Chemical Dynamics Simulations and Scattering Experiments for O2Collisions with GraphiteMoumita Majumder,† K. D. Gibson,‡ S. J. Sibener,‡ and William L. Hase*,†

†Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States‡The James Franck Institute and Department of Chemistry, The University of Chicago, 929 East 57th Street, Chicago, Illinois60637, United States

ABSTRACT: Energy transfer in collisions of O2 with agraphite surface was studied by chemical dynamicssimulations. The simulations were performed for threecollision energies Ei of 2.1, 7.4, and 15 kcal/mol, with theinitial incident angle fixed at θi = 45°. Simulations wereperformed for each Ei at a surface temperature Tsurf = 300 K.For the higher surface temperature of 1177 K, a simulationwas only performed for Ei = 15 kcal/mol. The followingproperties were determined and analyzed for the O2 +graphite collisions: (1) translational energy distributions ofthe scattered O2; (2) distribution of the final polar andazimuthal angle for the scattered O2; and (3) number ofbounces of O2 on the surface before scattering. The averageenergy transferred to the graphite surface and that remaining in O2 translation, i.e., ⟨ΔEsurf⟩ and ⟨Ef⟩, exhibit a lineardependence with the initial translational energy. For the O2 + graphite scattering, the physisorption/desorption residence timedistribution decays exponentially, with an increase in residence time with a decrease in Ei. The rate at which the distributiondecreases shows a near-linear dependence with an increase in Ei. For higher collisional energies of 7.4 and 15 kcal/mol, O2scattering from the surface follows a nearly quasi-trapping desorption process. However, for the lowest collision energy, itmostly follows conventional physisorption/desorption. For all of the scattering conditions considered experimentally, therelationship between the average final translational energy and average scattering angle for the O2 molecules found from thesimulations is in excellent agreement with the experimental results. This experimental validation of precise simulation outcomesis important as it indicates that collisional energy-transfer predictions for this system can be reliably used in assessing interfacialenergy flow in a variety of technological applications, including high-performance flight systems.

I. INTRODUCTION

Understanding energy-transfer dynamics at the gas−surfaceinterface1−5 provides fundamental information needed foraccurate modeling of many chemical and physical phenomena.The energy-transfer dynamics for collisions of gas moleculeswith a surface is a complicated process, dependent on anumber of properties, including the gas−surface potential,translational energy and incident angle of the projectile, gas−surface mass ratio, and surface temperature.Gas−surface collision dynamics have been investigated for a

variety of surfaces both theoretically and experimentally,including both organic6−13 and metal surfaces.14,15 Aparticularly interesting and important surface is graphite. It isone of the most prevalent carbon allotropes and has a layeredand planar structure,16,17 with the individual layers calledgraphene. The carbon atoms in each layer are arranged in ahoneycomb lattice with a C−C bond distance of 1.42 Å.16,17

The layers are stacked through a weak intermolecularinteraction, with an interlayer separation of 3.35 Å.16,17 Thestructure results in a large anisotropy in thermal propertiesparallel and perpendicular to the c-axis of the crystal.18−21

Since a defect-free graphite surface shows a minimum tendencytoward reactivity and heat conductivity, it is a possible choicefor a thermal protection system. It is also a model for ablativematerial on a spacecraft.22,23 An interest in gas−surfacescattering phenomena associated with graphite results frominterpreting microscopic details of the aerodynamic drag ofobjects with graphitic-like surfaces moving through theatmosphere. N2 + graphite serves as a prototype model forunderstanding highly energetic collisions of closed-shellmolecules with the surface of spacecraft in low Earth orbit(i.e., at 200−700 km altitude).24

Recently, several molecular beam experiments have beenperformed, wherein a wide range of projectiles (Ar, SF6, N2,CO, O2, Xe) collided with a graphite surface over a range ofexperimental conditions.10,25−31 Unlike the experiment for Arscattering from a graphite surface performed for high-energycollisions,10 the experimental data for lower-energy collisions

Received: March 16, 2018Revised: June 14, 2018Published: June 21, 2018

Article

pubs.acs.org/JPCCCite This: J. Phys. Chem. C 2018, 122, 16048−16059

© 2018 American Chemical Society 16048 DOI: 10.1021/acs.jpcc.8b02574J. Phys. Chem. C 2018, 122, 16048−16059

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are quite well described by a simple hard cube model(HCM).32,33 Oh et al.28 reported an extensive series ofmeasurements for the angular distribution of O2 moleculesscattered from a graphite surface. Their measurements werecarried out over a range of incident energies (291−614 meV)and surface temperatures (150−500 K). They proposed thatthe gas−surface collision is primarily a single-collision eventwith large cooperative motions of the carbon atoms in theoutermost graphene layer.28,29

For the present article, chemical dynamics simulations wereperformed to investigate energy transfer in collision of O2 witha graphite (0001) surface. The simulations only considernonreactive collisions between O2 and the graphite surface,and possible reactive events are not investigated. Thesimulations provide an atomic-level understanding of theenergy-transfer dynamics and mechanisms for energy transferto the translational and rotational degrees of freedom of the O2projectile. An important component of this study iscomparison with experiments by Sibener and co-workers.The simulations follow a recent study of the dynamics of N2collisions with a graphite (0001) surface.34

II. EXPERIMENTAL APPROACH

The design of the instrument has been previously covered,35 soonly a brief description follows. A molecular beam wasproduced in the source chamber and passed through severalregions of differential pumping before entering an ultra-high-vacuum chamber. The target was mounted on a manipulatorthat could be rotated with respect to the beam, giving avariable incident (polar) angle, θi. The target could beresistively heated to ∼1300 K. A differentially pumpedquadrupole mass spectrometer with an acceptance angle of∼1° could independently rotate around the target so that thefinal angle (θf) was variable. The scattering plane is defined bythe arc of this motion.There were two mechanical choppers, one before and one

after the target. The pre-collision chopper had narrow slots formeasuring the incident translational energy via time-of-flight.The post-collision chopper had a cross-correlation pattern andwas attached to the detector so that it rotated with the massspectrometer. This was used for all scattering measurements.The molecular beam was produced by expanding the gas

through a small pinhole (15 μm). Varying translational kineticenergies were produced by a combination of heating the nozzleand mixing the O2 with He. All of the gases used were of UHPgrade from Airgas.The target was highly oriented pyrolytic graphite (SPI, grade

3). Once mounted, the surface of the sample was refreshed byremoving the top layers with scotch tape. In vacuum, thesample was also exposed to O2 at a surface temperature of1200 K. No attempt was made to align the surfacecrystallographic directions with the scattering plane. Noreaction was observed between O2 and the surface in theexperiments. It may have been occurring, but the rate was toolow to observe experimentally.

III. COMPUTATIONAL DETAILS

III.I. O2 + Graphite Model and Potential EnergyFunctions. The potential energy function for the O2 +graphite system is given by

= + + +V V V Vgraphite O O graphite2 2 (1)

where Vgraphite is the graphite potential, VO2is the O2 potential,

and VO2+graphite is the O2 + graphite intermolecular potential.The graphite model consists of four layers stacked in an AB

sequence and is depicted in Figure 1. The carbon atoms in

each layer are arranged in a hexagonal pattern forming 15 ringsalong the x-direction and 12 along the y-direction. Thedetailed description of the graphite model is given elsewhere,34

and only salient features of the model are described here. Thepotential for a graphite layer is represented by C−C harmonicstretches, C−C−C valence angle bends, C−C−C−C dihedralangles, and Lennard-Jones (L-J) (6−12) van der Waalsinteractions for two C-atoms separated by four or moreatoms. Interactions between two C atoms that reside on twoadjacent layers are also described by these L-J (6−12)interactions. The parameters for the graphite potential aretaken from the all-atom optimized potentials for liquidsimulations (OPLS-AA) force field36 and are given in Table1 of ref 34. The OPLS scaling of 0.5 is not used for the van derWaals interactions of a 1−4 pair or across the graphene planes.Implementation of a large harmonic force field at the border ofthe graphite surface, to suppress its distortion, was discussed indetail in our earlier study of N2 + graphite.34 For the presentstudy, chemical dynamics simulations of O2 colliding withgraphite are studied at two surface temperatures of 300 and1177 K. The separations between surface layers at 300 and1177 K were determined previously as 3.5734 and 3.62 Å,respectively. The O2 potential is described by a Morse functionwith parameters De = 220.17 kcal/mol, βe = 2.78 Å−1, and re =1.2070 Å.37

Since benzene is the basic constituent of graphite, an abinitio potential of benzene interacting with O2 molecule is aquite appropriate choice to mimic the graphite + O2interaction. There have been several attempts made to obtainbenzene + O2 interaction energies, but the accuracy of thesecalculations greatly depends on the electronic structuremethod.38,39 Substantial differences are found in the literaturefor calculations of the interaction energy.40−44 However, alltheoretical calculations establish a common fact that theparallel orientation is the minimal geometry for the benzene−

Figure 1. Motion of the O2 center of mass along the z-direction, i.e.,perpendicular to the graphite surface, for the three trajectory types:(1) direct impulsive scattering; (2) trapping desorption orphysisorption/desorption; and (3) trapping. R is the z-distancebetween the center of mass of O2 and the bottom layer of the graphitesurface for the simulation with Ei = 2.1 kcal/mol and θi = 45°.

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O2 dimer with nearly free rotation of O2 in the benzenemolecular plane. The structure is therefore quite similar to thatobserved for the benzene−N2 dimer.39 In our present study,we used the benzene−O2 interaction potential proposed byGranucci and Persico.42 They obtained a value of D0 = 1.28kcal/mol (De = 1.48 kcal/mol at Re = 3.36 Å) using SCF/MP2calculations and corrected to account for the differencebetween calculated and experimental polarizabilities for bothmonomers. Their calculated D0 is only ca. 0.3−0.4 kcal/mollower than the experimentally reported D0 value by Grover andco-workers41 and Casero and Joens.43,44 The L-J parametersfor the O−C interaction, i.e., = − +−V A

rBrO C m n , used for

current simulations, are A = 486.3 kcal Åm/mol, B = 506900kcal Ån/mol, m = 6, and n = 12.42

As discussed above, a four-layer model was used for thegraphite surface and, in the previous study of N2 + graphitescattering,34 this model gave simulation results in excellentagreement with experiment. In a more recent study of N2 +graphite scattering,45 different simulation results were foundfor graphite models with four and six layers. This surface modelused springs with model force constants connecting the layerssuch that the number of layers changed the surface stiffness.For the current study, the graphene layers of the four-layersurface model interact via L-J (6−12) terms of the OPLS-AAforce field36 and the interaction between two layers isunaffected by other layers. The stiffness of the top layer, nextlayer, etc. is unaffected by the presence of underlying layers. Ina recent simulation study of Ar + graphite hyperthermalscattering,10 the scattering dynamics was found to be the samefor model surfaces with two and three layers.III.II. Procedure for the Chemical Dynamics Simu-

lations. Classical trajectories were used to simulate collisionsof a beam of O2 molecules with the graphite (0001) surface.The trajectory simulations were performed with the generalchemical dynamics computer program VENUS.46,47 Initialconditions for the trajectories were chosen to modelexperiments by Sibener and co-workers. Collisions betweenO2 and graphite were simulated for three incident beamtranslational energies Ei of 2.1, 7.4, and 15.0 kcal/mol. Theincident angle θi, defined by the angle between the O2 initialvelocity vector and the surface normal, was set to 45° for all ofthe trajectories. Chemical dynamics simulations for each Eiwere carried out at surface temperature Tsurf = 300 K. For thehigher surface temperature of 1177 K, a simulation was onlyperformed for Ei = 15 kcal/mol.Sampling of initial conditions follows our previous N2 +

graphite simulations.34 For each simulation, a beam of collidingO2 molecules was randomly aimed within a circular area ofradius 2.2 Å so that the area spanned by the O2 beam covered ahexagonal unit cell on the graphite surface. O2 was randomlyrotated about its Euler angles. Each trajectory was initiated

with a separation of 20 Å between the center of the beam andthe surface aiming point. The projection of the O2 beam ontothe graphite surface is defined by an azimuthal angle (χf) andchosen randomly between 0 and 360°. The initial ro-vibrational quantum states of the O2 molecules were sampledfrom a 300 K Boltzmann distribution for Ei = 2.1 and 7.4 kcal/mol and from a 500 K distribution for Ei = 15.0 kcal/mol.These are the temperatures of the nozzle in the molecularbeam experiments conducted by Sibener et al. The O2rotational angular momentum j was related to the O2 rotationalquantum number J via j = √[J(J + 1)]ℏ. Einstein−Brillouin−Keller (EBK) semiclassical quantization48 was used to add theO2 vibrational quantum number n. The O2 internal energy isgiven by

μ μ= + +E p V r j r/2 ( ) /22 2 2(2)

This sampling includes O2 zero-point energy.Periodic boundary conditions were employed along the x-

and y-directions of the graphite surface. The x, y, and zdimensions of the primary box are 29.5, 32.6, and 10.5 Å,respectively. For each trajectory, the bottom layer of thegraphite surface was held rigid and acted as an anchor layer.Initial conditions for the graphite surface were selected byassigning velocities to the carbon atoms of the first, second,and third layers, sampled from a Maxwell−Boltzmanndistribution at a given surface temperature. The surface wasthen equilibrated by a 50 or 75 ps molecular dynamicssimulation for surface temperatures of 300 or 1177 K,respectively, with velocity rescaling every 5 fs. This is followedby a 50 or 80 ps equilibration, without velocity rescaling. Theaverage surface temperature attained after the equilibration is300 or 1177 K, respectively.The trajectories were propagated with a combined fourth-

order Runge−Kutta and sixth-order Adams−Moulton algo-rithm, with a time step of 0.05 fs. Trajectories were terminatedby either a distance criterion, i.e., when the distance betweenthe aiming point and the outgoing O2 distance exceeds 30 Å,or a total integration time criterion, i.e., the total integrationtime exceeds 45 ps. The latter is used for trapped trajectorieswith O2 remaining on the surface, for the simulations with Ei of7.4 and 15 kcal/mol. For the lowest-energy simulations with Ei= 2.1 kcal/mol, the maximum integration time was set to 75 ps.Typically, 800 trajectories were calculated for each ensemble ofinitial conditions (Ei, θi, Tsurf). Energy conservation was within1% for each trajectory.At the end of each trajectory, the final translational and

internal energies of the O2 molecule and the internal energy ofthe surface are evaluated. The O2 rotational quantum numberis calculated from its final rotational angular momentum, andthe Einstein−Brillouin−Keller (EBK) semiclassical quantiza-tion48 is used to find the O2 vibrational quantum number. Thefinal angular distribution P(θf) of the scattered O2 molecule is

Table 1. Percentage of Each Trajectory Typea

trajectory types

Tsurf (K) Eib direct physisorption/desorption trappingc

300 ± 5 2.1 15 ± 1 15 ± 1 (22) 70 ± 2 (63)300 ± 5 7.4 46 ± 2 19 ± 1 35 ± 2301 ± 5 15.0 54 ± 2 19 ± 1 27 ± 21177 ± 20 15.0 60 ± 2 40 ± 2

aIncident angle is set to 45° for all simulations. bIncident energy given in kcal/mol. cO2 remains trapped on the surface when the trajectory isterminated at 45 ps. The numbers within parentheses are % of trajectory types at the maximum integration time of 75 ps.

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determined by calculating the angle between the final velocityvector of the projectile and the surface normal. Thedistribution of the final azimuthal angle, with respect to thescattering plane, P(χf) is also calculated. Statistical uncertain-ties were calculated for the simulation results. The uncertaintyin a component of a distribution is the standard deviation. Theuncertainty in an average value is the standard deviation of themean.

IV. RESULTS AND DISCUSSIONIV.I. O2 + Graphite Atomistic Collision Dynamics:

Inner Turning Point (ITP) and Residence Time. To

classify the trajectory type, the number of inner turning points(ITPs) was counted for each trajectory. From this analysis,

three types of trajectory were identified: direct (single ITP),physisorption/desorption with multiple ITPs (MITPs), andtrapping on the surface with MITPs, with O2 remaining on thesurface when the trajectory was terminated. Representativetrajectories of each trajectory type are demonstrated in Figure1, by showing the z-coordinate of O2 with respect to thegraphite rigid layer versus time. There were no trajectoriesfound for which O2 penetrated the top graphite layer, the samebehavior observed in N2 + graphite collisions.35 Trajectoriesfor which O2 remained trapped on the surface, when thetrajectories were halted, are excluded from analyses of Ef, θf,and χf.Table 1 presents percentages of the three trajectory types as

a function of incident energy and surface temperature. In our

Figure 2. Distribution of the residence time for physisorption/desorption trajectories.

Table 2. Percentage of Average Energies Transferred for Different Trajectory Types

trajectory type

direct scattering physisorption/desorption total

Tsurf Eib ⟨Ef⟩ ⟨ΔEsurf⟩ ⟨ΔEint⟩

a ⟨Ef⟩ ⟨ΔEsurf⟩ ⟨ΔEint⟩ ⟨Ef⟩ ⟨ΔEsurf⟩ ⟨ΔEint⟩

300 2.1 77 22 1 68 28 4 71 26 37.4 63 35 2 46 51 3 58 40 215.0 58 40 2 42 57 1 54 44 2

1177 15.0 58 35 7 66 25 9 62 31 7

aThe percentage for ΔEint is equivalent to ΔErot, since ΔEvib = 0 for all trajectories. bEnergy in kcal/mol.

Figure 3. Distributions of ΔEsurf, P(ΔEsurf), for Tsurf = 300 K and θi =45° with different Ei values.

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previous study of N2 + graphite,34 we found that at smallerincident angles with respect to the surface normal, themolecule−surface collisions are dominated by direct scattering,while physisorption/desorption becomes important at higherincident angles. In the present study, we have fixed the incidentangle at 45° to compare with experiment. As shown in Table 1,with increase in Ei, the direct scattering percentage increases to15, 46, and 54% for Ei = 2.1, 7.4, and 15 kcal/mol, respectively,for the surface temperature of 300 K.

For the Ei = 15 kcal/mol simulations and Tsurf = 300 K, O2interacts with the surface for a longer time than for thesimulations with Tsurf = 1177 K. For the latter Tsurf, there areno O2 molecules adsorbed/trapped on the surface when thetrajectories are terminated at 45 ps. Less trapping on thesurface is expected for the higher Tsurf. For the simulations withEi of 2.1 kcal/mol, 70 and 63% of the O2 molecules remainedtrapped on the surface for trajectory integration times of 45

Figure 4. Plots of fwhm and energy center Eo, for each P(Esurf), versus Ei; with fits to eq 3.

Figure 5. Distributions of Ef, P(Ef), for Tsurf = 300 K and θi = 45° withdifferent Ei values. The fits include Boltzmann and non-Boltzmanncomponents, i.e., BC and NB.

Figure 6. Angular distributions of θf, P(θf), for Ei = 2.1, 7.4, and 15kcal/mol; Tsurf = 300 K and θi = 45°. The solid line is the randomdistribution. P(θf) is for all azimuthal angles and not just in-planescattering. The square symbol represents the experimental angulardistributions.

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and 75 ps, respectively. If the trajectories were integrated for alonger period of time, a smaller percentage of O2 would haveremained trapped. At long time, it is expected that all of the O2will desorb. Similarly, for the simulations with Ei of 7.4 and 15kcal/mol and Tsurf = 300 K, all of the trapped trajectories areexpected to ultimately desorb. In Figure 2, histograms aregiven for the distribution of residence times for thephysisorption/desorption trajectories. For Ei of 15 and 7.4kcal/mol, a significant fraction of the O2 molecules leaves thesurface within 1−3 ps. However, for the lowest incidentenergy, a long tail extending to longer residence times isobserved. The physisorption/desorption residence timedistribution decreases exponentially, with an increase inaverage residence time with decrease in Ei. The rate at whichthe distribution decreases shows a near-linear dependence withEi.In previous chemical dynamics simulations of N2 collisions

with the graphite surface,34,45 the three trajectory types ofdirect scattering, physisorption/desorption, and trapping were

observed, as found here for O2 + graphite scattering. Incontrast, analyses with the hard cube and smooth surfacetheoretical models indicate that the dynamics is dominated bydirect scattering.28,29 The atomistic chemical dynamics withpotential energy surfaces results in dynamics different fromthat predicted by the theoretical models.Trampoline-like undulations of the graphite surface were

observed in simulations of the massive Xe-atom colliding withthe graphite surface.30 Such undulations were not seen in thecurrent simulations of the lighter O2 molecule colliding withgraphite.

IV.II. Energy-Transfer Efficiency. During the O2 collisionwith the graphite surface, part of Ei of O2 is transferred to itsinternal vibrational/rotational degrees of freedom (Eint) andsurface vibration energy (Esurf)

= Δ + Δ +E E E Ei int surf f (3)

where Ef is the O2 final translation energy. The values of ΔEint,ΔEsurf, and Ef are determined upon completion of eachtrajectory. This information is then presented as a histogram todetermine the distribution of each energy term.In Table 2, the average percentage energies transferred to

⟨ΔEint⟩, ⟨ΔEsurf⟩, and ⟨Ef⟩ are presented for the 300 K surfacetemperature simulations with Ei = 2.1, 7.4, and 15 kcal/mol,respectively. There are no restrictions on the final scatteringangles θf and χf. A negligible percentage of Ei is transferred tothe O2 rotation, with no transfer to vibration. Transfer to O2rotation is independent of Ei, with average energy-transfer

Table 3. Average Scattering Angles for Different TrajectoryTypes for the Surface Temperature of 300 K

trajectory type

Ei direct ⟨θf⟩ physisorption/desorption ⟨θf⟩ total ⟨θf⟩

2.1 56 46 507.4 63 63 6315.0 63 69 64

Figure 7. Scatter plots of Ef and θf versus residence time for physisorption/desorption trajectories, with Ei = 2.1, 7.4, and 15 kcal/mol. For thesesimulations, θi is fixed at 45° and Tsurf = 300 K. The solid line corresponds to the translational energy of 2RTsurf.

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percentages of 1−2%. Therefore, the loss of Ei is primarily tothe surface, with percentages of 26, 40, and 44% for Ei of 2.1,7.4, and 15 kcal/mol, respectively, for the total trajectories.Simultaneously, the percentages of the average energyremaining in O2 translation are 71, 58, and 54%, respectively.The increase in surface vibration with an increase in incidentenergy was also observed for N2 + graphite34 and CO2 + F-self-assembled monolayer (SAM) collisions.49 For the ensemble(Ei, Tsurf) = (15, 1177), 62% of Ei remained in O2 translationwith a 31% loss to the surface. For the above simulation, withthe same Ei but Tsurf = 300 K, the transfer to the surface is 44%.A separate analysis is done for each trajectory type, and the

percentages of the average energy transferred are listed inTable 2. It is evident from the analysis that physisorption/desorption plays a major role in energy transfer to the surface.The percentage transfers to ⟨ΔEsurf⟩ for direct scattering are22, 35, and 40%, whereas for physisorption/desorption, thevalues are 28, 51, and 57% for Ei = 2.1, 7.4, and 15 kcal/mol,respectively. The distributions of P(ΔEsurf) for the 300 Ksimulations are given in Figure 3, and all three are quite welldescribed by a Gaussian distribution.

= σ−f E A( ) e E E( ) /202 2

(4)

The full width at half-maximum (fwhm) and energy center(Eo) are determined for each distribution, and their variations

with Ei are depicted in Figure 4. A linear regression analysisclearly displays that both parameters are a linear function ofthe incident energy. This analysis helps to predict the energydistribution at any given Ei. A similar relationship was alsofound for N-protonated octaglycine collisions with an H-SAMsurface.50 The physical significance of this linear relationshiphas not been established.The probability distribution of the final O2 translational

energy is given in Figure 5. The extent of thermalization isdetermined by the fraction of P(Ef) described by theBoltzmann energy distribution. The value of f BC is determinedby nonlinear least-squares fitting of the total distribution P(Ef),given by

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where f NB is the non-Boltzmann component and f BC + f NB = 1.The temperature of the Boltzmann component is fixed at thesurface temperature. The fitting parameters are f BC, T2, ν2, andA. Equation 5 was used previously to analyze P(Ef) for Ne +squalane and Ar + H-SAM and HO-SAM scattering.51,52

Figure 5 clearly depicts that P(Ef) is mainly dominated by theNB component, and its contributions are 0.85, 0.96, and 1.00for Ei = 2.1, 7.4, and 15 kcal/mol, respectively. The fwhm andEf

max obtained from each distribution by fitting to a Gaussiandistribution are plotted against Ei in Figure 4. Like ⟨ΔEsurf⟩,⟨Ef⟩ also shows a strong linear dependence with Ei.As found for our previous N2 + graphite simulation,34 there

is no surface site dependence for the O2 + graphite scatteringdynamics. Energy transfer upon impact with the surfacedetermines whether O2 will directly scatter or physisorb withMITPs. This energy transfer is strongly influenced by theshort-range repulsion of the O2-graphite potential andexpected to be also affected by the orientation of O2 duringthe collision. Energy dissipation within the surface after O2impact is an interesting question, but was not investigated inthe current study.In the simplest models of energy transfer in gas−surface

collisions, it is only the normal component Ein of Ei which

participates in energy transfer and the parallel component isconserved. For the current simulations with θi = 45° and forthe direct scattering trajectories, a linear relationship was foundbetween the normal component of incident energy Ei

n = Eicos2 θi = Ei/2 and the energy transferred (Ei − Ef) to thesurface. For Ei = 7.4 and 15 kcal/mol, 37 and 42% of energywere transferred, respectively. These percentages are similar tothose reported using the hard cube model (HCM) for O2 +graphite energy transfer.28 For Tsurf = 500 K and Ei from 6.7 to14 kcal/mol, the HCM percentage energy transfer increasedfrom 30 to 38%. For Ei ∼ 6 kcal/mol and Tsurf = 300 K, theenergy transfer is 36%. In our previous study of N2 + graphitecollisions,34 we obtained an energy loss of ∼29%, whichmatched quite well with the estimated value for the HCM of∼27%.

IV.III. Scattering and Azimuthal Angle Distributions.The angular distribution P(θf) of scattered O2 for all azimuthaldirections is shown in Figure 6 for Ei of 2.1, 7.4, and 15 kcal/

Figure 8. Distributions of the change in the azimuthal angle Δχf = χf− χi; θi = 45°.

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mol. For random scattering, P(θf) follows sin(θ) cos(θ), andthese dynamics are approximately observed for the lowest Ei,but scattering with θf > 45° is more pronounced than for θf <45°. However, with increasing incident energy, the behaviorstarts to substantially deviate from this distribution, and themaximum θf

max in the angular intensity distribution appears atan angle much larger than the specular angle θf = θi. Thisimplies that during the collision, the particle has lost energy tothe surface, which is consistent with the dominance of directscattering for the larger Ei and transfer of a fraction of thenormal component of Ei to the surface. For low-incident-energy collisions with Ei = 2.1 kcal/mol, the angular deviationfrom the lobular maximum in the specular direction is only 5°,but for higher-energy collisions, the deviation becomes larger,and for Ei of 7.4 and 15.0 kcal/mol, the deviations are ∼18 and19°, respectively (see Figure 6). The distributions P(θf), shownin Figure 6, are for all scattering trajectories including both inand out of plane. The distributions are not divided by sin θf.To understand the contribution of each trajectory type to

the angular distribution, listed in Table 3 are the average finalscattering angles ⟨θf⟩ for the different trajectory types.Interestingly, ⟨θf⟩ for physisorption/desorption at highcollision energies shows a significant deviation from 45° andinstead has a value for a supraspecular angle. In our earlierstudy of N2 + graphite collisions,34 a similar behavior wasobserved and the trapping was categorized as quasi-trapping.53

Unlike conventional trapping, quasi-trapping involves veryrapid equilibration of the normal component of Ei but veryslow accommodation of the parallel component. Therefore, forhigher surface temperatures when the residence time of

projectile is very short, the projectile desorbs from the surfacebefore it is fully thermalized, resulting in memory of theparallel component.To further confirm whether the present system exhibits

quasi-trapping, the final scattered angle θf and energy Ef areplotted in Figure 7 as a function of residence time fordesorbing trajectories with Ei = 2.1, 7.4, and 15.0 kcal/mol. Forthermal desorption and full equilibration, ⟨Ef⟩ is 2RTs and ⟨θf ⟩is 45°. As depicted in Figure 7, for higher-energy collisions,most of the desorbing trajectories leave the surface after a shortresidence time of 5−10 ps, with a translational energy greaterthan 2RTs and not fully thermalized with the surface. Longerresidence times are more important for the low-energy Ei = 2.1kcal/mol collisions, and for times of ∼10 ps and greater,desorption follows the conventional definition of physisorp-tion/desorption with both the parallel and normal momenta ofO2 fully equilibrated and O2 scattered randomly.Distribution of the change in the azimuthal angle Δχf = χf −

χi is plotted in Figure 8. For Ei = 7.4 and 15.0 kcal/mol, withonly 19% physisorption/desorption, the Δχ distribution isstrongly peaked at 0 ± 10°, whereas for Ei = 2.1 kcal/mol, forwhich physisorption/desorption dominates, the Δχ distribu-tion is expected to be more uniform with the same probabilityat every final azimuthal angle. However, as shown in Figure 8,the population is not completely uniform, since populations ofsmaller values of Δχ are higher compared to those of largervalues. Only including desorbing trajectories with a residencetime greater than ∼10 ps results in a more uniform probabilityfor the azimuthal angle, and the uniformity increases withincrease in residence time. The scatter plots of both Ef and θf

Figure 9. Scatter plots of Ef and θf versus change in the azimuthal angle Δχ, with Ei = 2.1, 7.4, and 15 kcal/mol. For these simulations, θi is fixed at45° and Tsurf = 300 K.

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versus Δχ are given in Figure 9. The clustering of points in theregion of 0 ± 10° for the higher-energy collisions clearlydepicts that the scattering primarily remains in the incidentplane and for each θf retention of a relatively large fraction ofthe incident collision energy in the final translation. It is worthmentioning that even though the highest incident energyconsidered here is larger than 2RTs, it is not sufficient to crossthe threshold for a transformation in the scattering from thethermal to the structural regime.5,54

IV.IV. Comparison between Simulations and Experi-ments. Sibener and co-workers measured properties asso-ciated with the dynamics of O2 scattering off graphite in theincident plane at Ei = 2.1, 7.4, and 15.0 kcal/mol, θi = 45°, withsurface temperatures of 300 and 1200 K. In the experiments,all measurements were restricted to θf = 20−70°. For a directcomparison with experiment, it is essential to obtain simulationresults for in-plane scattering and, therefore, to accomplishthis, the simulation results for ∥Δχ∥ ≤ 10° were used toapproximate in-plane scattering.8,51,55,56 This approximation isquite acceptable; as shown in Figure 8 for high-energycollisions, there is a clustering of points in the Δχ region of0 ± 10°. For the three Ei = 2.1, 7.4, and 15.0 kcal/mol, at 300K, the respective percentages of trajectories that scatteredwithin ± 10° of the scattering plane are 38, 80, and 87%. Theaverage final translational energy of scattered O2 molecules as a

function of the final scattering angle θf is presented in Figure10, for both simulations and experiments. The agreementbetween simulation and experiment is excellent. Theprobability distributions of the final translational energy forin-plane scattering obtained from the simulations arecompared to the experimental P(Ef) distributions in Figure11. It should be noted that for the experimental distributions,θf = 50°; however, for the simulations, no such restriction wasmade and all θf are included. The average θf values for thesimulations, ⟨θf ⟩, are given in the figure.The experimental and simulation angular distributions of θf,

P(θf), are compared in Figure 6, and there is excellentagreement. However, it should be noted that the experimentaldistribution is for in-plane scattering, while that for thesimulations includes all azimuthal directions.When the Tsurf = 300 K simulations were terminated, some

of the O2 molecules remained trapped on the graphite surface.These molecules are expected to be thermally accommodatedwith the surface and thus desorb randomly in the 0−2π finalazimuthal angles χf. As a result, this scattering will contribute anegligibly small addition to the short time scattering, which isin (or near) the scattering plane, defined by the detector andthe O2 molecular beam. They will not affect comparison withthe experimental in-plane scattering.

Figure 10. Plots of ⟨Ef⟩ versus ⟨(θf)⟩ for the four ensembles Ei (kcal/mol), Tsurf (K) = (2.1, 300), (7.4, 300), (15, 300), and (15, 1177). For highersurface temperature, the experiment was carried out at 1200 K. Included are comparisons with experiment.

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V. CONCLUSIONSIn this study, chemical dynamics simulations were performedto study O2 + graphite gas−surface scattering. The simulationswere performed for three collision energies Ei of 2.1, 7.4, and15 kcal/mol, with the initial incident angle fixed at θi = 45°. O2scattering from graphite shows scattering dynamics similar tothat observed previously in N2 + graphite scattering.34 Thesimulations only considered nonreactive collisions between O2and the graphite surface, and possible reactive events were notinvestigated. The following are the important scatteringdynamics determined from the simulations:

(1) For larger Ei values of 15 and 7.4 kcal/mol, a significantfraction of the O2 molecules scatter from the surface in1−3 ps. However, for the lowest incident energy, there isa long tail extending to much longer residence times.The trapping desorption residence time distributionfollows an exponential decay with an increase inresidence time with decrease in Ei. The rate at whichthe distribution decreases shows a near-linear depend-ence with increase in incident energy.

(2) The average energy transferred to the surface and thatremaining in O2 translation, i.e., ⟨ΔEsurf⟩ and ⟨Ef⟩, alsoshow a strong linear dependence with initial translationalenergy, illustrating that their energy distributions may bepredicted for any initial collisional energy.

(3) Scattering for all incident angles is dominated by near in-plane scattering, with non-in-plane scattering becomingimportant for the low Ei of 2.1 kcal/mol and longresidence times. For higher collision energies Ei of 7.4and 15 kcal/mol, the angular distribution of thescattered O2 is nonrandom, with a single peak at anangle close to the specular angle. For these collisionenergies, most of the desorbing trajectories leave thesurface after a short residence time with a translationalenergy greater than the 2RTs value for full thermalequilibration with the surface. Low-energy (2.1 kcal/mol) collisions of O2 with graphite, for residence timesof ∼10 ps and longer, follow conventional trappingdesorption with both the parallel and normal momentaof the projectile fully equilibrated and the projectilescattered in random directions.

(4) For all of the scattering conditions consideredexperimentally, the relationship between the averagefinal translational energy and average scattering angle forthe O2 molecules found from the simulations is inexcellent agreement with the experimental resultsobtained by Sibener and co-workers.

An interesting question is whether the initial energy transferto the graphite surface is to the interplane or intraplanemotions. However, because of anharmonic couplings betweenthese motions, e.g., out-of-plane intraplane and interplanemotions, an unambiguous answer is not possible. Suchcouplings were observed in a simulation of Ne-atom collisionswith an alkylthiolate self-assembled monolayer (H-SAM)surface.55 During a collision, intramolecular vibrational energyredistribution occurred between low-frequency modes of H-SAM chains and chain−chain intermolecular motions. Mode-specific energy transfer to the graphite surface may be studiedusing a normal mode Hamiltonian for the surface,57 and suchsimulations may be pursued in future research.Finally, it would be of interest to study the O2 + graphite

energy-transfer dynamics, as well as those for N2 + graphite,34

as a function of the projectile’s orientation as it collides withthe surface. In the current study for O2 and in the previousstudy for N2,

34 the orientation of the projectile is chosenrandomly with a thermal rotational energy and it was notpossible to study these orientation dynamics. In futuresimulations, it would be of interest to fix the initial orientationof the O2/N2 projectile, without rotation excitation, andinvestigate how the energy-transfer dynamics is affected by theprojectile’s orientation.58

■ AUTHOR INFORMATIONCorresponding Author*E-mail: bill.hase@ttu.edu.ORCIDMoumita Majumder: 0000-0003-3928-957XS. J. Sibener: 0000-0002-5298-5484William L. Hase: 0000-0002-0560-5100NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe research reported here is based on work supported by theAir Force Office of Scientific Research grant FA9550-16-1-0133 and the Robert A. Welch Foundation grant D-0005.Support was also provided by the High Performance

Figure 11. Comparison between experimental and simulation P(Ef)distributions of the final translational energy for in-plane scattering; θi= 45° and θf fixed at 50° for the experiments.

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Computing Center at Texas Tech University under thedirection of Alan Sill. Some of the computations were alsoperformed on the Chemdynm cluster of the Hase ResearchGroup. S.J.S. acknowledges the support from the Air ForceOffice of Scientific Research grant FA9550-15-1-0428, as wellas support from the NSF-Materials Research Science andEngineering Center at The University of Chicago (Grant no.NSF-DMR-14-20709).

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