Inhibition of Hotspot Formation in Polymer Bonded ... · Inhibition of Hotspot Formation in Polymer Bonded Explosives Using an Interface Matching Low Density ... sensitive for propellants

Inhibition of Hotspot Formation in Polymer Bonded Explosives Usingan Interface Matching Low Density Polymer Coating at the Polymer−Explosive InterfaceQi An,† William A. Goddard, III,*,† Sergey V. Zybin,† and Sheng-Nian Luo‡

†Materials and Process Simulation Center, California Institute of Technology, Pasadena, California 91125, United States‡The Peac Institute of Multiscale Sciences, Chengdu, Sichuan 610207, People’s Republic of China

*S Supporting Information

ABSTRACT: In order to elucidate how shocks in heterogeneous materials affectdecomposition and reactive processes, we used the ReaxFF reactive force field inreactive molecules dynamics (RMD) simulations of the effects of strong shocks (2.5and 3.5 km/s) on a prototype polymer bonded explosive (PBX) consisting ofcyclotrimethylene trinitramine (RDX) bonded to hydroxyl-terminated polybuta-diene (HTPB). We showed earlier that shock propagation from the high densityRDX to the low density polymer (RDX → Poly) across a nonplanar periodicinterface (sawtooth) leads to a hotspot at the initial asperity but no additionalhotspot at the second asperity. This hotspot arises from shear along the interfaceinduced by relaxation of the stress at the asperity. We now report the case for shockpropagation from the low density polymer to the high density RDX (Poly → RDX)where we find a hotspot at the initial asperity and a second more dramatic hotspot at the second asperity. This second hotspot isenhanced due to shock wave convergence from shock wave interaction with nonplanar interfaces. We consider that this secondhotspot is likely the source of the detonation in realistic PBX systems. We showed how these hotspots depend on the densitymismatch between the RDX and polymer and found that decreasing the density by a factor of 2 dramatically reduces the hotspot.These results suggest that to make PBX less sensitive for propellants and explosives, the binder should be designed to providelow density at the asperity in contact with the RDX. Based on these simulations, we propose a new design for an insensitive PBXin which a low density polymer coating is deposited between the RDX and the usual polymer binder. To test this idea, wesimulated shock wave propagation from two opposite directions (RDX→ Poly and Poly→ RDX) through the interface matchedPBX (IM-PBX) material containing a 3 nm coating of low density (0.48 g/cm3) polymer. These simulations showed that this IM-PBX design dramatically suppresses hotspot formation.

I. INTRODUCTION

It is well-known that shocks can transform the structures ofmaterials while introducing defects, dislocations, melting, andchemical reactions.1−5 Understanding the interactions of shockwaves with materials is essential in many physical andengineering processes, such as inertial confinement fusion(ICF), Richtmyer-Meshkov instabilities (RMIs), supernovaexplosion, earthquakes, cavitation, and spallation. In particularfor the energetic materials (EMs) used in rocket propellantsand explosives, it is of interest to understand how the shocktriggers massive energy release (detonation) of these highenergy materials. To prevent accidental detonation in engineer-ing applications, explosive powders are normally bonded into apolymer matrix to form polymer bonded explosives (PBXs).The detonation sensitivity of EMs plays essential roles in thesafety storage and transportation, but the origin of detonationinitiation remains controversial despite numerous experimentaland theoretical studies.6−10 This is due to the heterogeneousstructures (defects, voids, grain boundaries, interfaces, etc.) andthe complex coupling of thermal, mechanical, and chemicalfactors.

It is generally accepted that a critical issue is the formation ofa hotspot whose high temperature accelerates the reactiveenergy releasing events that play a critical role indetonation.11−14 However, the mechanism of hotspot for-mation remains controversial, with multiple mechanismsproposed.15,16 An important observation17 is that a weakshock compression can desensitize the material so that it ismuch less sensitive to a strong shock or detonation wave. Thishas led to the speculation that the origin of hotspot is due tovoids that can be annealed by the initial weak shock.17,18

Indeed, atomistic simulations on molecular crystals and atomiccrystals containing voids confirmed that they lead to hotspotformation due either to void collapse or nanojets.19−22 It hadalso been observed that delamination and partial decom-position occur at micrograins boundaries or wedges betweenembedded EMs and the polymer, but not at the interior of thecrystals under the shear-impact experiments with weak

Received: June 30, 2014Revised: August 4, 2014Published: August 8, 2014

Article

pubs.acs.org/JPCC

© 2014 American Chemical Society 19918 dx.doi.org/10.1021/jp506501r | J. Phys. Chem. C 2014, 118, 19918−19928

pubs.acs.org/JPCC

shocks.23,24 This indicates that the interface between the EMand polymer also plays an important role in the hotspotformation.In a previous study,25 we considered a realistic model of PBX

N-106 involving 3.7 million atoms per periodic cell with anonplanar (sawtooth) interface between the RDX EM (Figure1a) and the HTPB (Figure 1b) based polymer binder. Usingthe ReaxFF in RMD we found that a system without defects orvoids leads to hotspot formation as the shock passing throughthe RDX encounters the initial asperity of the polymerinterface. We found that at this contact asperity with thenonplanar interface, relaxation of the longitudinal stress fromthe high density RDX to the low density polymer at the tipcauses shear localization that heats the RDX locally, leading todecomposition and energy release at the asperity of theheterogeneous material interface.25 Similarly, we recentlyreported similar studies of shock-induced hotspot formationat the nonplanar interface of silicon pentaerythritol tetranitrate(Si-PETN)26 based PBX model, where we found similar results.Indeed, for the colossally sensitive Si-PETN, we were able tosimulate the progress toward detonation initiation.Here we report simulations on a similar realistic model of

PBX N-106 to examine shock wave propagation across thenonplanar interface from the low density polymer to the highdensity RDX. We find again that a modest hotspot forms at thefront asperity of the sawtooth as shock wave passes from thepolymer to the RDX asperity, due to the shear localization.However, in this case we find that continuous propagation ofthe shock wave leads to a much hotter hotspot as the shockencounters the polymer asperity at the RDX contact on theback side of the sawtooth. This second hotspot is due to shockwave convergence arising from the shock wave in the lowdensity polymer interacting with the nonplanar interface to thehigh density RDX. Indeed we consider that this second hotspot is likely the source of the detonation in realistic PBXsystems.In order to meet the requirements of future space and

military applications, it is essential to develop new EMs withbetter performance while enhancing the insensitivity to thermalor shock response than the existing ones.27 In our previous

study,25 we demonstrated that decreasing the polymer densityby a factor of 2 (to 1/3 that of the RDX) essentially eliminatesthe hotspot formation at the front asperity for the RDX → Polyshock direction, while increasing the density of the polymer tomatch that of the RDX dramatically increases the hotspottemperature. Our current study finds that the strength of thesecond hotspot depends critically on both the shock impedanceand the density. Based on these results, we propose that apractical approach to make EMs less sensitive for propellantsand explosives would be to design the binder to provide a lowdensity at the interface while retaining the normal polymerproperties within the bulk polymer. To test this idea, we carriedout ReaxFF based reactive dynamics simulations for shockpropagation through the new interface matched-PBX (IM-PBX) material to show that coating a low density polymerbetween the normal polymer binder and the energetic materialdramatically reduces sensitivity.

II. RMD SIMULATION DESIGN AND METHODS

II-1. ReaxFF Reactive Force Field Method. ReaxFF hasbeen developed to simulate complex chemical reactions overlong time scales (pico to nano seconds) for large systems(millions of atoms) while retaining the accuracy of quantummechanics (QM). ReaxFF uses a general bond order−bonddistance relation and geometry-dependent charge adjustmentmethod to describe the bond breaking and bond formationaccurately and smoothly. The ReaxFF parameters aredetermined from fitting to numerous QM calculations ofreaction barriers and rates.28 The original ReaxFF accounts forthe van der Waals interaction by using a Morse type ofpotential form which we later found is too soft for theextremely small distance interactions found during high velocityshocks. Thus, the new version of ReaxFF used here includes atwo-body inner wall parameter29 needed to describe accuratelythe inner wall for the close contacts found in shock simulationsfor energetic materials. The new ReaxFF also includes a long-range London dispersion correction scaling like −C6/R

6 butdamped with the low-gradient dispersion correction term sothat valence forces are not affected. However, to be consistentwith our previous study of PBX with nonplanar interfaces,25 we

Figure 1. Molecular structures for PBX N-106 compositions: (a) RDX energetic molecule, (b) HTPB polymer chain, (c) IPDI cross-linker, and (d)DOA plasticizer.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp506501r | J. Phys. Chem. C 2014, 118, 19918−1992819919

did not include this vdW dispersion correction in the currentstudy. The parameters for this ReaxFF are included in theSupporting Information (SI), which we found gives a gooddescription of the mechanical properties and chemical reactionsin various explosives and polymers.10,25,26,29−32 Our MDsimulations used the ReaxFF engine incorporated into thelarge-scale atomic/molecular massively parallel simulator(LAMMPS).33

II-2. Atomic PBX Model. The PBX model in this study issimilar to our previous study.25 The polymer binder matrixconsists of hydrogen terminated polybutadiene (HTPB) andisophorone diisocyanate (IPDI)-based polyurenthane rubberusing a dioctyl adipate (DOA) molecule plasticizer (Figure 1).This composition optimizes the casting properties of thepolymer binder. The details of preparing the RDX and polymerbinder can be found in ref 25.We formed the periodic sawtooth triangular interface (Figure

2a) by carving out of an RDX cell the sawtooth shape, based onthe molecular center of mass to form (110) and (1−10)surfaces as previously discussed in refs 25 and 26. The periodicdimensions of the polymer were deformed to match the cross-section of the RDX (100) surface. Then a complementarysurface to RDX was built into the HTPB by eliminating eachpolymer chain having its center of mass outside the intendedregion and keeping the others intact. This led to some chainsextending outside the intended region for the polymer. Thenwe brought the EM and polymer piece together to a pointexpected to have 2% compression of polymer. We relaxed thesystem with minimization first and followed by a 10 psdynamics using isothermal-isochoric (NVT) ensemble at roomtemperature to form a smooth interface. The periodic cellcontains 1606106 atoms (625191 atoms of RDX and 980915atoms of HTPB-based binder) with cell dimensions of 26.5 nm(in the shock direction) × 27.1 nm (sawtooth direction) × 25.4nm (into the third periodic direction).

To examine how the polymer densities affect the hotspotformation, we decreased the binder density to half the originalvalue of 0.95 g/cm3 by scaling the atomic mass. We alsoexamined the case of high density binder by increasing itsdensity to 1.71 g/cm3 which is approximately the same as RDX.To incorporate the low density polymer coating into this PBXmodel, we chose a 3 nm thin layer of the HTPB polymer incontact with the RDX (based on molecular center of mass) andchanged its density to 0.48 g/cm3 (50% of the normal density)by scaling the atomic mass and leave the other part intact. Weused the same procedure to coat a 3 nm low density polymer tothe previous PBX model in ref 25. The coating PBX models areshown in Figure 2b,c.

II-3. Shock Simulations and Analysis. Shock waves weregenerated by driving thermalized two-dimensionally (2D)periodic slabs onto a Lennard-Jones 9−3 wall as in ref 25.The initial shock conditions were obtained by adding thedesired particle velocity to the thermal velocities (300 K) for allatoms in the slab. Periodic boundary conditions were notapplied along the shock direction (x-axis). We simulated theshock propagation using the microcanonical (NVE) ensemble.We used a time step of 0.1 fs in ReaxFF simulations integratingthe equations of motion with the Verlet algorithm. The particlevelocities are Up = 2.5 and 3.5 km/s for shock simulations.We used 1D and 2D binning techniques25 to analyze spatial

distributions of the physical properties (temperature, stress,particle velocity) at various stages of shock loading. Wepartitioned the simulation cell into fine bins (∼1 nm) along thex direction (1D binning analysis) or along the x−y plane (2Dbinning analysis). We averaged along the z-axis ([001]direction) for the 2D analysis. The center of mass velocitywas removed to calculate the temperature and stress in eachbin. The stress for each bin was the averaged virial stress plusthermal contributions. For chemical reactions, we did thefragment analysis based on the bond order cutoffs described inthe Supporting Information. Here we chose large values of

Figure 2. (a) Initial PBX sawtooth configuration with the shock propagation from the right (polymer binder region) to the left (RDX). This leads toformation of two hotspots, marked as i-LH and f-LH. (b) The PBX model coating with 3 nm low density (0.48 g/cm3) polymer where shockpropagates from polymer to RDX. (c) The PBX model coating with 3 nm low density (0.48 g/cm3) polymer where shock propagate from RDX topolymer.



bond order cutoffs (with different values for each element, seeTable S1 of the Supporting Information) than normally used(0.3)28 so that the normal vibrations of hot molecules wouldnot exhibit oscillations in fragments sizes for the hightemperatures and high pressures.

III. RESULTS AND DISCUSSIONS

III-1. Hotspot Formation as Shock Propagate fromPolymer to RDX. III-1a. Temperature. Figure 3a,b shows thetemperature profiles for shock wave propagation along the x-direction from low density polymer (0.95 g/cm3) to highdensity RDX (1.71 g/cm3) with an impact velocity Up = 3.5km/s. We find that a hotspot with a temperature increase of1480 K (leading to 1780 K) forms as the shock waveencounters the first angular tip in Figure 3a (this point isdenoted as i-LH for initial asperity and low to high impedance).The mechanism for this first hotspot formation is shearlocalization as we found in earlier simulations that examinedpropagation of the shock from the dense RDX to the lowdensity polymer,25 but the hotspot temperature of ∼1780 K is750 K lower than the hotspot found in the previoussimulations.25

Now, however, we find a new phenomenon arising as theshock wave continues propagating in the converging widthwithin the interface triangle of the low impedance polymerembedded in the higher impedance RDX. Here a much hotterhotspot with a temperature of 2540 K forms as the shock waveapproaches the second apex, which is denoted as f-LH (toindicate the final asperity for low impendence to highimpedance shock direction). This second hotspot was notobserved when shock waves pass through from RDX topolymer binder,25 because the conditions for converging shockswere absent.

Table 1 shows the temperature of the two asperity regions asshock passes through from two opposite directions. For the 3.5

km/s shock from polymer to RDX, the temperature of thesecond hotspot (2540 K) is similar to the first hotspot at theasperity from RDX to polymer (2530 K) but much higher thanthe first hotspot (1780 K). This temperature increase for thesecond hotspot is ∼750 K greater than the temperatureincrease for the first hotspot. Thus, for both directions ofpropagation the hot spot is at the asperity of RDX penetratinginto the polymer. Hence, we consider that the shockconvergence mechanism likely plays a critical role in strongshock induced detonation.For Up = 2.5 km/s the effects of the shock from polymer to

RDX are much less, with the initial asperity leading to a hotspotof 1220 K and the second asperity to 1310 K or an increasetemperature of 90 K. The temperature profiles for Up = 2.5 km/s are shown in Figure 3c,d.

III-1b. Chemistry. Figure 4a shows the evolution of numberof NO2 and NO3 fragments as the shock wave propagates inPBX for Up = 2.5 km/s. Only two NO2 fragments dissociatefrom RDX molecules in the 1 nm × 1 nm bin of the firsthotspot region within 0.5 ps after it forms, but 6 (∼3× asmany) NO2 fragments appear within 0.5 ps at the secondhotspot region (f-LH) where shock convergence occurs. For Up

Figure 3. (a) Up = 3.5 km/s for PBX. The first hotspot formation at i-LH (T = 1780 K). (b) Up = 3.5 km/s for PBX. The second, hotter hotspotformation at f-LH (T = 2540 K) due to shock convergence. (c) Up = 2.5 km/s for PBX. The first hotspot formation at i-LH (T = 1220 K). (d) Up =2.5 km/s for PBX. The second, hotter hotspot formation at f-LH (T = 1310 K) due to shock convergence. Note that the temperature scaling in (c)and (d) is much reduced compared to (a) and (b).

Table 1. Temperature (K) of Two Asperity Regions afterShock Passes through from Two Opposite Directions

shock direction Up (km/s) first hotspot (K) second hotspot (K)

RDX to polymer 2.5 1450 10933.5 2530 1834

polymer to RDX 2.5 1220 13103.5 1780 2540



= 3.5 km/s, the number of NO2 fragments in the f-LH (52) is∼2.2× as many as in the i-LH (24). Table 2 summarizes the

numbers of NO2 in a 1 nm × 1 nm bin of two asperity regionsafter 0.5 ps as shock passes through from two oppositedirections. The number of NO2 of the second hotspot frompolymer to RDX is similar to the first hotspot (the sameasperity region) from RDX to polymer and much more thanthe other asperity region.For Up = 2.5 km/s, the shock reaches the first asperity at 1.7

ps and the second asperity at 4.1 ps. Figure 4b,c shows the NO2spatial distributions at 4.4 and 4.8 ps, respectively. In the firsthotspot region (i-LH), the NO2 fragment number increasesslowly (from 0 to 6 within 0.7 ps in the whole hotspot region).As the second hotspot (f-LH) initiates, 5 NO2 fragments appearin the hotspot region (defined in terms of three 1 nm × 1 nmbins) at 4.4 ps, with the number increasing abruptly to 13 at 4.8

ps. This indicates that dramatically increased chemical reactionsoccur in the second hotspot region due to the shockconvergence effects. At this second hotspot we also observedformation of NO3 after ∼1 ps of NO2 dissociation.To examine the formation mechanism of NO2 and NO3

during shock wave propagation, we selected two RDXmolecules and traced the trajectories as the NO2 breaks off ofone RDX and reacts with a second one to form NO3. Thesnapshots are shown in Figure 4d. As the shock wave passes,the upper RDX molecule is compressed and rotated (2.55 to3.00 ps), leading to NO2 dissociation (3.00 to 3.45 ps). Thenfrom 3.45 to 3.55 ps this NO2 molecule extracts an oxygenatom from the NO2 group of the other RDX to form NO3,leaving behind two RDX radical fragments that subsequentlyreact.

III-1c. Shock Convergence Effects. The shock impedance, Z= ρ × v (where ρ is the density and v is the velocity) is offundamental importance, leading to wave refraction when shockwave propagation encounters a change in Z. The angle of theinterface with respect to shock direction determines the shockconvergence in the confinement geometry of the impedancemismatched materials. In our RDX/HTPB model, a pistonvelocity of Up = 3.5 km/s leads to a RDX shock wave velocityof Us = 7.9 km/s (Up = 2.5 km/s leads to RDX Us = 6.5 km/s),which agrees well with our previous study.4 The HTPB basedbinder has a similar shock wave velocity as RDX for the highlyshocked region, Us = 7.6 km/s for Up = 3.5 km/s (Us = 6.4 km/

Figure 4. Chemistry for Up = 2.5 km/s. (a) Evolution of the numbers of fragments (NO2, NO3) as the shock wave propagates in PBX. The totalnumber of NO2 produced at 4.8 ps (190) when the 2nd hotspot f-LH forms, is 2.3× larger than that at 3.1 ps (50) when the 1st hotspot i-LH forms,indicating that the shock convergence leading to the 2nd hotspot likely dominates initiation of detonation in PBX. (b, c) NO2 fragment distributionsat time 4.4 and 4.8 ps, respectively. The number of NO2 fragments increases abruptly near the second hotspot f-LH. (d) Mechanism of NO2 andNO3 formation as the shock wave propagates. At 2.55 ps, the upper RDX is compressed, which at 3.0 ps leads to dissociation of the NO2 which at3.45 ps interacts with the O of an adjacent RDX and by 3.55 ps forms NO3. At 3.45 ps, two NO2 appear. However, the left NO2 to the lower RDXradical is not truly dissociated, instead it rebonds to the RDX radical again at 3.55 ps. The C, H, O and N atoms are represented by black, green, redand blue filled balls, respectively.

Table 2. Number of NO2 and NO3 (in the bracket) inHotspot Region (a 1 nm × 1 nm bin in the xy plane) at aTime of 0.5 ps after the Shock has Passed through

shock direction Up (km/s) first hotspot second hotspot

RDX to polymer 2.5 8(1) 2(0)3.5 51(6) 22(3)

polymer to RDX 2.5 2(0) 6(0)3.5 24(2) 52(4)



s for Up = 2.5 km/s), which agrees very well with experimentalpolyurethane Up−Us relationships.34 Thus, the shock impe-dance ratio of RDX/HTPB is determined by the density ratio,which is ∼1.8 for both Up = 2.5 and 3.5 km/s.When the planar shock enters this sawtooth interface (i-LH

region), the impedance mismatch from low to high across theboundary of the confined region produces reflected wavesleading to Mach discs where both pressure and temperature areelevated.35,36 As these shock waves encounter the interface inthe f-LH region, the temperature increases due to the localshear, leading to hotspot formation. This initial temperatureincrease at the f-LH, coupled with the pressure increase,continues as time evolves, resulting in significantly enhancedmolecule decomposition compared to that at region i-LH at thesame time.Figure 5 displays the two-dimensional particle velocity (along

the shock direction, Vx) distribution as shock propagates in theconfined region with Up = 3.5 km/s. Figure 5a shows that theshock enters the confined region and the first hotspot forms at1.5 ps. The particle velocity becomes zero after the planarshock pass through. Later, the impedance mismatch causes theinterfacial reflection and lead to the reflected waves shown inFigure 5b. Subsequently, the reflections along interface aremore obvious at 3.15 ps and a new “center shock” forms behindthe planar shock along the axis passing through the f-LHhotspot. This “center shock” grows progressively until it finallyfills the channel cross-section at 3.45 ps, leading to the muchincreased temperature and pressure.III-2. Polymer Binder Density Effects on Hotspot

Formation as Shock Propagates from Polymer to RDX.Our earlier study showed that binder density affects the hotspotformation.25 To simulate this effect we reduced the polymerbinder density to half the density of HTPB (from 0.95 to 0.48g/cm3) by scaling the atomic masses. We also simulated the

case in which the polymer density was almost doubled to matchthe density of RDX (1.71 g/cm3). When Up = 2.5 km/s, thischange in the density changes the shock impedance of theHTPB from 6.08 × 106 Rayl (0.95 g/cm3) to 3.07 × 106 Rayl(0.48 g/cm3) and to 10.94 × 106 Rayl (1.71 g/cm3) comparedto a shock impedance of 11.12 × 106 Rayl for RDX.We examined the temperature changes inside a small

segment containing a hotspot, defined as 2 nm in the sawtoothdirection (y) by 1 nm in the shock direction (x). For the case ofUp = 3.5 km/s, Figure 6 shows the position time−temperaturediagrams up to 4.0 ps as the shock wave passes through thehotspot region. Compared to the case with normal binderdensity (0.95 g/cm3), the hotspot temperature increasesdramatically from 1780 to 3070 K at the first hotspot, andfrom 2540 to 2760 K at the second hotspot for the high densitybinder (1.71 g/cm3).For the half density case (0.48 g/cm3), the temperature of

first hotspot decreases from 1780 to 1700 K, while the secondhotspot decreases much more, from 2540 to 1690 K. Thus, forthe low density binder, the second hotspot has a temperaturesimilar to the first one. The reason is that a big shockimpedance mismatch increases the shock convergence effects,but the initially generated shock strength from the impact isdecreased due to the low densities. The trade-off between thesetwo effects leads to similar temperatures in both hotspots.The reason for the small temperature decrease at the first

hotspot is that there are two opposing effects: the lower densityleads to a less compressed polymer (P = ρ × Up × Us) that atthe asperity would normally lead to a temperature increasebecause of lower shear resistance. However, the lower densityalso leads to lower input shock energy (E = 1/2 × m × v2),which leads to a lower temperature in the polymer as shockapproaches asperity. This tends to decrease the temperature at

Figure 5. Distribution of particle velocities along shock direction (Vx) at various times for Up = 3.5 km/s as shock passes through low densitypolymer binder to high density RDX. (a) Planar shock enters the confined region; (b) the interfacial reflective waves from the impedance mismatch;(c) a new “center shock” forms behind the planar shock, and (d) planar shock passes through the f-LH and the “center shock” fills in the asperity,leading to much high temperature.



the asperity. The net effect is a small temperature decrease atthe first asperity.The chemical reactions also change as the binder density is

modified. Figure 7 shows the NO2 distribution of variouspolymer densities for Up = 3.5 km/s after shock passes throughthe second hotspot. Compared with the normal densitypolymer binder, the number of NO2 dramatically increases bya factor of 3 for the high density polymer, leading to thepronounced hotspots. In contrast, we find only one-fourth asmany chemical reactions in the low density polymer, decreasinghotspot formation.In contrast, our previous study25 shows that the hotspot

temperature dramatically decreased from 2530 to ∼1800 K asthe shock propagates from RDX to lower-density (0.48 g/cm3)polymer. This temperature decrease is similar to that at thesecond hotspot as shock propagates from lower-densitypolymer to RDX, indicating this half density polymer decreasesthe hotspot for both shock directions.III-3. Interface Modified PBX (IM-PBX) Material and Its

Effects on Hotspot Formation. The above results and our

previous study25 indicate that a binder with lower densityshould decrease hotspot formation, leading to a less sensitiveEM for propulsion and explosives applications. Of coursemodifying the entire polymer component of the PBX wouldrequire finding a dramatically different polymer that might leadto other problems with synthesis and stability. Instead wepropose here that a practical way to synthesize the less sensitivePBX is to coat the EM with a lower density polymer beforeintegration into the polymer binder matrix. To test this newstrategy, we modified out system by setting the density of a 3nm coating of polymer to 0.48 g/cm3. Then we examined theshock propagation with Up = 3.5 km/s from two oppositedirections.For the case in which the shock propagates from the low

density polymer to the high density EM, Figure 8a,b shows theposition time−temperature diagrams for i-LH and f-LHhotspots. For comparison, we also display the results for thenormal PBXs without coating in Figure 8c,d. For the i-LHhotspot, we see that the coating suppresses hotspot formation,decreasing the hotspot temperature from 1780 to 1340 K (30%

Figure 6. Position time−temperature diagrams for the Up = 3.5 km/s shock for three different binder density. Here we consider thin slicescontaining the first i-LH (a, c, e) and second f-LH (b, d, f) hotspots in Figure 2. Note that e and f have a much increased temperature legend than a−d. (a, b) Temperature increases of 1480 K (i-LH) and 2240 K (f-LH). (c, d) Low density polymer dramatically decreases this temperature increase to1400 K (i-LH) and 1390 K (f-LH), with a particularly large effect on f-LH. (e, f) Increased polymer density leads to dramatically larger increases inthe hotspot temperatures, 2770 K (i-LH) and 2360 (f-LH) with a particularly large effect at the iLH.



decrease in the temperature increase). For the f-LH hotspot,the hotspot temperature decreases from 2500 to 1870 K (29%decrease in the temperature increase). Thus, the coating effectsare similar for hotspots induced in the polymer to RDX shockat both asperities. This is because of the attenuation effects asthe shock passes the interface of different density polymers forshock propagation from low density polymer to high densityEM.We observe that coating a low density thin film (3 nm)

between RDX and polymer can dramatically decrease this firsthotspot from polymer to RDX from 1780 to 1340 K (Figure 8),while the thick half density polymer decreased it only to 1700K. Two effects are responsible. First, the low density polymercoating attenuates the strength of shock wave. Then, becausethe coating is only 3 nm, the shear effect will be lesspronounced compared to the whole low density polymer. Thisleads to the dramatically temperature decrease observed for thecoating.For the case in which the shock propagates from high density

RDX to low density polymer, Figure 9a shows the positiontime−temperature diagrams for the first (i-HL) hotspot. We

also include the normal cases without coatings in Figure 9b forcomparison. The hotspot temperature decreases from 2530 to2320 K (8.7%) for the coated material compared to ∼1800 Kfor the case in which the whole polymer is half density. Thus,the coating effect is much less significant for the shockpropagation from RDX to polymer. As the shock passes theinterface from RDX to polymer, the low-density (0.48 g/cm3)polymer matrix leads to a rarefaction wave.25 This relaxes thehotspot, decreasing it dramatically. For the coated material, thisrarefaction wave encounters the normal density polymer veryquickly after shock passes the asperity region. This causes ashock wave reflection at the low density-high density polymerinterface leading to shear along the RDX−polymer interface,resulting in a less pronounced decrease in the hotspot.Our previous study25 in which the whole polymer (∼20 nm

along shock direction) density is decreased to its half densityshowed that the hotspot is eliminated. This indicates that thesuppression effect of hot-spot formation depends on thecoating thickness. Thus, we recommend that a 20 nm thickreduced density polymer could be used, which shouldcompletely suppress hot spot formation for the RDX → Polyshock.We showed above, that if the whole polymer of thickness

(∼20 nm) is decreased to half value, the hotspot temperaturedecreases to ∼1700 K for Poly → RDX. Thus, we expect thatan IM-PBX model using a coating of ∼20 nm woulddramatically suppress the hotspot formation.As an example, we could use polymer cross-linked aerogels as

the coating material, which have a density below 0.5 g/cm.37

A cautionary note about the estimate of the temperatureincreases should be mentioned here. Sewell and co-work-ers38−40 pointed out that, for weak shocks (<1 km/sec), thepredicted temperature increase from classical MD is signifi-cantly underestimated. This is because the calculated RDX Cvfrom classical MD is a factor of ∼2.2 larger than the valueestimated from experiments.39 Our studies consider consid-erably stronger shocks, with significant local distortions, whichwe expect would lead to a smaller underestimate of thetemperature increase.

IV. SUMMARYSummarizing, we used reactive molecular dynamics to examinethe mechanical, chemical, and thermal response of mechanicallyshocked polymer-bonded explosives (PBXs) using a realisticmodel of a nonplanar (sawtooth) interface with 1.6 millionindependent atoms. We observe that hotspots develop at boththe front and back asperity regions as the shock wavepropagates from the low-density polymer to the high-densityEM. We find that the second hotspot (f-LH) leads to a muchhigher temperature than the first (i-LH) one, with dramaticallyincreased decomposition of the EM. These results contrast withthe case for propagation from the high density EM to the lowdensity polymer where only the i-HL hot spot is observed.Here there is no f-HL temperature spike because there is noconverging shock.Based on these results we consider that the source for the

hotspot formation of energetic materials (that otherwise haveno defects) arises equally from two effects. As the shockpropagates from RDX to polymer across an asperity, the hotspot arises from tangential shear along the interface due todifferential relations, as discussed previously.25 However, as theshock propagates from polymer to RDX, the major source ofthe hotspot arises from shock convergence as the shock

Figure 7. Distribution of NO2 fragments for various polymer densitiesas shock propagates from low density polymer to high density RDXunder Up = 3.5 km/s: (a) low density polymer; (b) normal densitypolymer; and (c) high density polymer.



proceeds from polymer to EM, which leads to a largetemperature increase that persists long after the shock fronthas passed the interface. This second hotspot is also at theasperity in which RDX penetrates the polymer. It strongly

coupled to increased chemical reactions (NO2 dissociation,followed by NO3 formation) that ultimately lead to detonation.We show that using a much lower density polymer

dramatically decreases the effects for both mechanisms ofhotspot formation, while using a much high density polymerbinder dramatically increases hotspot formation. This effectarises from the change in shock impedance, which decreases byapproximately 51% for low density compared to an increase byapproximately 80% for high density for the Up = 3.5 km/s case.However, the nonplanar interface will still lead to shockconvergence effects if the polymer impedance is lower than thatof the EM.Since PBXs are fabricated by mixing the EMs with the binder

matrix, enormous interfaces having such impedance mis-matches exist in a realistic PBX. Our results suggest thatshock convergence is a general hotspot formation mechanismin EMs and a critical design strategy in developing insensitiveEMs for propellants and explosives is to develop a low densitybinder (1/3 that of the explosive). This suggests that coating alow density polymer to wet the EM (or adding surfactants toaccomplish this decrease in interfacial energy) could dramat-ically decrease the sensitivity of PBX systems. We validated thisconcept by simulating the shock propagation along twoopposite directions (RDX → Poly and Poly → RDX) in thelow density polymer coating PBX models. Indeed, we find forthe 3.5 km/s case that the hot spot temperature increase isdecreased by ∼30%% as shock propagates from Poly to RDXand by 8.7% as shock propagates from RDX to Poly. To gainthe maximum effect we recommend that the low densitycoating could be ∼20 nm.

Figure 8. Position time−temperature diagrams for coated and normal PBX models as shock propagates from low density polymer to high densityRDX under Up = 3.5 km/s: (a) coated PBX model, the i-LH hotspot; (b) coated PBX model, the f-LH hotspot; (c) mormal PBX model, the i-LHhotspot; and (d) normal PBX model, the f-LH hotspot.

Figure 9. Position time−temperature diagrams for coated and normalPBX models as shock propagates from high density RDX to lowdensity polymer under Up = 3.5 km/s: (a) coated PBX model; (b)normal PBX model.



■ ASSOCIATED CONTENT

*S Supporting InformationText gives the full set of ReaxFF parameters used in thesecalculations. It also provides a table listing the bond-ordercutoffs used for bond fragment analyses. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*To whom correspondence should be addressed. E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

All computations were carried out on the Army HPC systems;we thank Betsy Rice and Larry Davis for assistance. Personnelwere supported mostly by ONR (N00014-09-1-0634), withsome assistance from ARO (W911NF-05-1-0345 andW911NF-08-1-0124). W.A.G. also received support from thePSAAP project at Caltech (DE-FC52-08NA28613).

■ REFERENCES(1) Ball, P. Material Witness: Shock Relief. Nat. Mater. 2012, 11, 747.(2) Holian, B. L.; Lomdahl, P. S. Plasticity Induced by Shock Wavesin Nonequilibrium Molecular Dynamics Simulations. Science 1998,280, 2085−2088.(3) Germann, T. C.; Holian, B. L.; Lomdahl, P. S.; Ravelo, R.Orientation Dependence in Molecular Dynamics Simulations ofShocked Single Crystals. Phys. Rev. Lett. 2000, 84, 5351−5354.(4) Strachan, A.; van Duin, A. C. T.; Chakraborty, D.; Dasgupta, S.;Goddard, W. A., III Shock Waves in High-Energy Materials: TheInitial Chemical Events in Nitramine RDX. Phys. Rev. Lett. 2003, 91,098301.(5) An, Q.; Luo, S. N.; Han, L. B.; Zheng, L. Q.; Tschauner, O.Melting of Cu under Hydrostatic and Shock Wave Loading to HighPressures. J. Phys: Condens. Matter 2008, 20, 095220.(6) Dick, J. J. Effect of Crystal Orientation on Shock InitiationSensitivity of Pentaerythritol Tetranitrate Explosive. Appl. Phys. Lett.1984, 44, 859−862.(7) Dick, J. J.; Ritchie, J. P. Molecular Mechanics Modeling of Shearand the Crystal Orientation Dependence of the Elastic PrecursorShock Strength in Pentaerythritol Tetranitrate. J. Appl. Phys. 1994, 76,2726−2737.(8) Yoo, C. S.; Holmes, N. C.; Souers, P. C.; Wu, C. J.; Ree, F. H.;Dick, J. J. Anisotropic Shock Sensitivity and Detonation Temperatureof Pentaerythritol Tetranitrate Single Crystal. J. Appl. Phys. 2000, 88,70−75.(9) Zybin, S. V.; Goddard, W. A., III; Xu, P.; van Duin, A. C. T.;Thompson, A. P. Physical Mechanism of Anisotropic Sensitivity inPentaerythritol Tetranitrate from Compressive-shear Reaction Dy-namics Simulations. Appl. Phys. Lett. 2010, 96, 081918.(10) An, Q.; Liu, Y.; Zybin, S. V.; Kim, H.; Goddard, W. A., IIIAnisotropic Shock Sensitivity of Cyclotrimethylene Trinitramine(RDX) from Compress-and-Shear Reactive Dynamics. J. Phys. Chem.C 2012, 116, 10198−10206.(11) Dear, J. P.; Field, J. E.; Walton, A. J. Gas Compression and JetFormation in Cavities Collapsed by a Shock Wave. Nature (London)1988, 332, 505−508.(12) Cheret, R. Detonation of Condensed Explosives; Springer-Verlag:New York, 1993.(13) Bowden, F. P.; Yoffe, A. D. Initiation and Growth of Explosions inLiquids and Solids; Cambridge University Press: Cambridge, England,1952.

(14) Maffre, P.; Peyrard, M. Molecular-Dynamics Investigations ofShock-Induced Detonations in Inhomogeneous Energetic Crystals.Phys. Rev. B 1992, 45, 9551−9561.(15) Field, J. E. Hot Spot Ignition Mechanisms for Explosives. Acc.Chem. Res. 1992, 25, 489−496.(16) Field, J. E.; Bourne, N. K.; Palmer, S. J. P.; Walley, S. M.;Sharma, J.; Beard, B. C. Hot-Spot Ignition Mechanisms for Explosivesand Propellants. Philos. Trans. R. Soc., A 1992, 339, 269−283.(17) Tarver, C. M. Corner Turning and Shock DesensitizationExperiments plus Numerical Modeling of Detonation Waves in theTriaminotrinitrobenzene Based Explosive LX-17. J. Phys. Chem. A2010, 114, 2727−2736.(18) Tarver, C. M.; Chidester, S. K.; Nichols, A. L., III CriticalConditions for Impact- and Shock-Induced Hot Spots in SolidExplosives. J. Phys. Chem. 1996, 100, 5794−5799.(19) Holian, B. L.; Germann, T. C.; Maillet, J. B.; White, C. T.Atomistic Mechanism for Hot Spot Initiation. Phys. Rev. Lett. 2002, 89,285501.(20) Mintmire, J. W.; Robertson, D. H.; White, C. T. Molecular-dynamics Simulations of Void Collapse in Shocked Model-MolecularSolids. Phys. Rev. B 1994, 49, 14859−14864.(21) Nomura, K.; Kalia, R. K.; Nakano, A.; Vashishta, P. ReactiveNanojets: Nanostructure-Enhanced Chemical Reactions in a DefectedEnergetic Crystal. Appl. Phys. Lett. 2007, 91, 183109.(22) Hatano, T. Spatiotemporal Behavior of Void Collapse inShocked Solids. Phys. Rev. Lett. 2004, 92, 015503.(23) Lecume, S.; Lefrancois, A.; Chabin, P. Structural and ChemicalChanges in PBX Induced by Rapid Shear Followed by Compression.12th Detonation Symposium, San Diego, California 92101, August 11−16th, 2002.(24) Skidmore, C. B.; Phillips, D. S.; Asay, B. W.; Idar, D. J.; Howe,P. M.; Bolme, D. S. Microstructural Effects in PBX 9501 Damaged byShear Impact. AIP Conf. Proc. 2000, 505, 659−662.(25) An, Q.; Zybin, S. V.; Goddard, W. A., III; Jaramillo-Botero, A.;Blanco, M.; Luo, S. N. Elucidation of the Dynamics for Hot-SpotInitiation at Nonuniform Interfaces of Highly Shocked Materials. Rhys.Rev. B 2011, 84, 220101.(26) An, Q.; Goddard, W. A., III; Zybin, S. V.; Jaramillo-Botero, A.;Zhou, T. T. Highly Shocked Polymer Bonded Explosives at aNonplanar Interface: Hot-Spot Formation Leading to Detonation. J.Phys. Chem. C 2013, 117, 26551−26561.(27) Sikder, A. K.; Sikder, N. A Review of Advanced HighPerformance, Insensitive and Thermally Stable Energetic MaterialsEmerging for Military and Space Applications. J. Hazard. Mater. 2004,112, 1−15.(28) Van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A., IIIReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A2001, 105, 9396−9409.(29) Jaramillo-Botero, A.; An, Q.; Cheng, M. J.; Goddard, W. A., III;Beegle, L. W.; Hodyss, R. Hypervelocity Impact Effect of Moleculesfrom Enceladus’ Plume and Titan’s Upper Atmosphere on NASA’sCassini Spectrometer from Reactive Dynamics Simulation. Phys. Rev.Lett. 2012, 109, 213201.(30) Nomura, K. I.; Kalia, R. K.; Nakano, A.; Vashishta, P.; van Duin,A. C. T.; Goddard, W. A., III Dynamic Transition in the Structure ofan Energetic Crystal during Chemical Reactions at Shock Front Priorto Detonation. Phys. Rev. Lett. 2007, 99, 148303.(31) Strachan, A.; Kober, E. M.; van Duin, A. C. T.; Oxgaard, J.;Goddard, W. A., III Thermal Decomposition of RDX from ReactiveMolecular Dynamics. J. Chem. Phys. 2005, 122, 054502.(32) Mattsson, T. R.; Lane, J. M. D.; Cochrane, K. R.; Desjarlais, M.P.; Thompson, A. P.; Pierce, F.; Grest, G. S. First-Principles andClassical Molecular Dynamics Simulation of Shocked Polymers. Phys.Rev. B 2010, 81, 054103.(33) Plimpton, S. Fast Parallel Algorithms for Short-Range MolecularDynamics. J. Comput. Phys. 1995, 117, 1−19.(34) van Thiel, M. V.; Shaner, J.; Salinas, E. Compendium of ShockWave Data; Lawrence Livermore National Lab: Berkeley, CA, 1977;Vol. 3, p 603.



http://pubs.acs.org

mailto:[email protected]

mailto:[email protected]

(35) Setchell, R. E.; Storm, E.; Sturtevant, B. An Investigation ofShock Strengthening in a Conical Convergent Channel. J. Fluid Mech.1972, 56, 505−522.(36) Brown, J. L.; Ravichandran, G. Shock Waves in ConvergingGeometries. AIP Conf. Proc. 2009, 1195, 747−750.(37) Katti, A.; Shimpi, N.; Roy, S.; Lu, H.-B.; Fabrizio, E.; Dass, A.;Capadona, L.; Leventis, N. Chemical, Physical, and MechanicalCharacterization of Isocyanate Cross-linked Amine-Modified SilicaAerogels. Chem. Mater. 2006, 18, 285−296.(38) Cawkwell, M. J.; Sewell, T. D.; Zheng, L. Q.; Thompson, D. L.Shock-Induced Shear Bands in an Energetic Molecular Crystal:Application of Shock-Front Absorbing Boundary Conditions toMolecular Dynamics Simulations. Phys. Rev. B 2008, 78, 014107.(39) Bedrov, D.; Hooper, J. B.; Smith, G. D.; Sewell, T. D. Shock-Induced Transformations in Crystalline RDX: A Uniaxial Constant-stress Hugoniostat Molecular Dynamics Simulation Study. J. Chem.Phys. 2009, 131, 034712.(40) Cawkwell, M. J.; Ramos, K. J.; Hooks, D. E.; Sewell, T. D.Homogeneous Dislocation Nucleation in Cyclotrimethylene Trinitr-amine under Shock Loading. J. Appl. Phys. 2010, 107, 063512.



Documents

Inhibition of Hotspot Formation in Polymer Bonded ... · Inhibition of Hotspot Formation in Polymer Bonded Explosives Using an Interface Matching Low Density ... sensitive for propellants