Inhibition of Hotspot Formation in Polymer Bonded Explosives Using

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Inhibition of Hotspot Formation in Polymer Bonded Explosives Using an Interface Matching Low Density Polymer Coating at the Polymer-Explosive Interface Qi An, William A. Goddard III, Sergey V. Zybin, and Sheng-Nian Luo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp506501r • Publication Date (Web): 08 Aug 2014 Downloaded from http://pubs.acs.org on August 18, 2014

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The Journal of Physical Chemistry

Submitted to J. of Phys. Chem. C Inhibition of Hotspot Formation in Polymer Bonded Explosives Using an Interface Matching Low Density Polymer Coating at the Polymer-explosive Interface Qi An,1 William A. Goddard III,1* Sergey V Zybin,1 and Sheng-Nian Luo2 1

Materials and Process Simulation Center, California Institute of Technology, Pasadena, California 91125, USA

2

The Peac Institute of Multiscale Sciences, Chengdu, Sichuan 610207, People’s Republic of China *

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

Abstract: In order to elucidate how shocks in heterogeneous materials affect decomposition and reactive processes, we used the ReaxFF reactive force field in reactive molecules dynamics (RMD) simulations of the effects of strong shocks (2.5 km/s and 3.5 km/s) on a prototype polymer bonded explosive (PBX) consisting of cyclotrimethylene trinitramine (RDX) bonded to hydroxyl-terminated polybutadiene (HTPB). We showed earlier that shock propagation from the high density RDX to the low density polymer (RDXPoly) across a nonplanar periodic interface (sawtooth) leads to a hotspot at the initial asperity but no additional hotspot at the second asperity. This hotspot arises from shear along the interface induced by relaxation of the stress at the asperity. We now report the case for shock propagation from the low density polymer to the high density RDX (PolyRDX) where we find a hotspot at the initial asperity and a second more dramatic hotspot at the second asperity. This second hotspot is enhanced due to shock wave convergence from shock wave interaction with non-planar interfaces. We consider that this 2nd hotspot is likely the source of the detonation in realistic PBX systems. We showed how these hotspots depend on the density mismatch between the RDX and polymer and found that decreasing the density by a factor of two dramatically reduces the hotspot. These results suggest that to make PBX less sensitive for propellants and explosives, the binder should be designed to provide low density at the asperity in contact with the RDX. Based on these simulations, we propose a new design for an insensitive PBX in which a low density polymer coating is deposited between the RDX and the usual polymer binder. To test this idea, we simulated shock wave propagation from two opposite directions (RDXPoly and PolyRDX) through the interface matched PBX (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.

Keywords: Energetic Material, PBX, Shock Wave, ReaxFF

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I. Introduction It is well known that shocks can transform the structures of materials, while introducing defects, dislocations, melting, and chemical reactions.1−5 Understanding the interactions of shock waves with materials is essential in many physical and engineering processes, such as inertial confinement fusion (ICF), Richtmyer-Meshkov instabilities (RMIs), supernova explosion, earthquakes, cavitation, and spallation. In particular for the energetic materials (EMs) used in rocket propellants and explosives, it is of interest to understand how the shock triggers massive energy release (detonation) of these high energy materials. Here to prevent accidental detonation in engineering applications, explosive powders are normally bonded into a polymer matrix to form polymer bonded explosives (PBXs). The detonation sensitivity of EMs plays essential roles in the safety storage and transportation, but the origin of detonation initiation remains controversial despite numerous experimental and theoretical studies.6−10 This is due to the heterogeneous structures (defects, voids, grain boundaries, interfaces, etc.) and the complex coupling of thermal, mechanical and chemical factors. It is generally accepted that a critical issue is the formation of a hotspot whose high temperature accelerates the reactive energy releasing events that play a critical role in detonation.11−14 However, the mechanism of hotspot formation remains controversial, with multiple mechanisms proposed.15,16 An important observation17 is that a weak shock compression can desensitize the material so that it is much less sensitive to a strong shock or detonation wave. This has led to the speculation that the origin of hotspot is due to voids that can be annealed by the initial weak shock.17,18 Indeed, atomistic simulations on molecular crystals and atomic crystals containing voids confirmed that they lead to hotspot formation due either to void collapse or nano-jets.19−22 It had also been observed that delamination and partial decomposition 2 ACS Paragon Plus Environment

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occur at micro-grains boundaries or wedges between embedded EMs and the polymer, but not at the interior of the crystals under the shear-impact experiments with weak shocks.23,24 This indicates that the interface between the EM and polymer also plays an important role in the hotspot formation. In a previous study,25 we considered a realistic model of PBX N-106 involving 3.7 million atoms per periodic cell with a non-planar (sawtooth) interface between the RDX EM (Fig. 1(a)) and the HTPB (Fig. 1(b)) based polymer binder. Using the ReaxFF in RMD we found that a system without defects or voids leads to hotspot formation as the shock passing through the RDX encounters the initial asperity of the polymer interface. We found that at this contact asperity with the nonplanar interface, relaxation of the longitudinal stress from the high density RDX to the low density polymer at the tip causes shear localization that heats the RDX locally, leading to decomposition and energy release at the asperity of the heterogeneous material interface.25 Similarly, we recently reported similar studies of shock-induced hotspot formation at 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 to simulate the progress toward detonation initiation. Here we report simulations on a similar realistic model of PBX N-106 to examine shock wave propagation across the nonplanar interface from the low density polymer to the high density RDX. We find again that a modest hotspot forms at the front asperity of the sawtooth as shock wave passes from the polymer to the RDX asperity, due to the shear localization. However, in this case we find that continuous propagation of the shock wave leads to a much hotter hotspot as the shock encounters the polymer asperity at the RDX contact on the back side of the sawtooth. This second hotspot is due to shock wave convergence arising from the shock 3 ACS Paragon Plus Environment


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wave in the low density polymer interacting with the non-planar interface to the high density RDX. Indeed we consider that this second hot spot is likely the source of the detonation in realistic PBX systems. In order to meet the requirements of future space and military applications, it is essential to develop new EMs with better performance while enhancing the insensitivity to thermal or shock response than the existing ones.27 In our previous study,25 we demonstrated that decreasing the polymer density by a factor of two (to 1/3 that of the RDX) essentially eliminates the hotspot formation at the front asperity for the RDXPoly shock direction, while increasing the density of the polymer to match that of the RDX dramatically increases the hotspot temperature. Our current study finds that the strength of the second hotspot depends critically on both the shock impedance and the density. Based on these results, we propose that a practical approach to make EMs less sensitive for propellants and explosives would be to design the binder to provide a low density at the interface while retaining the normal polymer properties within the bulk polymer. To test this idea, we carried out ReaxFF based reactive dynamics simulations for shock propagation through the new interface matched-PBX (IM-PBX) material to show that coating a low density polymer between the normal polymer binder and the energetic material dramatically reduces sensitivity. II. RMD Simulation Design and Methods II-1 ReaxFF Reactive Force Field Method. ReaxFF has been developed to simulate complex chemical reactions over long time scales (pico to nano seconds) for large systems (millions of atoms) while retaining the accuracy of quantum mechanics (QM). ReaxFF uses a general bond-order−bond-distance relation and geometry-dependent charge adjustment method to describe the bond breaking and bond formation accurately and smoothly. The ReaxFF 4 ACS Paragon Plus Environment

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parameters are determined from fitting to numerous QM calculations of reaction barriers and rates.28 The original ReaxFF accounts for the van der Waals interaction by using a Morse type of potential form which we later found is too soft for the extremely small distance interactions found during high velocity shocks. Thus, the new version of ReaxFF used here includes a 2-body inner wall parameter29 needed to describe accurately the inner wall for the close contacts found in shock simulations for energetic materials. The new ReaxFF also includes a long range London dispersion correction scaling like –C6/R6 but damped with the low-gradient dispersion correction term so that valence forces are not affected. However, to be consistent with our previous study of PBX with nonplanar interfaces,25 we did not include this vdW correction in the current study. The parameters for this ReaxFF are included in the supporting information (SI), which we found gives a good description of the mechanical properties and chemical reactions in various explosives and polymers.10, 25, 26, 29−32 Our MD simulations used the ReaxFF engine incorporated into the large-scale atomic/molecular massively parallel simulator (LAMMPS).33 II-2 Atomic PBX Model. The PBX model in this study is similar to our previous study.25 The polymer binder matrix consists of hydrogen terminated polybutadiene (HTPB) and isophorone diisocyanate (IPDI)-based polyurenthane rubber using a dioctyl adipate (DOA) molecule plasticizer (Fig.1). This composition optimizes the casting properties of the polymer binder. The details of preparing the RDX and polymer binder can be found in ref.25. We formed the periodic sawtooth triangular interface [Fig. 2(a)] by carving out of an RDX cell the sawtooth shape, based on the molecular center of mass to form (110) and (1-10) surfaces as previously discussed in ref. 25 and 26. The periodic dimensions of the polymer were deformed to match the cross-section of the RDX (100) surface. Then a complementary surface to RDX was built into the HTPB by eliminating each polymer chain having its center of mass 5 ACS Paragon Plus Environment


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outside the intended region and keeping the others intact. This led to some chains extending outside the intended region for the polymer. Then we brought the EM and polymer piece together to a point expected to have 2% compression of polymer. We relaxed the system with minimization first and followed by a 10 ps dynamics using isothermal-isochoric (NVT) ensemble at room temperature to form a smooth interface. The periodic cell contains 1,606,106 atoms (625,191 atoms of RDX and 980,915 atoms of HTPB-based binder) with cell dimensions of 26.5 nm (in the shock direction) × 27.1 nm (sawtooth direction) × 25.4 nm (into the 3rd periodic direction). To examine how the polymer densities affect the hotspot formation, we decreased the binder density to half the original value of 0.95 g/cm3 by scaling the atomic mass. We also examined the case of high density binder by increasing its density to 1.71 g/cm3 which is approximately the same as RDX. To incorporate the low density polymer coating into this PBX model, we chose a 3 nm thin layer of the HTPB polymer in contact with the RDX (based on molecular center of mass) and changed its density to 0.48 g/cm3 (50% of the normal density) by scaling the atomic mass and leave the other part intact. We used the same procedure to coat a 3 nm low density polymer to the previous PBX model in ref. 25. The coating PBX models are shown in figure 2(b) and figure 2(c). II-3 Shock Simulations and Analysis. Shock waves were generated 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 the desired particle velocity to the thermal velocities (300K) for all atoms in the slab. Periodic boundary conditions were not applied along the shock direction (x-axis). We simulated the shock propagation using the microcanonical (NVE) ensemble. We used a timestep of 0.1 fs in ReaxFF simulations integrating the equations of 6 ACS Paragon Plus Environment

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motion with the Verlet algorithm. The particle velocities are Up = 2.5 km/s, 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. We partitioned the simulation cell into fine bins (~1 nm) along the x direction (1D binning analysis) or along the x−y plane (2D binning analysis). We averaged along the z-axis ([001] direction) for the 2D analysis. The center of mass velocity was removed to calculate the temperature and stress in each bin. The stress for each bin was the averaged virial stress plus thermal contributions. For chemical reactions, we did the fragment analysis based on the bond order cutoffs described in the supporting information. Here we chose large values of bond order cutoffs (with different values for each element, see table S1 of the supporting information) than normally used (0.3)28 so that the normal vibrations of hot molecules would not exhibit oscillations in fragments sizes for the high temperatures and high pressures. III Results and Discussions III-1 Hotspot Formation as Shock Propagate from Polymer to RDX III-1a Temperature. Figures 3(a),(b) show the temperature profiles for shock wave propagation along the x-direction from low density polymer (0.95 g/cm3) to high density RDX (1.71 g/cm3) with an impact velocity Up = 3.5 km/s. We find that a hotspot with a temperature increase of 1480 K (leading to 1780 K) forms as the shock wave encounters the first angular tip in Fig. 3 (a) (this point is denoted as i-LH for initial asperity and low to high impedance). The mechanism for this first hotspot formation is shear localization as we found in earlier simulations that examined propagation of the shock from the dense RDX to the low density polymer,25 but 7 ACS Paragon Plus Environment


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the hotspot temperature of ~1780 K is 750 K lower than the hotspot found in the previous simulations.25 Now however, we find a new phenomenon arising as the shock wave continues propagating in the converging width within the interface triangle of the low impedance polymer embedded in the higher impedance RDX. Here a much hotter hotspot with a temperature of 2540 K forms as the shock wave approaches the 2nd apex, which is denoted as f-LH (to indicate the final asperity for low impendence to high impedance shock direction). This second hotspot was not observed when shock waves pass through from RDX to polymer binder,25 because the conditions for converging shocks were absent. Table 1 shows the temperature of the two asperity regions as shock passes through from two opposite directions. For the 3.5 km/s shock from polymer to RDX, the temperature of the 2nd hotspot (2540 K) is similar to the 1st hotspot at the asperity from RDX to polymer (2530 K) but much higher than the 1st hotspot (1780 K). This temperature increase for the second hotspot is ~750 K greater than the temperature increase for the first hotspot. Thus, for both directions of propagation the hot spot is at the asperity of RDX penetrating into the polymer. Hence we consider that the shock convergence mechanism likely plays a critical role in strong shock 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 hotspot of 1220 K and the 2nd asperity to 1310 K or an increase in the hot temperature of 90 K. The temperature profiles for Up = 2.5 km/s are shown in figure 3(c) and (d). III-1b Chemistry. Figure 4(a) shows the evolution of number of NO2 and NO3 fragments as the shock wave propagates in PBX for Up = 2.5 km/s. Only two NO2 fragments dissociate from RDX molecules in the 1 nm × 1 nm bin of the first hotspot region within 0.5 ps after it forms, but 8 ACS Paragon Plus Environment

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6 (~3 times as many) NO2 fragments appear within 0.5 ps at the second hotspot region (f-LH) where shock convergence occurs. For Up = 3.5 km/s, the number of NO2 fragments in the f-LH (52) is ~2.2 times as many as in the i-LH (24). Table 2 summarizes the numbers of NO2 in a 1 nm × 1nm bin of two asperity regions after 0.5 ps as shock passes through from two opposite directions. The number of NO2 of the 2nd hotspot from polymer to RDX is similar to the 1st hotspot (the same asperity region) from RDX to polymer and much more than the other asperity region. For Up = 2.5 km/s, the shock reaches the 1st asperity at 1.7 ps and the 2nd asperity at 4.1 ps. Figure 4(b),(c) show the NO2 spatial distributions at 4.4 ps and 4.8 ps, respectively. In the first hotspot region (i-LH), the NO2 fragment number increases slowly (from 0 to 6 within 0.7 ps in the whole hotspot region). As the second hotspot (f-LH) initiates, 5 NO2 fragments appear in the hotspot region (defined in terms of three 1 nm × 1 nm bins) at 4.4 ps with the number increasing abruptly to 13 at 4.8 ps. This indicates that dramatically increased chemical reactions occur in the second hotspot region due to the shock convergence effects. At this 2nd hotspot we also observed formation of NO3 after ~1 ps of NO2 dissociation. To examine the formation mechanism of NO2 and NO3 during shock wave propagation, we selected two RDX molecules and traced the trajectories as the NO2 breaks off of one RDX and reacts with a second one to form NO3. The snapshots are shown in Figure 4(d). As the shock wave passes, the upper RDX molecule is compressed and rotated (2.55 to 3.00 ps), leading to NO2 dissociation (3.00 to 3.45 ps). Then from 3.45 ps to 3.55 ps this NO2 molecule extracts an oxygen atom from the NO2 group of the other RDX to form NO3, leaving behind a two RDX radical fragments that subsequently react.



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III-1c Shock Convergence Effects. The shock impedance, Z = ρ × v (where ρ is the density and v is the velocity) is of fundamental importance, leading to wave refraction when shock wave propagation encounters a change in Z. The angle of the interface with respect to shock direction determines the shock convergence in the confinement geometry of the impedance mismatched materials. In our RDX/HTPB model, a piston velocity of Up = 3.5 km/s leads to a RDX shock wave velocity of 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 based binder has a similar shock wave velocity as RDX for the highly shocked region, Us = 7.6 km/s for Up = 3.5 km/s (Us = 6.4 km/s for Up = 2.5 km/s), which agrees very well with experimental polyurethane Up−Us relationships.34 Thus the shock impedance ratio of RDX/HTPB is determined by the density ratio which is ~1.8 for both Up = 2.5 km/s and 3.5 km/s. When the planar shock enters this sawtooth interface (i-LH region), the impedance mismatch from low to high across the boundary of the confined region produces reflected waves leading to Mach discs where both pressure and temperature are elevated.35,36 As these shock waves encounter the interface in the f-LH region, the temperature increases due to the local shear, leading to hotspot formation. This initial temperature increase at the f-LH, coupled with the pressure increase continues as time evolves, resulting in significantly enhanced molecule decomposition compared to that at region i-LH at the same time. Figure 5 displays the two dimensional particle velocity (along the shock direction, Vx) distribution as shock propagates in the confined region with Up = 3.5 km/s. Figure 5 (a) shows that the shock enters the confined region and the first hotspot forms at 1.5 ps. The particle velocity becomes zero after the planar shock pass through. Later, the impedance mismatch causes the interfacial reflection and lead to the reflected waves shown in figure 5 (b). 10 ACS Paragon Plus Environment

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Subsequently, the reflections along interface are more obvious at 3.15 ps and a new 'centre shock' forms behind the planar shock along the axis passing through the f-LH hotspot. This 'centre shock' grows progressively until it finally fills the channel cross-section at 3.45 ps, leading to the much increased 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 hotspot formation.25 To simulate this effect we reduced the polymer binder density to half the density of HTPB (from 0.95 to 0.48 g/cm3) by scaling the atomic masses. We also simulated the case in which the polymer density was almost doubled to match the density of RDX (1.71 g/cm3). When Up = 2.5 km/s, this change in the density changes the shock impedance of the HTPB 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) compared to 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 sawtooth direction (y) by 1nm in the shock direction (x). For the case of Up = 3.5 km/s, Figure 6 shows the position-time-temperature diagrams up to 4.0 ps as the shock wave passes through the hotspot region. Compared to the case with normal binder density (0.95 g/cm3), the hotspot temperature increases dramatically from 1780 K to 3070 K at the first hotspot, and from 2540 K to 2760 K at the second hotspot for the high density binder (1.71 g/cm3). For the half density case (0.48 g/cm3), the temperature of first hotspot decreases from 1780 K to 1700 K, while the second hotspot decreases much more, from 2540 K to 1690 K. Thus for the low density binder, the second hotspot has a temperature similar to the first one. The reason is 11 ACS Paragon Plus Environment


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that a big shock impedance mismatch increases the shock convergence effects, but the initially generated shock strength from the impact is decreased due to the low densities. The tradeoff between these two 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 density leads to a less compressed polymer (P = ρ × Up × Us) that at the asperity would normally lead to a temperature increase because of lower shear resistance. However, the lower density also leads to lower input shock energy (E = ½ × m × v2) which leads to a lower temperature in the polymer as shock approaches asperity. This tends to decrease the temperature at the asperity. The net effect is a small temperature decrease at the first asperity. The chemical reactions also change as the binder density is modified. Figure 7 shows the NO2 distribution of various polymer densities for Up = 3.5 km/s after shock passes through the second hotspot. Compared with the normal density polymer binder, the number of NO2 dramatically increases by a factor of 3 for the high density polymer, leading to the pronounced hotspots. In contrast, we find only one fourth as many chemical reactions in the low density polymer, decreasing hotspot formation. In contrast, our previous study25 shows that the hotspot temperature dramatically decreased from 2530 K to ~1800 K as the shock propagates from RDX to lower-density (0.48 g/cm3) polymer. This temperature decrease is similar to that at the 2nd hotspot as shock propagates from lower-density polymer to RDX, indicating this half density polymer decreases the hotspot for both shock directions. III-3 The Interface Modified PBX (IM-PBX) Material and its Effects on Hotspot Formation


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The above results and our previous study25 indicate that a binder with lower density should decrease hotspot formation, leading to a less sensitive EM for propulsion and explosives applications. Of course modifying the entire polymer component of the PBX, would require finding a dramatically different polymer that might lead to other problems with synthesis and stability. Instead we propose here that a practical way to synthesize the less sensitive PBX is to coat the EM with a lower density polymer before integration into the polymer binder matrix. To test this new strategy, we modified out system by setting the density of a 3 nm coating of polymer to 0.48 g/cm3. Then we examined the shock propagation with Up = 3.5 km/s from two opposite directions. For the case in which the shock propagates from the low density polymer to the high density EM, Figure 8(a) and (b) show the temperature-time-position diagrams for i-LH and f-LH hotspots. For comparison, we also display the results for the normal PBXs without coating in Figure 8(c) and (d). For the i-LH hotspot, we see that the coating suppresses hotspot formation, decreasing the hotspot temperature from 1780 K to 1340 K (30% decrease in the temperature increase). For the f-LH hotspot, the hotspot temperature decreases from 2500 K to 1870 K (29% decrease in the temperature increase). Thus the coating effects are similar for hotspots induced in the polymer to RDX shock at both asperities. This is because of the attenuation effects as the shock passes the interface of different density polymers for shock propagation from low density polymer to high density EM. We observe that coating a low density thin film (3 nm) between RDX and polymer can dramatically decrease this first hotspot from polymer to RDX from 1780 K to 1340 K (Figure 8) while the thick half density polymer decreased it only to 1700 K. Two effects are responsible. First the low density polymer coating attenuates the strength of shock wave. Then, because the 13 ACS Paragon Plus Environment


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coating is only 3 nm, the shear effect will be less pronounced compared to the whole low density polymer. This leads to the dramatically temperature decrease observed for the coating. For the case in which the shock propagates from high density RDX to low density polymer, Figure 9(a) shows the temperature-time-position diagrams for the first (i-HL) hotspot. We also include the normal cases without coatings in Figure 9(b) for comparison. The hotspot temperature decreases from 2530 K to 2320 K (8.7%) for the coated material compared to ~1800 K for the case in which the whole polymer is half density. Thus the coating effect is much less significant for the shock propagation from RDX to polymer. As the shock passes the interface from RDX to polymer the low-density (0.48 g/cm3) polymer matrix leads to a rarefaction wave.25 This relaxes the hotspot, decreasing it dramatically. For the coated material, this rarefaction wave encounters the normal density polymer very quickly after shock passes the asperity region. This causes a shock wave reflection at the low density-high density polymer interface 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 density, showed that the hotspot is eliminated. This indicates that the suppression effect of hot-spot formation depends on the coating thickness. Thus we recommend that a 20 nm thick reduced density polymer could be used, which should completely suppress hot spot formation for the RDXPoly shock. We showed above, that if the whole polymer of thickness (~20 nm) is decreased to half value, the hotspot temperature decreases to ~1700 K for PolyRDX. Thus we expect that an IM-PBX model using a coating of ~20 nm would dramatically suppress the hotspot formation.


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As an example, we could use as the coating material polymer cross-linked aerogels which have density below 0.5 g/cm.37 A cautionary note about the estimate of the temperature increases should be mentioned here. Sewell and coworkers38−40 pointed out that for weak shocks (

Inhibition of Hotspot Formation in Polymer Bonded Explosives Using

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