Ultrafast Molecular Transport on Carbon Surfaces: The Diffusion of Ammonia on Graphite
Anton Tamtögl, Marco Sacchi, Irene Calvo-Almazán, Mohamed Zbiri, Marek M. Koza, Wolfgang E. Ernst, Peter Fouquet
aa r X i v : . [ c ond - m a t . m t r l - s c i ] O c t Ultrafast Molecular Transport on Carbon Surfaces:The Diffusion of Ammonia on Graphite
A. Tamt¨ogl, ∗ M. Sacchi, I. Calvo-Almaz´an,
3, 4
M. Zbiri, M. M. Koza, W. E. Ernst, and P. Fouquet Institute of Experimental Physics, Graz University of Technology, 8010 Graz, Austria Department of Chemistry, University of Surrey, GU2 7XH, Guildford, United Kingdom Cavendish Laboratory, University of Cambridge,J. J. Thomson Avenue, CB3 0HE, Cambridge, United Kingdom. Material Science Division, Argonne National Laboratory, Argonne, Illinois, 60439, United States Institut Laue-Langevin, 71 Avenue des Martyrs, CS 20156, F-38042 Grenoble Cedex 9, France.
We present a combined experimental and theoretical study of the self-diffusion of ammonia onexfoliated graphite. Using neutron time-of-flight spectroscopy we are able to resolve the ultrafastdiffusion process of adsorbed ammonia, NH , on graphite. Together with van der Waals correcteddensity functional theory calculations we show that the diffusion of NH follows a hopping motionon a weakly corrugated potential energy surface with an activation energy of about 4 meV which isparticularly low for this type of diffusive motion. The hopping motion includes further a significantnumber of long jumps and the diffusion constant of ammonia adsorbed on graphite is determinedwith D = 3 . · − m / s at 94 K. Keywords: Ammonia; Graphite; Diffusion; Neutron scattering; DFT; Adsorption
I. INTRODUCTION
The diffusion of ammonia on graphite is particularlyinteresting for potential applications of graphene andgraphitic material surfaces. Those include chemical dop-ing of graphene, e.g., n-doping of graphene by ther-mal annealing in the presence of ammonia gas . Fur-thermore, the modification of the electronic structureof graphene upon adsorption of ammonia has been em-ployed for quantum sensing / gas sensor applications .It was shown that it is possible to use graphene as a gassensor with high sensitivity and high accuracy for detect-ing ammonia groups due to the fact that ammonia ad-sorbed on graphene induces the appearance of new sub-strate electronic states . The changes to the grapheneelectronic states could be reverted by annealing, wherein particular desorption is often dominated by the ki-netic processes on the surface. Moreover, the gas ad-sorption and diffusion on the graphene surface basicallydetermines the sensitivity of these graphene based gassensors .The adsorption and diffusion of molecular species ongraphene and graphitic materials is also of fundamen-tal interest in various fields. Several studies on thedynamics and the structure of physisorbed molecu-lar species on graphite have been carried out, includ-ing molecular hydrogen , alkanes and aromatichydrocarbons . The diffusion of adsorbates and clus-ters on carbon-based materials has also been subject tointensive research, in search for low-friction and superdif-fusive systems as well as for studying elementary dy-namic processes such as atomic-scale friction and thedevelopment of nanometer size motorization systems .However, little experimental data exists for the diffu-sion of ammonia (NH ) on graphite. This is quite sur-prising, given that NH represents one of the simplestheteroatomic molecules. Experimental results about the ammonia/graphite system are mainly based on ther-mal desorption studies of ammonia on graphitic sur-faces and some very early neutron and nuclear magneticresonance (NMR) diffusion data . While ammonia onhighly oriented pyrolytic graphite (HOPG) starts to des-orb at 90 K , slightly higher desorption temperatures(111 K) have been found for graphene/metal systems .According to density functional theory (DFT) calcula-tions, NH adsorbs in the centre of the carbon hexagon( E a = 31 −
48 meV ), almost invariant to rotations aroundthe axis perpendicular to the surface and through the ni-trogen atom . On the other hand, the adsorptionenergy from thermal desorption spectroscopy (TDS) is E a = (260 ±
20) meV and DFT calculations have pre-dicted that the barrier for translational diffusion is about10 meV .Here we present a combined neutron scattering and den-sity functional theory (DFT) study of the diffusion of am-monia on exfoliated graphite. Scattering techniques suchas quasi-elastic neutron scattering (QENS) and quasi-elastic helium atom scattering (QHAS) are powerful tech-niques to study very fast molecular dynamics, allowingto follow the atomic-scale motion of atoms and moleculesand resolving diffusion processes on timescales from nsto sub-ps . Ammonia on graphite is a fast diffus-ing system, accessible within the time-window of neu-tron time-of-flight spectroscopy. Together with van derWaals (vdW) corrected DFT calculations we show thatammonia follows a jump motion on a weakly corrugatedpotential energy surface. II. EXPERIMENTAL AND COMPUTATIONALDETAILSA. Sample preparation
We used exfoliated compressed graphite,
Papyex , a ma-terial that is widely employed for adsorption measure-ments due to its high specific adsorption surface area. Itexhibits an effective surface area of about 25 m g − andretains a sufficiently low defect density . In addition,exfoliated graphite samples show a preferential orienta-tion of the basal plane surfaces. We exploited this andoriented the basal planes parallel to the scattering planeof the neutrons. We used 7.39 g of Papyex exfoliatedgraphite of grade N998 ( > .
8% C, Carbone Lorraine,Gennevilliers, France). The prepared exfoliated graphitedisks were heated to 973 K under vacuum for 4 days be-fore transferring them into a cylindrical aluminium sam-ple cartridge. The sample cartridge was sealed by anindium gasket and connected to a gas sorption systemvia a stainless steel capillary.The sample temperature was controlled using a standardliquid helium cryostat. The sample was initially cooleddown to 4 K and the quantity corresponding to 0.5 mono-layer (ML) and 0.9 ML of ammonia gas, respectively,was dosed through the stainless steel capillary which wasconnected to a pressure control monitor. At monolayercoverage the area occupied by one NH molecule corre-sponds to Σ = 10 . (see ). Throughout the entireexperiment, connection to a 500 cm reservoir at roomtemperature was maintained, for safety and monitoringpurposes. In using this set-up any desorbed ammoniarises to the reservoir, where the desorbed quantity canbe deduced through pressure monitoring (Figure 1). FIG. 1. The adsorption process of NH on exfoliated graphitecan be followed by monitoring the pressure in the connectedreservoir. Left panel: Uptake during dosing from 0.5 to 0.9ML coverage at a sample temperature of 4 K.Right panel: During the measurements at 105 K desorptionslowly starts to commence. However, the pressure rise corre-sponds to a loss of less than 1% of the original coverage, sowe can still safely assume a coverage of 0.9 ML. B. Instrumental details (a) Two-dimensional contour plot of the dynamic scatteringfunction S ( Q, ∆ E ) that was extracted from neutron TOF dataobtained for exfoliated graphite covered by 0.9 ML of NH at 94K. The intense spot at about Q = 1 . − is due to the (002)Bragg reflection from the basal plane of graphite.(b) Comparison of the scattering functions S ( Q, ∆ E ) ata momentum transfer of Q = 0 .
65 ˚A − for severaltemperatures with the clean graphite measured at 4 K. FIG. 2. Neutron TOF spectra for 0.9 ML of NH on graphite,converted to the dynamic scattering function S ( Q, ∆ E ). The measurements were performed at the IN6 time-of-flight (TOF) neutron spectrometer and the IN11 neutronspin-echo (NSE) spectrometer of the ILL . The incom-ing neutron wavelengths were set to 5 .
12 ˚A and 5 . µ eV (IN6) and 1 µ eV (IN11). Neutronscattering TOF spectra of NH /graphite were obtainedover a large range of temperatures: 4 K, 15 K, 25 K, 37K, 85 K, 94 K (at 0.5 ML and 0.9 ML NH coverages)and 105 K (only at 0.9 ML NH coverage). Previousto the adsorption of NH , the scattering function of thegraphite substrate was measured at 4 K, in order to ob-tain an elastic scattering resolution of the clean graphitesample.The TOF spectra were converted to scattering functions, S ( Q, ∆ E ), where Q = | Q | = | k f − k i | is the momen-tum transfer and ∆ E = E f − E i is the energy trans-fer. Figure 2a shows a two-dimensional contour plot ofthe dynamic scattering function S ( Q, ∆ E ) for 0.9 MLof NH at a temperature of 94 K. The spectrum showsan intense elastic scattering region around ∆ E = 0 meVwhich is mainly due to scattering from the graphite sub-strate. The broader feature surrounding the elastic bandis the quasi-elastic broadening which appears due to scat-tering from the diffusing ammonia adsorbates.A cut of the scattering function S ( Q, ∆ E ) at Q =0 .
65 ˚A − is displayed in Figure 2b for several tempera-tures. Figure 2b shows that the quasi-elastic broadeningincreases with sample temperature. Up to a sample tem-perature of 37 K the broadening is relatively small andit is not possible to extract the quasi-elastic broadeningwith a reliable fit of the measured data. However, inthe temperature range from 60 K to 105 K we observea clearly discernible quasi-elastic broadening which willbe used in the following to extract information about thediffusion of ammonia on exfoliated graphite. C. Computational Details
The DFT calculations were performed usingCASTEP , a plane wave periodic boundary condi-tion code. The Perdew Burke Ernzerhof exchange-correlation functional, with the dispersion forcecorrections developed by Tkatchenko and Scheffler (TSmethod) , was employed for the calculations presentedin this work. The plane wave basis set was truncated toa kinetic energy cutoff of 360 eV. We have used (4 × ×
2) graphene unit cells composed of a three-layergraphene sheet to model the adsobate system at twocoverages. A vacuum spacing of 20 ˚A was imposedabove the graphite surface in order to avoid interactionswith the periodically repeated supercells. The substrateis frozen during the calculation and the Brillouin zone ofthe two unit cells are sampled with regular (4 × × × × k -point Monkhorst-Pack grids. Theelectron energy was converged up to a tolerance of 10 − eV while the force tolerance for structural optimizationswas set to 0.05 eV / ˚A. III. RESULTS AND DISCUSSION
The experimentally measured scattering function S ( Q, ∆ E ) was fitted using a convolution of the resolutionfunction of the neutron TOF spectrometer S res ( Q, ∆ E )with an elastic term I el ( Q ) δ (∆ E ) and the quasi-elasticcontribution S inc ( Q, ∆ E ): S ( Q, ∆ E ) = S res ( Q, ∆ E ) ⊗ [ I el ( Q ) δ (∆ E ) + S inc ( Q, ∆ E )]= S res ( Q, ∆ E ) ⊗ (cid:20) I el ( Q ) δ (∆ E ) + A ( Q ) 12 π Γ( Q )[Γ( Q )] + ∆ E (cid:21) . (1)Here, δ represents the Dirac delta and the quasi-elasticbroadening is modelled by a Lorentzian function, where I el ( Q ) is the intensity of the elastic scattering and A ( Q )is the intensity of the quasi-elastic scattering. Γ( Q ) is thehalf width at half maximum (HWHM) of the Lorentzian.We write S inc ( Q, ∆ E ) because the quasi-elastic part ofthe scattering function is nearly identical to the incoher-ent scattering function since the coherent scattering ofthe graphite substrate in the considered Q range is weakand the scattering of the ammonia is strongly dominatedby the H atoms . An exemplary fit is illustrated bythe thick grey line in Figure 2b.The hereby extracted quasi-elastic broadening Γ( Q ) ata temperature of 94 K is plotted versus the momentumtransfer Q in Figure 3. The error bars in Figure 3 rep-resent the confidence intervals of the least squares fits.The error bars at small momentum transfers are invisi-ble in the plot, since they are smaller than the size of thesymbols, but for momentum transfers Q > . − they grow rapidly as Γ approaches the widths of the spectro-scopic window of the spectrometer.For the case that the diffusion of the adsorbate is gov-erned by the interaction of the molecule with a corru-gated surface, its motion can be well described by theChudley-Elliott (CE) model of jump diffusion . TheCE model assumes that a particle rests for a time τ atan adsorption site, before it moves instantaneously to an-other adsorption site. In the simplest case, this motionhappens on a Bravais lattice and the HWHM Γ( Q ) canbe expressed as:Γ( Q ) = ~ N τ N X n =1 (cid:2) − e − i Q · l n (cid:3) , (2)where l n are the corresponding jump vectors. In the caseof scattering from a polycrystalline sample, isotropic an-gular averaging has to be performed since the scatteredneutron signal “sees” the jumping adsorbate from all pos-sible directions. In the case of 2D isotropy, integrationin the scattering plane (over the azimuth ϕ ) yields:Γ( Q ) = ~ τ [1 − J ( Q · l · sin θ )] , (3)where J ( Q · l · sin θ ) is the zeroth order cylindrical Besselfunction and l is the average jump length. Q · sin θ isthe component of the scattering vector in the plane ofdiffusion, and θ the angle between Q and the normal tothis plane . Papyex consists of planes with an inclina-tion that is normally distributed around θ = 90 ◦ witha HWHM of about 15 ◦ . This has been taken into ac-count by numerical integration of (3).It should be noted that the isotropic averaging is only Q ( ˚ A − ) Γ ( m e V ) FIG. 3. Extracted quasi-elastic broadening Γ( Q ) for 0.5 and0.9 ML NH at 94 K versus momentum transfer Q . Themomentum transfer dependence can be described by the 2Disotropic Chudley Elliot model, Eq. (3), with l = 1 . · a gr (red dash dotted curve). Γ( Q ) shows hardly any change withcoverage apart from a slightly reduced broadening at small Q with increasing coverage. The green dotted line shows thetheoretical Γ( Q ) for Brownian motion. an approximation and it omits the fact that for a cor-rect isotropic averaging one needs to integrate over the S ( Q, ∆ E ) rather than the broadening Γ( Q ), which pro-duces in general a non-Lorentzian QENS broadening .However, the deviation from the Lorentz distribution ismainly caused due to scattering processes which occuralmost perpendicular to the plane of diffusion. Whilethis contribution should not be neglected in the case ofthree-dimensional polycrystalline materials, in the caseof Papyex the scattering vector Q is approximately par-allel to the (0001) basal plane of graphite as mentionedabove. Hence we will rely on the approximate solution(3), which produces very good results.(3) is then fitted to the experimentally determined broad-ening Γ( Q ) using an iterative generalized least squares al-gorithm with weights (and a numerical integration over θ ). The red dash-dotted line in Figure 3 shows that(3) fits the data very well for l = (3 . ± .
02) ˚A and τ = (0 . ± .
08) ps. From the momentum transfer de-pendence we can clearly exclude other types of motion.E.g. ballistic diffusion, which represents a two dimen-sional ideal gas, is characterised by a linear dependenceof Γ( Q ). Moreover, Brownian diffusion which describes acontinuous motion, is characterised by a square law de-pendence of the momentum transfer (green dotted line inFigure 3) and cannot reproduce the momentum transferdependence of the broadening.Note that the average jump distance ( l = 3 .
45 ˚A) corre-sponds to 1 . a gr where a gr is the graphite lattice con-stant. Hence the average jump length suggests that a sig-nificant number of long jumps occurs at this temperature.Using the residence time τ and the average jump length l Einstein’s equation for diffusion (in the two-dimensionalcase) can be used to determine the diffusion constant D : D = h l i τ (4)with the mean jump length h l i . Using (4) we obtain adiffusion constant of D = (3 . ± . · − m / s at 94 K.The diffusion constant for ammonia adsorbed on graphi-tized carbon black has been determined to range from D = 0 . · − m / s at 180 K to D = 6 · − m / s at 230K using NMR with similar values at 205 K using neu-tron scattering . Considering that these values were de-termined at much higher temperatures (where ammoniaon graphite will already have been completely desorbed)and for a different substrate, the diffusion constants arewithin the same order of magnitude compared to our re-sults.The diffusion of small molecules on graphite andgraphene has been mainly treated by theoretical ap-proaches where typically a fast diffusion process ispredicted . E.g. Ma et al. report that H O ad-sorbed on graphene undergoes an ultra-fast diffusion pro-cess at 100 K with D = 6 · − m / s. The value deter-mined for ammonia in our study is even one order ofmagnitude larger showing that the diffusion of ammo-nia on graphite is a very rapid process. Compared toother experimental studies it is about the same size com-pared to the jump diffusion of molecular hydrogen (H )on graphite and again one order of magnitude largerthan the diffusion constant found for benzene (C H ) ongraphite .As a next step we consider the coverage and temperaturedependence of the diffusion process. Unfortunately, thesignal-to-noise ratio and the difference between the scat-tering function and the resolution function is too smallfor the data measured at 0.5 ML coverage to extract a re-liable quasi-elastic broadening. The only exception is thehighest temperature (94 K), measured at this coverage.This is due to the fact that with increasing temperaturethe broadening becomes larger, as one would expect foran activated motion. Figure 3 shows a comparison ofthe quasi-elastic broadening Γ( Q ) for 0.5 and 0.9 ML ofNH coverage as a function of momentum transfer Q .One may anticipate a slightly reduced broadening at thehigher coverage and thus a smaller hopping rate, which ishowever, only discernible at small Q due to the uncertain-ties. In general the experiments show no significant cov-erage dependence within the experimental uncertainties.Hence we cannot quantify the respective contributions ofthe molecule-molecule collisions or the molecule-surfaceinteractions to the diffusion process.In Figure 4a the quasi-elastic broadening Γ( Q ) is plot-ted for all temperatures measured at an NH coverage of0.9 ML. The broadening and hence the hopping rate be-comes larger with increasing temperature, but the overalldependence upon Q , i.e., the hopping distance, remainslargely constant.While at high Q the uncertainties in Figure 4a are toolarge to extract a meaningful temperature dependence,we can use the temperature dependence of Γ at small Q ,i.e., for long range diffusion, to obtain a diffusion bar-rier. For a thermally activated processes, Arrhenius’ lawpredicts a temperature dependence of the broadening Γ,as: Γ = Γ e − EakB T , (5)where Γ is the pre-exponential factor, E a is the activa-tion energy for diffusion, k B the Boltzmann constant and T the sample temperature. Taking the natural logarithmof (5) results in a linear relationship between the inverseof the temperature, 1 /T , and the natural logarithm ofthe broadening Γ.Figure 4b shows such an Arrhenius plot of the broaden-ing Γ for the three lowest momentum transfers Q . Theactivation energy, extracted form the linear fit varies be-tween 3.5 and 4.1 meV giving rise to a mean value of E a = (3 . ± .
7) meV.Note that the hereby determined diffusion barrier issmaller than the thermal energy ( k B T ) of the substrate,while on the other hand the thermal energy is still sig-nificantly below the desorption energy. Other experi-mental examples for the occurrence of jump-like diffu-sion in the case of a very low potential energy barrierinclude the case of Cs on Cu(001) . Nevertheless, it isquite unusual to observe hopping motion for a systemwith such a weakly corrugated potential energy surface.It suggests that substantial energy dissipation channelsmust be present in the ammonia/graphite system (e.g.,by molecular collisions or by energy dissipation to thesurface), in contrast to the diffusion of flat hydrocarbonssuch as pyrene on graphite .In general, at temperatures higher than the diffusion bar-rier height, the time spent by the adsorbate near theminimum of the adsorption potential is comparable tothe time in the in-between regions. In this case both dif-fusive and vibrational motions, associated with a tempo-rary trapping of an adsorbate inside the surface poten-tial well, contribute to the quasielastic broadening andare coupled . As theoretically proposed by Mart´ınez-Casado et al. in a generalised model for the quasi-elasticbroadening, a combination of both cases should give rise Q ( ˚ A − ) Γ ( m e V )
60 K85 K94 K105 K (a) Temperature dependence of the quasi-elastic broadeningΓ( Q ) at 0.9 ML coverage. While the speed of the diffusionchanges with temperature, the overall dependence upon Q remains constant.(b) Arrhenius plot showing the temperature dependence of thebroadening Γ at small Q . The activation energy for diffusion, E a , is extracted from the slope of the linear fit. FIG. 4. Temperature dependence of the quasi-elastic broad-ening for 0.9 ML of NH on graphite. to a more complicated dependence of the broadening onthe momentum transfer due to the diffusive hopping mo-tion and the friction parameter η . As shown by Jardine etal. , friction may become more apparent in the broaden-ing due to these vibrational motions, whereas the contri-bution of the effect to energy dissipation during diffusioncannot be decoupled due to the final energy resolution ofthe instrument. The internal degrees of freedom of theadsorbed molecule may even further complicate the un-derlying microscopic processes .However, based on the approach by Mart´ınez-Casado etal. , we can use the fact that the CE model containsBrownian diffusion as a long range diffusion limit, to ob-tain a crude estimate for the friction. For Q → η can be directly extracted using Einstein’s relation asused in the fluctuation-dissipation theorem by Kubo : D = k B Tηm , (6)where m is the mass of the ammonia molecule. Using thisapproximation we obtain an estimate of the atomic-scalefriction of η = 1 . − from the data in Figure 3, whichis a medium value for the atomic-scale friction comparedto previous studies .We would like to stress that the result should be takenwith care and can only serve as a crude estimate. Fric-tion in surface diffusion processes can be caused by avariety of energy dissipation channels, including also in-teractions between the adsorbates and interaction withthe substrate. Since the measurements were performedclose to the monolayer regime, the friction parameterextracted from the fitting of the quasi-elastic broaden-ing to a parabola at low momentum transfers cannot bewritten as a simple sum of contributions to the energydissipation . It is rather an averaged friction parameterwhich is related to the energy dissipation frequency of asingle molecule diffusing on the basal plane of graphiteand interacting with the surface phonon bath and itsneighbouring molecules.Nonetheless it suggests that friction plays a significantrole in the NH /graphite system. Indeed, for a systemwith non-negligible friction, one would expect that foreach single jump an energy equivalent to the height ofthe barrier is dissipated . I.e. energy dissipation viafrictional coupling is likely to be responsible for the oc-currence of the hopping motion. On the other hand withincreasing thermal energy compared to the potential en-ergy surface, more and more long jumps start to set induring jump diffusion , which is evident from the ex-perimental data, since the best fit Chudley-Elliott modelgives an average jump length of 1 . a gr .Note that a similar diffusive motion was observed formolecular hydrogen on graphite with jump diffusion andalso a very low activation energy . Although therole of atomic-scale friction was not explicitly discussedin those cases, it suggests together with the results pre-sented in our study, that friction may be partly causedby the geometry of the molecule when compared to theflat-lying polycyclic aromatic hydrocarbons which closelyresemble the structure of the graphite substrate .Finally, the occurrence of long jumps makes the deter-mination of a meaningful activation energy challengingsince under these circumstances jumps start to becomecorrelated as shown in theoretical studies . In the caseof exfoliated graphite this is further complicated by theazimuthal averaging as described above. Nevertheless wewill use this value as a rough estimate for the diffusionof ammonia on graphite and attempt in the following tocompare our experimental results with DFT calculations. A. DFT results
We have studied the adsorption of NH on graphite fora large number of different adsorption geometries. Thoseinclude 6 different adsorption sites within the graphiteunit cell, the orientation of the molecule with the hydro-gen atoms pointing upwards (U) or downwards (D) aswell as three different rotations around the axis perpen-dicular to the surface. Figure 5 shows the energeticallymost favourable adsorption site, with the molecule lo-cated at the C site (centre) and the H-atoms pointingtowards the surface, directed towards the onbond sites.Based on the vdW corrected DFT calculations the ad- CB side viewtop view T FIG. 5. Geometry of the NH /graphite system investigatedin this study. The high symmetry adsorption positions withrespect to the graphite lattice are labelled as T: on-top; B:onbond or bridge and C: centre. The most favourable adsorp-tion site according to vdW corrected DFT is for NH at thecentre position with the rotation axis perpendicular to thesurface and the hydrogen atoms directed towards the onbondsites. sorption energy of a single NH molecule on graphite is173 meV, which is slightly reduced to 151 meV in the highcoverage regime (about 1 ML). Note that the adsorptionenergy is much closer to the experimentally found val-ues from TDS than in previous DFT calculations whichyielded adsorption energies in the order of 25-30% of theexperimentally determined value. Hence it shows the im-portance of vdW interactions in this system and that pre-vious DFT results (without vdW interactions) should betaken cautiously when trying to make predictions.Interestingly B¨ottcher et al. obtain a similar adsorptionenergy of 146 meV for NH on graphene/Ni(111) fromvdW corrected DFT, however, the molecule is adsorbedin the upwards configuration on graphene/Ni(111). Onthe other hand, recent X-ray absorption spectroscopymeasurements provided evidence for a chemical contribu-tion to the adsorption bond in the case of NH adsorbedon graphene/Ni(111) . Hence it is possible that dueto the present metal substrate the adsorption geometryof the ammonia molecule on graphene/Ni(111) changescompared to ammonia adsorbed on graphite.Table I summarises six arrangements where the TABLE I. The adsorption energy E a and the energy difference∆ E a relative to the most favourable adsorption site for NH on graphite. The six different adsorption geometries are withthe H-atoms pointing upwards (U) or downwards (D) and thecentre (C), top (T) and bridge (B) adsorption site.Orientation Position E a (eV) ∆ E a (meV)D T − .
144 7D B − .
145 6D C − .
151 0U T − .
089 62U B − .
095 56U C − .
113 38 molecule is placed in the high symmetry positions (T,B, and C) at a rotation of 30 ◦ for an ammonia coverageof about 1 ML. For the complete set (including all con-sidered adsorption geometries and coverages) please re-fer to the supplementary information. We conclude fromTable I that the downwards configuration is definitivelyfavoured with respect to the upwards configuration, re-gardless of the adsorption site. For the down configura-tion the energy differences between different adsorptionsites are in general extremely small. Moreover, the dis-tance of the molecule with respect to the surface doesnot vary significantly, e.g., for a given rotation angle anddownwards orientation the minimum distance is 3.24 ˚Aat the C site and the maximum is 3.26 ˚A at the B site.Hence, the DFT calculations confirm that the diffusionof ammonia on graphite should be governed by a weaklycorrugated potential energy surface. It can also be seenfrom Figure 6 which shows a contour plot of the potentialenergy surface for NH adsorbed on different positionsof the graphite substrate. The adsorption energies forboth the upwards and the downwards configuration areillustrated, as extracted from the vdW corrected DFTcalculations with the minimum energy rotation of 30 ◦ and at a coverage of approximately 1 ML NH . For thedownwards configuration, Figure 6a, the top site locatedabove the second layer carbon atom is energetically lessfavourable by a significant amount but all other adsorp-tion positions vary only by several meV. Based on the“static snapshots” i.e. the energy differences between theadsorption sites from vdW corrected DFT (Table I andFigure 6a) the diffusion barrier would be 6 meV whichis in good agreement with the value extracted from theexperimental data. According to this the most likely tra-jectory would be from the C site via the B site to thenext C site. Furthermore, we have also calculated the energy differ- (a) Downwards configuration (b) Upwards configuration FIG. 6. Comparison of the potential energy surface as ob-tained by the vdW corrected DFT for NH in the downwardsand upwards configuration. Both calculations are for the min-imum energy rotation of 30 ◦ and at a coverage of approxi-mately 1 ML NH . The red and orange lines represent thefirst and second layer of the graphite substrate, respectively. ence for nitrogen inversion (the umbrella or symmetricdeformation vibration mode) on graphite. Here, the en-ergy difference between the up and down NH configura-tion in a given position can only serve as a lower limit tothe “real” inversion barrier and gives 38 meV for 1 MLof NH in our case. Therefore we have also calculatedthe transition state structure for NH inversion on theglobal minimum for both the (2 ×
2) and (4 ×
4) cells.At lower coverage the barrier is 157 meV (starting fromthe down configuration) and 142 meV (starting from theup configuration). At higher coverage, the barriers arereduced to 132 meV and 94 meV, respectively. Since thedown and up configurations are not symmetrical, thereis a slight difference in the barrier from the down and upstructures.There is quite a substantial activation energy changewhen going to the higher coverage. We suspect thatthis change may be caused by repulsive steric interac-tions between the hydrogen atoms of two adjacent NH molecules. In general the barrier is in line with the val-ues reported for other systems with adsorbed ammonia.E.g the energy of this mode is typically between 130-145meV for NH adsorbed on metal surfaces . For NH on HOPG the umbrella mode could only be observed inthe multilayer case where the value is similar to the onefor solid ammonia . upon adsorption on graphite. B. Spin-echo measurements
The neutron spin-echo experiments for deuteratedammonia (ND ) at a surface coverage of 0.9 ML wereconducted on IN11 for sample temperatures of 2 K(resolution) and for 60 K, 85 K, 94 K and 105 K. TheNSE measurement delivers the development of the spacecorrelation function with time t , i.e., the normalisedintermediate scattering function S ( Q, t ) /S ( Q, .This function can also be obtained by Fourier transform-ing the scattering function S ( Q, ∆ E ). Converting thequasi-elastic broadening determined in section III to abroadening in time gives rise to τ ≈ Q = 0 . − .This is below the spectral acceptance window of IN11and the corresponding decay does not appear in the IN11spectra. Nevertheless, the spin-echo measurements showthat there is no additional motion at longer timescales,confirming the fast diffusion process seen in the TOFmeasurements (see also the supplementary information). IV. SUMMARY AND CONCLUSION
We have studied the diffusion of ammonia on exfoli-ated graphite using quasi-elastic neutron scattering. Thedependency of the quasielastic broadening on the mo-mentum transfer shows that ammonia follows a hoppingmotion on the basal plane of graphite. The diffusionconstant at 94 K was determined as D = (3 . ± . · − m / s suggesting that the diffusion of ammonia ongraphite is a very rapid process, comparable to the dif-fusion of molecular hydrogen and much faster than thediffusion of larger molecules, such as benzene. Consider-ing in particular the mass of the molecule, together withthe unusual tilted NH − π bonding, makes the observeddiffusion in this system uniquely fast. In terms of possi-ble applications for gas sensing purposes, it implies thatafter adsorption the kinetics on the surface should not bethe limiting factor.The activation energy extracted from the temperaturedependence of the quasielastic broadening is about 4meV. The combination of jump diffusion and a low ac-tivation energy suggests that NH /graphite is a system with a rather unusual combination of a weakly corrugatedpotential energy surface together with a significant fric-tion. The combination of jump diffusion and a low activa-tion energy suggests that NH /graphite is a system witha rather unusual combination of a weakly corrugated po-tential energy surface together with a significant friction.We hope that our work will initiate further theoreticalinvestigations in order to address this interesting finding.The calculated potential energy surfaces is extremely flatfor a given orientation of the molecule. The configura-tion of the adsorbate with the reverse polarity (NH bondspointing upwards) is energetically unfavourable, there-fore breaking the symmetry of the umbrella inversionmode. Furthermore, the adsorption energy of ammoniaon graphite is determined as 173 meV from DFT, muchcloser to the experimental value compared to previousDFT calculations without dispersion corrections. Theclose agreement between the calculated adsorption en-ergy, diffusion barrier and the experimental results con-firm the accuracy of the TS dispersion corrections schemefor vdW bonded systems on graphite. V. ACKNOWLEDGEMENT
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SUPPLEMENTARY INFORMATION:ULTRAFAST MOLECULAR TRANSPORT ON CARBON SURFACES:THE DIFFUSION OF AMMONIA ON GRAPHITE
S1. FULL SET OF DFT CALCULATIONS
In this section we present the data for all adsorption geometries / configurations of ammonia on graphite whichhave been calculated using van-der-Waals corrected DFT. We have calculated the adsorption energy of NH adsorbedon several different positions on top of graphite, for several rotational angles as well as with hydrogen atoms of themolecule pointing upwards (U) or downwards (D).For the 6 considered adsorption positions and the rotation of the molecule ϕ see the illustration in Figure S1. Notethat the difference between the two top sites (position 1 and position 3) is given by the carbon atom sitting in thesecond layer underneath the top site. The results for a (2 ×
2) unit cell are summarised in Table S1 and the resultsfor a (4 ×
4) unit cell are given in Table S2. φ (a) Top view(b) Side view showing the nitrogen inversion FIG. S1. Geometry of the NH /graphite system investigated in this study. The considered adsorption positions with respectto the graphite lattice are labelled with the numbers 1 , , ...
6. Three different rotations around the axis perpendicular to thesurface ϕ have been considered as well. Finally, the adsorption of the molecule with the hydrogen atoms pointing towards thesurface and in an upwards configuration were considered as well. TABLE S1. Summary of the vdW corrected DFT calculations for NH on a (2 ×
2) graphite unit cell.Orient ... Orientation of NH with the H-atoms pointing downwards (D) or upwards (U)Rot ... Rotation of NH along the z -axisPos ... Adsorption position on graphite (Figure S1) E a ... Calculated adsorption energy∆ E ... Energy difference with respect to the most favourable adsorption geometry∆ E inv ... Energy difference for nitrogen inversionOrient Rot. ( ◦ ) Pos. E a (eV) ∆ E (meV) ∆ E inv (meV)D 0 1 − .
140 11 57D 0 2 − .
138 14 55D 0 3 − .
132 19 55D 0 4 − .
140 11 49D 0 5 − .
139 12 49D 0 6 − .
144 8 39D 30 1 − .
145 7 55D 30 2 − .
145 6 50D 30 3 − .
132 19 43D 30 4 − .
147 4 48D 30 5 − .
147 4 48D 30 6 − .
151 0 38D 60 1 − .
134 17 55D 60 2 − .
137 14 54D 60 3 − .
138 13 52D 60 4 − .
138 13 48D 60 5 − .
140 11 49D 60 6 − .
143 9 38U 0 1 − .
083 68U 0 2 − .
083 68U 0 3 − .
078 73U 0 4 − .
091 60U 0 5 − .
090 61U 0 6 − .
105 46U 30 1 − .
090 62U 30 2 − .
095 56U 30 3 − .
089 62U 30 4 − .
099 52U 30 5 − .
099 52U 30 6 − .
113 38U 60 1 − .
080 72U 60 2 − .
083 68U 60 3 − .
086 65U 60 4 − .
090 61U 60 5 − .
092 60U 60 6 − .
105 47
TABLE S2. Summary of the vdW corrected DFT calculations for NH on a (4 ×
4) graphite unit cell.Orient ... Orientation of NH with the H-atoms pointing downwards (D) or upwards (U)Rot ... Rotation of NH along the z -axisPos ... Adsorption position on graphite (Figure S1) E a ... Calculated adsorption energy∆ E ... Energy difference with respect to the most favourable adsorption geometry∆ E inv ... Energy difference for nitrogen inversionOrient Rot. ( ◦ ) Pos. E a (eV) ∆ E (meV) ∆ E inv (meV)D 0 1 − .
164 10 34D 0 2 − .
161 12 31D 0 3 − .
167 6 42D 0 4 − .
165 9 26D 0 5 − .
162 11 25D 0 6 − .
170 3 16D 30 1 − .
163 10 31D 30 2 − .
165 9 30D 30 3 − .
163 10 31D 30 4 − .
167 6 25D 30 5 − .
167 6 25D 30 6 − .
173 0 15D 60 1 − .
168 5 41D 60 2 − .
161 12 31D 60 3 − .
163 10 34D 60 4 − .
162 11 25D 60 5 − .
165 9 26D 60 6 − .
171 2 17U 0 1 − .
130 44U 0 2 − .
130 43U 0 3 − .
126 48U 0 4 − .
139 34U 0 5 − .
137 36U 0 6 − .
155 18U 30 1 − .
132 41U 30 2 − .
135 39U 30 3 − .
132 42U 30 4 − .
142 31U 30 5 − .
142 31U 30 6 − .
158 15U 60 1 − .
127 47U 60 2 − .
130 43U 60 3 − .
129 44U 60 4 − .
138 36U 60 5 − .
139 35U 60 6 − .
154 19
S2. NEUTRON SPIN-ECHO MEASUREMENTS
As already mentioned in the main text, the quasi-elastic broadening determined from the TOF measurementscorresponds to a broadening in time with τ ≈ − at Q = 0 . − . Diffusion at such a short timescale does not fitthe current spectral window of IN11. As an example, Figure S2 shows the normalised intermediate scattering function S ( Q, t ) /S ( Q,
0) at 105 K for deuterated ammonia (ND ) at a surface coverage of 0.9 ML. There appears no decayversus Fourier time within the given uncertainties. Only at the largest momentum transfer ( Q = 0 .
51 ˚A − ) one mightanticipate a small change at about 1 ns. Hence the spin-echo measurements show that there is no additional motionat longer timescales, confirming the fast diffusion process seen in the TOF measurements. S ( q , t) / S ( q , ) Fourier Time (ns) -graphite105 KQ = 0.15 Å -1 -1 -1 -1 FIG. S2. Neutron spin-echo spectra of 0.9 ML deuterated ammonia (ND ) adsorbed on exfoliated graphite. The normalisedintermediate scattering function S ( Q, t ) /S ( Q,
0) shows hardly any change with Fourier time at a temperature of 105 K.
S3. FITTING OF THE EXPERIMENTAL DATA
Figure S3 shows the result of the fit of the experimental data to (1) (of the main paper) at 94 K and severalmomentum transfers. The red curve illustrates the convolution of the resolution function with the quasi-elasticbroadening and the elastic term which is fitted to the experimental data. The orange curve is the resolution function,obtained by measuring the graphite sample measured at 4 K, and the green curve displays the single Lorentzian usedto describe the quasi-elastic broadening.