CP620, Shock Compression of Condensed Matter - 2001edited by M. D. Furnish, N. N. Thadhani, and Y. Hone© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00

WHAT IS A SHOCK WAVE TO AN EXPLOSIVE MOLECULE?Craig M. Tarver

Lawrence Livermore National LaboratoryP.O. Box 808, L-282, Livermore, CA 94551

An explosive molecule is a metastable chemical species that reacts exothermically given the correct stimulus.Impacting an explosive with a shock wave is a "wake-up call" or "trigger" which compresses and heats themolecule. The energy deposited by the shock wave must be distributed to the vibrational modes of theexplosive molecule before chemical reaction can occur. If the shock pressure and temperature are high enoughand last long enough, exothermic chemical decomposition can lead to the formation of a detonation wave.For gaseous, liquid, and perfect single crystal solid explosives, after an induction time, chemical reactionbegins at or near the rear boundary of the charge. This induction time can be calculated by high pressure,high temperature transition state theory. A "superdetonation" wave travels through the preshocked explosiveuntil it overtakes the initial shock wave and then slows to the steady state Chapman-Jouguet (C-J) velocity.In heterogeneous solid explosives, initiation of reaction occurs at "hot spots" created by shock compression.If there is a sufficient number of large and hot enough "hot spots," these ignition sites grow creating apressure pulse that overtakes the leading shock front causing detonation. Since the chemical energy isreleased well behind the leading shock front of a detonation wave, a mechanism is required for this energy toreinforce the leading shock front and maintain its overall constant velocity. This mechanism is theamplification of pressure wavelets in the reaction zone by the process of de-excitation of the initially highlyvibrationally excited reaction product molecules. This process leads to the development of the three-dimensional structure of detonation waves observed for all explosives. In a detonation wave, the leadingshock wave front becomes a "burden" for the explosive molecule to sustain by its chemical energy release.

INTRODUCTION

What is a shock wave to an explosive molecule?There are several answers to this question dependingupon the strength and time duration of the shockpulse. Since an explosive molecule (or a mixture offuel and oxidizer molecules) is inherently metastable,it requires only an increase in its internal energy toovercome its activation energy barrier to reaction.This decomposition process may eventually becomehighly exothermic and cause deflagration (subsonicflow) or detonation (supersonic flow). So a shockwave is the "wake-up call" or the "trigger" thatcauses the molecule to release its chemical energy.The shock pulse must be of sufficient strength andtime duration or self-sustaining exothermic chemicalreaction does not occur. In a heterogeneous solidexplosive, a weak shock wave can create acompressed material that does not react when

subjected to subsequent shock waves. Stronger shockwaves create reactive flows in their wake. Thesereactive flows can couple to, reinforce and strengthenthe shock front. The result is a detonation wave, inwhich the leading shock wave front is sustained bythe chemical energy released behind it. Then theshock front is not only a "trigger" but also a"burden" to the explosive molecule since the shockis sustained by its exothermic chemical reaction.

Therefore a shock wave can be many differentthings to an explosive molecule. In this paper thecurrent state of knowledge and future researchdirections for each of these regimes are brieflydiscussed in order of increasing pressure.

NON-SHOCK IMPACT IGNITION

When a heterogeneous solid explosive charge issubjected to a low velocity impact that produces a

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few kilobars of pressure, a two-stage compressionwave is formed. This wave consists of an elasticwave that propagates through the explosive atlongitudinal sound velocity followed by a plasticwave traveling at lower velocity (1,2), Within theflow field produced by the plastic wave, regions ofthe explosive can be heated by void collapse,friction, shear, and other possible mechanisms (3)."Hot spots" are foimed and can ignite and grow intoan explosive energy release. Most of theseignitions result in subsonic deflagration waves drivenby heat transfer from the hot reaction products intothe surrounding explosive molecules. Impactignition is one of the most important explosivesafety concerns, because it is causal by the smallestamount of energy delivered to the explosivemolecules. Several tests have been developed tostudy impact: drop hammers; drop weight impactmachines; the Skid test; the Susan test; etc. Inrecent years, the Steven Test at LLNL (4) and itsmodified version at LANL (5) have been used toyield quantitative experimental data that can besimulated with reactive flow computer models. TheSteven Test and other impact studies have resulted inan improved understanding of impact ignition.

WEAK SHOCK COMPRESSION

At slightly higher pressures, the elastic and plasticwaves merge into a relatively weak shock wave(1,2). For homogeneous explosives, these shockscompress and heat the explosive molecules slightly,but little or no chemical decomposition occurs. Forsome heterogeneous solid explosives, there exists anarrow range of shock pressures in which all of thevoids and other inhomogeneities can be compressedwithout creating growing hot spot reactions. Theresulting fully dense explosive material can not beshock initiated by subsequent strong shock waves oreven detonation waves. This phenomenon is called"dead pressing" or "shock desensitization"(6).Depending on the application, this can be a useful ora frustrating property of explosive molecules.

HOMOGENEOUS EXPLOSIVES

Homogeneous explosives include gases, liquidswithout bubbles or suspended solids, and perfectcrystals of solid explosives. In these materials,planar shock waves uniformly compress and heat theexplosive molecules. There has long been somedebate about the definition of the thickness of a

shock wave. Zeldovich and Raizer (7) define thewidth of a shock wave as the distance at which theviscosity and heat conduction become negligible.This occurs within a few molecular collisions in agas. At the same time, the internal modes ofgaseous explosive molecules are becoming excited:translational modes (a few collisions); rotationalmodes (tens of collisions); and vibrational modes(hundreds of collisions). These equilibrationprocesses have long been studied in shock tubes (8).Internal energy equilibration is now being studied inshocked liquid and solid explosives by Dlott et al. (9)and Payer et al(10). In condensed phases, the phononmodes are initially excited followed by multi-phononexcitation of the lowest frequency vibrational modesand then the higher frequency modes by multi-phonon up-pumping and internal vibrational energyredistribution (IVR)(11). Once the explosivemolecules have attained vibrational equilibrium,chemical decomposition can begin.

For gaseous explosives, the non-equilibriumprocesses which precede chemical reaction are easilymeasured, since they can be lengthened tonanosecond or even microsecond time frames bydilution with inert gases or by the use of low initialpressures. The calculation of these states is alsostraight forward, because the perfect gas law applies.The initial reaction rates for the dissociation of theweakest chemical bond present in the explosivemolecule/mixture are also easily measured in shocktube experiments and calculated using unimolecularArrhenius chemical kinetics. If the shock wave heatsthe explosive molecules to temperatures at whichsufficient dissociation occurs before the shockcompression ends and rarefaction cooling begins, thenewly formed atoms react with surroundingmolecules. An exothermic chain reaction processfollows in which reaction product gases are formed inhighly vibrationally excited states (12). Theseexcited products either undergo reactive collisionswith the surrounding explosive molecules or non-reactive collisions with their neighbors in which oneor more quanta of vibrational energy is transferred.Some collisions are "super-collisions"(13) in whichseveral quanta of vibrational energy are transferred.Since reaction rates increase rapidly with each quantaof vibrational energy available, reactive collisionsdominate and the main chemical reactions ateextremely fast. Once the chain reaction process iscompleted, the remainder of the reaction zone isdominated by the de-excitation of highlyvibrationally excited product molecules as chemical

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equilibrium is approached. This de-excitationprocess controls the length of the reaction zone andprovides the chemical energy necessary for shockwave amplification during shock-to-detonationtransition (SDT) and self-sustaining detonation.

The Non-Equilibrium Zeldovich - von Neumann-Doring (NEZND) theory of detonation (12,14-17)was developed to explain the various non-equilibriumprocesses that precede and follow chemical energyrelease in self-sustaining detonation waves. Aspressure wavelets pass through the subsonic reactionzone, they are amplified by vibrational de-excitationprocesses. The opposite effect - shock wave dampingby a non-equilibrium gas that lacks vibrationalenergy after expansion through a nozzle - is a well-known phenomenon (7). The pressure waveletsthen interact with the main shock front and replacethe energy lost during compression, acceleration andheating of the explosive molecules. During shockinitiation, this interaction process increases theshock front pressure and velocity. If the initial shockwave is accelerated to a velocity at which chemicalreaction occurs close to the front, then self-sustaining detonation occurs. The pressure waveletamplification process then provides the requiredchemical energy by developing a three-dimensionalMach stem shock front structure. This leading shockwave front is still a "wake-up call" or "trigger" forexplosive reaction, but it is also a "burden" for theexplosive molecules to sustain at supersonic velocitywith their energy release.

The three-dimensional structures of detonationwaves have been observed for gaseous, liquid andsolid explosives (18). In gaseous detonations, thedetails are very well known and several excellentreviews of the subject are available (19). For liquidand perfect single crystal solid explosives, thesituation is much more complex and thus moredifficult to observe and calculate than in gases. Thehigh initial densities of the condensed phases makethe measurement and calculation of the states attainedbehind a shock wave more difficult, because theprocesses now take tens and hundreds of picosecondsand the perfect gas law does not apply. Thedistribution of the shock compression energybetween the potential (cold compression) energy ofthe unreacted liquid or solid and its thermal energy isa complex function of shock strength. The lack ofvoids, cracks, particle boundaries, etc. eliminates"hot spot" formation as an initiation mechanism. Ifthe shock compressed state lasts long enough forexothermic reaction to begin at this shock

temperature, initiation of occurs at or near theboundary of the explosive charge in the moleculesfirst impacted by the shock. This "thermalexplosion" creates a "superdetonation" wave thatpropagates through the precompressed explosive at avelocity in excess of its equilibrium Chapman-Jouguet (C-J) velocity. When this wave overtakesthe leading shock wave, its velocity decreases rapidlyuntil steady state velocity is attained. Thisphenomenon has been measured and calculated forseveral detonating liquids (20) and solid perfectcrystals (21). Liquid explosives exhibit a wide rangeof shock sensitivity (22). Perfect single crystals ofrelatively sensitive solid explosives like PETN canbe shock initiatiated (21), but single crystals ofHMX can not be initiated by a detonation wave froman HMX-based plastic bonded explosive (6).

The "induction" time for the initial "thermalexplosion" can be calculated using the high pressure,high temperature transition state theory.Experimental unimolecular gas phase reaction ratesunder low temperature (<1000°) shock conditionsobey the usual Arrhenius law:

(1)

where K is the reaction rate constant, A is afrequency factor, E is the activation energy, and T istemperature, at low temperatures, but "fall-off' toless rapid rates of increase at high temperatures (23).Nanosecond reaction zone measurements for solidexplosives overdriven to pressures and temperaturesexceeding those attained in self-sustaining detonationwaves have shown that the reaction rates increasevery slowly with shock temperature (24). Eyring(25) attributed this "falloff' in unimolecular rates atthe extreme temperature and density states attained inshock and detonation waves to the close proximity ofvibrational states, which causes the high frequencymode that becomes the transition state to rapidlyequilibrate with the surrounding modes by IVR.These modes form a "pool" of vibrational energy inwhich the energy required for decomposition isshared. Any large quantity of vibrational energy thata specific mode receives from an excitation process isshared among the modes before reaction can occur.Conversely, sufficient vibrational energy from theentire pool of oscillators is statistically present inthe transition state long enough to cause reaction.When the total energy in the vibrational modesequals the activation energy, the reaction rateconstant K is:

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s-1K = (kT/h)e's E (E/RT)1 e~E/RT/ i! (2)

i=0

where k, h, and R are Boltzmann's, Planck's, and thegas constant, respectively, and s is the number ofneighboring vibrational modes interacting with thetransition state. The main effect of this rapid IVRamong s+1 modes at high densities and temperaturesis to decrease the rate constant dependence ontemperature. Reasonable reaction rate constantswere calculated for detonating solids and liquids usingEq. (2) with realistic equations of state and values ofs (15). For the lower temperatures attained in shockinitiation of homogeneous liquid and solidexplosives, the reaction rate constants calculatedusing Eq. (2) are larger than those predicted by Eq.(1). Reaction rate constants from Eqs. (1) and (2) arecompared to induction time results for gaseousnorbornene, liquid nitromethane, and single crystalPETN in Figs. 1-3, respectively (16). Despiteuncertainties in the calculated shock temperatures forvarious equations of state, it is clear that Eq. (2)agrees quite well with all three sets of data usingreasonable values of s. Thus high pressure, hightemperature transition state theory accuratelycalculates induction times for shock induced reactionsduring shock initiation and detonation ofhomogeneous gaseous, liquid, and solid explosives.

10 -

Arrhenius Rate Calculation-log A = 14.63, E = 45.39 kcal/m

(Barker and King - Ref. 16)

Experimental Data(Kieferetal.-Ref. 15)

High Temperature, High DensityTransition State Theory Calculations[Eq. (2) with s = 20]

0.7 0.8 0.9Inverse Temperature - 1000/T

FIGURE 1. Reaction rate constant versus inverse temperaturefor the unimolecular decomposition of norbornene

§O

Io

2-

Eq. (2)(s=14)

Cowperthwaiteand Shaw EOS

Lysne andHardesty EOS

0.6 0.8 1.0Inverse Temperature - 1/K (xlOOO)

1.2

FIGURE 2. Reaction rate constants for nitromethane asfunctions of shock temperature

7 -

oc 5 •

Eq. (2)(s=15)

Experimentalnduction Time Data

Eq. (2)(s=20)

0.4 0.6 0.8 1.0 1.2 1.4Inverse Temperature - 1/K (xlOOO)

FIGURE 3. Reaction rate constants for single crystal PETN asfunctions of shock temperature

HETEROGENEOUS EXPLOSIVES

For heterogeneous explosives (liquids withbubbles or suspended solid particles and pressed orcast solids with voids, binders, metal particles, etc.),an initiating shock wave does not have to heat theentire material to the point of thermal explosion.Thermal energy is concentrated in local sites by thephysical processes of void collapse, friction, shear,dislocation pile-up, etc. Liquid explosives whichcontain bubbles can undergo partial reactions known

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as low velocity detonation (LVD) at hot spot sitescreated by collapsing voids. LVD can propagatelong distances in metal pipes and is a major safetyconcern. LVD can cease to propagate or transition tofull detonation in various scenarios (26).

It has long been known that shock initiation ofsolid explosives is controlled by ignition of hotspots (3). How large and how hot does a hot spothave to be to react and begin to grow? Criticalconditions for the growth or failure of hot spots inHMX- and TATB-based explosives have beencalculated using multistep Arrhenius kineticchemical decomposition models derived from themialexplosion experiments (27). Figure 4 shows thecalculated critical spherical hot spot temperatures inHMX and TATB. Once ignited, the growth rates ofreacting hot spots into neighboring solid explosiveparticles and the interactions of several growing hotspots have been calculated for various geometries(28). Figure 5 shows the times required for sphericalHMX particles of various radii to complete inwarddeflagration under various boundary temperatureconditions. These relatively long times show thatlarge explosive particles must fragment, producingsmaller particles with more reactive surface area forhot gaseous reaction products to ignite. As growinghot spots coalesce at high pressures andtemperatures, the transition from shock inducedreaction to detonation occurs very rapidly. Thebuildup of pressure and particle velocity behind theshock wave front during shock initiation has beenthoroughly studied using embedded gauge (29,30) and

Shock Regime

~ 1200 -J

impact Regime

10Diameter -

Figure 4. Critical spherical hot spot temperatures inHMX and TATB at various diameters

laser interferometric (31) techniques. These reactiveflows have been modeled in multidimensional codesby the Ignition and Growth model of shock initiationand detonation (32). Figure 6 shows measured andcalculated pressure histories obtained for a shockinitiation experiment on HMX-based LX-04 (29).

1000 1500 2000 2500 3000 3500 4000Boundary Temperature - °K

FIGURE 5. Reaction times for HMX particles

£ 8.

0 mm 5 mm 10 mm

JL J

FIGURE 6. Pressure histories for ambient temperature LX-04shock initiated by a Teflon flyer plate at 0.956 mm/jis

Detonation wave reaction zone structures in solidexplosives and their metal acceleration propertieshave also been measured by embedded gauges and

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laser interferometry and calculated by the Ignition andGrowth model (33). Figure 7 shows the measuredand calculated interface velocity histories fordetonating LX-17, a TATB-based explosive,impacting various salt crystals (33). Figure 8illustrates the measured and calculated free surfacevelocities of 0.267 mm thick tantalum discs drivenby 19.871 mm of detonating LX-17

15mm LX-17KCI CrystalExperiment

'Calculation15mm LX-17NaCI Crystal

I IV^TV *"*. ^^^Calculation

30mm LX-17LiF CrystalExperimentCalculation

0.5 -

1.0 1.5Time - \&

I2.5

FIGURE 7. Interface particle velocity histories fordetonating LX-17 and various salt crystals

2.8 -

e^ 2.6 -&_p 2.4 -

tW

Calculated Record

Experimental Records

0.0 0.1 0.2 0.3 0.4 0.5Time - us

FIGURE 8. Free surface velocities for 0.267 mmthick tantalum disks driven by 19.871 mm of LX-17

MultiphononUp-pumping j

IntramolecularVibrational EnergRedistribution

EndothermicBond Breaking

Exothermic Reactions

Supercollisions

Vibrational Deexcitation

Solid Carbon Formation

Equilibrium

(CO2*,H2O*,N2*,C) (CO2**,H2O**,N2**)

C-J State VibrationallyExcited States

(CwHxOyNz*)

Transition ShockState (s) Front

FIGURE 9. The Non-Equilibrium Zeldovich - vonNeumann-Doring (NEZND) model of detonation forcondensed phase explosives

Since the main application of detonating solidexplosives is to accelerate metals and other materialsto high velocities, accurate measurements of theunreacted shock state (the "von Neumann spike"), thepressure profile of the chemical reaction zone, andthe subsequent expansion of the reaction products asthey deliver their momentum to the metal areessential. Currently the one-dimensional averages ofthese properties are known to within a few percentwith several nanosecond resolution (21,31,33,34).

Due to solid particle interactions, one expects thedetonation front structure to be more complex andless regular in heterogeneous explosives than inhomogeneous ones. The sub-nanosecond techniquesneeded to resolve this wave structure are becomingavailable. Figure 9 illustrates the various processesthat precede and follow exothermic chemicalreactions behind each wavelet of the three-dimensional structure comprising the reaction zoneof a condensed phase detonation wave. Eventuallyall of these non-equilibrium physical and chemicalmechanisms, along with those that have not beenidentified as yet, will need to be measuredexperimentally and modeled in advancedmultidimensional reaction flow models. Then theinteractions of shock waves with explosivemolecules and vice versa can be better understood.This understanding may lead to the production ofsafer, more energetic explosive molecules andformulations.

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FUTURE RESEARCH

While a great deal has been learned in recent yearsabout the interaction of shock waves with explosivemolecules, greater spatial and time resolution isneeded in shock wave experiments and calculations.For understanding low velocity impact ignitionmechanisms, the relative roles of void collapse,friction, shear, dislocation pile-up, etc. need to bedetermined by clever experimentation. Many ofthese postulated hot spot formation mechanismsdepend upon the magnitude of the viscosity in andbehind shock wave fronts, which has not yet beenmeasured for shock waves in condensed phaseexplosives. If the dominant hot spot mechanism (ormechanisms) can be identified experimentally andsuccessfully modeled, modifications to existingexplosive formulations can be made. New processesand new materials (explosives, binders, additives,etc.) can be developed to produce safer products.

Since chemical reaction rates are controlled by thelocal temperature of a region of molecules, the mostimportant need is for experimental measurements oftemperature in all regions of shocked explosives: inand around hot spots; in deflagration waves; in thereactive flows behind shock fronts and in detonationwaves. With this type of data, improved equationsof state and all-Arrhenius reactive flow models can bedeveloped to better predict the effects of shock waveson explosive molecules and vice versa (28).Eventually it will become possible to model shockinduced reactions as thermal decompositionmechanisms are modeled today by identifyingintermediate reaction product species and followingtheir concentration changes. To do this effectively,nanosecond or faster time resolved experimental dataon the rates of consumption of the unreactedexplosive, the concentrations of intermediate species,and the rates of production of the final stableproducts is needed. Accurate determination of thethree-dimensional structures of detonation waves incondensed phase explosives is required to determinehow much detail must be included in reactive flowmodels to yield more realistic and predictivesimulations in two- and three-dimensional codes.

SUMMARY

This short review can only begin to address thecomplex question: What is a shock wave to anexplosive molecule? Through several compressionand heating mechanisms, a shock wave is the "wake-

up call" or the "trigger" by which the exothermicpower of the metastable explosive molecule isunleashed. Many possible outcomes of the initialhot spot formation process are possible: no reaction;shock desensitization; weak explosion; violentexplosion; deflagration; shock wave formation; decayor amplification of the shock front; and transition todetonation. Detonation is the desired result of anintentional shock initiation, but must be avoided atall costs during unintentional initiations (accidents).At the maximum rate of energy delivery in adetonation wave, the leading shock wave initiates thechemical reaction but then must be sustained by thechemical energy released. This chemical energy isinitially released into highly vibrationally excitedreaction products, whose relaxation to chemicalequilibrium amplifies pressure wavelets propagatingthrough the subsonic reaction zone. These pressurewavelets then overtake the shock wave front,replacing its lost energy and creating the three-dimensional detonation wave front structure observedfor all explosives. Understanding this intimateconnection between non-equilibrium chemicalkinetics and the three-dimensional detonation wavestructure is one key to developing improved reactiveflow models and safer, more powerful explosives.Another major key is to understand hot spotformation, ignition, and growth induced by shockwaves in explosive molecules.

ACKNOWLEDGMENTS

The author would like to thank Jerry Forbes, PaulUrtiew, Steve Sheffield, Rick Gustavsen, DavidFunk, Riad Manaa, Maija Kukla, Steve Chidester,Larry Fried, Randy Simpson, Jon Maienschein, JoeShepherd, Tom Russell, Peter Haskins, MalcomCook, Langdon Bennett, and Mel Baer for recentdiscussions. Also essential was the research andfriendship of many excellent scientists: MichaelCowperthwaite; Bob Woolfolk; Bob Shaw; DonCurran; Lynn Seaman; LeRoy Green; LeroyErickson; Ed Lee; Bud Hayes; Bill Davis; WildonFickett; John Ramsay; John Kury; Don Breithaupt;Ray McGuire; Ed James; Bobby Craig; Pier Tang;Chuck Forest; Jace Nunziato; Albert Nichols; DanCalef; Milt Finger; Bill Von Holle; Steve Cochran;Ron Lee; Kerry Bahl; Frank Walker; Bob Frey; PhilHowe; Joe Foster; Steve Coffey; and many others.

This work was performed under the auspices of theU.S. Department of Energy by Lawrence LivermoreNational Laboratory (contract no.W-7405-ENG-48).

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4.

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