Isotopic Enrichment Resulting from Differential Condensation of Methane Isotopologues Involving Non-equilibrium Gas − Surface Collisions Modeled with Molecular Dynamics Simulations

: We employ molecular dynamics simulations to understand the energy transfer processes involved during the collisions of CH 4 and CD 4 with CH 4 layered surfaces at 20 K in order to explain our experimental finding of preferential adsorption of CD 4 compared to CH 4 . There is good agreement between our MD simulations and our experimental results. We find that gas − surface collisional energy accommodation is dominated by exchange involving the translational degrees of freedom of the incident molecule and intermolecular vibrations of the interface. This observation allows us to understand that the cause of CD 4 preferential sticking arises from its propensity to lose more energy during its first impact with the surface, inducing longer residence times and leading to increased probability of becoming trapped and condensed onto the surface. Systematic trends are seen for sticking probabilities and energy transfer when we explore the behavior of the other H/D-substituted isotopologues of methane. These molecular insights provide context into the adsorption behavior occurring on icy dust grains in our solar system. Because adsorption is often the first step, trapping efficiency differences between isotopologues have notable implications for condensed phase reaction probabilities involving isotopically substituted species and subsequent events leading to increased molecular complexity. Aside from astrophysical significance, our findings have direct implications for novel isotope enrichment mechanisms under non-equilibrium conditions involving the preferential condensation of heavier isotopes and isotopologues during gas − surface collisions under specifically selected substrate, gas mixture, and incident kinematic conditions.


■ INTRODUCTION
Understanding energy-transfer dynamics at the gas−surface interface helps to accurately model a variety of chemical and physical phenomena. 1,2The energy transfer that occurs when a gas molecule collides with a condensed surface is complicated and a result of many factors such as the gas−surface potential, translational energy and incident kinematics of the projectile, gas−surface mass ratio, density of states of the interface's degrees of freedom, surface morphology, and surface temperature.We present detailed molecular dynamics simulations to explicitly calculate energy transfer with the surface in order to understand our experimental observation 3 that preferential adsorption occurs for CD 4 when striking the CH 4 surface compared to CH 4 under non-equilibrium gas−surface collision conditions.
−12 In order to accurately model chemical abundances, we previously examined isotopologues to understand how differences in mass between the projectile and the surface influence the ability of the species to adsorb and thus lead to observed relative isotopic abundances. 13,14We studied methane and its isotopologue deuterated methane due to methane's interstellar abundance in both the gaseous and solid forms 15−21 and its ability to form larger hydrocarbon species through addition reactions. 22We determined, through two independent experimental methods (monitoring reflected species as well as those species adsorbed on the surface), that preferential sticking and condensation occurred for CD 4 compared CH 4 under specific non-equilibrium gas−surface collision conditions. 3−31 For isotopologues, the gas−surface potentials are intrinsically identical; hence, any difference in sticking probabilities is directly correlated to the dynamics of the gas−surface collision.Here, we refine our computational parameters and perform molecular dynamics (MD) simulations using VENUS 23 to fully investigate this energy transfer during the collision of CH 4 and CD 4 with CH 4 layered surfaces that results in these differing trapping efficiencies.We conclude that the dominant energy exchange occurs between the incident translational degrees of freedom and intermolecular lattice surface vibrations.Because CD 4 loses more translational energy upon impact compared to CH 4 , the CD 4 projectiles interact with the surface longer and are therefore more likely to be trapped onto the surface.
Understanding the refined details of intermolecular energy exchange responsible for gaseous condensation is in itself quite important as it has a direct linkage to many technological applications.One such avenue pertains to water condensation in high-velocity gas flows as experienced by aircraft in lowtemperature situations, while another example is condensation on windmill blades for power generation operating in cold environments.
Additionally, these findings can be incorporated into the development of novel heterogeneous isotopic enrichment and separation techniques.More broadly, this work is also critical to understanding the nature of methane adsorption within astrophysical environments.Trapping efficiency differences and energy exchange mechanisms can be incorporated into astrophysical models to explain molecular abundances and increased deuterium abundance in cometary ices and outer solar system planets.Moreover, aside from astrophysical environments, adsorption has implications into fields such as heterogeneous catalysis or thin film growth where the adsorption process serves as the first step in film formation. 32COMPUTATIONAL DETAILS Potential Energy Surface.As detailed in our earlier publication and summarized here, 3 the potential energy function for the (CH 4 ) beam and (CH 4 ) surface on top of a Au(111) crystal is given by where V beam is the beam CH 4 intramolecular potential, V surface is composed of intramolecular CH 4 potentials (same as V beam ) as well as the intermolecular CH 4 −CH 4 and Au−CH 4 potentials using the 6−12 Lennard-Jones formulation, and V beam+surface is the intermolecular CH 4 −CH 4 potential.Each intramolecular CH 4 potential is expressed as a sum of Morse potentials for the C−H stretches and quadratic potentials for the H−C−H bends: the Morse parameters are D = 4.878 eV, β = 1.86 Å −1 , and r 0 = 1.086Å, 28 and each HCH quadratic bend has f = 0.585 mdyn Å/rad 2 and θ = 109.47°. 28,33These parameters were also used for the CD 4 beam.The methane harmonic frequencies are 3193, 3021, 1583, and 1413 cm −1 .The surface model consists of 6 methane layers stacked in an AB sequence on top of a layer of gold to form a cubic closepacked structure (Figure 1). 34There are 789 CH 4 molecules in alternating layers of 120/143 molecules to prepare a methane surface area of 1600 Å 2 (40 × 40 Å 2 in the x−y plane).The total surface height of all of the stacked layers is 18 Å including the gold layer on the bottom.All intermolecular potentials are written as sums of 6−12 Lennard-Jones two-body potentials with a cutoff distance of 10 Å and are summarized in Table 1. 35,36For the Au(111) base, ε 0 = 0.229 eV and σ 0 = 2.951 Å 37 were used to give an atomic spacing of 2.93 Å, closely matching that determined from STM images of the reconstructed (111) surface. 38In the current surface model, the CH 4 molecules are spaced by an average C−C distance of 3.8 Å, which is comparable to calculated CH 4 intermolecular potentials. 39The Au−CH 4 interactions are described by Au−C Lennard-Jones potentials with parameters derived from the Au−Au and C−C interactions using standard mixing rules, 37,40 which are ε 0 = 0.0318 eV and σ 0 = 2.99 Å.
Prior to trajectory simulations, the surface configuration was fully relaxed to a potential energy minimum after a geometry optimization step and a thermal equilibration step at 20 K.The surface configuration at 20 K is similar to a flat crystalline surface, which is a model representation of a local section of the experimental methane surface prepared from beam deposition of methane on a Au(111) substrate, which in reality may contain domains of small, imperfect crystallites.However, even with this difference, there is qualitatively similar energy-transfer dynamics and thus appropriate to use for our study. 29lthough the surface retains a layered crystalline configuration of methane molecules in the z-direction at 20 K, the orientations of the hydrogens of a particular methane molecule within a layer are randomized.Thus, as the surface relaxes into its configuration, there may be some regions that can adsorb incident projectiles more efficiently.
The easiest test to determine a small radial area acceptable for gas−surface collision simulations is to calculate the methane binding enthalpy with different impact parameters (BMAX, Å) where BMAX is the radial distance in angstroms in the X−Y plane from a head on collision to a methane on the surface.A microcanonical ensemble averaged intermolecular potential curve for CH 4 approaching the surface is obtained by  The Journal of Physical Chemistry C averaging the potential energies of over 1000 randomly oriented CH 4 molecules as a function of CH 4 −surface distance. 41Comparing the interfacial potential energy curves evaluated at several BMAX impact parameters (Figure 2), we find that the potential minimum decreases as the impact parameter traverses the unit cell.The potential energy curve at 4 Å is close to the curve at 0 Å, but not identical because our average C−C distance is 3.8 Å.We then decided to use a BMAX impact parameter of 8 Å to sample the equivalence of two unit cells for a representative sampling of the surface.Procedure for the Molecular Dynamics Simulations.Molecular dynamics simulations were performed using the VENUS general chemical dynamics computer program. 23,42lassical trajectories were used to simulate collisions of a beam of CH 4 or CD 4 with the CH 4 surface.Initial conditions for the trajectories were selected to sample the beam's translational and vibrational energy at the experimental conditions; rotations were frozen at 0 K given the supersonic expansion of the incident beam.The selection of initial conditions follows from previous VENUS studies. 30,43For each simulation, a beam of colliding molecules was aimed at a circular area.Each trajectory was initialized with a separation of 10 Å between the center-of-mass of the beam molecule and the surface aiming point.Unless otherwise specified (in the simulations with an angle of 45°between the beam and the surface), the beam molecule collides perpendicularly to the surface to match the predominant configuration of the experimental apparatus.For each beam, the initial vibrational levels were sampled from Boltzmann distributions at 300, 700, 900, or 1100 K including the vibrational zero-point energy.Our experimental studies employ essentially monoenergetic seeded supersonic beams so that the CH 4 and CD 4 have the same incident velocity but different kinetic energies and momenta (0.49, 1.16, 1.48, and 1.79 eV for CH 4 and 0.67, 1.41, 1.74, and 2.19 eV for CD 4 ).
We also ran classical trajectories to simulate collisions of a beam of CH 3 D, CH 2 D 2 , and CD 3 H with the CH 4 surface.These trajectories were compared to those of the 1.79 eV CH 4 and 2.19 eV CD 4 beams (the highest initial velocity, 4613 m/ s).Thus, the initial vibrational levels were sampled from a Boltzmann distribution at 1100 K, and the rotational levels were frozen at 0 K.The kinetic energies were 1.93 2.02, and 2.1 eV for CH 3 D, CH 2 D 2 , and CD 3 H, respectively.
For each trajectory, the gold and bottom three layers were held rigid and acted as anchor layers.Additionally, the mass of carbon atoms in rim CH 4 molecules was artificially increased by 10000 to truncate the surface.Initial conditions for this surface were selected by assigning velocities to the carbon atoms of these layers, sampled from a Maxwell−Boltzmann distribution at 20 K.The surface was equilibrated by a 50 ps molecular dynamics simulation with velocity scaling every 1000 steps and another equilibration without velocity scaling.The trajectories were propagated with a Velocity-Verlet integrator with a time step of 0.01 fs.Trajectories were terminated either when the distance between the central methane molecule and the outgoing product exceeded 30 Å or when the total integration exceeded 50 ps.Typically, 1900− 2000 trajectories were calculated for each ensemble of initial conditions, including the surface composition and beam conditions.

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■ RESULTS AND DISCUSSION Sticking Probability.First, the theoretical predictions of the sticking probabilities from the trajectory simulations agree well with the experimentally determined sticking probabilities.Computationally, the sticking probability is the fraction of trajectories with CH 4 or CD 4 remaining on the surface after 50 ps.Our VENUS calculations demonstrate (1) a decrease in sticking probability with increasing incident velocity as well as (2) a significant isotopic effect as seen in the difference between CH 4 and CD 4 sticking probabilities on the CH 4 surface (Figure 3) as a function of incident velocity.In general, we f ind that the CD 4 and CH 4 sticking probabilities are identical for the lowest velocity beam before diverging for the higher velocity beams as more CD 4 trajectories become preferentially trapped on the surface.For comparison, the VENUS calculations are overlaid with our experimental King and Wells 44 sticking probability measurements (solid circles). 3Although the theoretical sticking probabilities are slightly lower than the experimental values, the trend and differential sticking between CH 4 and CD 4 at each initial condition are in excellent agreement (Figure 3b).This offset could result from structural differences between our disordered experimental surface and our layered flat theoretical surface.Additionally, Lennard-Jones potentials are not fully optimized for the repulsive region. 45egardless, there is qualitatively similar energy-transfer dynamics between crystalline and domains of small, imperfect crystallites 29 so that we can use our theoretical system to explain how the two isotopologues are differentially condensed.
Direct/Indirect Scattering.The trajectories that eventually scattered off the surface can experience different dynamics on the surface.In particular, these trajectories are categorized as two types: (1) direct scattering with only 1 inner turning point (ITP) and ( 2) physisorption/desorption with multiple ITPs, where an ITP occurs when the CH 4 /CD 4 center-of-mass height changes from decreasing to increasing. 30epresentative CH 4 trajectories of both types at an incident velocity of 4613 m/s are shown in Figure 4a as well as a comparison to a sticking/trapped trajectory, where the centerof-mass height from the layered surface is plotted as a function of time.The direct scattering trajectory bounces on the surface with a shorter residence time near the surface, while the physisorption/desorption trajectory can experience multiple hops on the surface until a successful escape from the surface.The trapped trajectory remains about 3.5 Å above the surface, in agreement with the CH 4 −CH 4 intermolecular Lennard-Jones potentials and surface spacing.At our selected incident velocities, we do not find any CH 4 or CD 4 projectiles contain enough incident energy to penetrate into the bulk film.
Separating the scattered trajectories into direct and physisorption/desorption trajectories, we find that with increasing incident velocity, the percentage of direct trajectories and physisorption/desorption trajectories both increase as fewer projectiles are trapped on the surface.Additionally, the relative percentage of direct trajectories compared to physisorption/desorption trajectories decreases.This difference is particularly stark for the highest velocity (4613 m/s) beam where among the scattered trajectories there is a larger percentage of direct trajectories for CH 4 than for CD 4 .This provides mechanistic support for why trapping efficiencies differ between these two isotopologues and how energy loss to the surface plays an important role.
Scattered Trajectory Energy Distributions.For each trajectory that does not stick on the surface, we conducted additional analyses to determine the post-collision velocity distributions, translational and internal energy lost to the surface, residence time on the surface, and angle scattered from the surface.When CH 4 and CD 4 collide with the CH 4 surface, in order for trapping to occur, the CH 4 or CD 4 molecule must lose enough of its initial energy to avoid bouncing back.To align with our experimental setup employing monoenergetic seeded supersonic beams, the molecular dynamics simulations consider CH 4 and CD 4 molecules with identical incident velocities but different kinetic energies and momenta.Thus, we

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first examine the final velocity distributions for the projectiles that scatter off the surface (Figure 5a,b) before calculating the translational energy exchange to the surface.
As expected, with increasing incident velocity, the scattered molecules leave the surface with a higher final velocity.For the lowest incident velocity (2483 m/s) molecules, there is essentially no difference between CH 4 and CD 4 .However, when the incident velocity is increased to 4613 m/s, the CH 4 molecules scatter with a larger final velocity (Figure 5b).The velocity distributions are well described by either one or the sum of two Maxwell−Boltzmann distributions. 31,46,47We see that there is an inelastic collision with the surface, but the molecules are not thermally equilibrated with the surface, as the fitting temperature is greater than 20 K (Figure 5b).
We next examine the translational, vibrational, and rotational energy transfer upon impact with the CH 4 surface because trapping only occurs when a molecule loses enough energy to the surface (Figure 6).The incident projectiles contain no rotational energy (to be consistent with our supersonic beam expansion conditions) 3 so we calculated the rotational energy gain due to collisions with the surface; the vibrational and translational energy losses are calculated by taking the initial − final energy (in electronvolts) for each scattered trajectory.With increasing initial incident velocity, more energy (translational and vibrational) is lost to the surface while nevertheless still leading to the overall decrease in sticking probability (Figure 3).For the translational energy at the faster incident velocity (Figure 6a), we see the largest divergence; CD 4 loses 2.07 eV to the surface compared to 1.67 eV for CH 4 .The larger translational energy loss for CD 4 is what enables it to be trapped on the surface with a greater relative probability.Additionally, even at the highest velocity with 1100 K initial vibrational energy and 0 K initial rotational energy, both CH 4 and CD 4 lose less than 0.25 eV vibrational energy to the surface and gain less than 0.06 eV rotational energy (Figure 6b,c).We find that the vibrational energy lost and rotational energy gained are all at least an order of magnitude smaller than the translational energy lost to the surface.This indicates that it is the translational energy exchange that dominates the condensation behavior between incident CH 4 and CD 4 and the CH 4 surface, leading to trapping of these molecules rather than rotational and vibrational energy exchange.
As a comparison and to further generalize our energy exchange occurring for CH 4 and CD 4 , we also ran additional trajectories for CH 3 D, CH 2 D 2 , and CD 3 H impinging on the 20 K CH 4 surface.These trajectories were for the highest initial velocity (4613 m/s), corresponding to kinetic energies of 1.93 2.02, and 2.10 eV for CH 3 D, CH 2 D 2 , and CD 3 H, respectively.The trajectories contained vibrational energies sampled from a Boltzmann distribution at 1100 K and 0 K rotational energy to directly compare to CH 4 and CD 4 .First, we examined the sticking probability (Figure 7) and found that the increased  surface at 20 K.The translational energy (a) is calculated from the momenta at the final step of the trajectory.The vibrational energy (b) is calculated from the momenta at the final step of the trajectory and using the harmonic bend and Morse parameters for methane.The rotational energy (c) is calculated from the angular momentum evaluated at the final step of the trajectory.Energy loss is calculated by taking the initial − final energy (in eV) for each scattered trajectory.Because the initial rotational energy is 0, the rotational energy gained (final − initial) is equal to the final energy (in eV).Translational energy exchange is an order of magnitude higher than vibrational and rotational energy exchange with the surface and is responsible for trapping the methane molecules.

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condensation is directly proportional to the number of deuterated atoms in the methane molecule.Thus, CD 4 , with four deuterium atoms, has the highest sticking probability as compared to CH 4 and the other isotopologues (CH 3 D, CH 2 D 2 , and CD 3 H).
Next, we examine the translational energy loss (Figure 8a), vibrational energy loss (Figure 8b), and rotational gain (Figure 8c) for these five beams (CH 4 , CH 3 D, CH 2 D 2 , CD 3 H, and CD 4 ) with the same initial velocity but increasing initial kinetic energies.We confirm that translational energy exchange dominates and is an order of magnitude higher than vibrational and rotational energy exchange.Additionally, the translational energy loss increases monotonically to preferentially trap the deuterated methane molecules.
Residence Time Distributions.To further understand how this translational energy loss is dissipated to trap the methane isotopologues, we examine their time on the surface (residence time).For all scattered trajectories, the residence time is the duration of time that an incident CH 4 or CD 4 has its center-of-mass (COM) height within 10 Å of the surface.The residence time distributions for the lowest velocity (2483 m/s) and highest velocity (4613 m/s) of CH 4 /CD 4 molecules are shown in Figure 9a,b.These distributions are fit to an exponentially modified Gaussian (EMG) function which is a convolution of an exponential and a Gaussian distribution probability distribution: 48 where the complementary error function is defined as In eq 2a, a is the amplitude, σ is the Gaussian width, S is the skew or shift in the time from a normal Gaussian distribution, and k is the exponential decay.For the lowest velocity beams (Figure 9a), the CH 4 and CD 4 distributions are quite similar to Gaussian peak widths of ∼0.3 ps, a relaxation time (1/k) of 0.77 ps, and an amplitude of 0.2.For the higher velocity beams, although both Gaussian widths are ∼0.17ps, there are some clear differences between the CH 4 and CD 4 results (Figure 9b).First, when considering the Gaussian component of the fit, CH 4 has a much higher amplitude (0.064) compared to CD 4 (0.048).Second, when considering the exponential decay component, the relaxation time is longer for CD 4 (1.31 ps) compared to CH 4 (0.98 ps).This supports the finding that CH 4 molecules spend less time interacting with the surface (1.5 vs 1.7 ps at the highest initial velocity).Thus, we can clearly see in Figure 9c that with increasing initial velocity, on average, the molecules spend less time on the surface.To avoid convolution between different mechanisms, the average residence time on the surface (Figure 9c) considers only direct scattering trajectories.For these direct scattering trajectories, the translational energy loss during one bounce with the surface directly impacts the residence time.We f ind that because CD 4 projectiles lose more translational energy to the surface during collision (particularly for the highest velocity beam), they end up interacting with the methane surface longer than the CH 4 projectiles and are therefore more likely to be trapped.
Scattering Angle Distributions and 45°Incident Angle Trajectories.The final scattering angle (θ f ) is defined as the angle between the final velocity vector of CH 4 or CD 4 and the surface normal.With increasing incident velocity, the average scattered angle decreases for both CH 4 and CD 4 , but it decreases more for CD 4 .The final average angles are 48°and  vibrational energy (sampled from a Boltzmann at 1100 K), and 0 K rotational energy.The energy exchange is calculated using the momenta at the final step of the trajectory and the initial energy (in eV).Translational energy loss increases monotonically with increasing initial kinetic energy and is an order of magnitude higher than the vibrational and rotational energy.

The Journal of Physical Chemistry C
44°for CH 4 at the lowest and highest incident velocity, respectively, and 47°and 40°for CD 4 .For all incident conditions, we find that the emitted trajectories do not scatter with a cosine distribution, indicating dominance of direct scattering and the lack of reemitted thermalized trajectories.
We also ran an additional set of simulations with trajectories that approach the surface from 45°instead of normal.The initial conditions for these trajectories were v i = 2483 m/s and v i = 4613 m/s with vibrational energy sampled from Boltzmann distributions at 300 and 1100 K, respectively, to match the experimental conditions and the trajectories impinging upon the surface at normal.We also included CH 4 and CD 4 trajectories with an initial velocity of 6579 m/s and vibrational energy sampled from a Boltzmann distribution at 1100 K so that the normal velocity component was 4613 m/ s.In general, we find a lower overall sticking probability for trajectories incident at 45°versus normal.Therefore, our mechanism involving direct translational energy exchange with the intermolecular vibrations of the surface lattice upon one impact with the surface is broadly applicable regardless of the incident angle.Because the sticking probabilities are much lower for the 45°trajectories, we propose that perpendicular components of the incident momentum are especially important in this translational energy transfer to the surface lattice.

■ CONCLUSION
In conclusion, we performed detailed molecular dynamics simulations to understand our experimental result of differential condensation between CH 4 isotopologues impinging onto a CH 4 surface at 20 K. First, we have good agreement between our MD simulations and our experimental results, where there was increased adsorption of CD 4 compared to CH 4 , particularly for the highest velocity beam.Second, we find that gas−surface collisional energy accommodation is dominated translational energy exchange with intermolecular vibrations of the methane surface lattice.CD 4 preferential sticking arises from its propensity to lose more energy during its first impact with the surface, inducing longer residence times and leading to increased probability of becoming trapped and condensed onto the surface.Systematic trends are seen for sticking probabilities and energy transfer when we explore the behavior of the other H/D substituted isotopologues of methane.
In general, our increased understanding of this gas−surface energy exchange under non-equilibrium conditions at cold substrate temperatures from these numerical simulations has important astrophysical and technological implications.Two such technological applications are water condensation in highvelocity gas flows as experienced by aircraft in low-temperature situations and condensation on windmill blades for power generation operating in cold environments.
Importantly, these results offer a novel route for isotope enrichment and separation via the preferential condensation of heavier isotopes during gas−surface collisions under carefully selected substrate, gas mixture, kinematic, and incident velocity conditions.
These novel trapping efficiency differences and energy exchange mechanisms can also be incorporated into astrophysical models.Adsorption is often the first step for many cold temperature reactions occurring on dust grains, with trapping efficiency differences having notable implications for allowed reaction probabilities and subsequent events, leading to increased molecular complexity.Our investigations of gas− surface collisional energy transfer processes can help to not only explain increased abundance of deuterium in solar system planets, 53,54 but these mechanisms can be incorporated into astrophysical models of the icy dust grain processes including those in the interstellar region. 5

■ ACKNOWLEDGMENTS
This work was supported by the Air Force Office of Scientific Research, Grant FA9550-19-1-0324, with focus on the dynamics of energetic gas−surface interactions in extreme environments.The computer simulations were performed on the Midway cluster at the University of Chicago Research Computing Center (RCC).Infrastructure support from the NSF-Materials Research Science and Engineering Center at the University of Chicago, Grant NSF-DMR-2011854, is also gratefully acknowledged.

Figure 1 .
Figure 1.Schematic model of the optimized methane surface comprised of methane layers on top of a layer of gold.The methane surface area is 1600 Å 2 and is in a cubic close-packed structure.

Figure 2 .
Figure 2. Orientation averaged CH 4 (beam)−CH 4 (surface) intermolecular potential.The incident methane experiences a slightly different potential based on where it hits on the unit cell.

Figure 3 .
Figure 3. Sticking probabilities (a) calculated from the number of CH 4 and CD 4 direct and physisorption scattering trajectories (open circles) on a CH 4 surface at 20 K. Error bars represent the standard error of a binomial distribution of at least 1900 trajectories for each velocity.The experimental sticking probabilities (solid circles) 3 are from at least three King and Wells measurements on at least three different days.The differential sticking probability (b) is the ratio of the CH 4 /CD 4 sticking probability at the CD 4 initial velocity.The experimental and VENUS CH 4 sticking probabilities are extrapolated using the linear fit in (a), so that the ratio is taken at the same initial condition.Excellent agreement between experiment and theory is readily seen in (b).

Figure 4 .
Figure 4. (a) Example representative trajectory types plotted as center-of-mass height from the surface versus time.Direct scattering trajectories have one ITP, physisorption/desorption trajectories have MITPs, and trapped trajectories have MITPs and remain on the surface after 50 ps.(b) Percentage (%) of each trajectory type for the CH 4 and CD 4 projectiles at each incident velocity.A total of 1922 to 1979 MD trajectories were run for each incident condition.

Figure 5 .
Figure 5. Final velocity distributions for CH 4 and CD 4 scattering off of a CH 4 surface at 20 K.The velocity is calculated from the momenta at the final step of the trajectory.The distributions are curve fit to either one Maxwell−Boltzmann distribution (panel a, v i = 2483 m/s) or the sum of two Maxwell−Boltzmann distributions (panel b, v i = 4613 m/s).The average final velocity is plotted in (c).As the incident velocity increases, the projectiles scatter off with an average faster final velocity; CH 4 scatters off with a higher velocity.

Figure 6 .
Figure 6.Average translational energy loss (a), vibrational energy loss (b), and rotational energy gain (c) for CH 4 and CD 4 scattering off a CH 4surface at 20 K.The translational energy (a) is calculated from the momenta at the final step of the trajectory.The vibrational energy (b) is calculated from the momenta at the final step of the trajectory and using the harmonic bend and Morse parameters for methane.The rotational energy (c) is calculated from the angular momentum evaluated at the final step of the trajectory.Energy loss is calculated by taking the initial − final energy (in eV) for each scattered trajectory.Because the initial rotational energy is 0, the rotational energy gained (final − initial) is equal to the final energy (in eV).Translational energy exchange is an order of magnitude higher than vibrational and rotational energy exchange with the surface and is responsible for trapping the methane molecules.

Figure 7 .
Figure 7. Sticking probabilities calculated from the number of 4613 m/s CH 4 , CH 3 D, CH 2 D 2 , and CD 3 H, and CD 4 direct and physisorption trajectories scattering off a CH 4 surface at 20 K. Error bars represent the standard error of a binomial distribution of at least 1900 trajectories for CH 4 and CD 4 and between 400 and 800 trajectories for CH 3 D, CH 2 D 2 , and CD 3 H.The sticking probability increase is proportional to the number of deuterated atoms.

Figure 8 .
Figure 8.Average translational energy loss (a), vibrational energy loss (b), and rotational energy gain (c) for 4613 m/s CH 4 , CH 3 D, CH 2 D 2 , and CD 3 H and CD 4 scattering off a CH 4 surface at 20 K.The methane and deuterated methane molecules have identical initial velocity (4613 m/s),vibrational energy (sampled from a Boltzmann at 1100 K), and 0 K rotational energy.The energy exchange is calculated using the momenta at the final step of the trajectory and the initial energy (in eV).Translational energy loss increases monotonically with increasing initial kinetic energy and is an order of magnitude higher than the vibrational and rotational energy.