Motion of water monomers reveals a kinetic barrier to ice nucleation on graphene
Anton Tamtögl, Emanuel Bahn, Marco Sacchi, Jianding Zhu, David J. Ward, Andrew P. Jardine, Steven J. Jenkins, Peter Fouquet, John Ellis, William Allison
DDynamics of water monomers on a hydro-phobic surface
Anton Tamt¨ogl, ∗ , † Emanuel Bahn, † , ‡ Marco Sacchi, ¶ , § Jianding Zhu, † David J. Ward, † AndrewP. Jardine, † Steven Jenkins, ¶ Peter Fouquet, ‡ John Ellis, † and William Allison † † Cavendish Laboratory, J. J. Thompson Avenue, Cambridge CB3 0HE, United Kingdom ‡ Institut Laue-Langevin, 71 Avenue des Martyrs, 38000 Grenoble, France ¶ Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UnitedKingdom. § Department of Chemistry, University of Surrey, Guildford GU2 7XH, United Kingdom
E-mail: [email protected]
The interfacial behaviour of water remains a central question to fields as diverse as protein foldingand surface wetting.
Much of our existing knowledge concerning the microscopic motion comesfrom computational simulation but the dynamics of molecules, on an atomic scale, is largelyunexplored by experiment. Here we present experimental results that provide a detailed insightinto the behaviour of water monomers on a graphene surface. We show that motion occurs byactivated hopping on a primitive lattice that corresponds to the centres of the graphene hexagons.The motion is remarkable because of a strong signature for cooperative behaviour due to repulsiveforces between the monomers. The repulsive forces enhance the monomer lifetime ( t m ≈ s at T S = 125 K), providing a precursor gaseous phase that precedes the nucleation of ice islands and, inturn, provides the opportunity for our experiments to be performed. The initial stages of ice growthare generally believed to be dominated by attractive interactions through hydrogen-bonding. Ourevidence provides an alternative perspective and suggests that, at least in some cases, nucleation onsurfaces may be a process that is kinetically hindered. D iffusion and motion of water at surfaces controlsmany phenomena in physics, chemistry and bi-ology as well as being a central contributor totechnological processes such as corrosion and catalysis.Even though water/solid interactions are omnipresent,detailed molecular-level understanding of water/solidinterfaces is mainly based on studies of water on flatmetal substrates. Here, several structural studies re-veal the role of attractive, short range forces in the earlystages of ice formation but experimental studies regard-ing the motion at surfaces are scarce. Yet the diffusionof atoms and molecules across the surfaces of materialsis of paramount importance to an endless list of phe-nomena.The atomic-scale motion of adsorbates on surfaces istypically described by adsorbates moving or hoppingalong the surface while the substrate provides the ther-mal energy for the motion. We have prepared a sys-tem where we can observe the motion of isolated watermolecules on a hydrophobic graphene surface. The ad-sorption of water on graphene is attracting most atten-tion at present due to its great technological relevanceand direct impact on graphene-based devices as well asa model system to understand the interaction betweenwater and carbonaceous surfaces. Our results are of im-portance for understanding the water-graphene interac-tion in more complex systems: for the development of graphene as a novel separation technology includ-ing the utility of graphene to act as a material for watertreatment and for biological and chemical sensorsbased on graphene as well as carbon nanotubes in biol-ogy and medicine. Gaining direct images of water on non-metallic surfacesremains challenging and one is often restricted in termsof the substrate to e.g. NaCl.
In particular ongraphene, water has only been visualised when subsur-face, due to its dynamic nature.
He atom scatter-ing (HAS) has the advantage that it is sensitive to Hatoms in the top layer irrespective of the substrate.Moreover the scattering of neutral He atom beams withenergies of typically 8 meV is perfectly suited to probethese systems in an inert, completely non-destructivemanner whereas earlier experimental conclusions of wa-ter structures were partly caused by electron damage. The schematic principle of He spin-echo spectroscopy isillustrated in Figure (a): A polarised He beam, illus-trated by the blue wavepacket is split into two compo-nents which are separated in time by t SE . After scat-tering from the surface, the separated wavepackets arerecombined. If the scattered surface changes betweenscattering of the two parts of the wavepacket, a loss ofpolarisation is observed in the detected beam (see Jar-dine et al. for more information). The onset of dy-namical processes on the surface can be seen by the loss1 a r X i v : . [ c ond - m a t . m t r l - s c i ] O c t f correlation in the so-called intermediate scatteringfunction (ISF) (Figure (b) where we see a clear singleexponential decay within the measured time window. Diffusion of H O on graphene
Fig. 1 : Diffusion of Water monomers ongraphene. (a)
Illustration of the helium spin-echomethod: Two wavepackets, scatter from the surfacewith a time difference t SE , allowing the motion ofmolecules on the surface to be interrogated through theloss in correlation, measured through the polarisationof the beam. (b) Typical measurements of polarisa-tion for the diffusion of water on graphene ( T S = 125K, ∆ K = 0 . − ). The change in polarisation withincreasing spin-echo time follows a single exponentialdecay (solid line), characterised by the dephasing rate, α . (c) Structural model for the graphene lattice (black)on the Ni(111) substrate (green). The inset shows theprinciple symmetry directions of the Brillouin zone. (d)
The momentum transfer dependence of the dephasingrate, α (∆ K ), at T S = 125 K from which the mecha-nism for diffusion follows. Blue data points show single-particle, or incoherent α (∆ K ), deduced from the coher-ent scattering data (grey points, see text). An analyti-cal model (red curve) shows the expected behaviour forjumps between the centres of the graphene hexagons.By dosing a controlled amount of water ontographene, within a certain temperature window, in-dividual water molecules are diffusing between islandsof water on bare graphene. Therefore, we are able tostudy the movement of water monomers on this surface(see A precursor gaseous phase - adsorption on a hy-drophobic surface and supplementary information for more details): We deposit water on a graphene/Ni(111)surface under ultra-high-vacuum (UHV) conditions. At100 K water forms three-dimensional clusters and fi-nally covers the whole substrate if a sufficient amountof water has been deposited. Upon heating to 110 K atransition starts: The movement of water is no longerkinetically hindered and the deposited water starts toform separated islands while leaving uncovered regionsof graphene behind (Figure ). A similar behaviourhas been observed for water on other metal supportedgraphene systems. Within a small temperature window, between 113 and130 K, a dynamical equilibrium between adsorption,desorption and the area covered by water islands canbe maintained by continuously depositing water. Un-der these conditions individual water molecules arediffusing between islands of water on the bare graphenesurface and we are able to study the movement of watermonomers on graphene.Figure (d) shows the experimentally determined de-phasing rate α (∆ K ) as a function of the momentumtransfer ∆ K = | ∆ K | for a relative coverage of 0.02monolayers of water monomers (see supplementary in-formation for the coverage calibration). It exhibits asinusoidal ∆ K dependence that is characteristic of jumpdiffusion; the periodicity of about 2 . − in the ΓMdirection suggests a jump distance that corresponds tothe size of the graphene unit cell. The steep rise in thebeginning is indicative of repulsive interactions betweenthe adsorbates. The coherent dephasing rate can becorrected in order to consider the incoherent decay ratewhich describes motion in a non-interacting system.By correcting with the static structure factor one ob-tains the dependence for a non-interacting system. (More information about this aspect can be found inthe supplementary information as well as in Ref. )In doing so, the dephasing rate can now be described bya simple analytic equation which considers jumps be-tween equivalent sites on a lattice. For the case of waterdiffusion governed by the interaction of the moleculeswith a corrugated surface, its motion can be well de-scribed by the Chudley-Elliott model of jump diffusion.It assumes that a particle rests adsorbed for a time τ at an adsorption site, before it moves instantaneouslyto another adsorption site: α (∆ K ) = 2 τ X m p m · sin (cid:18) ∆ K · j m (cid:19) (1)where ∆ K is the momentum transfer parallel to thesurface and j m is the jump vector. Here, p m is theprobability that a jump to the corresponding site oc-curs.We observe that the analytical model fits the experi-mental data really well for jumps on a hexagonal lattice,where the jump length is equal to the lattice constantand multiples thereof (red solid curve in Figure (d)).It suggests, that hopping occurs between hollow ad-sorption sites on the graphene surface. Fitting a sum of2umps to nearest, next-nearest, and next-next-nearestneighbours produces a most probable fit with a resi-dence time τ = (65 ±
3) ps and a relative contributionof p n = 63 %, p nn = 20 %, and p nnn = 17 % for nearest,next-nearest, and next-next-nearest neighbour jumps,respectively.For ∆ K close to zero and around the diffraction peakthe experimental data points do not go to zero and asmall constant offset occurs (Figure (d)). Note that itis an artefact of the correction procedure used obtainthe incoherent from the coherent decay rate.Notably, the jump model only describes the experimen-tal data if the water molecule is adsorbed in the centreof the hexagon formed by the carbon rings. Jumps withother adsorption geometries would either give rise toa different dependence upon the momentum transferor to the appearance of two exponential decays in theISF (see supplementary information). Hence we canidentify the adsorption site of H O on graphene.Our findings are in good agreement with angle-resolved photoelectron spectroscopy of H O ongraphene/Ni(111) which have been interpreted in termsof a preferential adsorption on either hollow or bridgeadsorption sites. Adsorption of H O on the hollowsite is also in accordance to the findings of most densityfunctional theory (DFT) studies. While we obtain thesame adsorption site on free-standing graphene in ourvan der Waals corrected DFT calculations, inclusion ofthe Ni substrate favours adsorption of water on top ofthe carbon atoms (see supplementary information) incontrast to the experimental results.Furthermore, the diffusion coefficient D for two-dimensional motion can be calculated from the resi-dence time τ as determined from the CE model using: D = 14 τ (cid:10) l (cid:11) (2)where h l i is the average jump length with 3 . D = (4 . ± . · − m / s (0 .
041 ˚A / ps).The diffusion of water on graphene has been recentlystudied by means of molecular dynamics (MD) sim-ulations. Tocci et al. predict a substantially lowermacroscopic friction coefficient in comparison to adsorp-tion on a hexagonal boron nitride surface and Park etal. predicted fast diffusion with a diffusion constant D = 2 . · − m / s. MD simulations of water nan-odroplets on freestanding graphene revealed a diffu-sion constant between 2 · − m / s and 8 . · − m / sdepending on the size of the droplet (at 298 K). Bothvalues are way beyond the diffusion constant found inour experiments, yet they are considering the motionof water clusters and droplets at much higher temper-atures (room temperature) rather than the diffusion ofmonomers.The diffusion coefficient for single water molecules ongraphene has been estimated to be 6 · − m / s at a temperature of 100 K by Ma et al. which is some-what closer to the conditions in our experiments. Indeedtheir value is closer to our result but still one order ofmagnitude larger. However all calculations mentionedabove were performed on free standing graphene whileour measurements are on graphene/Ni(111) where themotion of the ripples which gives rise to the ultra-fastdiffusion is suppressed. In order to obtain further information about the dif-
Fig. 2 : Temperature dependence and signatureof repulsive interactions in the diffusion process.(a)
The temperature dependence of α can be used todetermine the activation energy for diffusion of water ongraphene. (b) Charge density difference for two watermolecules adsorbed on graphene (red/blue isosurfacescorrespond to ± . / ˚A ) illustrating the dipole mo-ment. The dipole moment of a water monomer ongraphene is 6 . · − C · m, which is slightly larger thanfor an isolated water molecule. (c) The coherent signal(Figure 1c) which describes the collective motion can bereproduced using a Monte-Carlo simulation when long-range repulsive forces (
A >
0) between the individualwater molecules are considered.fusion of water on graphene, temperature dependentmeasurements at a fixed momentum transfer ∆ K havebeen performed. For thermally activated processes, Ar-rhenius’ law predicts a temperature dependence of thedephasing rate, α , as α = α · exp (cid:16) − E a k B · T S (cid:17) (3)where α is the pre-exponential factor describing thejump attempt frequency, E a is the activation energyfor diffusion, k B the Boltzmann constant and T S thetemperature of the sample surface. Taking the naturallogarithm of Equation 3 results in a linear relationshipbetween the inverse of the temperature, 1 /T S , and thenatural logarithm of the dephasing rate α .The plot of ln( α ) at different temperatures (see Fig-ure (a)) clearly shows a linear dependence upon 1 /T S
3s expected for activated motion. To ensure a constantsurface coverage of 0 .
02 ML at all temperatures, an over-pressure was applied for each measurement, which cor-responded to an attenuation of the specularly reflectedsignal by a factor of 4. The activation energy is obtainedfrom the slope of Figure (a) as E a = (60 ±
4) meVwhereupon the intercept gives α = (5 ±
1) ps − . Thereis hardly any difference between the two different mo-mentum transfers shown in Figure (a).To investigate the origin of the steep rise of α atsmall ∆ K (Figure (d), we have performed kineticMonte Carlo (MC) simulations for a model of theH O/graphene system. We are now considering thecollective motion rather than the motion of the individ-ual water molecules described by the analytic model.Therefore we assume that the water molecules moveon a hexagonal grid between adjacent sites (basedon the results of the analytical model above). Re-pulsive/attractive inter-adsorbate interactions were in-cluded with a pairwise dipole-dipole potential. Usingthe trajectories of the MC simulation, the dephasingrate α is then determined from the calculated ISFs(see supplementary information for more details).Figure (c) shows the α (∆ K ) curves obtained fromthe MC simulations. For no interaction between themolecules we obtain the same dependence as the analyt-ical model for hopping motion. Attractive interactions( A <
0) between the molecules cannot explain the steeprise at small ∆ K . However, the introduction of repul-sive forces ( A >
0) in the MC simulation can reproducethe steep rise observed in the experimental data. Notealso, that due to the periodicity in ∆ K we see the samephenomenon around the minimum at 2 . − .While attractive forces and hydrogen bonding play amajor role in the clustering of water, we conclude thatfor the diffusion of water monomers, long-range repul-sive forces between the individual water molecules needto be considered. We believe that this is possible dueto the dipole moment of the water molecules, whichare adsorbed in the same configuration on graphene(see Figure (b)). According to DFT calculations thedipole moment of a water monomer on graphene is6 . · − C · m, i.e. slightly larger than for an isolatedwater molecule. A precursor gaseous phase - adsorptionon a hydrophobic surface
Previous to the dynamics measurement, we have car-ried out extensive adsorption and desorption measure-ments of H O on a graphene/Ni(111) surface preparedin situ. The processes of adsorption and desorptionwere observed by following in real time the specularbeam intensity of helium atoms scattered from the crys-tal surface during the deposition of water. At a temper-ature of 100 K the intensity of the specular peak fallsoff sharply, corresponding to the commencement of ad-sorption and diffuse scattering from the adsorbates. Thespecular intensity decays almost to zero which is typi- cal for the absence of any ordered structure. This isconfirmed by subsequent diffraction experiments whichdo not show any diffraction signal. We interpret it asbeing due to the formation of amorphous solid waterat the surface. After heating the surface to 110 K,diffraction scans reveal peaks at the same position asthe graphene diffraction peaks (Figure (g)). From sub-sequent thermal desorption measurements, we can con-clude that no desorption occurs at this temperature.The diffraction pattern could thus stem only from aperfect (1 ×
1) H O over-structure, or from the forma-tion of separated islands upon melting, which would ex-pose free graphene to the helium beam. Comparisonwith the structures of ice I h and ice I c shows that thelattice spacing is too large, to give rise to this peri-odicity, even for a spacing as in the recently discoveredsquare ice structure. We thus conclude in accor-dance with the strong hydrophobicity of graphene andgraphite, that the deposited water clusters togetherto form separated islands upon heating to 110 K. Theisland formation can also be followed by monitoring thespecular reflection upon slowly heating to 110 K (Fig-ure (a)): The specular intensity recovers as the waterdeposited at 100 K starts to form islands while leavingregions of bare graphene behind (see supplement for thesize of the islands). A similar behaviour is seen whendosing H O while the surface is constantly held at 110 K(Figure (f)). Firstly, the intensity of the specular peakfalls again off sharply and decays to almost zero, but,after several minutes the specular signal recovers – thisprocess, i.e. the nucleation of islands is much slowerthan the molecular diffusion. When comparing the uptake curves at 100 K and 110K we see another interesting feature: After starting thedosing, the specular intensity at 110 K seems to de-cay at a faster rate than at 100 K. While it might seemcounter-intuitive at first glance it can again be explainedin terms of the mobility of H O at 110 K. The watermolecules are not mobile at 100 K hence they adsorbat the site where they hit the surface and remain attheir initial position. At 110 K however, the moleculesare mobile. If they tend to stay apart from each other(as shown in the dynamics measurements) the apparentscattering cross section of water on the surface will belarger compared to the same water coverage at 100 K(illustrated in Figure (e)). Therefore the specular sig-nal decays faster at 110 K.Upon further heating to temperatures above 113 K thedeposited water slowly starts to desorb form the sur-face. From 113 K to 130 K it is necessary to applyan overpressure of water to maintain a constant cover-age. Under these conditions water monomers are diffus-ing between islands of ice providing a precursor gaseousphase to the nucleation of the islands. The lifetime thateach H O molecule spends on the surface before it sticksto an island is roughly 2 seconds at 125 K, where mostdiffusion measurements where performed.Finally, we conclude that the desorption of watermolecules is likely to happen from the edges of water4 ig. 3 : Adsorption and island formation of wateron graphene. (a)-(c)
Water deposited at low temper-atures on graphene forms unordered amourphous layers (b) . Upon heating the water molecules become mo-bile (observed by an exponential decay in the spin-echomeasurement), starting to form separated islands andleaving areas of bare graphene behind (c) . The diffrac-tion scan (g) gives the same periodicity as for the cleansurface but with smaller intensity. (f )
He atoms areonly scattered coherently from regions of the surfacethat are not covered by water. Due to the mobility ofthe water molecules at 110 K (e) , the intensity falls offmore rapidly than compared to 100 K (d) upon deposi-tion of water. However, the intensity at 110 K recoversafter the island formation starts (f ) . islands. Based on the experimentally determined des-orption energy of (520 ±
20) meV which is close to thedesorption enthalpy from ice, it is unlikely that in-dividual water molecules are desorbing from graphene.This is further supported by DFT results where a muchsmaller adsorption energy for a single water moleculeon graphene/Ni(111) is obtained. From van der Waalscorrected DFT we obtain an adsorption energy of 225meV (see supplementary information) similar to the183 meV by Li et al. , while DFT calculations of wa-ter on graphene (without a metal substrate) typicallygive even smaller adsorption energies. Fur-thermore, according to DFT, the binding energy be-tween molecules in a water cluster is much larger thanthe adsorption energy between the water cluster andgraphene. Summary and Conclusion
In summary, we have studied the diffusion of wateron graphene/Ni(111) using He spin-echo spectroscopyand identified the principles of the diffusion mechanism.Within a small temperature window, individual watermolecules are diffusing between islands of water on thebare graphene surface and we are able to study themovement of water monomers on graphene. Our studyunravels the unique nature in the structure and dynam-ics of water on the hydrophobic substrate graphene/Ni,involving long-range repulsive interactions between theindividual water molecules. It illustrates that the struc-ture and dynamics of water on a surface is typicallydetermined by an intricate interplay of intermolecularinteractions and molecule-surface interactions definingthe two extremes of hydrophobic and hydrophilic be-haviour.The water molecules undergo an activated jump diffu-sion process where jumps occur between the hollow ad-sorption sites in the centre of the carbon hexagon. Theactivation energy for the process is (60 ±
4) meV, mean-ing that there exists a significant barrier for the motionof water on graphene/Ni. The self-diffusivity of wa-ter on graphene/Ni corresponds to a diffusion constant D = (4 . ± . · − m / s at 125 K, showing that thetransport on metal supported graphene is slower thanthe diffusivity theoretically predicted for free-standinggraphene.The diffusion of water monomers indicates also thatlong-range repulsive forces between the individual watermolecules play an important role in the low-coverage dif-fusion mechanism, even though attractive forces and hy-drogen bonding are much more important for the assem-bly and clustering of water at higher coverages. Whilerepulsive interactions have been observed e.g. for hydro-carbons on metal substrates, this is to our knowledgethe first report for such a behaviour of water moleculeson a surface. The hydrophobic graphene substrate andthe adsorption geometry may play an important role inthat aspect and we hope that our work will initiate fur-ther investigations in this direction. Notably long-range5epulsive interaction have recently also been predictedfor van der Waals dimers which are confined on a sur-face. Our study shows that the diffusion of water on surfacesis governed by the molecule-surface interaction and sub-tle atomistic details of the substrate. The observed dif-fusion mechanism can have a significant impact on thetransport of water at the nanoscale with implicationsranging from nanofluidics to biology.
Code availability
The code for the kinetic Monte Carlo simulationsis available from https://doi.org/10.5281/zenodo.3240428 under the GNU/GPL-3.0 license.
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Acknowledgements
The authors would like to thank G.Alexandrowicz for many helpful discussions. A. Tamt¨ogl ac-knowledges financial support provided by the FWF (AustrianScience Fund) within the project J3479-N20. This work is part ofthe Ph.D. project of E. Bahn who would like to thank the EcoleDoctorale de Physique of the Universit de Grenoble for funding. ynamics of water monomers on a hydro-phobic surface:Supplementary Information Sample preparation
All measurements have been performed on the Cam-bridge helium-3 spin-echo spectrometer (HeSE). Thecharacterisation and growth of the graphene layer ona Ni(111) surface has been published elsewhere. S1 Inshort, a nickel (Ni) (111) single crystal used in the studyis mounted onto a sample holder, which can be heatedusing radiative heating from a filament on the backsideof the crystal or cooled down to 100 K using liquid ni-trogen. Prior to the measurements, the Ni surface wascleaned by Ar + sputtering and annealing at 870 K. Amonolayer of graphene on Ni(111) was grown by dosingethene (C H ) while heating the Ni crystal (730 K) overseveral hours.The sample temperature was measured using a chromel-alumel thermocouple. While absolute temperatures canbe determined with an uncertainty of ± ± . Ois dosed up to a certain attenuation (corresponding toa certain H O coverage) of the specularly reflected he-lium signal. Therefore the partial pressure of water inthe scattering chamber is adjusted using an automaticleak valve and the reflected helium signal is monitoreduntil equilibrium is obtained. Throughout the dynamicsmeasurements it was constantly checked that the equi-librium is maintained over the length of the experiment,by monitoring the specular attenuation as well as by re-peating several dynamics measurements under the sameconditions to prove the reproducibility of the results.
Further details on water dosing and up-take
The microcapillary array beam doser used for depositingwater is situated in a dosing arm that can be separatedform the scattering chamber. During dosing the micro-capillary is brought close to the surface (5 cm distance)using a linear translator of the dosing arm. In doing so,a well defined flux can be brought to the sample surfaceand the H O gas load in the scattering chamber can bereduced compared to backfilling of the whole chamber.Water was dosed from the vapour pressure over the liq-uid phase at room temperature.Therefore, a previously baked stainless steel tube wasfilled with de-ionised water and connected to the dos-ing arm. The cleaning process consists of severalfreeze-pump-thaw cycles, where the water inside the tube was frozen and the gas phase above the frozenice was pumped away. Several repeated cycles ofthis freeze-thaw procedure were performed until thequadrupole mass spectrometer in the scattering cham-ber only showed pure water from the gas phase abovethe water in the reservoir during dosing. Prior to ev-ery series of adsorption, diffraction, or He spin-echomeasurements, the water was again purified by severalfreeze-thaw cycles. In addition, at regular intervals amass spectrometer signal was monitored to exclude acontamination of the water sample.The processes of adsorption and desorption was ob-served by monitoring the specular reflected helium sig-nal while dosing H O onto the graphene/Ni(111) sur-face. A precise pressure control has been obtained withthe use of a leak valve that is attached to the top of thedosing arm. The leak valve itself was usually regulatedby a feedback control system in order to maintain a con-stant pressure. Adsorption has been monitored at 100,110, 125, 130, and 150 K at a typical dosing pressure atthe surface between (1 − · − mbar.As shown in Figure 3(f) of the article, at 100 K thespecular intensity does not level off, it decays to full at-tenuation and does not recover when the dosing pressureis decreased. As already mentioned in the main body ofthe text, this is typical if no ordered structure forms, i.e.for the growth of an amorphous layer. The formationof amorphous ice layers on surfaces, commonly namedamorphous solid water (ASW) has been observed sincethe 1960s. S2 For example, recent isothermal desorptionmeasurements of water on HOPG at 100 K, showed aglass transition accompanied by a change in desorptionrate and a growth of 3D water islands rather than a wet-ting of the graphite surface. S3 In addition, no diffractionwas observed.At 110 K and 125 K, the signal decays as well but doesnot fully attenuate. Based on the fact that the samediffraction pattern as on clean graphene is observed, thishas been interpreted by the formation of separated wa-ter islands, leaving areas of bare graphene behind.For sample temperatures above 120 K, when reducingpressure, the signal recovers at a very fast rate. The sys-tem is, thus, in an adsorption-desorption equilibrium.Small changes in the pressure immediately change thespecular reflection and hence the coverage. While withincreasing overpressure the coverage increases, with in-creasing surface temperature the dynamic equilibrium isreached faster. Within the available temperature range- where we could observe diffusion and where we areable to obtain a constant coverage by applying an over-pressure - it was found that measurements at 125 K pro-vided the best trade-off in order to clearly see dynamicsand maintain constant experimental conditions. (Thelower panel of Figure S1 shows that the dephasing rate1 a r X i v : . [ c ond - m a t . m t r l - s c i ] O c t ig. S1 : Upper panel: Normalised specular at-tenuation versus water coverage.
Here, the cover-age has been determined from the exposure as describedin the text. The dashed line corresponds to equation 1with Σ = 138 ˚A . At 125 K a kink in the adsorp-tion curve appears due to the onset of island formation.From this point onwards the coverage is no longer in-creasing. Lower panel: Dephasing α (∆ K ) at two temper-atures. α shows the same functional behaviour versusmomentum transfer ∆ K with increasing temperature,the only difference being the absolute value of α for afixed ∆ K which increases with temperature accordingto Arrhenius’ law. α follows the same functional behaviour vs. momentumtransfer ∆ K irrespective of the temperature).Finally when going to even higher surface temperatures,i. e. at 150 K, no adsorption has been observed evenwhen dosing up to 1 . · − mbar. Coverage and island size determination
The water exposure during dosing can be related to thesurface coverage Θ in monolayer (ML). Here, exposureis defined as the impinging flux of molecules on the sur-face integrated over the time of exposure. In literature,a monolayer equivalent has been defined in several casesfor water on graphite and graphene, where 1 ML corre-sponds to 0 .
115 molecules / ˚A = 0 .
603 molecules / uc(uc: graphene unit cell), which is equivalent to the den-sity of an ice I h overlayer. S4 This allows us to relate thesurface coverage with the exposure through the kinetictheory of gases.The fact that the presence of water on the surface sub- stantially attenuates the specular beam indicates thatwater covered parts of the surface do not contribute tothe specular intensity. Hence the attenuation of thespecular intensity during water adsorption can be usedas a direct measure of diffuse scattering. I.e., the ad-sorbed H O molecules scatter the He beam diffusivelyand the specular intensity arises exclusively from sub-strate areas not covered by water. S5 The normalisedspecular intensity
I/I can then be related to the watercoverage Θ via: I/I = (1 − Θ) n · Σ / cos ϑ i (S1) ≈ − Θ · n · Σ / cos ϑ i for Θ (cid:28) n = 1 / .
69 ˚A − is the adsorbate density at (hy-pothetical) monolayer (ML) coverage, Σ is the heliumscattering cross section and the term cos( ϑ i ) accountsfor the increase of the apparent scattering cross sectionsince scattering happens at an incident angle ϑ i = 22 . ◦ .Equation S1 follows a strict geometrical overlap ap-proach of the scattering cross sections, assuming ran-dom adsorption of the adsorbates. S5,S6
In case of low coverage, a linear dependence of the in-tensity on the coverage can be assumed (S1) and thescattering cross section Σ can be determined from theinitial slope of the adsorption curve. Figure S1 showsthe normalised specular reflection I/I versus coverageplotted on a logarithmic scale for 100 K and 125 K. Thedashed line in Figure S1 corresponds to a fit of the 100K data according to Equation S1. We obtain a heliumscattering cross section of Σ = (138 ±
4) ˚A which isin good agreement with values found in the literature(Σ = 130 ˚A in Ref S7 ).When the formation of islands starts, the reflectivity isdetermined by the much smaller geometrical size of theadsorbates in the 2D condensed phase. This is typicallyseen by a kink in the adsorption curve as evident for thecurve at 125 K in Figure S1 . From this point onwardsthe coverage as determined from the exposure becomesmeaningless and is in fact even decreasing as seen bythe specular attenuation.The dynamics measurements have been performed atan attenuation of I / S1 . This is also the same value towhich the signal at 125 K recovers after some time. Anattenuation of I / . .
02 ML.We can also estimate the size of the islands. Basedon the rate of adsorption, the lifetime that each H O2olecule spends on the surface before it sticks to an is-land or desorbs is roughly 2 seconds. From the dynam-ics measurements in the main part of the manuscriptwe know that the hopping rate at 125 K is 1 . · Hz.Together with the above mentioned estimate for thelifetime and the mean jump length for diffusion ongraphene each molecule travels about 50 µ m before itsticks to an island - in other words: the islands are 50 µ m apart. Isobaric adsorption
Further information about the adsorption behaviourcan be obtained in another kind of experiment. Fig-ure S2 shows an isobaric deposition curve of water onthe graphene/Ni(111) surface: At a constant partialpressure of H O of 1 . · − mbar the temperature ofthe crystal is decreased from 180 K down to 100 K.There is no significant decrease in the intensity untilthe crystal reaches about 140 K where the intensity ofthe specular peak falls off sharply corresponding to thecommencement of adsorption. The specular intensitydrops to almost zero when the crystal temperature hasreached 100 K. Upon starting to heat the system underthe same conditions the specular intensity does not in-crease before we reach temperatures above 160 K. Hencewe are observing a hysteresis, with desorption occurringat a higher temperature than adsorption.One reason for this behaviour might be the higher heat-ing rate - i.e. with increasing heating rate the desorp-tion maximum shifts to higher temperatures. However,it cannot explain a shift of this magnitude. Instead thehysteresis shows that there is a kinetic barrier to nucle-ation on the surface. Upon cooling the system down,the drop occurs much later because adsorption on thehydrophobic bare graphene surface is less likely. Thewater growth on the graphene surface is delayed becausesome clustering centres on the surface are necessary toallow the process to start. S8 On the other hand, uponheating, the surface is now covered with amorphous icewhere it is harder to remove a molecule (see illustrationson the right-hand side of Figure S2 ). Thermal desorption
Several groups have conducted thermal desorption spec-troscopy (TDS) measurements of water on the (0001)basal plane of graphite. Consistently, a single des-orption peak was observed that corresponds to a des-orption energy in the range of 0 . . .
49 eV.
S4,S9,S10
This energy was observed not to changewith coverage, indicating the formation of separatedislands on the graphene surface. S9 On the surfaces ofgraphene/Ni(111) and of graphene/Ir(111), TDS spec-tra reveal pseudo-zeroth order desorption and desorp-tion energies of (356 ±
23) meV in the first case, and(585 ±
31) meV in the latter case, respectively, were
Fig. S2 : Isobaric adsorption curve for a partialH O pressure of 1 . · − mbar, showing the variationof the specular He reflection as a function of the sur-face temperature T S . Starting from the top right cor-ner ( T S = 180 K), the sample is cooled down to 100 Kand then heated up again. The signal follows a hystere-sis, with desorption occurring at a higher temperaturethan adsorption, caused by the nucleation kinetics onthe surface which is illustrated on the right-hand side.The shaded temperature region represents the temper-ature window where dynamics is observable.found. S8 We have also conducted thermal desorption spec-troscopy while monitoring the m/z = 18 peak on amass spectrometer and simultaneously measuring thespecularly reflected He signal. A single desorption peakwith a maximum at 163 K coincides with a rapid recov-ery of the specular signal. The Redhead equation canbe applied, in order to estimate the desorption energy E d . Using ν = 9 · − s − according to Ulbricht etal. S9 for the peak maximum at (163 ±
5) K at a heatingrate β = 0 .
22 K · s − we obtain a desorption energy of E d = (520 ±
20) meV.Furthermore, we can use the recovery of the He signal todetermine the desorption energy. Therefore, we exposedthe graphene surface to 2 · − mbar H O overpressureand waited until the system was in equilibrium. Wethen turned off the exposure and monitored the spec-ular signal recovery. From this we calculated the cor-responding surface coverage as a function of time. Thesurface coverage first rises during exposure and then de-cays exponentially after exposure has been turned off.The initial desorption rate, which is identical to the ex-ponential decay rate, exhibits an activated temperaturedependence. The desorption energy can then be deter-mined from the slope in an Arrhenius plot. Hereby weobtain a desorption energy of E d = (510 ±
10) meV.As already mentioned in the main text, the results fromour desorption studies suggest that water moleculestend to desorb rather form the edge of water islandsand not as individual molecules which are adsorbed onthe bare graphene surface. These findings are also sup-ported by the diffraction measurements mentioned inthe main text.3 etails on the DFT calculations
The density functional theory approach has been ap-plied a number of times for the adsorption of water ongraphene. DFT calculations generally agree that thepotential energy surface is rather flat and that the bind-ing energy depends more on the orientation than on theposition of the adsorbent. Most calculations predict apreferential water adsorption with the hydrogen atomspointing downwards. An adsorption energy E ads in therange of about 130 meV is calculated, but results varyconsiderably. A general agreement on an adsorptiondistance of about 3 . S11–S14
Thestructure of H O clusters adsorbed on graphite has alsobeen calculated by several groups where the associationenergy to the cluster is in the range of 450 −
500 meV,while the binding energy of a molecule to the graphenesurface is much lower.
S11,S12
We have performed DFT calculations using CASTEP,
S15 a plane wave periodic boundary condition code. ThePerdew Burke Ernzerhof
S16 exchange correlation func-tional, with the dispersion force corrections developedby Tkatchenko and Scheffler (TS method),
S17 was em-ployed for all the calculations presented in this work.The plane wave basis set was truncated to a kinetic en-ergy cutoff of 360 eV. The calculations are performed ona (6 ×
6) graphene cell, carbon atoms are fixed, k -pointsampling has been done with a (2 × ×
1) MP grid.
S18
Avacuum layer of 15 ˚A was imposed above the graphenesurface in order to avoid spurious interactions with theperiodically repeated supercells. All the calculationsuse Vanderbilt Ultrasoft Pseudopotentials
S19 and the x , y coordinates of the O-atoms are fixed. The electronenergy was converged up to a tolerance of 1 · − eVwhile the force tolerance for the geometrical optimisa-tions was 0 .
05 eV / ˚A.The Ni(111) surface has been modelled as a five-layersnickel slab with a ( √ × √
7) surface unit cell. Spin-polarisation was included in the calculations with thenickel substrate. The graphene overlayer was kept freeto relax during the structural optimisations, while thenickel substrate atoms were kept frozen in the initialpositions. The lateral position of the oxygen atom ofthe water molecule was also kept fixed, while its dis-tance from the surface was free to vary. The hydrogenatoms positions were left fully unconstrained.For adsorption of H O on free-standing graphene theenergetically most favourable adsorption site is the hol-low site in down configuration. I.e. the water moleculeis adsorbed in the centre of the hexagon formed bythe carbon rings with the two OH bonds pointing to-wards the surface (down configuration), so that theplane of the molecule is perpendicular to the surfaceFigure S3 (a).The barrier for the formation of water dimers was cal-culated to be about 90 meV. The binding energy inthe dimer is 320 meV which suggests that once a dimerforms it will rarely dissociate. This result supportsour explanation of the hysteresis mentioned above Fig- Fig. S3 : Adsorption geometries of water accord-ing to DFT calculations. (a) Adsorption geome-try for H O on free-standing graphene according to ourDFT calculations. (b) Optimised adsorption geometryfor H O on graphene/Ni(111).ure S2 .When including the Ni substrate, adsorption of wateron top of the carbon atoms becomes more favourable.There are two types of top sites, one with the carbonatom on top of a nickel atom and one on top of anhcp site of nickel. The fcc top site is the slightly mostfavourable one. The orientation of water changes duringthe optimisation from the configuration with the OHbonds initially pointing towards the surface to finallybeing almost horizontal over the surface (Figure S3 (b)).The “static snapshots” from DFT i.e. the energy dif-ferences between the adsorption sites can be used asan approximative measure for the diffusion barrier. Inthe case of the expected jump diffusion between hollowsites the activation energy would correspond to the po-tential energy difference between a hollow and a bridgeadsorption site, which would need to be overcome dur-ing a jump. The calculated differences of adsorptionenergies between hollow and bridge sites are in moststudies in the order of only a few meV while accordingto our calculations it is about 20 meV. Details on the jump diffusion process
In the measured ∆ K -range, the decay rate is in the or-der of 10 ns − at 125 K. This temperature correspondsto a mean kinetic energy in the order of 10 meV. Asdiscussed in the main part of the text, the adsorptionenergy of an H O molecule in an ice cluster is predictedto be in the order of 500 meV,
S11 while for the ad-sorption energy of a molecule on the graphene surface,values in the order of 100 −
200 meV have been calcu-lated. Thus one would expect to observe the diffusion ofH O on graphene, rather than on the surface of an icecluster. Together with the adsorption and diffractionresults this is another evidence that we are seeing themotion of single water molecules on graphene.As described in the main part of the text, the exper-imental data is best described for an analytical model4hat assumes jumps between the hollow adsorption sitesin the centre of the carbon hexagons. The possibilitiesof jumps for water adsorbed on top of the carbon atomsis also an important option to consider. The adsorptionsites on top of a carbon atom are in general not degen-erate because of the Ni(111) surface that lies below thegraphene layer; instead the geometry can be describedby two hexagonal Bravais lattices with different adsorp-tion energies. A generalised jump diffusion model fornon-equivalent adsorption sites has been established byTuddenham et al.
S20
The jump distance between topadsorption sites is the C-C distance with 1 .
44 ˚A andthe jump signature is the same as for fcc - hcp jumpson the underlying Ni(111) substrate. If the top adsorp-tion sites were degenerate, a second, faster decay wouldappear along ΓM which we do not observe in our exper-imental data. In particular if the data is fitted with asingle exponential decay this would give rise to a differ-ent momentum transfer dependence as for hollow-hollowjumps in the ΓM direction (see Figure S4 ): The cleardip along ΓM is not reproduced by this model at all.In general, the top adsorption sites are not degen- Fig. S4 : Illustration of the analytical jump dif-fusion model for different jumps.
Top-top jumpsfor degenerate top sites (assuming a single exponentialdecay) would give rise to a different momentum transferdependence. In particular the clear dip along ΓM is notreproduced at all.erate because of the Ni(111) surface that lies belowthe graphene layer. However, DFT calculations sug-gest that the non-degeneracy between the top-fcc andtop-hcp sites is rather small. Nevertheless, for non-degenerate sites, a second, faster decay appears for bothcrystal directions, with an amplitude that is very low upto about 1 . − , and then rises steeply (see Figs. 7 and8 in Ref. S20 ). While we do not observe such a contri-bution in our experimental data, an analysis with a sin-gle exponential decay would again give rise to the samemomentum transfer dependence as shown in Figure S4 which cannot reproduce the dip along ΓM. Bridge tobridge jumps bear a similar geometry as top jumps andby the same reasoning, we do not expect this to be anoption. Details on the MC simulations
In the kinetic Monte-Carlo (MC) simulation watermolecules can move on a hexagonal lattice with jumps up to third nearest neighbour sites. A periodic (60 × O atoms wereinitially put down on the grid in turn at random. Thepotential energy for an atom at each site of the gridwas calculated for the initial configuration, taking intoaccount inter-adsorbate interactions. Therefore, repul-sive/attractive interactions were included with a pair-wise dipole-dipole potential of the form: ± Ar = p π(cid:15) r (S2)where p is the effective value of the dipole moment and r is the distance separating the two dipoles and + / − accounts for repulsive/attractive interactions.An MC event consists of choosing a water molecule atrandom which may then hop to one of its neighbour-ing sites, with different probabilities for jumps to first,second and third nearest neighbours. Provided that thewater molecule is not blocked from entering the new siteby another molecule the probabilities are weighted bythe difference in the potential of the molecule at the twosites. If several new sites with lower potential energy ex-ist, one of them is chosen at random and the moleculeis moved into the new site. Evaluation of the ISF and incoherentscattering
The trajectories of the molecules versus time obtainedfrom the MC simulation can be used to calculate theintermediate scattering function (ISF) which is also ob-tained in the experiment. From the MC simulation boththe coherent and the incoherent ISF can be calculated.The subtle difference between the coherent and incoher-ent ISF is the averaging procedure. While the coherentISF is obtained by averaging over all particles, the in-coherent ISF is obtained by first calculating the ISF ofa single particle followed by averaging over all particles.Details on how to obtain both the coherent and the in-coherent ISF can be found elsewhere.
S21
The ISFs obtained from the simulation are then anal-ysed in the same way as the experimental data: TheISF is fitted with a single exponential decay which al-lows to determine the dephasing rate α (∆ K ) from thesimulation in analogy to the curve determined from theexperiments. The trajectories from the MC simulationcan be used to calculate both the coherent and the inco-herent ISF. On the other hand, He spin-echo is a coher-ent scattering method, hence the measurements providethe coherent ISF. As shown for neutron scattering S22 aswell as for X-ray photocorrelation spectroscopy
S23 onecan correct for the effect of adsorbate interactions inthe coherent α coh (∆ K ) to obtain the corresponding in-coherent α inc (∆ K ).We can clearly see from Figure S5 (a) that α coh (∆ K )extracted from the coherent ISF of the MC simulationexhibits the same shape as the experimentally deter-mined coherent α (∆ K ) (grey circles in Figure S5 (b).5he coherent ISF shows the dynamics of the moleculein the context of its neighbourhood which is influencedby repulsive interactions in our case. On the other hand, α inc (∆ K ) extracted from the incoherent ISF (blue linein Figure S5 (a)) follows the same shape as one wouldexpect for a system with no interactions - i.e. the in-dividual motion of the adsorbates. It follows the ap-proach by Pusey, S22 where the effect of adsorbate inter-actions in the coherent α coh (∆ K ) is corrected by mul-tiplying α coh (∆ K ) with the corresponding static struc-ture factor S (∆ K ). Here we use the amplitude A (∆ K ) Fig. S5 : Relation between coherent and incoher-ent scattering data. (a) Coherent and incoherent de-phasing α (∆ K ) extracted from the trajectories of theMC simulation for the ΓM azimuth. (b) The coherentexperimental data can be corrected to give an incoher-ent α (∆ K ) similar to the one obtained from the MCsimulation.of the fitted exponential decay as an approximate mea-sure of S (∆ K ). An approximation of the incoherent α inc (∆ K ) can then be calculated by multiplying the co-herent α coh (∆ K ) with a factor given by the ratio of theamplitude of the exponential decay, A (∆ K ), and theamplitude in regions where no structural contributionis expected. α inc (∆ K ) in Figure 5(b) illustrates thisprocedure for the ΓM azimuth: The blue dots repre-sent the corrected incoherent data. A comparison withthe MC simulation in Figure S5 (a) shows that it clearlyapproximates the incoherent α inc (∆ K ), i.e. the ∆ K de-pendence of a non-interacting system, very well. S21
The only region where this approach does not apply isin the vicinity of the substrate diffraction peaks. Herethe structure factor of the substrate becomes impor-tant while at the same time the uncertainty of A (∆ K )becomes very large. As a consequence the blue dotsin Figure S5 (b) show an offset for ∆ K close to zeroand around the diffraction peak. The MC simulationon the other hand considers only the dynamics of theadsorbates so the coherent α (∆ K ) in Figure S5 (a) ap-proaches zero at these positions as expected.Finally, here we note again that the implementation ofrepulsive interactions in the MC simulation alone canreproduce the peak-and-dip structure as evident in theexperimental data. Figure S6 shows both the dephas-ing rate α (dash-dotted lines) and the correspondingstatic structure factor S (∆ K ) (solid lines) as extractedfor the MC simulations along the ΓK-azimuth. We seethat only for ( A >
0) there appears a clear peak in S (∆ K ) at the same position where α (∆ K ) shows a dipas illustrated by the arrow a the top of the plot. We Fig. S6 : Comparison between the dephasing rate α (dash-dotted lines) and the corresponding static struc-ture factor S (∆ K ) (solid lines) along the ΓK-azimuth,as extracted from the MC simulations. Only repulsiveinteractions ( A >
0) give rise to a clear peak in S (∆ K )at the same position where α (∆ K ) shows a dip as illus-trated by the arrow.should note that this does not exclude the possibilityof short-range attractive interactions and it is the im-plementation of long-range repulsive interactions in thekinetic MC that reproduces the feature in the experi-mental data. Short-range interactions may rather occurwithin a length scale that corresponds to intra-cell dif-fusion S24 while the discrete grid in terms of the MCsimulations allows just for interactions at the the inter-cell diffusion length-scale to be taken care of.
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