Ultrafast Detonation of Hydrazoic Acid HN3

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week ending, PRL 109 038301 2012 PHYSICAL REVIEW LETTERS 20 JULY 2012. zone of explosives with analytical equations of state shock steady shock solutions at the chosen shock speed The ideal. waves in amorphous Lennard Jones and amorphous detonation velocity of an explosive was shown to be. Tersoff carbon 17 18 Simulations in this work utilized bounded by the shock speed of a simulation that exhibits. an orthorhombic computational cell containing 64 mole divergence and the shock speed of a simulation that does. cules and employed periodic boundary conditions see not when all chemical reactions have been completed The. Supplemental Material 20 for additional details final state of the lowest shock speed simulation that does. Results and discussion Figure 1 shows temperature not diverge before chemistry completion corresponds to. stress and volume versus time behind the shock front for the CJ state In Fig 1 the smallest shock speed that does. shocks of various speeds propagating through HN3 In all not exhibit the volume divergence is 6 km s Figure 2. cases the volume decreases rapidly during the initial com shows that the chemical species populations in this simu. pression before chemical reactions occur Initial compres lation have achieved constant values by the end of the. sion is followed by a slower volume increase as chemistry simulation indicating 6 km s is near the ideal detonation. occurs The slower expansion is accompanied by a tem velocity Our calculated initial shock pressure and. perature increase as heat is evolved from the reaction temperature or Zeldovich von Neumann Doering theory. Our previous work on the MSST has shown that the ideal spike conditions are approximately 20 GPa and 2300 K. detonation velocity for an infinite charge diameter can be respectively The calculated CJ state pressure and tempera. determined from first principles 17 This velocity is the ture are approximately 11 GPa and 4400 K respectively. natural propagation speed of the detonation shock wave an Nonequilibrium molecular dynamics calculations of deto. intrinsic property of the material The MSST exhibits a nation in condensed phase model systems have been found. volume divergence computational cell volume rapidly to yield detonation velocities and CJ conditions within a. increases to infinity when the mechanical stability con few percent of those predicted by 1D continuum theory. ditions for a shock wave are not met indicating there are no utilized here 4 21. While experimental results on HN3 are sparse the deto. nation velocity has been reported to range from 7 1 to. 7 6 km s 22 23 The detonation velocity is determined. largely by the magnitude of energy released by reactions. and by the composition and equation of state of the final. reaction products It is likely that the DFTB representations. of both of these play some role in the difference between. FIG 2 color online Top panel shows time dependence of the. population of most prevalent molecules for a 6 km s shock near. FIG 1 color online Temperature stress shock propagation detonation speed The time required for completion of the. direction component and volume versus time behind the shock reaction is approximately 10 ps substantially shorter than the. front for shocks of various speeds propagating through HN3 A nanosecond and greater time scales of secondary explosives. volume divergence observed at the lowest shock speeds indicates Bottom panel shows deviation from vibrational equilibrium. that these speeds are below the Chapman Jouguet CJ detona given by time dependent temperature fluctuations expressed as. tion velocity The smallest shock speed that does not exhibit the time dependent heat capacity for the 6 km s shock The feature. volume divergence before completion of chemistry is 6 km s at 2 ps corresponds to shock compression subsequent excursions. indicating this is near the CJ detonation velocity see text for are associated with chemical reactions and fluctuations occur. details around a constant value after chemistry is complete. week ending, PRL 109 038301 2012 PHYSICAL REVIEW LETTERS 20 JULY 2012. our calculated detonation velocity and experiments The scale slower than reactions that do not require any atomic. energy of formation without zero point energy using the diffusion The reaction zone length is reported to be on the. DFTB scheme is 0 083 Eh slightly less than the value of order of tens of microns in nitromethane and on the order of. 0 092 Eh calculated using DFT at the B3LYP 6 31G level 1 mm in TATB 27 much longer than the 40 nm length of. and 0 114 calculated at the quadratic configuration inter HN3 Hydrazoic acid lacks carbon and therefore might be. action with single and double substitutions QCISD expected to have a faster decomposition time scale. cc PVTZ level 24 These deviations are consistent with Another condition for fast chemistry is that the tempera. a simulated shock speed being lower than experimental ture at the shock front is sufficiently high to yield fast. values see Supplemental Material 20 kinetics The temperature at the shock front is determined. Figure 2 shows the time dependence of the population of by the equation of state of the material and the magnitude of. most prevalent molecules for a 6 km s shock near deto energy release during detonation both parameters that are. nation speed HN3 molecules react to form N2 NH3 and a unrelated to the activation barrier magnitudes in the system. small amount of H and H2 as final products The overall The time scale for chemistry here is sufficiently fast. reaction can be approximately written as follows that reacting intermediates could be out of vibrational. 64HN3 86N2 20NH3 H2 2H 1 equilibrium It has been proposed that vibrational dis. equilibrium might play an important role in shock induced. N3 is formed as the most dominant intermediate Charged chemistry 28 30 While vibrational equilibrium in. species include N 0 3 3 H2 N 0 4, 3 and a small amount of molecular solids is established on time scales longer than. NH4 formed from the ammonia The atomic hydrogen 1 ps 31 the reaction intermediates observed here. charge is found to be neutral Several intermediate reac have lifetimes that are much shorter The primary inter. tions are given in the Supplemental Material 20 mediate N3 has an average lifetime of 330 fs Some direct. Figure 2 shows that the time required for completion of evidence for vibrational disequilibrium can be observed in. the reaction is approximately 10 ps This short time scale the magnitude of kinetic energy fluctuations or instanta. corresponds to a reaction zone extending a distance of neous temperature fluctuations In analog with the NPH. approximately 40 nm in space behind the shock front ensemble where temperature fluctuations are related to the. It is interesting to note that this reaction is likely one of heat capacity at constant pressure 32 the MSST tem. the fastest naturally occurring chemical reactions in nature perature fluctuations at equilibrium are expected to be. Only ultrafast photon induced reactions are faster because related to a heat capacity at constant shock speed. excitations into vibrationally unstable states can be achieved hT t 2 i hT t i2. 3N 1 3k2cB For a fixed heat capacity c and, on subpicosecond time scales In the case of detonating. HN3 the time scale is an intrinsic material property as is number of atoms N the magnitude of fluctuations is ex. the case for all explosives and is not determined by the time pected to be time independent at equilibrium Significant. scale of an external impulse The picosecond time scale deviations from a constant value can occur if the system is. response of shocked materials is potentially observable us not in vibrational equilibrium The bottom panel in Fig 2. ing existing experimental techniques 25 26 shows that the magnitude of c deviates from equilibrium. The calculated reaction rates are likely sensitive to values by more than an order of magnitude while chemistry. errors in reaction barrier heights calculated with DFTB occurs indicating that vibrational equilibrium is not. A crude Arrhenius estimate of the variation of kinetic rates established during this period Supplementary detail can. with DFTB representation of reaction barriers gives a be found in the Supplemental Material 20 Detonating. reaction zone time scale of 100 ps factor of 10 slower HN3 is an unusual state of matter where statistical. than observed in simulations for a DFTB reaction barrier mechanics based approaches to kinetic descriptions e g. 0 8 eV lower than actual and a reaction zone time scale of transition state theory are questionable. 1 ns for a DFTB reaction barrier 1 6 eV lower than Figure 3 shows the time dependence of electronic den. actual The calculated DFTB barrier for dissociation sity of states in HN3 with a shock speed of 6 km s near. of a gas phase HN3 molecule into N2 and HN one of the detonation speed The Fermi energy is depicted by the. initial reactions see Supplemental Material 20 is 0 6 eV white line The band gap of the material decreases upon. higher than QCISD cc PVTZ calculations suggesting that shock compression and states can be observed within the. Arrhenius kinetics may be slower in the DFTB case gap during the region of peak chemical reactions from 2 to. The anomalously fast reaction times might be partially 10 ps Similar behavior was observed on longer time scales. understood in terms of the lack of significant chemical in earlier studies of detonation in nitromethane 2. diffusion Carbon containing explosives like nitromethane The ultrafast kinetics of HN3 detonation may play a role. CH3 NO2 and triaminotrinitrobenzene TATB C6 N6 O6 H6 in the extreme sensitivity of this material to mechanical. are thought to initially form small molecules such as CO2 perturbations The initiation of detonation is thought to. N2 H2 O etc followed by carbon clusters on longer time occur through localized hot regions in the material hot. scales 3 Formation of such clusters requires the diffusion spots that react and release energy before the heat can. and accumulation of carbon atoms a process that has a time diffuse away from the hot spot 33 The critical hot spot. week ending, PRL 109 038301 2012 PHYSICAL REVIEW LETTERS 20 JULY 2012.
2 E J Reed M R Manaa L E Fried K R Glaesemann,and J D Joannopoulos Nature Phys 4 72 2007. 3 M R Manaa E J Reed L E Fried and N Goldman,J Am Chem Soc 131 5483 2009. 4 D W Brenner D H Robertson M L Elert and C T,White Phys Rev Lett 70 2174 1993. 5 C T White D R Swanson and D H Robertson in, Chemical Dynamics in Extreme Environments edited by. R A Dressler World Scientific London 2001 Vol 11,Chap 11 p 547.
6 J J C Barrett D H Robert and C T White Chem Phys. Rep 18 1969 2000,7 B L Evans A D Yoffe and P Gray Chem Rev 59 515. 8 B P Aduev E D Aluker G M Belokurov Y A,Zakharov and A G Krechetov Zh Eksp Teor Fiz 89. 906 1999 JETP 89 906 1999, FIG 3 color online Time dependence of electronic density 9 P Gray Nature London 179 576 1957. of states in shocked HN3 near detonation conditions The 10 M R Manaa and G E Overturf in International Detonation. Fermi energy is depicted by the white line The band gap of Symposium Proceedings http www intdetsymp org. the material decreases upon shock compression and states can be detsymp2010 2010. observed within the gap during the region of peak chemical 11 M Elstner D Porezag G Jungnickel J Elsner. reactions from 2 to 10 ps M Haugk Th Frauenheim S Suhai and G Seifert. Phys Rev B 58 7260 1998, 12 M R Manaa L E Fried and E J Reed J Comput Aided. size decreases with increasing reaction kinetics leading to a Mater Des 10 75 2003. material more sensitive to mechanical and other perturba 13 D Margetis E Kaxiras M Elstner T Frauenheim and. tions It is possible to speculate that the ultrafast chemistry M R Manaa J Chem Phys 117 788 2002. of this nitrogen compound may also play a role in other 14 B Aradi B Hourahine and T Frauenheim J Phys. polynitrogen compounds that have been long sought as Chem A 111 5678 2007. ultrahigh energy density materials like N4 N5 ions and 15 E J Reed L E Fried and J D Joannopoulos Phys Rev. Lett 90 235503 2003, polynitrogen 34 35 The relationship of the present results.
16 E J Reed L E Fried M R Manaa and, to the kinetics of metal azides is less clear since the metal J D Joannopoulos A Multi scale Approach to. chemistry may be quite different than that of hydrogen Molecular Dynamics Simulations of Shock Waves. Conclusions We have performed molecular dynamics in Chemistry at Extreme Conditions edited by. simulations of detonating HN3 from the shock front to the M R Manaa Elsevier New York 2005 Chap 10. final CJ state These are the first simulations of detonation p 297. in an azide material from beginning to end The simulations 17 E J Reed L E Fried W D Henshaw and C M Tarver. show that the material decomposes into stable products in Phys Rev E 74 056706 2006. about 10 ps Deviations from vibrational equilibrium occur 18 E J Reed A Maiti and L E Fried Phys Rev E 81. during chemistry a feature associated with the fast kinetics 016607 2010. of this material 19 E J Reed J Phys Chem C 116 2205 2012. 20 See Supplemental Material at http link aps org, This work was performed in part under the auspices of the. supplemental 10 1103 PhysRevLett 109 038301 for addi. U S Department of Energy by Lawrence Livermore tional computational details and method validation. National Laboratory under Contract No DE AC52 21 B M Rice W Mattson J Grosh and S F Trevino Phys. Ultrafast Detonation of Hydrazoic Acid HN 3 The fastest self sustained chemical reactions in nature occur during detonation of energetic materials where reactions are thought to occur on nanosecond or longer time scales in carbon containing materials Here we perform the rst atomistic simulation of an azide energetic material HN 3 from the beginning to the end of the chemical

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