. Comparative Infrared and Raman (26) Li, Y.; Vashishta, P.; et al. Multistage Reaction Pathways in Spectroscopy of Energetic Polymers. J. Mol. Struct. 2003, 661−662, Detonating High Explosives. Appl. Phys. Lett. 2014, 105, 204103. 561−566. (27) Rom, N.; Zybin, S. V.; van Duin, A. C. T.; Goddard, W. A.; (7) Brown, K. E.; McGrane, S. D.; Bolme, C. A.; Moore, D. S. Zeiri, Y.; Katz, G.; Kosloff, R. Density-Dependent Liquid Nitro- Ultrafast Chemical Reactions in Shocked Nitromethane Probed with methane Decomposition: Molecular Dynamics Simulations Based on Dynamic Ellipsometry and Transient Absorption Spectroscopy. J. Phys. ReaxFF. J. Phys. Chem. A 2011, 115, 10181−10202. Chem. A 2014, 118, 2559−2567. (28) Liu, L.; Liu, Y.; Zybin, S. V.; Sun, H.; Goddard, W. A. ReaxFF- (8) Dlott, D. D. New Developments in the Physical Chemistry of Lg: Correction of the ReaxFF Reactive Force Field for London Shock Compression. Annu. Rev. Phys. Chem. 2011, 62, 575−597. Dispersion, with Applications to the Equations of State for Energetic (9) Bassett, W. P.; Dlott, D. D. High Dynamic Range Emission Materials. J. Phys. Chem. A 2011, 115, 11016−11022. Measurements of Shocked Energetic Materials: Octahydro-1,3,5,7- (29) Budzien, J.; Thompson, A. P.; Zybin, S. V. Reactive Molecular Tetranitro-1,3,5,7-Tetrazocine (HMX). J. Appl. Phys. 2016, 119, Dynamics Simulations of Shock Through a Single Crystal of 225103. Pentaerythritol Tetranitrate. J. Phys. Chem. B 2009, 113, 13142− (10)Moore,D.S.;McGrane,S.D.;Funk,D.J.Ultrafast 13151. Spectroscopic Investigation of Shock Compressed Energetic Polymer (30) Zhou, T.; Song, H.; Liu, Y.; Huang, F. Shock Initiated Thermal Films. AIP Conf. Proc. 2003, 706, 1285−1288. and Chemical Responses of HMX Crystal from ReaxFF Molecular (11) Patterson, J. E.; Lagutchev, A.; Huang, W.; Dlott, D. D. Ultrafast Dynamics Simulation. Phys. Chem. Chem. Phys. 2014, 16, 13914− Dynamics of Shock Compression of Molecular Monolayers. Phys. Rev. 13931. Lett. 2005, 94, 015501. (31) Tersoff, J. Empirical Interatomic Potential for Carbon, with (12) McGrane, S. D.; Moore, D. S.; Funk, D. J. Shock Induced Applications to Amorphous Carbon. Phys. Rev. Lett. 1988, 61, 2879− Reaction Observed via Ultrafast Infrared Absorption in Poly(Vinyl 2882. Nitrate) Films. J. Phys. Chem. A 2004, 108, 9342−9347. (32) Brenner, D. W. Empirical Potential for Hydrocarbons for Use in (13) Rom, N.; Hirshberg, B.; Zeiri, Y.; Furman, D.; Zybin, S. V.; Simulating the Chemical Vapor Deposition of Diamond Films. Phys. Goddard, W. A.; Kosloff, R. First-Principles-Based Reaction Kinetics Rev. B: Condens. Matter Mater. Phys. 1990, 42, 9458−9471. for Decomposition of Hot, Dense Liquid TNT from ReaxFF (33) Ashraf, C.; van Duin, A. C. T. Extension of the ReaxFF Multiscale Reactive Dynamics Simulations. J. Phys. Chem. C 2013, Combustion Force Field toward Syngas Combustion and Initial 117, 21043−21054. Oxidation Kinetics. J. Phys. Chem. A 2017, 121, 1051−1068. (14) Shan, T.-R.; Wixom, R. R.; Mattsson, A. E.; Thompson, A. P. (34) Islam, M. M.; Zou, C.; van Duin, A. C. T.; Raman, S. Atomistic Simulation of Orientation Dependence in Shock-Induced Interactions of Hydrogen with the Iron and Iron Carbide Interfaces: A Initiation of Pentaerythritol Tetranitrate. J. Phys. Chem. B 2013, 117, ReaxFF Molecular Dynamics Study. Phys. Chem. Chem. Phys. 2016, 18, 928−936. 761−771. (15) Wood, M. A.; van Duin, A. C.; Strachan, A. Coupled Thermal (35) Van Duin, A. C.; Strachan, A.; Stewman, S.; Zhang, Q.; Xu, X.; and Electromagnetic Induced Decomposition in the Molecular Goddard, W. A. ReaxFFSiO Reactive Force Field for Silicon and Explosive αHMX; A Reactive Molecular Dynamics Study. J. Phys. Silicon Oxide Systems. J. Phys. Chem. A 2003, 107, 3803−3811. Chem. A 2014, 118, 885−895. (36) Islam, M. M.; Ostadhossein, A.; Borodin, O.; Yeates, A. T.; (16) Schweigert, I. V. Quantum Mechanical Simulations of Tipton, W. W.; Hennig, R. G.; Kumar, N.; van Duin, A. C. T. van. Condensed-Phase Decomposition Dynamics in Molten RDX. J. Phys. ReaxFF Molecular Dynamics Simulations on Lithiated Sulfur Cathode Conf. Ser. 2014, 500, 052039. Materials. Phys. Chem. Chem. Phys. 2015, 17, 3383−3393. (17) Schweigert, I. V. Ab Initio Molecular Dynamics of High- (37) Mortier, W. J.; Ghosh, S. K.; Shankar, S. Electronegativity- Temperature Unimolecular Dissociation of Gas-Phase RDX and Its Equalization Method for the Calculation of Atomic Charges in Dissociation Products. J. Phys. Chem. A 2015, 119, 2747−2759. Molecules. J. Am. Chem. Soc. 1986, 108, 4315−4320. (18) Joshi, K. L.; Chaudhuri, S. Reactive Simulation of the Chemistry (38) Russo, M. F., Jr.; van Duin, A. C. T. Atomistic-Scale Simulations behind the Condensed-Phase Ignition of RDX from Hot Spots. Phys. of Chemical Reactions: Bridging from Quantum Chemistry to Chem. Chem. Phys. 2015, 17, 18790−18801. Engineering. Nucl. Instrum. Methods Phys. Res., Sect. B 2011, 269, (19) Riad Manaa, M.; Reed, E. J.; et al. Early Chemistry in Hot and 1549−1554. Dense Nitromethane: Molecular Dynamics Simulations. J. Chem. Phys. (39) Islam, M. M.; Kolesov, G.; Verstraelen, T.; Kaxiras, E.; van Duin, 2004, 120, 10146−10153. A. C. T. eReaxFF: A Pseudoclassical Treatment of Explicit Electrons (20) Strachan, A.; van Duin, A. C. T.; Chakraborty, D.; Dasgupta, S.; within Reactive Force Field Simulations. J. Chem. Theory Comput. Goddard, W. A. Shock Waves in High-Energy Materials: The Initial 2016, 12, 3463−3472. Chemical Events in Nitramine RDX. Phys. Rev. Lett. 2003, 91, 098301. (40) Strachan, A.; Kober, E. M.; van Duin, A. C.; Oxgaard, J.; (21) Van Duin, A. C.; Dasgupta, S.; Lorant, F.; Goddard, W. A. Goddard, W. A., III Thermal Decomposition of RDX from Reactive ReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A Molecular Dynamics. J. Chem. Phys. 2005, 122, 054502. 2001, 105, 9396−9409. (41) Haley, B. P.; Li, C.; Wilson, N.; Jaramillo, E.; Strachan, A. (22) Chenoweth, K.; van Duin, A. C. T.; Goddard, W. A. ReaxFF Atomistic Simulations of Amorphous Polymers in the Cloud with Reactive Force Field for Molecular Dynamics Simulations of PolymerModeler. ArXiv Prepr. ArXiv150303894, 2015. Hydrocarbon Oxidation. J. Phys. Chem. A 2008, 112, 1040−1053. (42) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. DREIDING: a (23) Senftle, T. P.; Hong, S.; Islam, M. M.; Kylasa, S. B.; Zheng, Y.; generic force field for molecular simulations. J. Phys. Chem. 1990, 94, Shin, Y. K.; Junkermeier, C.; Engel-Herbert, R.; Janik, M. J.; Aktulga, 8897−8909.

L DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX The Journal of Physical Chemistry C Article

(43) Ravelo, R.; Holian, B. L.; Germann, T. C.; Lomdahl, P. S. Constant-Stress Hugoniostat Method for Following the Dynamical Evolution of Shocked Matter. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 014103. (44) Reed, E. J.; Fried, L. E.; Joannopoulos, J. D. A Method for Tractable Dynamical Studies of Single and Double Shock Compression. Phys. Rev. Lett. 2003, 90, 235503. (45) Tokmakoff, A.; Fayer, M. D.; Dlott, D. D. Chemical Reaction Initiation and Hot-Spot Formation in Shocked Energetic Molecular Materials. J. Phys. Chem. 1993, 97, 1901−1913. (46) Xue, X.; Wen, Y.; Zhang, C. Early Decay Mechanism of Shocked ε-CL-20: A Molecular Dynamics Simulation Study. J. Phys. Chem. C 2016, 120, 21169−21177. (47) Maharrey, S.; Behrens, R. Thermal Decomposition of Energetic Materials. 5. Reaction Processes of 1,3,5-Trinitrohexahydro-S-Triazine below Its Melting Point. J. Phys. Chem. A 2005, 109, 11236−11249. (48) NIST WebBook http://webbook.nist.gov/ (accessed Jun 7, 2017). (49) Wood, M. A.; Strachan, A. Nonequilibrium Reaction Kinetics in Molecular Solids. J. Phys. Chem. C 2016, 120, 542−552. (50) Oyumi, Y.; Brill, T. B. Thermal Decomposition of Energetic Materials 3. A High-Rate, in Situ, FTIR Study of the Thermolysis of RDX and HMX with Pressure and Heating Rate as Variables. Combust. Flame 1985, 62, 213−224. (51) Rahaman, O.; van Duin, A. C.; Goddard, W. A., III; Doren, D. J. Development of a ReaxFF Reactive Force Field for Glycine and Application to Solvent Effect and Tautomerization. J. Phys. Chem. B 2011, 115, 249−261. (52) van Duin, A. C. T.; Damste,́ J. S. S. Computational Chemical Investigation into Isorenieratene Cyclisation. Org. Geochem. 2003, 34, 515−526. (53) Ostadhossein, A.; Cubuk, E. D.; Tritsaris, G. A.; Kaxiras, E.; Zhang, S.; van Duin, A. C. T. van. Stress Effects on the Initial Lithiation of Crystalline Silicon Nanowires: Reactive Molecular Dynamics Simulations Using ReaxFF. Phys. Chem. Chem. Phys. 2015, 17, 3832−3840. (54) Ge, N.-N.; Wei, Y.-K.; Ji, G.-F.; Chen, X.-R.; Zhao, F.; Wei, D.- Q. Initial Decomposition of the Condensed-Phase β-HMX under Shock Waves: Molecular Dynamics Simulations. J. Phys. Chem. B 2012, 116, 13696−13704.

M DOI: 10.1021/acs.jpcc.7b06154 J. Phys. Chem. C XXXX, XXX, XXX−XXX