Molecular dynamics simulations of melting of perfect crystalline hexahydro-1,3,5-trinitro-1,3,5- s -triazineLianqing Zheng and Donald L. Thompson

Citation: The Journal of Chemical Physics 125, 084505 (2006); doi: 10.1063/1.2238860 View online: http://dx.doi.org/10.1063/1.2238860 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/125/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Molecular dynamics characterization of void defects in crystalline (1,3,5-trinitro-1,3,5-triazacyclohexane) J. Chem. Phys. 131, 204903 (2009); 10.1063/1.3265986 1,3,5-trinitro-1,3,5-triazine decomposition and chemisorption on Al(111) surface: First-principles moleculardynamics study J. Chem. Phys. 126, 234702 (2007); 10.1063/1.2200352 Nonreactive molecular dynamics force field for crystalline hexahydro-1,3,5-trinitro-1,3,5 triazine J. Chem. Phys. 124, 104508 (2006); 10.1063/1.2176621 Molecular dynamics in n -alkanes: Premelting phenomena and rotator phases J. Chem. Phys. 124, 054901 (2006); 10.1063/1.2148909 Molecular dynamics studies of melting and some liquid-state properties of 1-ethyl-3-methylimidazoliumhexafluorophosphate [ emim ] [ PF 6 ] J. Chem. Phys. 122, 154704 (2005); 10.1063/1.1880932

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THE JOURNAL OF CHEMICAL PHYSICS 125, 084505 �2006�

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Molecular dynamics simulations of melting of perfect crystallinehexahydro-1,3,5-trinitro-1,3,5-s-triazine

Lianqing Zheng and Donald L. Thompsona�

Department of Chemistry, University of Missouri, Columbia, Missouri 65211

�Received 22 March 2006; accepted 30 June 2006; published online 24 August 2006�

The melting mechanism of superheated perfect crystalline hexahydro-1,3,5-trinitro-1,3,5-s-triazine��-RDX� has been investigated using molecular dynamics simulations with the fully flexible forcefield developed by Smith and Bharadwaj �J. Phys. Chem. B 103, 3570 �1999��. Sequential 50 psequilibration simulations of the constant stress–constant temperature ensemble were performed at10 K intervals over the range of 300–650 K, corresponding to a heating rate of 2.0�1011 K/s. Asolid-solid phase transition is observed between 480 and 490 K, followed by melting, which occursbetween 500 and 510 K. The solid-solid phase transition, both displacive and rotational, ischaracterized by an abrupt decrease in the lengths of the unit cell edges a and b and an increase ofthe length of edge c. The molecular conformation in the new phase is AAE, although the axial nitrogroups have different changes: one shift is more axial and the other is more equatorial. Phases otherthan �-RDX have been observed experimentally, however, there are insufficient data forcomparisons to ascertain that the new phase observed here corresponds to a real phase. At the highheating rate �2.0�1011 K/s� used in the simulations, the melted RDX reaches full orientationaldisorder at about 540 K and translational freedom at around 580 K. If the simulation at the meltingtemperature �510 K� is run sufficiently long complete rotational freedom is achieved in a fewhundreds of picoseconds, while complete translational freedom requires much longer. These resultsshow that given a sufficiently high heating rate, the system can exist for significant periods of timein a near-liquid state in which the molecules are not as free to rotate and diffuse as in the true liquidstate. The bond lengths and bond angles undergo little change upon melting, while there aresignificant changes in the dihedral angles. The molecular conformation of RDX changes from AAEto EEE upon melting. The ramification of this for formulating force fields that accurately describemelting is that it is important that the torsional motions are accurately described. © 2006 AmericanInstitute of Physics. �DOI: 10.1063/1.2238860�

I. INTRODUCTION

Direct measurements of molecular-level details of melt-ing are difficult. Molecular dynamics �MD� simulations pro-vide a practical means of gaining insights that are not acces-sible experimentally into the microscopic mechanisms bywhich a solid is transformed to a liquid. Many MD studies ofmelting of atomic solids have been reported, but only a fewof molecular solids. We have reported a series of studiesusing MD simulations to investigate the melting of complexmolecular and ionic solids.1–6 We have used nitromethane asa prototypical molecular solid. We have developed a forcefield that accurately describes the solid, liquid, and meltingproperties of nitromethane. Agrawal et al.7 compared the re-sults of MD simulations of melting of rigid and flexible mod-els of nitromethane, concluding that the melting point is pre-dicted equally well with either model. The molecularstructure does not undergo significant change upon melting.8

In a study of a somewhat larger, more flexible molecule,dimethylnitramine, we found that molecular torsional mo-tions are important for accurately modeling the meltingtransition.9 These results prompt us to investigate melting of

a�

Electronic mail: thompsondon@missouri.edu

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crystals of larger, floppier molecules. Here we report the re-sults of MD simulations of perfect crystalline hexahydro-1,3,5-trinitro-1,3,5-s-triazine C3N6O6H6 �RDX�, a widelyused energetic material, and an excellent prototypical large,flexible molecule.

Figure 1 shows the molecular configuration of �-RDX;the labeling of the atoms will be used in subsequent discus-

FIG. 1. The molecular structure of �-RDX with the labeling of the atomsthat is used in the discussions. The coordinates were based on the x-ray data

�Ref. 11�.

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084505-2 L. Zheng and D. L. Thompson J. Chem. Phys. 125, 084505 �2006�

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sions. RDX has close to Cs symmetry. The molecule consistsof three CH2NNO2 units arranged in a six-member ring, withtwo nitro groups �N2N5O3O4 and N3N6O5O6 in Fig. 1� ofthe molecule in the �-RDX crystal arranged in the pseudo-axial �A� position about the ring and a third in the pseu-doequatorial �E� position, i.e., the AAE conformation. Ex-periments indicate that there are considerable differences inthe molecular structure in the two crystalline phases forwhich there are data, in solution, and in the gas phase.10 Themajor change is in the relative orientations of the nitrogroups. It seems reasonable that if there are intramolecularchanges in transitions from the solid to the solution or gasphase, there would be similar changes upon melting.

Crystalline RDX exists in several polymorphic forms.The most stable phase at ambient conditions is �-RDX,which is orthorhombic and belongs to the space group Pbcawith eight molecules in the unit cell.11 The second crystallinephase, �-RDX, was first observed by McCrone12 by recrys-tallizing RDX on a microscope slide from high boiling-pointsolvents. It is highly unstable and therefore crystallographicdata for it are not available.13 Olinger et al.14 first observedthe third crystalline phase, RDX III, at 293 K when theyapplied a pressure of over 4 GPa on �-RDX. RDX III isorthorhombic and belongs to the Pbca space group. Themelting point �462 K� of �-RDX has been measured.15 Baeret al.16 used Raman spectroscopy to study the phase diagramof RDX at pressures up to 16 GPa and over the temperaturerange of 150–450 K. They determined the pressure for the�-RDX→RDX III transition to be 3.8±0.2 GPa and inde-pendent of temperature from 150 to 375 K. They found the�-RDX→RDX III transition to be reversible. They also ob-served a metastable phase of RDX at high pressure and hightemperature, which they concluded was �-RDX based oncomparisons of their Raman spectra with the IR spectra of�-RDX.17 However, there have been no further results toconfirm this.

When a crystal is subjected to ultrafast heating inducedby intense radiation or shock waves, it can undergo super-heating before melting.18–20 An explosive when shocked orrapidly heated is very likely to undergo some superheatingbefore it melts and detonates.21,22 Our main interest in thepresent study is the melting mechanism of superheated per-fect crystalline RDX, thus the present study is for perfectcrystals. We have not attempted to calculate the thermody-namic melting point of RDX.

II. COMPUTATIONAL METHODS

A. Force field

The fully flexible force field developed by Smith andBharadwaj23 �SB� was used for the simulations. This forcefield was at first developed for dimethylnitramine24 by usingquantum-chemistry calculations and later extended tooctahydro-1,3,5,7-tetranitro-1,3,5,7-tetra-azacyclooctane�HMX�. Smith and co-workers have applied this force fieldto study the physical properties of crystalline and liquidHMX’s, such as density, lattice parameters,25 elasticproperties,26 shear viscosity coefficient,27 and thermal

28

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structures of HMX and RDX, we assume that the force fieldrealistically describes RDX without any modifications exceptfor the atomic partial charges. The total potential energy�Utotal� of this force field is the summation of the electrostatic�UES�, van der Waals �UvdW�, bond stretching �Ubond�, bond-angle bending �Uangle�, and dihedral �Udih, which includesproper dihedrals and out-of-plane bends� energies,

Utotal = �i=1

N

�j=i+1

N �kcqiqj

Rij+ Aij exp�− BijRij� −

Cij

Rij6 �

+ �bonds

Ks

2�r − r0�2 + �

angles

KB

2�� − �0�2

+ �proper dihedrals

KT

2�1 − cos�n���

+ �out−of−plane bends

KO

2�2, �1�

where Aij, Bij, and Cij are parameters for the intermolecularvan der Waals interactions; qi, Rij, r, �, �, and � are thepartial charges, nonbonded interatomic distances, bondlengths, bond angles, proper dihedral angles, and out-of-plane bending �improper dihedral� angles, respectively; KS,KB, and KO are the harmonic force constants for bondstretching, bond-angle bending, and out-of-plane bending,respectively; KT and n are the barrier and periodicity for thetorsional motions, respectively; N and kc are the number ofatoms in the simulation supercell and Coulomb constant, re-spectively. The electrostatic and van der Waals interactionsare applied to all intermolecular atoms and atoms separatedby three or more bonds in a molecule. The values of theparameters Aij, Bij, Cij, KS, KB, KO, KT, and n are given inRef. 23 and the partial charges are taken from Ref. 29.

B. Molecular dynamics simulations

The MD supercell consisted of 2�3�3 unit cells �144molecules, 3024 atoms� of �-RDX. The initial atomic coor-dinates were calculated according to experimental crystallo-graphic data and the initial supercell was of size 26.364�34.722�32.127 Å3. Three-dimensional periodic boundaryconditions were applied. All simulations were performed us-ing the DLPOLY program30 for the constant-temperature and-stress �NST� ensemble.31–33 The same relaxation time,1.0 ps, was used for the thermostat and barostat. The timestep for trajectory integration was 1.0 fs. The cutoff distanceof 11.0 Å was used for the van der Waals interactions andthe electrostatic interactions were calculated using thesmooth particle mesh Ewald algorithm.34 The average valueof the pressure in all simulations was constrained at 1 atm.

Simulations of 50 ps duration were performed at 10 Kincrements, equivalent to a heating rate of 2.0�1011 K/s.The starting configuration of each simulation was the lastconfiguration of the previous simulation at a lower tempera-ture. The duration of each simulation was 50 ps. The initialtemperature was 300 K and then increased to 350 and400 K, after which the temperature increment was set to be

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To monitor the changes in the system with increasingtemperature, we define translational ��T� and orientational��O� order parameters,

�T =1

Nm�i=1

Nm �cos�2ri

ref · ri

�riref�2 ��2

�2�

and

�O =1

Nm�i=1

Nm

�nCCC,i . nCCC,iref �2. �3�

Here, Nm is the number of molecules in the supercell, and thevectors ri and nCCC,i are, respectively, the coordinates of thecenter of mass and normal vector of the C¯C¯C plane ofthe ith molecule. The superscript “ref” denotes the valuesexpected when the MD supercell undergoes only linear ther-mal expansion. Similar order parameters have been used tostudy the melting of nitromethane.8

To determine the changes in the molecular orientationsin the solid-solid phase transition �see below�, we have cal-culated the distribution of an angle-order parameter definedas

cos�i� = nCCC,i · nCCC,iref . �4�

III. RESULTS AND DISCUSSION

The values of the density and lattice parameters of crys-talline RDX predicted by the SB potential at ambient condi-tions are in good agreement with experiment.11 The com-puted density at 300 K and 1 atm is 1.83 g/cm3, about 1.2%larger than the measured value of 1.81 g/cm3. The calculatedcrystal unit cell lengths a, b, and c are 13.330, 11.497, and10.532 Å, respectively, compared to the experimental valuesof 13.182, 11.574, and 10.709 Å.11 The calculated unit cellangles �, �, and � are 90.02°, 89.98°, and 90.00°, in excel-lent agreement with the measured value of 90.0° for the threeangles. The calculated 300 K isotherm �see Fig. 2� is also inexcellent agreement with the experimental data14 up to4 GPa, where the �→ III phase transition is expected. TheSB potential does not predict the �→ III transition, possiblybecause the repulsive part of the potential is not accurate athigh pressure. The bulk modulus B and its pressure deriva-tive B� were calculated by fitting the isotherm up to 4 GPa tothe third-order Birch-Murnaghan equation35

P�V� =3

2B� V

V0�−7/3

− � V

V0�−5/3��1 −

3

4�4 − B��

�� V

V0�−2/3

− 1� , �5�

where V0 is the volume at 1 atm. The calculated values of Band B� are, respectively, 12.3 GPa and 9.95 compared to12.1 GPa and 8.65, which were obtained by fitting the ex-perimental data14 to Eq. �5�. The reported experimental val-ues of B range from 11.1 to 11.9 GPa,36,37 thus our calcu-lated value of B is in good agreement with all the available

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The density � and diffusion coefficient D of the carbonatoms over the temperature range of 300–650 K are shownby the solid circles in Fig. 3. These results were obtainedusing a heating rate of 2.0�1011 K/s. There are abruptchanges in � and D between 500 and 510 K due to melting.About 10 K below the melting transition, there is a small�0.9%� abrupt decrease in the density, which we discuss be-low. The density of RDX abruptly decreases by 6.2% at510 K and there is a sharp increase in the diffusion coeffi-cient from near zero to 10−10 m2/s. This melting temperatureof the perfect RDX crystal is comparable to the value of504 K calculated using a force field that is a combination ofthe generalized AMBER �Ref. 38� intramolecular interactionsand the Sorescu-Rice-Thompson �SRT� force field.29 TheAMBER-SRT force field predicts 439 K for the thermody-namic melting point, in reasonable agreement with the mea-

FIG. 2. Comparison of the calculated �circles� and experimental �squares�isotherms of RDX crystal at 300 K. �a� Relative volume as a function ofpressure; �b� unit cell edge lengths as functions of pressure. The experimen-tal data were taken from Olinger et al., Ref. 14.

FIG. 3. Calculated �a� density and �b� diffusion coefficient of RDX as func-11

tions of temperature. The rate of heating was 10 K/50 ps �2.0�10 K/s�.

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084505-4 L. Zheng and D. L. Thompson J. Chem. Phys. 125, 084505 �2006�

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sured value of 462 K.39 We did not compute the thermody-namic melting point for the SB force field, but given theagreement with the AMBER-SRT for the perfect solid, wewould expect good agreement for the thermodynamic melt-ing point, and thus good agreement with experiment.

The small drop in the density values shown in Fig. 3 thatoccurs below the melting point is the result of a solid-solidphase transition. Note that there is not a corresponding in-crease in the diffusion coefficient. The changes in the volumeand shape of the unit cell for this phase change are shown bythe circles in Fig. 4. Figure 4 shows the volume and thelengths of the edges of the unit cell for both heating �circles�and cooling �squares� over the range of 300–500 K. Heatingresults in a small but significant change in the volume be-tween 480 and 490 K, however, upon cooling at the samerate as the heating there is no abrupt change in volume, in-dicating that the transition is not reversible. The lengths ofthe unit cell edges a, b, and c are shown, respectively, inpanels �b�, �c�, and �d� of Fig. 4. There are abrupt changes ina, b, and c in the interval of 480–490 K from 13.46, 11.64,and 10.71 Å to 13.35, 11.23, and 11.29 Å �−0.8%, −3.5%,and 5.4%�, respectively. The average values of the unit cellangles remain 90°. This phase is likely an artifact of the SBforce field, and we will refer to it as RDX-SB. There areinsufficient data for the crystal phases of RDX to determinewhether the RDX-SB phase approximates a real phase. It isreasonable to assume that a solid passes through such tran-sitory phases as the temperature approaches the meltingpoint, although it is expected that it would be less orderedthan the one predicted by the SB force field. Though thedifference of the densities of the two solid phases is quitesmall, the unit cell edge lengths differ significantly, espe-

FIG. 4. Calculated �a� unit cell volume V and ��b�–�d�� edge lengths a, b,and c as functions of temperature. The circle symbols are the results of aheating simulation and the squares are the results for cooling simulation.The points are connected by straight lines for clarity. The rate of heating/cooling was 10 K/50 ps �2.0�1011 K/s�.

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ferent crystalline phases. The fractional coordinates ofRDX-SB show that it also belongs to the space group Pbca.

Figure 5 shows the distributions of at 480 and 490 Kcomputed using Eq. �4�. Apparently, the distribution for480 K peaks 7.2° and that for 490 K at 12.5°. The distribu-tion for 490 K is broader; the full width at half maximum is13.6° at 480 K and 17.6° at 490 K. These differences indi-cate that relatively significant orientational changes occur inthe solid-solid phase transition. The orientational fluctuationsare limited to the peak region, showing that the RDX-SBphase is crystalline, with no dynamic orientational disorder.

The mean-squared displacements �msd� of the C, N, O,and H atoms at 490 K are shown in Fig. 6 as functions oftime. Comparing the msd of the C atoms at 480 K �dashedcurve�, we see that significant increases in the msd occurduring the solid-solid phase transition �e.g., the msd of the Catoms increases from 0.45 to 1.1 Å2� and the fluctua-tions also significantly increase from about ±0.05 to about±0.125 Å2. These results show that there is significant ther-mal fluctuation in the RDX-SB phase.

The van der Waals, electrostatic, bond stretching, bond-angle bending, and dihedral energies and enthalpy �H=total energy+ PV� of the RDX supercell as functions oftemperature up to 650 K are shown in Fig. 7. The UvdW,Ubond, and H undergo no abrupt change at the solid-solidphase transition, while abrupt changes are found in all ener-

FIG. 5. Distributions of the order angles i �see Eq. �4�� of the RDXmolecules at 480 K �dashed curve� and 490 K �solid curve�.

FIG. 6. Mean-squared displacements �msd� of the C, N, O, and H atoms asfunctions of time at 490 K. The dashed curves denote the msd of the C

atoms at 480 K and serve as a reference for those at 490 K.

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084505-5 Melting of RDX J. Chem. Phys. 125, 084505 �2006�

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gies �except the bond stretching energy� and enthalpy uponmelting. The electrostatic energy is increased by 2.5% from480 to 490 K and by 6.9% from 500 to 510 K. The bendingenergy is decreased by 0.9% at the solid-solid phase transi-tion and by 1.8% at the melting. After the RDX supercellbecomes the liquid phase, the bending energy begins to in-crease again with increasing temperature. The dihedral en-ergy �including the proper dihedral and out-of-plane bendingenergies� first is increased by 2.6% when the temperature isincreased from 480 to 490 K, drops by 8.6% at the melting,and then begins to increase again with increasing tempera-ture.

Figure 8 shows the temporal evolution of the supercelledge lengths, volume, and translational and orientational or-der parameters at the solid-solid phase transition temperature�490 K� and superheating melting temperature �510 K�. At490 K, the supercell edge lengths a and b abruptly drop atabout 15 ps of the simulation time, while the edge length csuddenly increases �see Fig. 8�a��. At the same time, both the

FIG. 7. �a� van der Waals, �b� electrostatic, �c� bonding, �d� bending, and �e�dihedral energies and �f� enthalpy per molecule as functions of temperature.The arrows point to where the solid-solid phase transition �490 K� and melt-ing �510 K� occur, respectively.

FIG. 8. �a� The MD supercell edge lengths and �b� translational and orien-tational order parameters as functions of time at the solid-solid phase tran-sition temperature 490 K; �c� supercell volume and �d� translational andorientational order parameters as functions of time at the melting tempera-

ture of 510 K.

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translational and orientational order parameters undergoabrupt drops from 0.99 and 0.96 to 0.94 and 0.92, respec-tively, indicating that this solid-solid phase transition is bothdisplacive and rotational �see Fig. 8�b��. When the tempera-ture is increased to the melting temperature, the supercellvolume begins to expand abruptly �see Fig. 8�c��, and theorder parameters are found to drop quickly �see Fig. 8�d��.The values of the translational and orientational order param-eters for a fully disordered system are, respectively, 0.5 and0.35.8 Apparently, the given simulation duration of 50 ps isnot long enough for both order parameters to reach the equi-librium values. Hence, we extended the simulation time at510 K to 300 ps �see Fig. 9� to investigate the further evolu-tion of the order parameters. It is found that it takes almost300 ps for the orientational order parameter to reach the finalvalue of 0.35 while the translational order parameter seemsto reach an equilibrium value of 0.77, well above the finalvalue of 0.5 for complete disorder, at around 150 ps and doesnot decrease further. These results suggest that the meltedRDX retains some translational order, but complete rota-tional freedom at 510 K.

Further insight is gained from the temperature depen-dences of the order parameters, which are shown in Fig. 10.The translational and orientational order parameters are rep-resented by the circles and squares, respectively, in Fig. 10;each point in Fig. 10 is an average of the property of all themolecules in the simulation cell over the time interval of50–55 ps; straight lines have been sketched in the figure toillustrate the different stages �including the transitions� of thesystem as the temperature increases. Both order parametersremain close to 1.0 up to 480 K, then abruptly drop at 490 Kdue to the solid-solid phase transition. Larger decreases inthe order parameters occur when the RDX crystal melts at510 K. The orientational order parameter reaches its finalvalue of 0.35 at 540 K, while the translational order pa-rameter reaches 0.5 at 580 K. At the given heating rate, themelted RDX retains partial translational order, but there isorientational disorder between 540 and 580 K.

We have analyzed the molecular structural changes ofRDX at the solid-solid phase transition and melting. We will

FIG. 9. Plots of the logarithm of the orientational and translational orderparameters vs the simulation time at 510 K.

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084505-6 L. Zheng and D. L. Thompson J. Chem. Phys. 125, 084505 �2006�

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undergo significant changes �as indicated by the bonding en-ergy�; changes in the bond angles are less than 5°. Figure 11shows three examples of changes in the dihedral angle dis-tributions upon the solid-solid and solid-liquid transitions:C3–N3–C2–N2, H5–C3–N3–C2, and H1–C1–N2–N5 �theatom labels are given in Fig. 1�. The peak positions of theC3–N3–C2–N2 dihedral angle shift to smaller angles whentemperature is increased from 480 to 490 K, i.e., from 51° to46°. The two pronounced peaks in each of these distributionsmerge to one broad flat peak ranging between ±50° after theRDX crystal is melted �see Fig. 11�a��. This indicates that thering structure of RDX in the liquid phase changes signifi-cantly with time. The peaks in the H5–C3–N3–C2 dihedralangle distribution shift to larger angles �from 69° to 84°� in

FIG. 10. Orientational �squares� �Eq. �2�� and translational �circles� �Eq. �3��order parameters as functions of temperature. The rate of heating was10 K/50 ps �2.0�1011 K/s�. Straight lines have been drawn to illustrate thevarious stages the system passes through as the temperature is increased.

FIG. 11. Examples of distributions of the �a� C–N–C–N, �b� H–C–N–C, and�c� H–C–N–N dihedral angles of the RDX molecules at 480, 490, and

510 K.

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the solid-solid phase transition �see Fig. 11�b��. When RDXmelts the peak widths in the distributions become muchlarger �at least twice those for crystalline RDX� and the peakheights decrease significantly. There is a shoulder at 135°on the distribution for the liquid phase. Figure 11�c� showsthat the peaks of the H1–C1–N2–N5 dihedral move towardlarger angles �from 130° to 157°� and their magnitudes in-crease when the temperature is increased from 480 to 490 K.Unlike the broadening in the distributions of the C–N–C–Nand H–C–N–C dihedral angles at 510 K, this dihedral angleundergoes a pronounced shift when the crystal melts: from157° at 490 K to 65° at 510 K. A small peak at 165° ispresent in the distribution for the melted RDX. Table I liststhe peak positions of all the dihedral angles of the RDXmolecules in the simulation supercell at 480, 490, and510 K.

The N–C–N–N dihedral angles are of particular interestbecause they define the nitro group positions in the mol-ecules. Figure 12 shows the distributions of three represen-tative N–C–N–N dihedrals at 480, 490, and 510 K. After thesolid-solid phase transition the peaks of the N2–C1–N1–N4�see Fig. 12�a�� shift slightly, from 180° to 160°, while theN1–C3–N3–N6 and N1–C1–N2–N5 dihedral angles undergomore pronounced changes �see Figs. 12�b� and 12�c��. TheN1–C3–N3–N6 dihedral angle shifts from 93° to 137°, how-ever, the N1–C1–N2–N5 dihedral angle shifts from 116° to85°. These results show that though the molecular conforma-tion in the RDX-SB phase remains AAE, the two axial-positioning nitro groups have different changes, that is, onebecomes more axial while the other becomes more equatorial�see Fig. 13�. At 510 K, all N–C–N–N dihedral angles peakat 180°, indicating an AAE to EEE conformational changeupon melting.

IV. CONCLUSIONS

We have studied the melting of perfect crystalline RDXusing molecular dynamics simulations with the fully flexibleSmith and Bharadwaj force field.23 The purpose of the studywas to investigate molecular and structural changes that oc-cur during the melting of a large, flexible molecule. Themolecular structure of RDX �see Fig. 1� is a flexible six-member ring with three nitro groups attached at alternatingring atoms—thus, it should be fairly representative of large,complex, floppy molecules. The simulations were carried outover the temperature range of 300–650 K for the NST �con-stant stress, constant temperature� ensemble. The tempera-ture was increased incrementally �followed by equilibra-tions� corresponding to a rate of 2.0�1011 K/s. The changesin the solid upon heating were investigated by computingtranslational and orientational order parameters. The molecu-lar structural changes were monitored by computing bondlengths, bond angles, and dihedral angles. The major mo-lecular structural changes upon melting are due to changes inthe torsional angles.

A solid-solid phase transition was observed between 480and 490 K, and melting temperature between 500 and510 K. The solid-solid phase transition is characterized by

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084505-7 Melting of RDX J. Chem. Phys. 125, 084505 �2006�

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crease and c increases�, density, and electrostatic, bond-anglebending, and dihedral energies. This predicted crystallinephase �RDX-SB� is orthorhombic and belongs to the Pbcaspace group. The �-RDX→RDX-SB transition involvesboth molecular translation and reorientation. It is irreversibleupon cooling from 500 to 300 K. The molecular conforma-

TABLE I. Peak positions in the dihedral angle distribatom labels are given in Fig. 1�.

Dihedralangle

Peak position �deg�

480 K 490 K 510 K

C3–N1–C1–N2 37 37 a

C1–N2–C3–N3 40 30 a

C2–N3–C3–N1 47 35 a

C3–N3–C2–N2 51 46 a

C1–N2–C2–N3 47 53 a

C2–N2–C1–N1 40 50 a

N2–C1–N1–N4 180 160 180N1–C3–N3–N6 93 134 180N2–C2–N3–N6 90 120 180N1–C1–N2–N5 116 85 180N3–C2–N2–N5 107 83 180N3–C3–N1–N4 161 180 180H1–C1–N1–C3 75 75 80H2–C1–N1–C3 165 165 150H1–C1–N2–C2 75 66 75H2–C1–N2–C2 165 180 180H3–C2–N2–C1 180 180 180H4–C2–N2–C1 65 62 75H3–C2–N3–C3 180 180 180H4–C2–N3–C3 65 70 90H5–C3–N3–C2 69 84 84H6–C3–N3–C2 180 159 180H5–C3–N1–C1 75 87 87H6–C3–N1–C1 167 154 150

aBroad flat peak ranging between ±50° �see Fig. 11�

FIG. 12. Distributions of the �a� N2–C1–N1–N4, �b� N1–C3–N3–N6, and�c� N1–C1–N2–N5 dihedral angles of the RDX molecules at 480, 490, and

510 K.

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tion in the RDX-SB phase remains AAE, however, the twoaxial-positioning nitro groups have shifted slightly, that is,one becomes more axial and the other becomes more equa-torial. While the RDX-SB phase may be an artifact of thepotential �we have no evidence that it corresponds to a realphase�, it may be representative of the kinds of premeltingsolid-solid phase transitions that likely characterize the be-havior of a molecular crystal when heated to melting point.

Melting occurs when the temperature is increased from500 to 510 K. The melting transition is characterized byabrupt changes in the order parameters, density, diffusioncoefficient, potential energy, and dihedral angles. At the highheating rate �2.0�1011 K/s� used in the simulations, themelted RDX reaches full orientational disorder at about540 K and translational freedom at around 580 K. If thesimulation at the melting temperature �510 K� is run suffi-ciently long complete rotational freedom is achieved in a fewhundreds of picoseconds, while complete translational free-dom requires much longer �see Fig. 9�. These results showthat given a sufficiently high heating rate �as might be gen-erated by a shock�, the system can exist for long times in anear-liquid state in which the molecules are not as free torotate and diffuse as in the true liquid state.

The bond lengths and bond angles undergo little changeupon melting, while there are significant changes in the di-hedral angles. The distributions of the dihedral angles gener-ally become much broader and flatter and the peak positionsshift upon melting. The molecular conformation of RDX

s of the RDX molecules at 480, 490, and 510 K �the

Dihedralangle

Peak position �deg�

480 K 490 K 510 K

H1–C1–N1–N4 82 87 65H2–C1–N1–N4 40 33 55H1–C1–N2–N5 130 157 65H2–C1–N2–N5 0 43 53H3–C2–N2–N5 0 47 52H4–C2–N2–N5 140 161 66H3–C2–N3–N6 39 0 53H4–C2–N3–N6 157 126 66H5–C3–N3–N6 154 102 62H6–C3–N3–N6 33 0 58H5–C3–N1–N4 80 78 62H6–C3–N1–N4 35 42 55C1–N1–N4–O1 180 180 180C1–N1–N4–O2 0 0 0C3–N1–N4–O1 0 0 0C3–N1–N4–O2 180 180 180C1–N2–N5–O3 180 162 180C1–N2–N5–O4 0 20 0C2–N2–N5–O3 10 20 0C2–N2–N5–O4 170 160 180C2–N3–N6–O5 15 0 0C2–N3–N6–O5 165 180 180C3–N3–N6–O5 165 180 180C3–N3–N6–O6 16 0 0

ution

a��.

changes from AAE to EEE upon melting. The ramification ofct to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

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084505-8 L. Zheng and D. L. Thompson J. Chem. Phys. 125, 084505 �2006�

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this for formulating force fields that accurately describe melt-ing is that it is important that the torsional motions be accu-rately described.

ACKNOWLEDGMENTS

We would like to thank Dr. Thomas D. Sewell for help-ful discussions. This work was supported by a DOD MURIgrant managed by the Army Research Office.

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FIG. 13. �Color� Molecular configurations of RDXmolecules: �a� 480 K and �b� 490 K. The C, N, O, andH atoms are denoted by gray, blue, red, and green,respectively.

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