Chemical Dynamics Simulation of Low Energy N2 Collisions with

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Chemical Dynamics Simulation of Low Energy N Collisions with Graphite Moumita Majumder, Hum N. Bhandari, Subha Pratihar, and William Louis Hase J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10338 • Publication Date (Web): 04 Dec 2017 Downloaded from http://pubs.acs.org on December 6, 2017

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The Journal of Physical Chemistry

Chemical Dynamics Simulation of Low Energy N2 Collisions with Graphite Moumita Majumder,1 Hum N. Bhandari,2 Subha Pratihar,1 and William L. Hase1* 1

Department of Chemistry and Biochemistry Texas Tech University, Lubbock, Texas 79409, USA 2

Department of Mathematics and Statistics Texas Tech University, Lubbock, Texas 79409, USA

corresponding author email address: [email protected]

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT

A chemical dynamic simulation was performed to study low energy collisions between N2 and a graphite surface. The simulations were performed as a function of collision energy (6.34 and 14.41 kcal/mol), incident polar angle (20o - 70o) and random azimuthal angle. The following properties were determined and analyzed for the N2 + graphite collisions: (1) translational and rotational energy distributions of the scattered N2; (2) distribution of the final polar angle for the scattered N2; and (3) number of bounces of N2 on the surface before scattering. Direct scattering with only a single bounce is dominant for all incident angles. Scattering with multiple collisions with the surface becomes important for incident angles far from the surface normal. For trajectories that desorb, the parallel component of the N2 incident energy is conserved due to the extremely short residence times of N2 on the surface. For scattering with an incident energy of 6.34 kcal/mol, incident polar angle of 40o, and final polar angle of 50o the percentage incident energy loss is 29% from the simulations, while the value is 27% for a hard cube model used to interpret experiment (J. Phys.: Condes. Matter 2012, 24, 354001). The incident energy is primarily transferred to surface vibrational modes, with a very small fraction transferred to N2 rotation. An angular dependence is observed for the energy transfer, with energy transfer more efficient for incident angles close to surface normal.


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I. INTRODUCTION Understanding energy transfer processes at the gas-surface interface provides fundamental information concerning gas–surface chemical dynamics,1-5 which is needed for accurate modelling of many chemical or physical phenomena. Any detailed understanding of gas-surface energy transfer processes requires fundamental knowledge of the relevant gassurface interaction potential that helps describe gas-surface collision events such as direct scattering, temporary physisorption, trapping on and penetration of the surface, chemisorption, and sputtering and etching which occur at high incident energies. Trapping desorption becomes important at low collision energies. The dynamics and energy transfer in collisions of a gas molecule with a surface is a complicated process and, in addition to the gas-surface potential, depends on experimental conditions such as the translational energy and incident angle of the projectile, gas/surface mass ratio, and surface temperature. A variety of surfaces including both organic6-13 and inorganic metal surfaces14,15 have been studied in gas-surface collision dynamics, both theoretically and experimentally. A particularly interesting and important surface is graphite. It is one of the most prevalent carbon allotropes, and has a layered and planar structure, with the individual layers called graphene. The carbon atoms in each layer are arranged in a honeycomb lattice with a C-C bond distance of 1.42 Å. The layers are stacked on each other through weak intermolecular interactions, with an interlayer separation of 3.35 Å. The structure results in a large anisotropy in thermal properties parallel and perpendicular to the z-axis of the crystal.16-19 An interest in gas-surface scattering phenomena associated with graphite results from interpreting microscopic details of the aerodynamic drag of objects with graphitic-like surfaces moving through the atmosphere. N2 + graphite serves as a prototype model for understanding highly energetic collisions of closed-shell molecules with surfaces of



spacecraft in low Earth orbit (i.e., at 200-700 km altitude).20 Since a defect free graphite surface shows a minimum tendency toward reactivity and heat conductivity, it is a possible choice for a thermal protection system. It is also a model for ablative material on a spacecraft.21,22 Physisorption of H2 on graphene has been considered as a storage media for molecular hydrogen.23,24 However, when such storage devices are in contact with air, the H2 storage capacity may be affected by the most abundant molecule in the air, N2. Recently, Oh et al25 reported an extensive series of measurements for the angular distribution of N2 and CO molecules scattered from a graphite surface. Their measurements were carried out over a range of incident energies [275-625 meV] and surface temperatures [150 – 400 K]. Unlike scattering from a metallic surface,26-28 salient features of the angular distributions for the scattered CO and N2 molecules were quite similar for all measurements. They proposed that the gas-surface collision is primarily a single collision event with large cooperative motions of the carbon atoms in the outermost graphene layer. They also studied scattering of O2 from a graphite surface.29,30 Since, direct inelastic scattering is the major event in these experiments, the hard cube model (HCM)31,32 is an appropriate choice to explain the scattering experiments.

Kinefuchi and co-workers33 studied out-of-plane

scattering of N2 with a graphite surface using molecule beam experiments and found a small fraction of out-of-plane scattering which is an outcome of trapping desorption. This fraction diminishes as the incident energy increases. To explain the out-of-plane scattering they used a multistage gas-surface interaction model.9 In a recent study, ReaxFF and AI-Rebo model potentials for HOPG were used to study non-reactive scattering from graphene. Though, the simulations provide a qualitative comparison with experiment, they failed to capture important details of the experiments.11 For the present article chemical dynamics simulation were performed to investigate energy transfer in collision of N2 with a graphite (0001) surface. The simulations provide an


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atomic-level understanding of the energy transfer dynamics and mechanisms for energy transfer to the translational and rotational degrees of freedom of the N2 projectile. An important component of this work is comparison with the experiments of Oh et al.25

II. COMPUTATIONAL DETAILS A. Potential Energy Functions The potential energy function for N2 + graphite is given by

V = Vgraphite + VN2 + VN2+graphite

(1)

Vgraphite is the graphite potential, VN2 is the N2 potential, and VN2+graphite is the N2 + graphite intermolecular potential. 1. Graphite potential The graphite model consists of four layers stacked in an AB sequence and is depicted in Figure 1. Carbon atoms in each layer are arranged in a hexagonal pattern forming fifteen rings along the x-direction and twelve along the y-direction. The 0 K graphite structure has an interlayer separation of 3.35 Å with a C-C bond distance of 1.42 Å. The graphite potential for a layer is represented by C-C harmonic stretches, C-C-C valence angle bends, C-C-C-C dihedral angles, and C-C Lennard -Jones (LJ) (6-12) van der Waals interactions for two atoms separated by four or more atoms. Interaction between two carbon atoms that reside on two adjacent layers is also described by C-C (6-12) LJ interactions. The functional form for the potential is given as:



= ∑" $ " ∑* +, " %

&

( )

+ ∑# "

( )

+ ∑ !"

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( )

+

#

− ( )

(2)

The parameters for the intramolecular potential are taken from the OPLS-AA force field34 and are listed in Table 1. To avoid any unphysical distortion of the interior rings, boundaries of the surface were held nearly rigid by introducing an additional interaction term Vrigid to the graphite potential, which is a large harmonic potential applied between C atoms of terminal hexagonal rings of one layer and its second consecutive layer, i.e.

- = ∑ 5! 6 ,5" ."

// (01234 )

(3)

S0 (Tsurf) in Eq. (3) is the interlayer separation between the nth and (n+2)th layers of graphite at the desired surface temperature. For the 0 K structure of graphite, this parameter equals two times 3.35 Å. In the present study, the surface temperature is 300 K and, therefore, the separation between the two layers is expected to be larger than S0(0K). To determine S0 (Tsurf), a 300 K molecular dynamics (MD) simulation was performed for the graphite model without employing Vrigid at the borders of the surface. The line density distribution (LDD) was calculated for the C-atoms along the z-direction, i.e., perpendicular to the interface, with the border atoms of the surface which showed large oscillations excluded from this analysis. This 300 K LDD is shown in Figure 2, along with a 800 K LDD for comparison. The average zdistances between adjacent layers at the surface temperature of 300 and 800 K were found to


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be 3.57 and 3.60 Å, respectively.

This gives clear indication that the graphite surface

expands upon heating. The parameter S0 (300K) is then fixed at 2×3.57 = 7.14 Å, and the surface layers are separated by 3.57 Å instead of 3.35 Å. A very large value (> 100 mdyn/Å) was chosen for the harmonic force constant Ks. 2. N2 and N2 + graphite potentials The N2 potential is described by a Morse function with parameters De = 228.3 kcal/mol, βe = 2.699 Å-1, and re = 1.0945 Å.35,36 Ab initio electronic structure calculations and fits were used to obtain an analytic potential energy function for the N2 + graphite intermolecular interaction VN2+graphite. Since benzene is the basic constituent of graphite, ab initio potentials were calculated for N2 + benzene to model VN2+graphite. In previous studies, MP2 was found to provide accurate intermolecular potentials for azulene + N237 and benzene + Na+38. For the current study MP2/6-311++G(d, p) theory was used and it gives a benzene + N2 global minimum in which N2 is parallel to the benzene plane, has a benzene + N2 center-of-mass separation of 3.46 Å, and a potential energy of -1.30 kcal/mol. These properties are in excellent agreement with experiment39-41 and higher level theoretical values.42-45 This structure is identified as orientation 1. Another structure was found, orientation 4, in which the internuclear axis of N2 coincides with the C6 axis of benzene. It has not been observed in experiments. It is less attractive than the global minimum, with a potential energy of -0.53 kcal/mol, and has a larger internuclear separation of 3.95 Å, values which agree well with previous theoretical studies.42,45 An N2 + benzene analytic intermolecular potential energy function was developed by first calculating the potential energy for 342 randomly selected N2 + benzene geometries at the MP2/6-311++G(d,p) level of theory and then fitting the MP2 potential energies. The MP2 energies were corrected for a basis set superposition error (BSSE).46 Each random N2 +



benzene geometry is obtained by following the three successive steps: (1) the position of the center-of-mass of N2 with respect to the benzene molecular plane is sampled randomly; (2) the center-of-mass separation between N2 and benzene is then sampled randomly between 2.5 to 12.0 Å; and (3) N2 molecule is then rotated randomly about its center-of-mass. This random sampling of the N2 + benzene orientations emphasizes interactions between N2 and the benzene C-atoms. The 342 MP2 energies were then fit with an analytic function written as a sum of two body N-C and N-H potentials; i.e.

6AB

DAB

78 = 978 exp=>78 ?@ + C + E (4)

A Particle Swarm Optimization (PSO) algorithm47 was used to fit the data points and the fitted parameters for N-C are A = 278655.32 kcal/mol, B = 4.456 Å-1, C = -168.40 kcal Å6/mol, D = 3337.92 kcal Å10/mol, n = 6, and m = 10 and for N-H are A = 47104.65 kcal/mol, B = 2.954 Å-1, C = -105930.94 kcal Å9/mol, D = 0.0001 kcal Å13/mol, n = 9, and m = 13. The N-C parameters are the ones used for the current simulations. To test the analytic potential energy function, MP2/6-311++G(d,p) was used to calculate potential energy curves for the six different orientations depicted in Figure 3 and compare with the curves predicted by the analytic function. The two sets of curves are in excellent agreement. The minimum energy center-of-mass separation for each curve, Ro, and the values of the minima, Vo, are given in Table 2. There is also quite good agreement between the MP2 and analytic function values for these properties. For orientations 1 to 3 the nitrogen internuclear axis is parallel to the benzene molecular plane: for 1 the center-of-mass of N2 approaches the center-of-mass of benzene; for 2 the N-N bond bisects a C-C bond; and for 3 the N-N bond is parallel to a C-C bond. For orientations 4 to 6 the nitrogen axis 8 ACS Paragon Plus Environment

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approaches the benzene molecular plane perpendicularly: for 4 the N2 axis coincides with the C6 axis of benzene; for 5 a N atom of N2 approaches a C atom of benzene; and for 6 the N2 axis bisects a C-C bond of benzene. Orientation 1 is that for the global potential energy minimum and orientation 4 is that for the other minimum discussed above. Though the analytic intermolecular potential gives an excellent representation of the ab initio potential energy curves, previous work has shown that intermolecular energy transfer (IET) dynamics are not sensitive to fine details of the intermolecular potential,34 such as the accuracy of potential energy minima for different orientations. B. Classical Trajectory Simulations The trajectory simulations were performed with the general chemical dynamics computer program VENUS.48,49 Initial conditions for the trajectories were chosen to model the experimental conditions in reference 25. Collisions between N2 and graphite were simulated for the two incident beam translational energies Ei of 6.34 and 14.41 kcal/mol, the lowest and highest incident energies at which the gas-surface experiment was conducted. The incident angle θi, defined by the angle between the N2 initial velocity vector and the surface normal, was varied from 20o to 70o. A beam of colliding N2 molecules was randomly aimed within a circular area of radius 2.2 Å, so that the area spanned by the beam of N2 molecules covered a hexagonal unit cell on the graphite surface. The initial separation between the center of the beam and the surface aiming point was set to 20 Å. The projection of the N2 beam onto the graphite surface is defined by an azimuthal angle χ and chosen randomly between 0o and 360o. The initial ro-vibrational quantum states of the N2 molecules were sampled from a 30 K Boltzmann distribution to match experiment. Periodic boundary conditions (PBC) were employed along the x- and y-directions of the graphite surface. For each trajectory, the bottom layer of the graphite surface was held rigid with initial atomic velocities of the carbon atoms of the 1st, 2nd, and 3rd layers assigned



by sampling their 300 K Boltzmann distributions. The surface is then equilibrated by a 50 ps MD simulation with velocity rescaling every 0.5 ps. This is followed by a 50 ps equilibration without velocity rescaling to ensure that the temperatures of individual surface layers are 300 K. Using this final geometry, the LDD is calculated and compared with that in Figure 2 to assure that it is correct. The trajectories were propagated with a combined fourth-order Runge-Kutta and sixthorder Adams-Moulton algorithm, with a time step of 0.05 fs. Trajectories were terminated by either a distance criterion, i.e., when the distance between the aiming point and the outgoing N2 exceeds 30 Å, or a total integration time criterion, i.e., the total integration time exceeding 25 ps. The latter is used for trapped trajectories, for which N2 remains on the surface. Typically, 1000 trajectories were calculated for each Ei, θi initial condition. At the end of each trajectory, the final translational and internal energy of the N2 molecule and the internal energy of the surface are evaluated. The N2 rotational quantum number is calculated from its final rotational angular momentum. The final angular distribution P(θf) of the scattered N2 molecule is determined by calculating the angle between the final velocity vector of the projectile and the surface normal. The distribution of the final azimuthal angle, with respect to the scattering plane, P(χf) is also calculated.

III. SIMULATION RESULTS A. N2 + Graphite Atomistic Collison Dynamics Depending on the number of inner turning points (ITPs) in the motion of N2, with respect to the surface normal, three trajectory types were identified: direct, trapping desorption, and trapping on the surface. The former has only one ITP. The second type has multiple ITPs. For the third type N2 remained trapped on the surface when the trajectory was terminated. There were no trajectories for which N2 penetrated the top graphite layers. This is


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understandable as the N2 van der Waals radius is much larger than the available gap between any two extreme carbon atoms of a hexagonal ring. Trajectories for which N2 remained trapped on the surface, when the trajectory was concluded at 25 ps, are excluded from analyses that involve Ef, θf, and χf. The distance between the N2 center-of-mass and the bottom rigid layer of the graphite surface, versus time, is shown in Figure 4 for representative trajectories of each trajectory type. The initial and final scattering angles, θi and θf, are depicted in Figure 4. The probabilities of the three trajectory types depend on Ei and θi. Table 3 lists the percentages of the three trajectory types as a function of Ei and θi. At small θi the moleculesurface collisions are dominated (i.e., 98-99%) by direct scattering, irrespective of Ei. At large θi, the direct trajectory percentage is reduced but it remains dominant. For the low Ei of 6.34 kcal/mol, trapping desorption becomes important for large incident angles, with percentages of 17 and 29% for θi of 60o and 70o, respectively. When N2 encounters the surface, it transfers energy from the normal component of its momentum as discussed in detail below. For grazing collisions the initial value of the normal component is quite small. Therefore, the N2 + graphite motion is mostly governed by the parallel component and N2 may undergo multiple collisions with the surface until it attains the necessary normal momentum to recoil from the surface. For the higher Ei of 14.41 kcal/mol, the trapping desorption probability decreases substantially to only 3% and 14% for θi of 60o and 70o, respectively. Accordingly, trapping desorption decreases with increase in Ei, but increases with increase in θi. A very small fraction of the trajectories remained trapped on the surface when the trajectories were terminated; the percentage ranges from 0.1 - 1% for θi ≤ 60o. For the N2 + graphite collisions, the Ei values considered here are larger than the attractive well of -1.17 kcal/mol for the N2-graphite interaction. Therefore, trapping of N2 is unlikely.



As discussed above direct scattering is the dominant event for the simulations reported here. Depending on the incident energy, direct scattering occurs in two different regimes; thermal and structure.5 The thermal regime occurs when the time scale of the surface motion is nearly resonant with the incident energy, i.e., Ei ≤ 2RTs, where Ts is the surface temperature and 2RTs is the thermal desorption energy. The structure regime occurs when Ei is significantly larger and an individual surface atom is responsible for repelling the particle in the gas-surface collision. In the present study, Ei is similar to 2RTs = 1.2 kcal/mol and the direct scattering is expected to be dominated by the thermal regime. B. Energy Transfer Efficiency During the N2 + graphite collision, part of Ei is transferred to N2 internal energy, Eint, and surface vibration Esurf, with the remaining in N2 translation Ef;

G = ∆G + ∆G"IJ + GJ (6)

Values of , , and are presented in Table 4 for Ei of 6.34 and 14.41 kcal/mol and θi of 20o, 40o, 60o, and 70o. A small percentage of Ei is transferred to N2 rotation, with no transfer to vibration. Transfer to N2 rotation is weakly dependent on Ei and θi, with average energy transfer percentages of 10 - 11%, 7 - 8%, 4%, and 4% for θi of 20o, 40o, and 60o, and 70o, respectively. For the N2 + graphite collisions, the loss in N2 translational energy Ei is primarily to the surface. Unlike , the average energy transfer to shows a strong angular dependence. For Ei of 6.34 kcal/mol, the average percentages are 39, 23, 8, and -0.7% for θi of 20o, 40o, 60o, and 70o, respectively. Upon increasing Ei to 14.41 kcal/mol, energy transfer percentages to the surface increase and are 57, 34, 9, and 2% for θi of 20o, 40o, 60o, and 70o.


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An incident angle close to the surface normal increases the energy transfer probability, establishing that the normal component of Ei plays the key role in energy transfer to the surface. For grazing collisions, such as at θi = 70o, the normal component of Ei is very small and N2 leaves the surface when it acquires a sufficiently large normal component. This may require energy from the surface. For the simulation at Ei = 6.34 kcal/mol and θi = 70o, is -0.04 ± 0.7 kcal/mol with 97% of the energy retained in N2 translation. In the simplest models of energy transfer in gas–surface collisions,5 it is only the normal component Ein of Ei which participates in energy transfer. The normal component is Ein = Ei cos2θi and in Figure 5, Ein for the different θi are plotted versus the average percentage of the available energy in translation of the scattered N2 molecules, . As shown in the Figure, this model gives a good representation of versus θi, particularly for Ei = 6.34 kcal/mol. The energy remaining in N2 translation shows an interesting feature with change in θi. For the large θi of 70o and 60o, the percentages are the same for Ei of 6.34 and 14.41 kcal/mol. However, for the smaller θi = 20o they are different, e.g. the percentages are 50 and 33% for incident energies of 6.34 and 14.41 kcal/mol, respectively. To summarize, the normal component of Ei gives a good description of energy transfer to the surface and N2 rotation, which equals Ei - . The fractional energy loss from Ei is given by [1 - /Ei] and percentages for this fraction are 50, 31, 11, and 1% for Ei = 6.34 kcal/mol at θi of 20o, 40o, 60o, and 70o, respectively. For Ei 14.41 kcal/mol these percentages are 67, 41, 12, and 5%. Energy transfer becomes more important with increase in Ei and for large θi energy transfer becomes negligible. As shown in Table 4, energy transfer to N2 rotation is unimportant for the large θi. Distributions of Ef, P(Ef), for the different of Ei and θi are shown in Figure 6. They are far from Boltzmann and instead Gaussian in nature. As discussed above, trapping desorption trajectories become important for small Ei and large θi. Of interest is whether the collision



energy transfer efficiency is affected by the residence time of N2 on the graphite surface. Scatter plots of Erot and Ef, versus time, are given in Figure 7 for trapping desorption trajectories, with Ei = 6.34 kcal/mol and θi of 60o and 70o. For these trajectories there is one or more ITPs in the N2 + graphite normal motion. There is not a strong time dependence for Erot and Ef, and there is not one Ef value as low as 1.2 kcal/mol for thermal desorption. The same time independence is seen for Ei = 14.41 kcal/mol, but there are fewer events since trapping desorption is less important. It is of interest to determine if there is a surface site dependence for the scattering dynamics. To investigate this, scatter plots of Ef and θf versus a collision impact parameter, b, are given in Figure 8 for Ei = 6.34 kcal/mol and θi = 40o. For b = 0 N2 strikes a carbon atom and for b = 1.42 N2 targets the center of a ring. As shown in Figure 8 there is no significant site dependence on the range of Ef and θf, and their average values, with every site contributing both low and high Ef and θf values. For these Ei = 6.34 kcal/mol and θi = 40o simulations direct scattering dominates, as shown in Table 3, and for such scattering the repulsive part of the potential is most important for the scattering dynamics.2 As shown in Figure 3 for orientations 1, 2, and 3, the repulsive potential is similar for different impact sites, consistent with scattering dynamics independent of the impact site. It is worth noting that no-site dependence was found for the scattering dynamics in simulations of protonated diglycine collisions with the diamond {111} surface.50 For comparison with experiment a pristine, perfectly structured graphite surface model was used for the simulations. However, a graphite surface for practical applications is expected to have defects, such as step edges and carbon vacancies, and possible damage, which may affect the scattering dynamics. A recent experiment of Ar beam scattering from bare and defect induced graphite surfaces, provides insight into how vacancies affect energy transfer.51 The STM measurement clearly showed that the electronic state of the graphite


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surface is modified around the defect and induces heterogeneity to the surface. A new component appeared in the scattering distribution of Ar projectiles for an Ar+ sputtered graphite surface and this new component has a peak that appeared at a larger final scattering angle than that for the pristine graphite surface. An approximate estimation showed that the energy loss to the surface is increased from 33% to 58% when a defect induced graphite surface is used. Since Ar + graphite (effective mass = 114 amu, based on analysis with a hard cube model32) is a prototype model for N2 + graphite (effective mass = 108 amu25) system, one may expect similar behaviour for scattering of N2 from a defect induced graphite surface. C. Rotational distribution of the scattered N2 The rotational quantum number of the scattered N2 is given by j = [J(J + 1)]1/2ħ, where j is the angular momentum and J the rotational quantum number. P(J) distributions for all the trajectories, at the different Ei and θi, are shown in Figure 9. Each P(J) distribution may be fit by a sum of low and high temperature Boltzmann distributions, and the fraction of each component and its temperature are listed in Table 5. The low temperature component dominates and its fraction increases with increase in θi. However, for θi = 20o the fractions of the low and high temperature components are similar, suggesting that at smaller θi the high temperature component may dominate. Interestingly, the fractions of the low and high temperature components are similar for a broader range of θi at the higher Ei of 14.41 kcal/mol. The low temperature component is higher than the 30 K temperature of the colliding N2 molecules and remarkably similar for all the P(J), particularly for Ei = 6.34 kcal/mol, and ranges from 87 - 118 K. In contrast, the temperature of the high temperature component decreases precipitously with increase in θi. P(J) distributions were also determined for the direct and trapping desorption trajectory types. For θi of 20o and 40o, for which trapping desorption is unimportant, the P(J) for the direct trajectories are the same as for all the trajectories given in Figure 9. For Ei = 14.41



kcal/mol and θi = 60o the trapping desorption probability is also small, and P(J) for the direct trajectories is similar to that for all the trajectories; see Table 5. P(J) for the direct and trapping desorption trajectories at Ei = 6.34 kcal/mol for both θi of 60o and 70o, and at Ei = 14.41 kcal/mol for θi of 70o, are shown in Figure 10. As for all of the trajectories the direct P(J) are fit by a sum of low and high temperature Boltzmann distributions, and each component’s fraction and temperature are listed in Table 5. The low temperature component ranges from 85 - 118 K and similar to the low temperature component for all of the trajectories. The high temperature component is higher in temperature than for all of the trajectories. For θi from 20o to 70o, the high temperature component changes from 1024 to 457 K for Ei = 6.34 kcal/mol and 1703 to 510 K for Ei = 14.41 kcal/mol. P(J) for the trapping desorption trajectories is well-described by a single Boltzmann distribution, with temperatures given in Table 5. For the simulations at θi of 60o the fitted temperature is only slightly lower than the surface temperature of 300 K and, as shown in Figure 10, the P(J) are quite similar at Ei = 6.34 kcal/mol with the fitted temperature and 300 K. Given the uncertainties in the simulation P(J), both temperatures provide a good fit. However, at θi of 70o the fitted temperature is substantially smaller than 300 K and, as shown in Figure 10, for Ei of both 6.34 and 14.41 kcal/mol the P(J) for the fitted temperature and 300 K are different. Though the P(J) at θi = 60o is well represented by the surface temperature, there is not thermal accommodation with the surface as described by the above P(Ef) distributions and the angular distributions in the next section. D. Angular distribution of the scattered N2 Figure 11 presents polar plots of the scattered N2 angular distribution for the different Ei and θi. For each plot there is a lobular pattern, with the maximum in the angular intensity distribution, RJ57 , at an angle slightly larger than the specular angle of θf = θi. This implies that N2 has lost energy to the surface. For low incident angle collisions, with θi = 20⁰ and


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40o, the angular deviation of the lobular maximum from the specular direction is nearly 11o. The deviation becomes smaller with increase in the incident angle. For incident angles of 60o and 70o, the deviations are ~ 8o and ~ 2o, respectively. As shown in Figure S1, for all incident angles the angular distribution P(θ) of scattered N2 is quite different from the random scattering with sin(θ)cos(θ). Since direct scattering is dominant for all conditions, this is quite expected. The collisions are dominated by in-plane scattering. This is illustrated in Figure 12, where the probability of the change in the azimuthal angle, ∆χ, is plotted for θi of 20o, 40o, and 70o. The probability of in-plane scattering increases with increase in θi. To understand the contribution of each trajectory type to the angular distribution, the average final scattering angle for each trajectory type is listed in Table 6. For trapping desorption shows a significant deviation from 45o, the value for thermal desorption, and the maximum in θf is approximately at the specular angle for each incident angle, as shown in Figure 13. This conflicts with the conventional definition of trapping desorption where the projectile is expected to be desorbed from the surface after being fully equilibrated and scattered in a random way. In the present system desorbed N2 retains memory of the initial conditions. This trapping desorption is consistent with work by Head-Gordon and coworkers52 for Ar-Pt(111) systems at high surface temperatures. They concluded that unlike conventional trapping desorption, their experiments involve very rapid equilibration of the normal component but very slow accommodation of the parallel component. Therefore, for higher surface temperatures when the residence time of projectile is very short, the projectile desorbs from the surface before it is fully thermalized, resulting in memory of the parallel component for the desorbing trajectories. The possibility of thermal accommodation for the trapping desorption trajectories, with longer residence times, was investigated by preparing scatter plots of θf versus the N2 residence time on the graphite surface. The residence time is defined as the time between the first and last ITPs in the N2 center-of-mass motion with



respect to the surface. The plots are given in Figure S2 of the Supporting Information and it is seen that there is no statistical change in for residence times as long as 20-25 ps.

IV. COMPARISON BETWEEN SIMULATION AND EXPERIMENT In previous experiment, Oh et al25 studied in-plane N2 + graphite scattering by varying the incident angle θi and fixing the angle between θi and the detector at by 90o. The incident energy was 275 - 625 meV and surface temperature 150 – 400 K. The present simulations may be compared with these experiments for the incident energies Ei of 275 and 625 meV (6.34 and 14.41 kcal/mol) and surface temperature Tsurf of 300 K. In interpreting the experiments, Oh et al25 concluded that N2 + graphite scattering is predominantly a singlecollision event with an effective mass of 10.8 carbon atoms on the graphite surface. This collective effect of the surface arises from strong in-plane C-atom bonding in the graphene surface layer, so that on average 1.8 benzene rings interact simultaneously with N2. This cooperative motion of the graphene surface layer has been reported in other experimental studies of graphite and massive projectiles.53-55 In the simulations, direct scattering, a single collision event, is dominant for all of the initial conditions in agreement with experiment. In the experiments, for Ei of 275 meV (6.34 kcal/mol) and Tsurf of 300 K, the angular distribution intensity has a single peak appearing at a final scattering angle θf = 90 - θi = 49.4o. This suggests that for an incident angle close to 40.6o most of the N2 scatters off the surface at a slightly larger angle of ~ 10o than its specular position. From the simulation with Ei of 6.34 kcal/mol, Tsurf of 300 K, and θi of 40o and as shown in Figure 11, the angular deviation from the lobular maximum for specular scattering is nearly 11o. This simulation result is in excellent accord with experiment. Also, as shown in Figure 11, the value for the final angular distribution P(θf) is nearly zero, for a final scattered


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angle defined by θf = 90 – θi and for the incident angles θi of 20o, 60o, and 70o. This characteristic of P(θf) agrees well with the experimental results. In the N2 + graphite experimental study25 the energy transfer efficiency for N2 was not reported, but for CO + graphite scattering it was measured25 that 32% of the collision energy is transferred at the most probable final scattering angle, with Ei = 277 meV and Tsurf = 300 K. From the N2 + graphite simulations it is found that 31% of the energy is transferred for Ei = 6.34 kcal/mol (275 meV) and θi = 40o, with all θf included. However, as discussed above the simulation P(θf) distribution is narrow, making the experimental and simulation analyses of the energy transfer similar. In Figure 14, is plotted versus for both incident energies and θi = 40o (For other incident angles, see Figure S3). The plots are nearly linear with a negative slope. For Ei = 6.34 kcal/mol, of 49.4o, the most probable θf in the experiments, correlates with of 4.53 kcal/mol, leading to a 28.5% energy loss. According to a hard cube model (HCM), used to analyse the N2 + graphite experiments,25 the energy loss is 26.5% and in excellent agreement with the simulation value.

V. CONCLUSIONS In this work, chemical dynamics simulations were performed to study N2 + graphite gas-surface scattering. The N2 + graphite intermolecular potential used for the simulations was developed from MP2/6-311++G(d,p) calculations. The simulations were performed for two collision energies Ei of 6.34 and 14.41 kcal/mol, and four incident angles θi = 20o, 40o, 60o, and 70o for each Ei. The following are the scattering dynamics determined from the simulations: 1. Direct, i.e. impulsive, scattering is dominant for all the Ei, θi initial conditions. The trapping probability of N2 on the surface is nearly zero for small θi, but for the larger θi of 70o the probability goes to ~ 45% for Ei of 6.34 kcal/mol. This presumably indicates corrugation



on the surface. Most of the trapping is temporary with N2 desorbing during the trajectory integrations. 2. The transfer of N2 collision energy to the graphite surface is higher for θi close to surface normal. For these collisions, the parallel component of Ei is conserved. The percentage energy transfer for N2 + graphite collisions is in excellent agreement with experimental results for CO + graphite scattering.25 For N2 + graphite, with Ei = 6.34 kcal/mol and θi = 40o, the percentage energy loss from Ei is 29% from the simulations, while 27% for a hard cube model used to interpret the experiments.25 Most of the incident energy goes to the surface’s vibration modes and a very small fraction goes to the N2 rotation. For grazing collisions, the overall energy transfer is quite small. The N2 + graphite energy transfer found from the simulations is in excellent agreement with experiment. 3. The angular distribution of the desorbing N2 shows non-random scattering, with a single peak at an angle close to the specular angle. The scattering for all incident angles is dominated by near in-plane scattering, with in-plane scattering more dominant as the incident angle is further from normal. For the 25 ps simulations performed here, some of the trajectories are trapped on the surface, with the vast majority desorbing before the trajectories are terminated. For the trajectories that desorb, the parallel component of the N2 incident energy is conserved due to the extremely short residence times of the N2 molecules on the surface. The agreement found here between chemical dynamics simulations and experiment for N2 + graphite collisions is consistent with findings from previous studies of projectiles colliding with organic surfaces.3,7,13,56-61 For Ne collisions with an alkylthiolate selfassembled monolayer surface (H-SAM),3,56 CO27,57,58 and Ar59 collisions with a perfluorinated F-SAM surface, Ar collisions with a HO-terminated HO-SAM surface,60 and Ne collisions with a squalane surface61 the scattering dynamics from the simulations are in


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very good agreement with experiment. If sufficiently accurate potential energy surfaces are used classical chemical dynamics accurately represents the experiments. In future work if may be of interest to extend the research reported here. The manner in which the N2 vibrational and rotational energies and the graphite temperature affect the scattering dynamics could also be investigated. There have been limited studies of such collision dynamics. Simulations of collisions of N2 with highly vibrationally excited molecules,35-37 and the current simulations, indicate that exciting N2 vibration should not significantly affect the scattering dynamics, since transfer of energy from N2 vibration should be negligible. However, N2 rotational excitation may transfer to the surface and/or to translational energy of the scattered N2 molecule. In previous simulations of CO2 collisions with a F-SAM surface,7,58 transfer of CO2 vibrational angular momentum between CO2 rotational angular momentum and surface vibration was studied. Possible effects on the scattering dynamics, of changing the graphite temperature, is an interesting question. In N2 + graphite scattering experiments25 it is seen that increasing the surface temperature moves the final angular distribution to lower scattering angles, implying less efficient energy transfer. In contrast, in simulations of protonated diglycine ions with a diamond {111} surface,62 increasing either the ions’ or surface temperature from 300 to 2000 K had, at most, only a negligible effect on the energy transfer dynamics. To a good approximation, the initial surface and ion energies ae nearly adiabatic during the collision energy transfer, the latter agreeing with experiment.63 It may also be of interest to consider graphite surface damage for high energy N2 collisions and/or high surface temperatures. This could be done by QM/MM simulations,64 in which a QM region of the surface is reactive.65

SUPPORTING INFORMATION



Angular distribution P(θ) of scattered N2 for all Ei, θi (Figure S1), scattered plots of θf vs. residence time for desorption trajectories (Figure S2) and variation of with (Figure S3) are given in the Supporting Information.

ACKNOWLEDGEMENTS The research reported here is based upon work supported by the Air Force Office of Scientific Research (AFOSR) grant FA9550-16-1-0133 and the Robert A. Welch Foundation Grant No. D-0005. Support was also provided by the High Performance Computing Center (HPCC) at Texas Tech University, under the direction of Philip W. Smith. Some of the computations were also performed on the Chemdynm cluster of the Hase Research Group.


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Table 1. Parameters for the Graphite Potentiala

Potential Type

Potential Parameters

Harmonic Stretch (C—C)

r0 = 1.42, kr = 6.52

Harmonic bend (C—C—C)

θ0 =120o, kθ = 0.88

Dihedral (C—C—C—C)

Φ1 = 180.0, v1 = 7.25

L-J

a = 1121755, b = - 560.4387

a

Stretching and bending force constants have units of mdyn/Å and mdyn-Å/rad2, respectively. Angles are in degrees and torsion energy is in kcal/mol. The units of the L-J parameters a and b are kcal Å12/mol, and kcal Å6/mol


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Table 2. Comparison between Fitted and Ab Initio Parameters for Orientations in Figure 3.a Orientations

a

Fit

Ab initio

R0

-V0

R0

-V0

1

3.491

1.1773

3.46

1.3022

2

3.653

0.9119

3.61

0.8917

3

3.697

0.8720

3.62

0.9276

4

3.877

0.9201

3.95

0.5348

5

4.114

0.6559

4.32

0.2810

6

4.168

0.6028

4.29

0.2954

Energies are in kcal/mol and R0 is in Å.



Page 32 of 67

Table 3. Percentage of each Trajectory Type Trajectory Types

Eia

θi

Direct

Trapping Desorption

Trappingb

6.34

20o

99.6

0.4

---

40o

98.0

1.5

0.5

60o

76.4

17.1

6.5

o

56.0

29.0

15.0

20o

99.9

0.1

---

o

98.7

1.2

0.1

60o

96.0

3.0

1.0

70o

81.0

14.0

5.0

70

14.41

40

a

Incident energy in kcal/mol.

b

N2 remains trapped on the surface when the trajectory is terminated at 25 ps.


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Table 4. Percentage of Average Energies Transferred for Different Trajectory Types

Ei

c

6.34

θi

20o 40o 60o 70o

Trajectory Type Direct Scattering Trapping Desorption b

50 69 89 99

39 23 8 -2

11 8 3 3

a

a

a

a

a

a

84 93

10 5

6 2

50 69 88 97

a a a 14.41 20o 33 57 10 33 o a a a 40 59 34 7 59 o 60 88 8 4 79 17 4 87 o 70 95 3 2 90 7 3 94 a The number of trajectories too small to determine meaningful average percentages. b The percentage for ∆G is equivalent to ∆G, , since ∆GU# = 0 for all trajectories. c Energy in kcal/mol.


Total

39 23 8 -0.7

11 8 4 3.7

57 34 9 2

10 7 4 4


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Table 5. Parameters for the Boltzmann Fits to the P(J) Distributionsa, c

Trajectory Type Direct

Ei

θi

6.34

20o 40o 60o 70o

Trapping Desorption

Low T Frac. T (K)

High T Frac. T (K)

0.57 0.64 0.87 0.89

0.43 0.36 0.13 0.11

95 94 87 95

Total

1024 798 450 457

Low T Frac. T (K)

High T Frac. T (K)

b

b

b

b

-----

-----

1.00 1.00

267 211

Low T Frac. T (K)

High T Frac. T (K)

0.57 0.64 0.70 0.71

0.43 0.36 0.30 0.29

95 94 87 99

1024 798 370 321

b b 14.41 20o 0.51 112 0.49 1703 0.51 112 0.49 1703 b b 40o 0.55 118 0.45 1354 0.55 118 0.45 1354 60o 0.67 94 0.33 828 ----- 1.00 258 0.66 93 0.34 804 70o 0.79 85 0.21 510 ----- 1.00 190 0.75 88 0.25 471 a Energies in kcal/mol and angles in degrees. b The number of trajectories too small to determine meaningful average properties. c Surface temperature is maintained at 300 K and initial N2 rotational temperature at time t = 0 ps is 30 K.


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Table 6. Average Scattering Angles for Different Trajectory Typesa Trajectory Type

Direct

Trapping Desorption

Total

Ei

θi

31.4 51.3 67.4 71.3

b

6.34

20o 40o 60o 70o

31.4 51.5 68.2 72.2

b

72.1 74.2

b 20o 36.8 36.8 o b 40 54.4 54.6 60o 66.7 74.7 67.0 70o 74.4 78.2 75.0 a Energies in kcal/mol and angles in degrees. b The number of trajectories too small to determine meaningful average properties.

14.41



Figure Captions

Figure 1. Top and side view of the simulated graphite surface at Tsurf = 0 K. Figure 2. Line density distribution (LDD) function for the graphite surface at 300 K and 800 K surface temperatures.

Figure 3. Ab initio calculations (open circle) and the fits (solid line) to the benzene-N2 intermolecular potential for the six different orientations. Ab initio energy points are obtained at the MP2/6-311G++(d,p) level of theory with BSSE correction.

Figure 4. Motion of the N2 center-of-mass along the z-direction, i.e. perpendicular to the graphite surface, for three trajectory types: 1) direct impulsive scattering; 2) trapping desorption; and 3) trapping. R is the z-distance between the center-of-mass of N2 and the bottom layer of the graphite surface for the simulation with Ei =6.34 kcal/mol and θi = 60⁰. Figure 5. Ein for the different θi are plotted versus the average percentage of the available energy in translation of the scattered N2 molecules, . Figure 6. Distributions of Ef, P(Ef), for the different Ei and θi. Figure 7. Scatter plots of Erot and Ef , versus residence time, for trapping desorption trajectories, with Ei = 6.34 kcal/mol and θi of 60o and 70o. 36 ACS Paragon Plus Environment

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Figure 8. Scatter plots of Ef and θf versus impact parameter, b, with Ei = 6.34 kcal/mol and θi = 40o.

Figure 9. P(J) distributions for all the trajectories, at the different Ei and θi. Fits were made with a sum of two Boltzmann distributions and their temperatures are given in legends. The fraction of each component and its temperature are given in Table 5.

Figure 10. P(J) for the direct and trapping desorption trajectories at Ei = 6.34 kcal/mol for both θi of 60o and 70o, and at Ei = 14.41 kcal/mol for θi of 70o. The direct P(J) are fit as in Figure 9. For trapping desorption P(J) is fit by a single Boltzmann.

Figure 11. Polar plots of the angular distribution for N2 scattering from the 300 K graphite surface for collision energies Ei of 6.34 kcal/mol and 14.41 kcal/mol, and incident angles θi of 20o, 40o, 60o, and 70o. Figure 12. Probability of the change in the azimuthal angle, ∆χ, for θi of 20o, 40o, and 70o, and Ei of 6.34 and 14.41 kcal/mol. Figure 13. Angular distribution of desorbed N2 for trapping desorption trajectories with Ei = 6.34 kcal/mol, and θi = 60o and 70o; 17% and 29% of the trajectories are trapping desorption for θi of 60o and 70o, respectively. Figure 14. Plot of versus for both incident energies and θi = 40o; Ei = 6.34 kcal/mol (red) and 14.41 kcal/mol (blue) .



Figure 1. Top and side view of the simulated graphite surface at Tsurf = 0 K.


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Figure 2. Line density distribution (LDD) function for the graphite surface at 300 K and 800 K surface temperatures.

Figure 3. Ab initio calculations (open circle) and the fits (solid line) to the benzene-N2 intermolecular potential for the six different orientations.

Ab initio energy points are

obtained at the MP2/6-311G++(d,p) level of theory with BSSE correction.


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Figure 4.

Motion of the N2 center-of-mass along the z-direction, i.e. perpendicular to the

graphite surface, for three trajectory types: 1) direct impulsive scattering; 2) trapping desorption; and 3) trapping. R is the z-distance between the center-of-mass of N2 and the bottom layer of the graphite surface for the simulation with Ei =6.34 kcal/mol and θi = 60⁰.



Figure 5. Ein for the different θi are plotted versus the average percentage of the available energy in translation of the scattered N2 molecules, .


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Figure 6. Distributions of Ef, P(Ef), for the different Ei and θi.



Figure 7. Scatter plots of Erot and Ef , versus residence time, for trapping desorption trajectories, with Ei = 6.34 kcal/mol and θi of 60o and 70o.


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Figure 8. Scatter plots of Ef and θf versus impact parameter, b, with Ei = 6.34 kcal/mol and θi = 40o.



Figure 9. P(J) distributions for all the trajectories, at the different Ei and θi. Fits were made with a sum of two Boltzmann distributions and their temperatures are given in legends. The fraction of each component and its temperature are given in Table 5.


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Figure 10. P(J) for the direct and trapping desorption trajectories at Ei = 6.34 kcal/mol for both θi of 60o and 70o, and at Ei = 14.41 kcal/mol for θi of 70o. The direct P(J) are fit as in Figure 9. For trapping desorption P(J) is fit by a single Boltzmann.



Figure 11. Polar plots of the angular distribution for N2 scattering from the 300 K graphite surface for collision energies Ei of 6.34 kcal/mol and 14.41 kcal/mol, and incident angles θi of 20o, 40o, 60o, and 70o.


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Figure 12. Probability of the change in the azimuthal angle, ∆χ, for θi of 20o, 40o, and 70o, and Ei of 6.34 and 14.41 kcal/mol.



Figure 13. Angular distribution of desorbed N2 for trapping desorption trajectories with Ei = 6.34 kcal/mol, and θi = 60o and 70o; 17% and 29% of the trajectories are trapping desorption for θi of 60o and 70o, respectively.


Page 50 of 67

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Figure 14. Plot of versus for both incident energies and θi = 40o; Ei = 6.34 kcal/mol (red) and 14.41 kcal/mol (blue) .



TOC.


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Figure1. Top and side view of the simulated graphite surface at Tsurf = 0 K. 313x140mm (120 x 120 DPI)

ACS Paragon Plus Environment


Figure 2. Line density distribution (LDD) function for the graphite surface at 300 K and 800 K surface temperatures. 254x254mm (120 x 120 DPI)


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Figure 3. Ab initio calculations (open circle) and the fits (solid line) to the benzene-N2 intermolecular potential for the six different orientations. Ab initio energy points are obtained at the MP2/6-311G++(d,p) level of theory with BSSE correction. 250x194mm (120 x 120 DPI)



Figure 4. Motion of the N2 center-of-mass along the z-direction, i.e. perpendicular to the graphite surface, for three trajectory types: 1) direct impulsive scattering; 2) trapping desorption; and 3) trapping. R is the zdistance between the center-of-mass of N2 and the bottom layer of the graphite surface for the simulation with Ei =6.34 kcal/mol and θi = 60o. 156x156mm (96 x 96 DPI)


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Figure 5. Ein for the different θi are plotted versus the average percentage of the available energy in translation of the scattered N2 molecules, . 254x254mm (120 x 120 DPI)



Figure 6. Distributions of Ef, P(Ef), for the different Ei and θi. 381x508mm (120 x 120 DPI)


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Figure 7. Scatter plots of Erot and Ef , versus residence time, for trapping desorption trajectories, with Ei = 6.34 kcal/mol and θi of 60o and 70o. 296x254mm (120 x 120 DPI)



Figure 8. Scatter plots of Ef and θf versus impact parameter, b, with Ei = 6.34 kcal/mol and θi = 40o. 131x197mm (96 x 96 DPI)


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Figure 9. P(J) distributions for all the trajectories, at the different Ei and θi. Fits were made with a sum of two Boltzmann distributions and their temperatures are given in legends. The fraction of each component and its temperature are given in Table 5. 381x592mm (120 x 120 DPI)



Figure 10. P(J) for the direct and trapping desorption trajectories at Ei = 6.34 kcal/mol for both θi of 60o and 70o, and at Ei = 14.41 kcal/mol for θi of 70o. The direct P(J) are fit as in Figure 9. For trapping desorption P(J) is fit by a single Boltzmann. 508x381mm (120 x 120 DPI)


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Figure 11. Polar plots of the angular distribution for N2 scattering from the 300 K graphite surface for collision energies Ei of 6.34 kcal/mol and 14.41 kcal/mol, and incident angles θi of 20o, 40o, 60o, and 70o. 141x196mm (120 x 120 DPI)



Figure 12. Probability of the change in the azimuthal angle, ∆χ, for θi of 20o, 40o, and 70o, and Ei of 6.34 and 14.41 kcal/mol. 508x254mm (120 x 120 DPI)


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Figure 13. Angular distribution of desorbed N2 for trapping desorption trajectories with Ei = 6.34 kcal/mol, and θi = 60o and 70o; 17% and 29% of the trajectories are trapping desorption for θi of 60o and 70o, respectively. 169x254mm (120 x 120 DPI)



Figure 14. Plot of versus for both incident energies and θi = 40o; Ei = 6.34 kcal/mol (red) and 14.41 kcal/mol (blue) . 169x169mm (120 x 120 DPI)


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59x59mm (96 x 96 DPI)


Chemical Dynamics Simulation of Low Energy N2 Collisions with

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