The Reactivity of Energetic Materials at Extreme...

CHAPTER 4

The Reactivity of Energetic Materialsat Extreme Conditions

Laurence E. Fried

Chemistry, Materials Science, and Life Sciences DirectorateLawrence Livermore National Laboratory, Livermore, California

INTRODUCTION

Energetic materials are unique for having a strong exothermic reactivity,which has made them desirable for both military and commercial applications.Energetic materials are commonly divided into high explosives, propellants,and pyrotechnics. We will focus on high explosive (HE) materials here,although a great deal of commonality exists between the classes of energeticmaterials. Although the history of HE materials is long, their condensed-phaseproperties are poorly understood.

Understanding the condensed-phase properties of HE materials is impor-tant for determining stability and performance. Information regarding HEmaterial properties [such as the physical, chemical, and mechanical behaviorsof the constituents in plastic-bonded explosive (PBX) formulations] isnecessary for efficiently building the next generation of explosives as the questfor more powerful energetic materials (in terms of energy per volume) movesforward.1

There is a need to better understand the physical, chemical, and mechan-ical behaviors when modeling HE materials from fundamental theoreticalprinciples. Among the quantities of interest in PBXs, for example, are thermo-dynamic stabilities, reaction kinetics, equilibrium transport coefficients,mechanical moduli, and interfacial properties between HE materials and the

Reviews in Computational Chemistry, Volume 25edited by Kenny B. Lipkowitz and Thomas R. Cundari

Copyright � 2007 Wiley-VCH, John Wiley & Sons, Inc.

159

polymeric binders. These properties are needed (as functions of stress state andtemperature) for the development of improved micro-mechanical models,2

which represent the PBX at the level of high explosive grains and polymericbinder.3,4 Improved micro-mechanical models are needed to describe theresponses of PBXs to dynamic stress or thermal loading, thus yielding informa-tion for use in developing continuum models.

Detailed descriptions of the chemical reaction mechanisms of condensedenergetic materials at high densities and temperatures are essential for under-standing events that occur at the reactive front under combustion or detona-tion conditions. Under shock conditions, for example, energetic materialsundergo rapid heating to a few thousand degrees and are subjected to a com-pression of hundreds of kilobars,5 which results in almost 30% volume reduc-tion. Complex chemical reactions are thus initiated, in turn releasing largeamounts of energy to sustain the detonation process. Clearly, understandingof the various chemical events at these extreme conditions is essential in orderto build predictive material models. Scientific investigations into the reactiveprocess have been undertaken over the past two decades. However, thesub-microsecond time scale of explosive reactions, in addition to the highlyexothermic conditions of an explosion, make experimental investigation ofthe decomposition pathways difficult at best.

More recently, new computational approaches to investigate con-densed-phase reactivity in energetic materials have been developed. Herewe focus on two different approaches to condensed-phase reaction model-ing: chemical equilibrium methods and atomistic modeling of condensed-phase reactions. These complementary approaches assist in understandingthe chemical reactions of high explosives. Chemical equilibrium modelinguses a highly simplified thermodynamic picture of the reaction process,which leads to a convenient and predictive model of detonation and otherdecomposition processes. Chemical equilibrium codes are often used inthe design of new materials, both at the level of synthesis chemistry andformulation.

Atomistic modeling is a rapidly emerging area. The doubling of compu-tational power approximately every 18 months that is predicted by Moore’slaw has made atomistic condensed-phase modeling more feasible. Atomisticcalculations employ far fewer empirical parameters than chemical equili-brium calculations. Nevertheless, the atomistic modeling of chemicalreactions requires an accurate global Born–Oppenheimer potential energysurface. Traditionally, such a surface is constructed by representing thepotential energy surface with an analytical fit. This approach is only feasiblefor simple chemical reactions involving a small number of atoms. Morerecently, first principles molecular dynamics, where the electronic Schrodin-ger equation is solved numerically at each configuration in a moleculardynamics simulation, has become the method of choice for treatingcomplicated chemical reactions.6

160 The Reactivity of Energetic Materials at Extreme Conditions

CHEMICAL EQUILIBRIUM

The energy content of an HE material often determines its practical uti-lity. Accurate estimates of the energy content are essential in the design of newmaterials1 and for understanding quantitative detonation tests.7 The usefulenergy content is determined by the anticipated release mechanism. Becausedetonation events occur on a microseconds time frame, chemical reactions sig-nificantly faster than this may be considered to be in an instantaneous chemi-cal equilibrium. It is generally believed that reactions involving the productionof small gaseous molecules (CO2, H2O, etc.) are fast enough to be treated inchemical equilibrium for most energetic materials. This belief is based partlyon success in modeling a wide range of materials with the assumption of che-mical equilibrium.8–12

Unfortunately, direct measurements of chemical species involved in thedetonation of a solid or liquid HE material are difficult to perform. Blais,Engelke, and Sheffield13 have measured some of the species produced in deto-nating nitromethane using a special mass spectroscopic apparatus. Thesemeasurements pointed to the importance of condensation reactions in detona-tion. The authors estimate that the hydrodynamic reaction zone of detonatingbase-sensitized liquid nitromethane is 50 m in thickness, with a reaction timeof 7 ns. The hydrodynamic reaction zone dictates the point at which the mate-rial ceases to release enough energy to drive the detonation wave forward.Reactions may continue to proceed behind the reaction zone, but the timescales for such reactions are harder to estimate. Typical explosive experi-ments are performed on parts with dimensions on the order of 1–10 cm. Inthis case, hydrodynamic confinement is expected to last for roughly 1 ms,based on a high-pressure sound speed of several centimeters/microsecond.Thus, chemical equilibrium is expected to be a valid assumption for nitro-methane, based on the time scale separation between the 7-ns reaction zoneand the microsecond time scale of confinement. The formation of solids, suchas carbon, or the combustion of metallic fuels, such as Al, is believed to yieldsignificantly longer time scales of reaction.14 In this case, chemical equili-brium is a rough, although useful, approximation to the state of matter of adetonating material.

Thermodynamic cycles are a useful way to understand energy releasemechanisms. Detonation can be thought of as a cycle that transforms theunreacted explosive into stable product molecules at the Chapman–Jouguet(C-J) state,15 which is simply described as the slowest steady-state shockstate that conserves mass, momentum, and energy (see Figure 1). Similarly,the deflagration of a propellant converts the unreacted material intoproduct molecules at constant enthalpy and pressure. The nature of theC–J state and other special thermodynamic states important to energeticmaterials is determined by the equation of state of the stable detonationproducts.

Chemical Equilibrium 161

A purely thermodynamic treatment of detonation ignores the importantquestion of reaction time scales. The finite time scale of reaction leads tostrong deviations in detonation velocities from values based on theChapman–Jouguet theory.16 The kinetics of even simple molecules underhigh-pressure conditions is not well understood.

High-pressure experiments promise to provide insight into chemicalreactivity under extreme conditions. For instance, chemical equilibrium analy-sis of shocked hydrocarbons predicts the formation of condensed carbon andmolecular hydrogen.17 Similar mechanisms are at play when detonatingenergetic materials form condensed carbon.10 Diamond anvil cell experimentshave been used to determine the equation of state of methanol under high pres-sures.18 We can then use a thermodynamic model to estimate the amount ofmethanol formed under detonation conditions.19

Despite the importance of chemical kinetic rates, chemical equilibrium isoften nearly achieved when energetic materials react. As discussed, this is auseful working approximation, although it has not been established throughdirect measurement. Chemical equilibrium can be reached rapidly underhigh-temperature (up to 6000 K) conditions produced by detonating energeticmaterials.20 We begin our discussion by examining thermodynamic cycle the-ory as applied to high explosive detonation. This is a current research topicbecause high explosives produce detonation products at extreme pressuresand temperatures: up to 40 GPa and 6000 K. These conditions make it extre-mely difficult to probe chemical speciation. Relatively little is known about theequations of state under these conditions. Nonetheless, shock experiments ona wide range of materials have generated sufficient information to allowreliable thermodynamic modeling to proceed.

Energy

Volume

Unreacted

Chapman– Jouguet

Expandedproducts

Combustion in air

Figure 1 A thermodynamic picture of detonation: The unreacted material is compressedby the shock front and reaches the Chapman–Jouguet point. From there adiabaticexpansion occurs, which leads to a high-volume state. Finally, detonation products maymix in air and combust.


One of the attractive features of thermodynamic modeling is that itrequires very little information regarding the unreacted energetic material;elemental composition, density, and heat of formation of the material arethe only information needed. As elemental composition is known once thematerial is specified, only density and heat of formation need to be predicted.

The C–J detonation theory15 implies that the performance of an explo-sive is determined by thermodynamic states, the C–J state, and the connectedexpansion region, as illustrated in Figure 1. As detonation processes are sorapid, there is insufficient time for thermal conduction during expansion,which implies that the expansion from the C–J state lies on an adiabat:dE ¼ �pdV. The adiabatic expansion of the detonation products releasesenergy in the form of PV work and heat. Subsequent turbulent mixing ofthe detonation products in air surrounding the energetic material leads to com-bustion processes that release more energy.

Thermochemical codes use thermodynamics to calculate statesillustrated in Figures 1 and 2 and, thus, predict explosive performance. Theallowed thermodynamic states behind a shock are intersections of the Rayleighline (expressing conservation of mass and momentum) and the shockHugoniot (expressing conservation of energy). The C–J theory assumes thata stable detonation occurs when the Rayleigh line is tangent to the shockHugoniot, as shown in Figure 2.

This point of tangency can be determined, assuming that the equation ofstate P ¼ PðV;EÞ of the products is known. The chemical composition of theproducts changes with the thermodynamic state, so thermochemical codesmust solve for state variables and chemical concentrations simultaneously.This problem is relatively straightforward, given that the equation of state(EOS) of the fluid and solid products are known.

Fully reacted Hugoniot

Unreacted state

V

P

Chapman–Jouguet

Rayleighline

Figure 2 Allowed thermodynamic states in detonation are constrained to the shockHugoniot. Steady-state shock waves follow the Rayleigh line.


One of the most difficult parts of this problem is describing the EOSof the fluid components accurately. Because of its simplicity, the Becker–Kistiakowski–Wilson (BKW)21 EOS is used in many practical applicationsinvolving energetic materials. Numerous parameter sets have been proposedfor the BKW EOS.22–25 Kury and Souers7 have critically reviewed these setsby comparing their predictions to a database of detonation tests. They con-cluded that the BKW EOS does not model the detonation of a copper-linedcylindrical charge adequately. The BKWC parameter set26 overcomes this defi-ciency partially through multivariate parameterization techniques. However,the BKWC parameter set is not reliable when applied to explosives that arevery high in hydrogen content.

It has long been recognized that the validity of the BKW EOS is question-able.12 This is particularly important when designing new materials that mayhave unusual elemental compositions. Efforts to develop better EOSs havebeen based largely on the concept of model potentials. With model potentials,molecules interact via idealized spherical pair potentials. Statistical mechanicsis then employed to calculate the EOS of the interacting mixture of effectivespherical particles. Most often, the exponential-6 (exp-6) potential is used forthe pair interactions:

VðrÞ ¼ ea� 6

6 exp a� ar

rm

� �� a

rm

r

� �6� �

½1�

Here, r is the distance between particles, rm is the minimum of the potentialwell, E is the well depth, and a is the softness of the potential well.

The Jacobs–Cowperthwaite–Zwissler (JCZ3) EOS was the first success-ful model based on a pair potential that was applied to detonation.27 This EOSwas based on fitting Monte Carlo simulation data to an analytic functionalform. Ross, Ree, and others successfully applied a soft-sphere EOS based onperturbation theory to detonation and shock problems.10,28–30 Computationalcost is a significant difficulty with an EOS based on fluid perturbation theory.Byers Brown31 developed an analytic representation of the Kang et al. EOSsusing Chebyshev polynomials. The accuracy of the Byers Brown EOS hasbeen evaluated by Charlet et al.;12 these authors concluded that Ross’sapproach is the most reliable. Fried and Howard32 have used a combinationof integral equation theory and Monte Carlo simulations to generate a highlyaccurate EOS for the exp-6 fluid.

The exp-6 model is not well suited to molecules with large dipolemoments. To account for this, Ree9 used a temperature-dependent well depthE(T) in the exp-6 potential to model polar fluids and fluid phase separations.Fried and Howard have developed an effective cluster model for HF.33 Theeffective cluster model is valid for temperatures lower than the variablewell-depth model, but it employs two more adjustable parameters than doesthe latter. Jones et al.34 have applied thermodynamic perturbation theory to


polar detonation-product molecules. Despite these successes, more progressneeds to be made in the treatment of polar detonation-product molecules.

Efforts have been made to develop EOS for detonation products basedon direct Monte Carlo simulations instead of on analytical approaches.35–37

This approach is promising given recent increases in computational capabil-ities. One of the greatest advantages of direct simulation is the ability to gobeyond van der Waals 1-fluid theory, which approximately maps the equationof state of a mixture onto that of a single component fluid.38

In most cases, interactions between unlike molecules (treated as singlespherical sites) are treated with Lorentz–Berthelot combination rules.39 Therules are used to determine the interactions between unlike molecules and thoseof like molecules. The rules specify the interactions between unlike molecules tobe the arithmetic or geometric averages of single-molecule pairwise interactions.It seems that these rules work well in practice, although they have not beenextensively tested through experiment. Highly non-additive pair interactionshave been proposed for N2 and O2.30 The resulting N2 model accuratelymatches double-shock data, but it is not accurate at lower temperatures anddensities.32 A combination of experiments on mixtures along with advance-ments in theory is needed to develop reliable unlike-pair interaction potentials.

The exp-6 potential has also proved successful in modeling chemicalequilibrium at the high pressures and temperatures characteristic of detona-tion. However, to calibrate the parameters for such models, it is necessaryto have experimental data for product molecules and mixtures of molecularspecies at high temperature and pressure. Static compression and sound-speedmeasurements provide important data for these models.

Exp-6 potential models can be validated through several independentmeans. Fried and Howard33 have considered the shock Hugoniots of liquidsand solids in the ‘‘decomposition regime’’ where thermochemical equilibriumis established. As an example of a typical thermochemical implementation,consider the Cheetah thermochemical code.32 Cheetah is used to predict deto-nation performance for solid and liquid explosives. Cheetah solves thermody-namic equations between product species to find chemical equilibrium for agiven pressure and temperature. From these properties and elementary detona-tion theory, the detonation velocity and other performance indicators arecomputed.

Thermodynamic equilibrium is found by balancing chemical potentials,where the chemical potentials of condensed species are functions of only pres-sure and temperature, whereas the potentials of gaseous species also dependon concentrations. To solve for the chemical potentials, it is necessary toknow the pressure-volume relations for species that are important productsin detonation. It is also necessary to know these relations at the high pressuresand temperatures that typically characterize the C–J state. Thus, there is a needfor improved high-pressure equations of state for fluids, particularly formolecular fluid mixtures.


In addition to the intermolecular potential, there is an intramolecularportion of the Helmholtz free energy. Cheetah uses a polyatomic model toaccount for this portion including electronic, vibrational, and rotational states.Such a model can be expressed conveniently in terms of the heat of formation,standard entropy, and constant-pressure heat capacity of each species.

We now consider how the EOS described above predicts the detonationbehavior of condensed explosives. The overdriven shock Hugoniot of anexplosive is an appropriate EOS test, because it accesses a wide range ofhigh pressures. Overdriven states lie on the shock Hugoniot at pressures abovethe C–J point (see Figure 2). The Hugoniot of penta-erythritol tetranitrate(PETN) is shown in Figure 3. Fried, Howard and Souers40 have calculatedthe Hugoniot with the exp-6 model and with the JCZS41 product library.Figure 3 shows that the exp-6 model lies within 1% of the measured datafor pressures up to 120 GPa (1.2 Mbar). The JCZS model is accurate to within1% up to a pressure of 90 GPa, but it shows a disagreement with experimentat 120 GPa. As the exp-6 model is not calibrated to condensed explosives, suchagreement is a strong indication of the validity of the chemical equilibriumapproximation to detonation.

Despite the many successes in the thermochemical modeling of energeticmaterials, several significant limitations exist. One such limitation is that realsystems do not always obtain chemical equilibrium during the relatively short(nanoseconds-microseconds) time scales of detonation. When this occurs,quantities such as the energy of detonation and the detonation velocity arecommonly predicted to be 10–20% higher than experiment by a thermoche-mical calculation.

Figure 3 The shock Hugoniot of PETN as calculated with exp-6 (solid line) and theJCZS library (dotted line) vs. experiment (error bars).


Chemical kinetic modeling is another way to treat detonation. Severalwell-developed chemical kinetic mechanisms exist for highly studied materialssuch as hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX) and 1,3,5,7-tetrani-tro-1,3,5,7-tetraazacyclooctane (HMX).42 Unfortunately, detailed chemicalkinetic mechanisms are not available for high-pressure conditions. Someworkers have applied simplified chemical kinetics to detonation processes.16

The primary difficulty in high-pressure chemical kinetic models is a lack ofexperimental data on speciation. First principles simulations, discussed below,have the potential to provide chemical kinetic information for fast processes.This information could then conceivably be applied to longer time scales andlower temperatures using high-pressure chemical kinetics.

Finally, there are several issues to be addressed in determining the EOS ofdetonation products. Although the exp-6 model is convenient, it does not treatelectrostatic interactions adequately. In a condensed phase, effects such asdielectric screening and charge-induced dipoles need to be considered. Also,non-molecular phases are possible under high-pressure and temperatureconditions. Molecular shape is also neglected in exp-6 models. Although thesmall size of most detonation product molecules limits the importance ofmolecular shape, lower temperature conditions could yield long-chainmolecules, where molecular shape becomes more important.

The possible occurence of ionized species as detonation products is a furthercomplication that cannot be modeled using the exp-6 representation alone.Recent results on the superionic behavior of water at high pressures (see discus-sion below) provide compelling evidence for a high-pressure ionization scenario.These results suggest, for example, that polar and ionic species interactions mayaccount for approximately 10% of the (C–J) pressure of PETN. In addition, wenote that thermochemical calculations of high explosive formulations rich inhighly electronegative elements—such as F and Cl—typically have substantiallyhigher errors than calculations performed on formulations containing onlythe elements H, C, N, and O. The difficulty in modeling the C–J states of theseformulations successfully may be from the neglect of ionic species.

Bastea, Glaesemann, and Fried43 have extended the exp-6 free energyapproach to include the explicit thermodynamic contributions arising fromdipolar and ionic interactions. The main task of their theory involves calculat-ing the Helmholtz free energy (per particle) of the detonation products—f. Thetheory starts with a mixture of molecular species whose short-rangeinteractions are well described by isotropic, exp-6 potentials. This mixtureincludes, for example, all molecules commonly encountered as detonation pro-ducts, such as N2, H2O, CO2, CO, NH3 and CH4. As documentedpreviously,44 a one-fluid representation of this system, where one replacesthe different exp-6 interactions between species by a single interaction depend-ing on both individual interactions and mixture composition, is a very goodapproximation. Bastea, Glaesemann, and Fried therefore, chose this nonpolarand neutral one-component exp-6 fluid to be the reference fluid. If the mixture


components possess no charge or permanent dipole moments, the calculationof the corresponding free energy per particle, designated as fexp�6, suffices toyield the mixture thermodynamics and all desired detonation properties. Thisphysical model has been used in many thermochemical codes for the calcula-tion of high explosives behavior.

It is worth noting that at high detonation pressures and temperatures thebehavior of the exp-6 fluid so introduced is dominated by short-range repulsionsand is similar to that of a hard repulsive sphere fluid. In fact, the variational theorytreatment45 of the exp-6 thermodynamics employs a reference hard sphere systemwith an effective, optimal diameter seff that depends on density and temperature.Bastea, Glaesemann, and Fried pursued this connection to the hard sphere fluid byconsidering first a fluid of equisized hard spheres of diameter s with dipolemoments m. For this simple model of a polar liquid, Stell et al.46,47 had previouslysuggested a Pade approximation approach for calculating the free energy fd,

fd ¼ f0 þ�fd ½2�

�fd ¼f2

1� f3=f2½3�

where f0 corresponds to the simple hard sphere fluid and f2 and f3 are terms(second and third order, respectively) of the perturbation expansion in thedipole–dipole interaction ð� m2Þ such that

fd ¼ f0 þ f2 þ f3 þ . . . : ½4�

The first order term f1 can be shown to be identically zero, whereas f2 and f3

have been calculated explicitly.46 The resulting thermodynamics can be writ-ten in scaled variables as

�fd ¼ �fdðr�; b�dÞr� ¼ rs3

b�d ¼m2

kBTs3

½5�

where r is the (number) density and T is the temperature. The same Padeapproximation also holds for a mixture of identical hard spheres with differentdipole moments mi.

48,49 We note that within this approximation, it is easy toshow that the mixture thermodynamics is equivalent with that of a simplehard spheres polar fluid with an effective dipole moment m given by

m2 ¼X

i

xim2i ½6�

where xi ¼ ri=r is the concentration of particles with dipole moment mi.


We also adopt the above combination rule (Eq. [6]) for the general caseof exp-6 mixtures that include polar species. Moreover, in this case, we calcu-late the polar free energy contribution �fd using the effective hard spherediameter seff of the variational theory.

We show a comparison of this procedure with MD simulation results foran exp-6 model of polar water in Figures 4 and 5. Also shown are the results of

40

30

20

10

01 1.5 2 2.5

r[G

Pa]

r[g/cc]

Figure 4 Comparison of pressure results for a model of polar water at T ¼ 2000 K: MDsimulations (symbols), newly developed theory for polar fluids (lower line) and exp-6calculations alone (upper line).

E/N

k B[1

03 k]

8

4

01 2

r[g/cc]

Figure 5 Same as Figure 4 for energy per particle.


exp-6 thermodynamics alone. For both the pressure and the energy, theagreement is very good and the dipole moment contribution is sizeable.

The thermodynamic theory for exp-6 mixtures of polar materials is nowimplemented in the thermochemical code Cheetah.32 We considered first themajor polar detonation products H2O, NH3, CO, and HF. The optimalexp-6 parameters and dipole moment values for these species were determinedby fitting to a variety of available experimental data. We find, for example,that a dipole moment of 2.2 Debye for water reproduces very well all availableexperiments. Incidentally, this value is in very good agreement with valuestypically used to model supercritical water.50

A comparison of our Cheetah polar water model predictions with bothhigh-pressure Hugoniot data,51 and low-density (steam at 800 K) experimentaldata52 is presented in Figure 6. The agreement is very good for both cases.

The newly developed equation of state was applied to the calculation ofdetonation properties. In this context, one stringent test of any equation of stateis the prediction of detonation velocities as a function of initial densities, and wechose for this purpose PETN. The Cheetah results are shown in Figure 7 alongwith the experimental data.53 The agreement is again very good.

Advances continue in the treatment of detonation mixtures that includeexplicit polar and ionic contributions. The new formalism places on a solidfooting the modeling of polar species, opens the possibility of realistic multiplefluid phase chemical equilibrium calculations (polar—nonpolar phase segrega-tion), extends the validity domain of the EXP6 library,40 and opens thepossibility of applications in a wider regime of pressures and temperatures.

15

10

5

00.8 1.3 1.8

r[g/cc]

P[G

Pa]

Figure 6 Comparison of theory for polar water: experimental data (Hugoniot—circlesand steam at T ¼ 800 K—diamonds) and theory (lines).


Predictions of high explosive detonation based on the new approach yieldexcellent results. A similar theory for ionic species model43 compares verywell with MD simulations. Nevertheless, high explosive chemical equilibriumcalculations that include ionization are beyond the current abilities of theCheetah code, because of the presence of multiple minima in the free energysurface. Such calculations will require additional algorithmic developments. Inaddition, the possibility of partial ionization, suggested by first principlessimulations of water discussed below, also needs to be added to the Cheetahcode framework.

ATOMISTIC MODELING OF CONDENSED-PHASEREACTIONS

Chemical equilibrium methods provide useful predictions of the EOS ofdetonation processes and the product molecules formed, but no details of theatomistic mechanisms in the detonation are revealed. We now discuss con-densed-phase detonation simulations using atomistic modeling techniques toevaluate reaction mechanisms on the microscopic level.

Numerous experimental studies have investigated the atomistic details ofHE decomposition by examining the net products after thermal (low-pressure)decomposition (see, for example, Ref. 54). For RDX and HMX, the rate limitingreaction is most likely NO2 dissociation and a plethora of final products in thedecomposition process have been isolated. Several theoretical studies have also

10

8

6

4

20 0.5 1 1.5 2

r0[g/cc]

DC

J[km

/s]

Figure 7 PETN detonation velocity as a function of initial density; experiments(symbols) and Cheetah calculation (line).

Atomistic Modeling of Condensed-Phase Reactions 171

been reported on the energetics of gas-phase decomposition pathways for HEmaterials using a variety of methods. For example, we point to work on RDXand HMX where both quantum chemistry42,55–57 and classic simulations ofunimolecular dissociation58,59 were used.

Gas-phase results provide insight into the reaction pathways for isolated HEmolecules; however, the absence of the condensed-phase environment is believedto affect reaction pathways strongly. Some key questions related to condensed-phase decomposition are as follows: (1) How do the temperature and pressureaffect the reaction pathways? (2) Are there temperature or pressure-inducedphase-transitions that play a role in the reaction pathways that may occur?(3) What happens to the reaction profiles in a shock-induced detonation? Thesequestions can be answered with condensed-phase simulations, but such simula-tions would require large-scale reactive chemical systems consisting of thousandsof atoms. Here we present results of condensed-phase atomistic simulations,which are pushing the envelope toward reaching the required simulation goal.

In our group, we are considering whether non-molecular phases of suchspecies could be formed at conditions approaching those of detonation.Condensed phase explosives typically have C–J pressures in the neighborhoodof 20–40 GPa and temperatures between 2500 K and 4000 K. Early in thereaction zone, energetic materials are thought to be cooler but morecompressed. The Zeldovich–von Neumann–Doring60–62 (ZND) state is definedby the Hugoniot of the unreacted material, which can be probed by shockexperiments carefully designed to avoid HE initiation. Estimates of the tem-perature at the ZND state are in the neighborhood of 1500 K, whereas pres-sures as high as 60 GPa are possible.

One possible non-molecular phase that may exist is a superionic solid.Superionic solids are compounds that exhibit exceptionally high ionic con-ductivity, where one ion type diffuses through a crystalline lattice of theremaining types. In this unique phase of matter, chemical bonds are breakingand reforming rapidly. Since their discovery in 1836, a fundamental under-standing of superionic conductors has been one of the major challenges incondensed matter physics.63 In general, it has been difficult to create a simpleset of rules governing superionic phases. Studies have been limited mostly tometal-based compounds, such as AgI and PbF2.63 However, the existence ofsuperionic solid phases of hydrogen-bonded compounds had been theorizedpreviously.64,65

Recent experimental and computational results indicate the presence of ahigh-pressure triple point in the H2O phase diagram,66–68 including a so-calledsuperionic solid phase with fast hydrogen diffusion.68,69 Goldman et al. havedescribed the emergence of symmetric hydrogen bonding in superionic waterat 2000 K and 95 GPa.69 In symmetric hydrogen bonding, the intramolecularX–H bond becomes identical to the intermolecular X–H bond, where X is anelectronegative element. It has been suggested that for superionic solids amixed ionic/covalent bonding character stabilizes the mobile ion during the


diffusion process.63 Symmetric hydrogen bonding provides mixed ionic/cova-lent bonding and thus could be a key factor in superionic diffusion inhydrogen-bonded systems. Because of current limitations in diamond anvilcell techniques, the temperatures and pressures that can be investigated experi-mentally are too low to probe the role of hydrogen bonding in previouslystudied hydrides (i.e., H2O and NH3). On the other hand, current shockcompression experiments have difficulty resolving transient chemical species.

The density profiles of large planets, such as Uranus and Neptune, sug-gest that a thick layer of ‘‘hot ice’’, exists which is thought to be 56% H2O,36% CH4, and 8% NH3.70 This hot ice layer has lead to theoretical investiga-tions of the water phase diagram,64 in which Car-Parrinello MolecularDynamics (CPMD) simulations6 were conducted at temperatures and pres-sures ranging from 300 K to 7000 K and 30–300 GPa.65 In these moleculardynamics simulations, the electronic degrees of freedom are treated explicitlyat each time step, effectively solving the electronic Schrodinger equation ateach step. At temperatures above 2000 K and pressures above 30 GPa, asuperionic phase was observed in which the oxygen atoms had formed a bcclattice, and the hydrogen atoms were diffused extremely rapidly (ca. 10�4 cm2/s)via a hopping mechanism between oxygen lattice sites. Experimental results forthe ionic conductivity of water at similar state conditions71,72 agree well withthe results from Ref. 3, confirming the idea of a superionic phase and indicatinga complete atomic ionization of water molecules under extreme conditions(P > 75 GPa;T > 4000 K).72

More recent quantum-based MD simulations were performed attemperatures up to 2000 K and pressures up to 30 GPa.73,74 Under theseconditions, it was found that the molecular ions H3Oþ and OH� are the majorcharge carriers in a fluid phase, in contrast to the bcc crystal predicted for thesuperionic phase. The fluid high-pressure phase has been confirmed by X-raydiffraction results of water melting at ca. 1000 K and up to 40 GPa ofpressure.66,75,76 In addition, extrapolations of the proton diffusion constantof ice into the superionic region were found to be far lower than a commonlyused criterion for superionic phases of 10�4 cm2/s.77 A great need exists foradditional work to resolve the apparently conflicting data.

The superionicphasehasbeenexploredwithmore extensiveCPMDsimula-tions.69 Calculated power spectra (i.e., the vibrational density of states or VDOS)have been compared with measured experimental Raman spectra68 at pressuresup to 55 GPa and temperatures of 1500 K. The agreement between theory andexperiment was very good. In particular, weakening and broadening of the OHstretch mode at 55 GPa was found both theoretically and experimentally.

A summary of our results on the phase diagram of water is shown inFigure 8. We find that the molecular to non-molecular transition in wateroccurs in the neighborhood of the estimated ZND state of HMX. Thistransition shows that the detonation of typical energetic materials occurs inthe neighborhood of the molecular to non-molecular transition.


For our simulations, we used CPMD v.3.91, with the BLYP exchange-correlation functional,78,79 and Troullier–Martins pseudo-potentials80 forboth oxygen and hydrogen. A plane wave cut-off of 120 Ry was employed toensure convergence of the pressure, although all other properties were observedto converge with a much lower cut-off (85 Ry). The system size was 54 H2Omolecules. The temperature was controlled by using Nose–Hooverthermostats81 for all nuclear degrees of freedom. We chose a conservative valueof 200 au for the fictitious electron mass and a time step of 0.048 fs.

Initial conditions were generated in two ways: (1) A liquid configurationat 2000 K was compressed from 1.0 g/cc to the desired density in sequentialsteps of 0.2 g/cc from an equilibrated sample. (2) An ice VII configurationwas relaxed at the density of interest and then heated to 2000 K in steps of300 degrees each, for a duration of 0.5–1 ps. While heating, the temperaturewas controlled via velocity scaling. We will refer to the first set of simulationsas the ‘‘L’’ set and the second as the ‘‘S’’ set. Unless stated otherwise, theresults (including the pressures) from the ‘‘S’’ initial configurations are thosereported. Once the desired density and/or temperature was achieved, allsimulations were equilibrated for a minimum of 2 ps. Data collection fromthe simulations was obtained for 5–10 ps after equilibration.

The calculated diffusion constants of hydrogen and oxygen atoms areshown in Figure 9. The inset plot shows the equation of state for this isothermfor both ‘‘L’’ and ‘‘S’’ simulations. The two results are virtually identical upuntil 2.6 g/cc. At 34 GPa (2.0 g/cc), the hydrogen atom diffusion constanthas achieved values associated with superionic conductivity (greater than

ZND2000

1500

1000

500

00 20 40 60 80 100

Pressure (GPa)

ice VII

ice VIII

ice X

superionicphasemolecular liquid

Tem

pera

ture

(K

)

Figure 8 The phase diagram of H2O as measured experimentally68 (black solid) andthrough first principles simulations of the superionic phase (gray dash).68,69 Theestimated ZND state of HMX is shown as a square for reference.


10�4 cm2/s). The diffusion constant remains relatively constant with increasingdensity, in qualitative agreement with the experimental results of Chau et al.72

for the ionic conductivity.In contrast, the O diffusion constant drops to zero at 75 GPa (2.6 g/cc)

for both ‘‘L’’ and ‘‘S’’ initial configurations. The surprisingly small hysteresisin the fluid to superionic transition allows us to place the transition pointbetween 70 GPa (2.5 g/cc) and 77 GPa (2.6 g/cc). The small hysteresis ismost likely caused by the weak O–H bonds at the conditions studied, whichhave free energy barriers to dissociation comparable with kBT (see below).Simulations that start from the ‘‘L’’ initial configurations are found to quenchto an amorphous solid upon compression to 2.6 g/cc.

The transition pressure of 75 GPa is much higher than the 30 GPapredicted earlier.65 This difference is likely caused by the use of a much smallerbasis set (70 Ry) by Cavazzoni et al. Our results are also in disagreement withsimple extrapolations of the proton diffusion constant to high temperatures.77

Radial distribution functions (RDFs) for the ‘‘S’’ simulations are shownin Figure 10. Analysis of the oxygen–oxygen RDF (not shown) for all pressuresyields a coordination number of just over 14 for the first peak, which isconsistent with a high-density bcc lattice in which the first two peaks arebroadened because of thermal fluctuations. The RDF can be further analyzedby calculating an ‘‘average position’’ RDF in which the position of eachoxygen is averaged over the course of the trajectory. The results for

3.0x10–4

2.5

2.0

1.5

1.0

0.5

0.0

2.0 2.2 2.4 2.6 2.8 3.0Density (g/cc)

Diff

usio

n co

nsta

nt (

D, c

m2 /

s)

120

100

80

60

40

2.0 2.2 2.4 2.6 2.8 3.0Density (g/cc)

Pre

ssur

e (G

Pa)

××

××

××

Figure 9 Diffusion constants for O and H atoms at 2000 K as a function of density. Thelines with circles correspond to hydrogen and the lines with squares to oxygen. The solidlines correspond to a liquid (‘‘L’’) initial configuration and the dashed lines to an ice VII(‘‘S’’) initial configuration. The inset plot shows the pressure as a function of density at2000 K, where the triangles correspond to ‘‘L’’ and the Xs to ‘‘S.’’


75–115 GPa indicate the presence of a bcc lattice undergoing large amplitudevibrations, even though each RDF in Figure 10 has width similar to that of aliquid or a glass. The RDFs for the amorphous phase (not shown) are similarto those of the solid phase obtained in the ‘‘S’’ simulations.

The O–O and H–H RDFs (not shown) indicate that no O–O or H–Hcovalent bonds are formed during the simulations at all densities. Theg(ROH) shows a lattice-like structure at 115 GPa, which is consistent withproton diffusion via a hopping mechanism between lattice sites.65 At34 GPa, the coordination number for the first peak in g(ROH) is 2, whichindicates molecular H2O. Between 95 GPa and 115 GPa, however, thecoordination number for the first peak in g(ROH) becomes four, whichindicates that water has formed symmetric hydrogen bonds where eachoxygen has four nearest-neighbor hydrogens.

Concomitant with the change in the oxygen coordination number is ashift of the first minimum of the O–H RDF from 1.30 A at 34 GPa to 1.70A at 115 GPa. We observe a similar structural change in the H–H RDF inwhich the first peak lengthens from 1.63 A (close to the result for ambient con-ditions) to 1.85 A. These observations bear a strong resemblance to the ice VIIto ice X transition in which the covalent O–H bond distance of ice becomesequivalent to the hydrogen bond distance as pressure is increased.82 However,the superionic phase differs from ice X, in that the position of the first peak ing(ROH) is not half the distance of the first O–O peak.82 We analyze the effect

Figure 10 O–H radial distribution function as a function of density at 2000 K. At34 GPa, we find a fluid state. At 75 GPa, we show a ‘‘covalent’’ solid phase. At 115 GPa,we find a ‘‘network’’ phase with symmetric hydrogen bonding. Graphs are offset by 0.5for clarity.


of the change in g(ROH) below in terms of the molecular speciation in thesimulations.

We determined the free energy barrier for dissociation by defining a freeenergy surface for the oxygen–hydrogen distances, viz. WðrÞ ¼ �kBTln [g(ROH)], where WðrÞ is the free energy surface (potential of mean force).The results are shown in Figure 11.

The free energy barrier can then be defined as the difference in heightbetween the first minimum and the second maximum in the free energy surface.The free energy barrier is 11 kcal/mol at 34 GPa and 8 kcal/mol at 115 GPa. Theremainder of the results discussed below are for the ‘‘S’’ simulations.

We now analyze the chemical species prevalent in water at these extremeconditions by defining instantaneous species based on the O–H bond distance.If that distance is less than a cut-off value rc, we count the atom pair as beingbonded. Determining all bonds in the system gives the chemical species at eachpoint in time. Species with lifetimes less than an O–H bond vibrational period(10 fs) are ‘‘transient’’ and do not represent bound molecules. The optimalcut-off rc between bonded and nonbonded species is given by the location ofthe maximum in the free energy surface.83

Using the free energy maximum to define a bond cut-off provides a clearpicture of qualitative trends. As expected from the g(ROH), at 34 GPa, the freeenergy peak is found at 1.30 A, which is approximately the same valueobtained from simulations of ambient water. At 75 GPa, the free energypeak maintains almost the same position but broadens considerably. At115 GPa, the peak has sharpened once again, and the maximum is now at1.70 A.

Figure 11 ROH free energy surface at 2000 K. The lines are spaced by a factor of 4 kcal/mol for clarity.


Given the above definition of a bond distance, we can analyze specieslifetimes. The lifetime of all species is less than 12 fs above 2.6 g/cc, whichis roughly the period of an O–H bond vibration (ca. 10 fs). Hence, waterdoes not contain any molecular states above 75 GPa and at 2000 K but insteadforms a collection of short-lived ‘‘transient’’ states. The ‘‘L’’ simulations at2.6 g/cc (77 GPa) and 2000 K yield lifetimes nearly identical to that found inthe ‘‘S’’ simulations (within 0.5 fs), which indicates that the amorphous statesformed from the ‘‘L’’ simulations are closely related to the superionic bcccrystal states found in the ‘‘S’’ simulations.

Species concentrations are shown in Figure 12. At 34 GPa (2.0 g/cc),H2O is the predominant species, with H3Oþ and OH� having mole fractionsof ca. 5%. In addition, some aggregation has occurred in which neutral andionic clusters containing up to six oxygens have formed. The concentrationsof OH� and H3Oþ are low for all densities investigated and nonexistent at95 and 115 GPa (2.8 and 3.0 g/cc, respectively). The calculated lifetimes forthese species are well below 10 fs for the same thermodynamic conditions(less than 8 fs at 34 GPa). At pressures of 95 and 115 GPa, the increase inthe O–H bond distance leads to the formation of extensive bond networks(Figure 13). These networks consist entirely of O–H bonds, whereas O–Oand H–H bonds were not found to be present at any point.

A maximally localized Wannier function analysis84–86 was performed tobetter analyze the bonding in our simulations. The maximally localizedWannier functions express the quantum wave function in terms of functionslocalized at centers, rather than as delocalized plane waves. The positions ofthese centers give us insight into the localization of charge during the

Figure 12 Mole fraction of species found at 34–115 GPa and 2000 K. The filled circlescorrespond to H3Oþ, whereas the open circles correspond to OH�.


simulation. We computed the percentage of O–H bonds with a Wannier centeralong the bond axis. Surprisingly, the results for pressures of 34–75 GPaconsistently showed that 85–95% of the O–H bonds are covalent. For95 GPa and 115 GPa, we find about 50–55% of the bonds are covalent.This result is consistent with symmetric hydrogen bonding, for which the splitbetween ionic and covalent bonds would be 50/50. The above simulationsshow that the molecular to non-molecular transition in H2O lies just abovethe operating range of most typical condensed explosives—about 50 GPa.This range presents a considerable challenge for thermochemical calculations,because a simple statistical mechanical treatment of non-molecular phasessuch as superionic water does not yet exist.

FIRST PRINCIPLES SIMULATIONS OF HIGHEXPLOSIVES

Quantum mechanical methods can now be applied to systems with up to1000 atoms;87 this capacity is not only from advances in computer technologybut also from improvements in algorithms. Recent developments in reactiveclassical force fields promise to allow the study of significantly larger systems.88

Many approximations can also be made to yield a variety of methods, each ofwhich can address a range of questions based on the inherent accuracy of themethod chosen. We now discuss a range of quantum mechanical-based methodsthat one can use to answer specific questions regarding shock-induced detona-tion conditions.

Atomistic simulations have been performed on condensed-phase HMX,which is a material that is widely used as an ingredient in various explosivesand propellants. A molecular solid at standard state, it has four known

Figure 13 Snapshots of the simulations at 75 GPa (left) and 115 GPa (right). Thetemperature for both is 2000 K. At 75 GPa, the water molecules are starting to cluster,and at 115 GPa, a well-defined network has been formed. The protons dissociate rapidlyand form new clusters (at 75 GPa) or networks of bonds (at 115 GPa).

First Principles Simulations of High Explosives 179

polymorphs, of which d-HMX is believed to be the most highly reactive. Infact, b-HMX often transforms into d-HMX before reacting violently.89

Manaa et al.20 have conducted quantum-based molecular dynamics simula-tions of the chemistry of HMX and nitromethane90 under extreme conditions,which are similar to those encountered at the C–J detonation state. They stu-died the reactivity of dense (1.9 g/cm3) fluid HMX at 3500 K for reaction timesup to 55 ps, using the ‘‘Self-Consistent Charge Density-Functional Tight-Binding’’ (SCC-DFTB) method.91 Stable product molecules are formed rapidly(in a less than 1 ps) in these simulations. Plots of chemical speciation, however,indicate a time greater than 100 ps is needed to reach chemical equilibrium.Reactions occur rapidly in these simulations because the system is ‘‘preheated’’to 3500 K. In a detonation, on the other hand, a temperature close to 3500 Kwould only be found after stable product molecules had been formed. Theinitial temperature of unreacted nitromethane, after being shocked, has beenestimated to be 1800 K.13 HMX likely has a similar initial temperature tothat of nitromethane. Nonetheless, the simulations of Manaa et al. provideuseful insight into the chemistry of dense, hot energetic materials, whichdemonstrate that they are a useful complement to more traditional gas phasecalculations.

Numerous experimental characterizations of the decomposition productsof condensed-phase HMX exist at low temperatures (i.e., < 1000 K, well belowdetonation temperature).54, 92–100 These studies tend to identify final gas pro-ducts (such as H2O, N2, H2, CO, and CO2) from the surface burn, and theauthors aspire to establish a global decomposition mechanism. Similar experi-mental observations at detonation conditions (temperatures 2000–5000 K andpressures 10–30 GPa) have not been realized to date, however. Computer simu-lations provide the best access to the short time scale processes occurring in theseregions of extreme conditions of pressure and temperature.101 In particular,simulations employing many-body potentials102,103 or tight-binding modelshave emerged as viable computational tools, the latter of which has beendemonstrated successfully in the studies of shocked hydrocarbons.104,105

Lewis et al.106 calculated four possible decomposition pathways of thea-HMX polymorph: N–NO2 bond dissociation, HONO elimination, C–Nbond scission, and concerted ring fission. Based on energetics, it wasdetermined that N–NO2 dissociation was the initial mechanism of decomposi-tion in the gas phase, whereas they proposed HONO elimination and C–Nbond scission to be favorable in the condensed phase. The more recent studyof Chakraborty et al.42 using density functional theory (DFT), reporteddetailed decomposition pathways of b-HMX, which is the stable polymorphat room temperature. It was concluded that consecutive HONO elimination(4 HONO) and subsequent decomposition into HCN, OH, and NO are themost energetically favorable pathways in the gas phase. The results alsoshowed that the formation of CH2O and N2O could occur preferably fromsecondary decomposition of methylenenitramine.


The computational approach to simulate the condensed-phase chemicalreactivity of HMX employed by Manaa et al.20 is based on implementing theSCC-DFTB scheme.91 This approach is an extension of the standard tight-binding approach in the context of DFT that describes total energies, atomicforces, and charge transfer in a self-consistent manner. The initial conditionsof the simulation included six HMX molecules, which correspond to a singleunit cell of the d-phase, with a total of 168 atoms. The density was 1.9 g/cm3

and the temperature 3500 K in the simulations. These thermodynamic quanti-ties place the simulation in the neighborhood of the C–J state of d-HMX(3800 K, 2.0 g/cm3) as predicted through thermochemical calculations. Theclosest experimental condition corresponding to this simulation would be asample of HMX that is suddenly heated under constant volume conditions,such as in a diamond anvil cell. A molecular dynamics simulation of the168-atom system was conducted at constant volume and constant tempera-ture. Periodic boundary conditions, whereby a particle exiting the super cellon one side is reintroduced on the opposite side with the same velocity,were imposed.

Under the simulation conditions, the HMX was found to exist in a highlyreactive dense fluid. Important differences exist between the dense fluid(supercritical) phase and the solid phase, which is stable at standardconditions. One difference is that the dense fluid phase cannot accommodatelong-lived voids, bubbles, or other static defects, whereas voids, bubbles, anddefects are known to be important in initiating the chemistry of solidexplosives.107 On the contrary, numerous fluctuations in the local environ-ment occur within a time scale of tens of femtoseconds (fs) in the dense fluidphase. The fast reactivity of the dense fluid phase and the short spatial coher-ence length make it well suited for molecular dynamics study with a finite sys-tem for a limited period of time; chemical reactions occurred within 50 fsunder the simulation conditions. Stable molecular species such as H2O, N2,CO2, and CO were formed in less than 1 ps.

Figure 14 displays the product formation of H2O, N2, CO2, and CO.The concentration C(t) is represented by the actual number of product mole-cules formed at time t. Each point on the graphs (open circles) represents anaverage over a 250-fs interval. The number molecules in the simulation weresufficient to capture clear trends in the chemical composition of the speciesinvolved. It is not surprising to find that the rate of H2O formation is muchfaster than that of N2. Fewer reaction steps are required to produce atriatomic species like water, whereas the formation of N2 involves a muchmore complicated mechanism.108 Furthermore, the formation of water startsaround 0.5 ps and seems to have reached a steady state at 10 ps, withoscillatory behavior of decomposition and formation clearly visible. Theformation of N2, on the other hand, starts around 1.5 ps and is stillprogressing (as the slope of the graph is slightly positive) after 55 ps ofsimulation time, albeit slowly.


Because of the lack of high-pressure experimental reaction rate data forHMX and other explosives with which to compare, we produce in Figure 15 acomparison of dominant species formation for decomposing HMX that havebeen obtained from entirely different theoretical approaches. The concentra-tion of species at chemical equilibrium can be estimated through thermody-namic calculations with the Cheetah thermochemical code.32,109

The results of the MD simulation compare well with the formation ofH2O, N2, and HNCO predicted by Cheetah. The relative concentrations ofCO and CO2, however, are reversed, possibly because of the limited timeduration of the simulation. Another discrepancy is that Cheetah predictscarbon in the diamond phase is in equilibrium with the other species at aconcentration of 4.9-mol/kg HMX. No condensed carbon was observed inthe simulation. Several other products and intermediates with lowerconcentrations, common to the two methods, have also been identified,including HCN, NH3, N2O, CH3OH, and CH2O. A comparison between

Figure 14 Product particle-number formations for H2O, N2, CO2, and CO as a functionof time.


the two vastly different approaches needs to be established when using muchlonger simulation times. Also, the product-molecule set of the thermochemicalcode needs to be expanded with important species determined from quantum-based simulations. It should also be noted that the accuracy of DFT calcula-tions for chemistry under extreme conditions needs further experimentalvalidation.

One expects the Cheetah results where more CO2 than CO is formed asfinal products, because disproportionation of CO to condensed Cþ CO2 isenergetically favorable. The results displayed in Figure 14 show that at asimulation time of 40 ps the system is still in the second stage of reactionchemistry. At this stage, the CO concentration is rising but has not yetundergone the water gas shift reaction ðCOþH2O! CO2 þH2Þ conversion.Interestingly, this shift occurs around 50 ps in the simulation, when CO2

molecules are being formed while the CO concentration is correspondinglydiminished.

Although the simulation sheds light on the chemistry of HMX underextreme conditions, some methodological shortcomings need to be overcomein the future. The demanding computational requirements of the quantum-based MD method limit its applicability to short times and high-temperatureconditions. For example, the simulations discussed on HMX took over a yearof wall clock time. Moreover, the SCC-DFTB method is not as accurate ashigh-level quantum-based methods. Nonetheless, the SCC-DFTB approachcould still be considered as a promising direction for future research on thechemistry of energetic materials.

Figure 15 Comparison of relative composition of dominant species found in the MDsimulation and in a thermodynamic calculation.


CONCLUSIONS

The ability to model chemical reaction processes in condensed-phaseenergetic materials at the extreme conditions typified by a detonation isprogressing. Chemical equilibrium modeling is a mature technique withsome limitations. Progress in this area continues, but it is hampered by alack of knowledge of condensed-phase reaction mechanisms and rates. Auseful theory of the equation of state for ionic and highly polar molecularspecies needs to be more fully developed. The role of unconventionalmolecular species in detonation needs to be investigated, and high-pressurechemical kinetics needs to be developed further as a field of study.

Atomistic molecular dynamics modeling is computationally intensiveand is currently limited in the realm of detonations to picosecond time scales.Nonetheless, this methodology promises to yield the first reliable insights intothe condensed-phase processes responsible for high explosive detonation. Firstprinciples simulations reveal that the transition to non-molecular phases liesclose to the operating range of common explosives such as HMX. Additionalwork is necessary to extend the time scales involved in atomistic simulations.Alternatively, advanced force fields may offer the ability to model the reactionsof energetic materials for periods of many picoseconds. Recent work inimplementing thermostat methods appropriate to shocks110,111 may promiseto overcome time scale limitations in the non-equilibrium molecular dynamicsmethod itself and allow the reactions of energetic materials to be determinedfor up to several nanoseconds.

ACKNOWLEDGMENTS

The author is grateful for the contributions of many collaborators to the work reviewedhere. Nir Goldman and M. Riad Manaa played a central role in the atomistic simulations. W.Michael Howard, Kurt R. Glaesemann, P. Clark Souers, Peter Vitello, and Sorin Bastea developedmany of the thermochemical simulation techniques discussed here. This work was performedunder the auspices of the U. S. Department of Energy by the University of California LawrenceLivermore National Laboratory under Contract W-7405-Eng-48.

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