Understanding frictional duality and bi-duality: Sb-nanoparticles on HOPG

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Nanotechnology 22 (2011) 085704 (5pp) doi:10.1088/0957-4484/22/8/085704

Understanding frictional duality andbi-duality: Sb-nanoparticles on HOPGJan Brndiar1, Robert Turansky1, Dirk Dietzel2,Andre Schirmeisen2 and Ivan Stich1

1 Center for Computational Materials Science, Institute of Physics, Slovak Academy ofSciences, 84511 Bratislava, Slovakia2 Physikalisches Institut and Center for Nanotechnology (CeNTech), WestfalischeWilhelms-Universitat Munster, Germany

E-mail: ivan.stich@savba.sk

Received 6 September 2010, in final form 13 December 2010Published 17 January 2011Online at stacks.iop.org/Nano/22/085704

AbstractAntimony nanoparticles deposited under UHV conditions on HOPG are found to exhibit anintriguing frictional behavior characterized by a distinct clearly separated double dual behaviorof dependence of the frictional force on contact area. We present the first realistic simulations,density functional modeling adapted to accommodate van der Waals interactions, of the(double) dual frictional behavior. The simulations provide insights into the physics/chemistry ofall the frictional branches in terms of incommensurable interfaces, mobile spacer molecules aswell as a novel concept of mobile oxidized multi-nanoasperities.

(Some figures in this article are in colour only in the electronic version)

Friction is one of the most easily and commonly observedphenomena of our everyday life. Yet, when it comesto atomic/molecular-scale origins of friction or nanotribol-ogy [1–3], the underlying physics and chemistry of theprocesses leading to friction still remain to be understood.Macroscopically, Amonton’s law applies and the frictionforce Ff = µFl, where Fl is the external loading forceand µ the friction coefficient. Since µ is constant for agiven interface, Ff is independent of the contact area A ofthe interface. However, at the nano-scale, this behaviorchanges, in particular, linear scaling of friction force Ff withcontact area A has been observed [3, 4]. Recent experimentsperformed under UHV conditions found even more intriguingbehavior not observed on the macroscale. Friction forceshave been measured in a static AFM apparatus for antimonynanoparticles sliding on highly oriented pyrolytic graphite(HOPG) substrate [5, 6]. Antimony particles were preparedunder UHV conditions and friction was measured duringlateral manipulation at sliding speeds of about 1000 nm s−1,as shown in figure 1(a). In a second experimental set theparticles were exposed to air for several days and subsequentlyfriction was measured inside the UHV system again [5, 6](figure 1(b)). The accumulated data indicate the presence ofa double duality in the frictional behavior. The first duality isrepresented by antimony nanoparticles prepared under UHV

conditions which show either vanishing friction forces orfriction forces increasing linearly with the contact area, heretermed non-vanishing friction. Surprisingly, the nanoparticlesafter extensive exposure to ambient conditions exhibit againa dual friction behavior. This time data points from thesame non-vanishing friction branch as in UHV coexist withnanoparticles showing very high friction of roughly an orderof magnitude larger.

The frictional behavior of this system, which exhibitsclearly separated friction regimes under UHV conditions,provides a unique and hitherto unrealized possibility to studyand understand the different friction regimes at the nano-scale. Can the observed behavior be reconciled with theexisting nanotribology models? The lattice mismatch betweenantimony and HOPG is about 4% [7]. For incommensuratestructures, such as antimony on HOPG under UHV conditions,the concept of structural superlubricity applies [9, 10] andhence the observed vanishing friction is to be expected.However, even under UHV conditions the ubiquitous residual‘dirt particles’, such as water, hydrocarbons, etc will lock theinterfaces [11], leading to linear dependence of the frictionforce with contact area, as observed on the non-vanishingfriction branch, see, figure 1. We note that mobility ofthe spacer particles is of key importance, as the effect ofrigidly bound particles would again lead to incommensurate

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Nanotechnology 22 (2011) 085704 J Brndiar et al

Figure 1. Experimental results for antimony nanoparticles of varying contact areas sliding over HOPG substrate uncovering double duality offriction behavior with three different frictional regimes. (a) Particles prepared and manipulated under UHV conditions show a coexistence ofvanishing friction (red squares) and non-vanishing friction (black squares). (b) After exposure to air for several days the particles showcoexistence of the same non-vanishing friction level as before (gray triangles) together with a very high friction branch (blue circles) withroughly one order of magnitude larger friction. The dashed line indicates the position of a 30 × 103 nm2 particle used as a reference forcomparison of experiment and simulation.

structures and superlubricity as illustrated in figure 2. Both theconcepts of superlubricity and of mobile spacer particles havebeen studied and understood at least for model Lennard-Jonessystems [12, 13]. However, to the best of our knowledge, nomolecular-scale simulations and insights for realistic systemsare available to date. Even more difficult to reconcilewith the existing models is the second duality observed fornanoparticles exposed to ambient conditions. Invoking largeconcentrations of dirt particles may not be compatible withUHV conditions and the observed dual behavior. One couldcommend formation of an oxide layer in the Sb–HOPGinterface. However, such an oxide layer would again resultin formation of an incommensurate interface and superlubricbehavior in stark contradiction with experimental observations.Hence, the high friction dual branch, figure 1(b), if notgenerated by mobile dirt particles, will require the presence ofhigh friction ‘mobile’ multiasperities. In order to shed light onthe experimentally observed double dual frictional behavior,figure 1, we will need predictions for required densities ofdirt particles and/or mobile high friction multiasperities. Inturn, modeling beyond the simple empirical force field picturewill require a full model of the structure and chemistry ofthe interface. In this communication we present results ofsuch quantitative simulations. While they reveal details ofthe friction duality of clean nanoparticles, they are accurateand predictive enough to shed light also on the other dualityappearing after exposure to ambient conditions.

All simulations, based on density functional (DFT) mod-eling, were performed with the plane-wave pseudopotentialCPMD [14] simulation package using the PBE [15] exchangecorrelation functional and a plane waves basis set at 30 Rydwith an ultrasoft pseudopotential [16] for carbon, oxygen

Figure 2. Schematic illustration of the scenario corresponding toimmobile (black lines) and mobile (red lines) spacers for twoparticles moving on a model potential energy surface. The upperpanels show the respective energy profiles with the average shown ingreen.

and hydrogen and a norm-conserving pseudopotential [17]for antimony. The Sb–HOPG interface has a strong van derWaals (vdW) bonding component and a pure DFT description

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Nanotechnology 22 (2011) 085704 J Brndiar et al

of the Sb–HOPG interface does not provide binding of Sbn

to HOPG or the vdW bonding in HOPG itself. The vdWcomponent was fixed by adding Grimme’s correction [18].A schematic simulation set up is shown in figure 3. Whilethe vdW component provides most of the ‘bonding’ betweenantimony and HOPG, it provides very little corrugation of thepotential energy surface (PES) for sliding. For example, for theSb4–HOPG interface, figure 3, the vdW interaction accountsfor ∼0.9 eV, or ∼0.3 eV/atom, and the short-range chemicalinteraction accounts for corrugation of the PES of ∼20 meV.In all simulations only one fixed graphene layer was includedin the chemical region with the number of vdW layers chosenso as to bring the energies and atomic forces to convergence.Inclusion of only one fixed graphene layer in the chemicalregion compared to a graphite surface (six layers, with twosurface layers kept fixed) with an appropriate number of vdWlayers modified neither energy profiles nor forces and resultedin a change of energy of the order of only ≈0.005 eV [19].Approximants to the incommensurate Sb–HOPG interfaceswere constructed by considering a 7 × 7 HOPG hexagonalcell and an antimony slab consisting of three bilayers, the topbilayer kept fixed, rotated by 30◦ with the antimony latticeparameter slightly adjusted so as to form a periodic supercell,see figure 4(a). Other approximants to incommensuratestructure could be generated by choosing a different cell sizeand rotation. We have considered a range of different dirtmobile particles associated with imperfect vacuum in the Sb–HOPG interface: oxygen atom and molecule, water molecule,propane molecule, Sb4 and Sb4O6 clusters. While details ofthe friction generation by these very different systems differ,as does the complexity of their simulation and analysis, theemerging picture from these simulations in the respectivefriction branches is qualitatively similar. Therefore we revealhere only results for the water molecule, Sb4, Sb4O6 clusters,and oxygen atom. The rest of the technically more involvedresults will be discussed elsewhere [19]. All simulations aredone at zero temperature by sliding the interface in a staticmanner. From the resulting PES approximate friction forceand/or dirt concentration estimates are made.

We have tested the accuracy of the above model byconsidering HOPG, antimony crystal, and small Sbn clusters.The geometries and energetics of all these systems weredescribed with the usual DFT accuracy [19]. Taking thestructure of the Sb crystal as a typical example, we findfor this partially vdW bonded system an agreement with theexperimentally determined lattice constants to within 1.5%. Inorder to demonstrate the accuracy of description of the Sb–HOPG interface, we quote the results for diffusion barriersof Sb4 on HOPG, see figure 3. A rough simulation estimateobtained from placement of Sb4 at the transition state andallowing it to slide downhill on the PES yields Ed > 20 meVcompared to experiments which yield 40–60 meV [8, 20].

Let us now consider a nanoparticle with a contact area of≈30 × 103 nm2, figure 1. For atomically clean Sb particles onHOPG the friction is below the experimental detection limitof 5 nN (lower branch in figure 1(a)), which coexists witha linear high friction branch yielding 30 nN for the samesize particles. Frictional duality was again found, but at a

Figure 3. Schematics of the simulation set up illustrated on a Sb4

nanoparticle on HOPG. Two different partitions between the‘chemically active’ and van der Waals regions tested are shown onthe left and right, with the scheme on the right used in the productionsimulations.

much higher level, after exposing the Sb particles to air forseveral days with subsequent low temperature annealing inUHV to remove residual surface molecules [6]. Figure 1(b)shows that then the 30 × 103 nm2 Sb particles coexist in avery high friction state with values reaching 300 nN togetherwith the previously identified contaminated friction branch of30 nN. Obviously oxidation of Sb plays an important rolein achieving this very high friction state. Below we givecomputational estimates which represent upper/lower boundsof the friction forces/contaminant concentrations consistentwith these numbers.

Let us start with the vanishing friction branch of the Sb–HOPG interface. In the case of superlubric sliding the frictionscales in a sub-linear fashion with the contact area. Foramorphous interface structures friction is known to scale withthe square root of the contact area and for crystalline interfaceseven more weakly [10]. The simulation results for thecrystalline incommensurate structure are shown in figure 4(a),yielding a friction value of ≈0.8 pN for the considered contactarea of 2.6 nm2 or ≈8 nN for a 30 × 103 nm2 particleassuming linear scaling or ≈0.08 nN assuming a square rootscaling. Another estimate can be based on an amorphousinterface. Therein Sb4 clusters tend to form three-dimensionalnanoparticles [8]. Using the simulation result in figure 4(c)yields an energy barrier of 15 meV for the considered Sb4

cluster. As an upper estimate we can use this result togetherwith the square root scaling to predict a theoretical frictionvalue of ≈3 nN for a 30 × 103 nm2 particle consistentwith the experimentally observed vanishing friction branch infigure 1(a).

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Nanotechnology 22 (2011) 085704 J Brndiar et al

0

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Figure 4. Left panel: PESs (green triangles) and angles (black dots) as indicated in the right panel, for an incommensurate Sb–HOPGinterface (a) and with one dirt particle (b)–(e) during sliding of the interface. From top to bottom: pure incommensurate Sb–HOPG interface,water, Sb4, one oxygen atom, and Sb4O6 bonded to the antimony surface.

Having elucidated the vanishing friction branch, we nowproceed with the normal friction branch. The results fora water molecule and Sb4 shown in figures 4(b) and (c)indicate energy barriers of ≈100 meV and ≈15 meV forwater and Sb4, respectively. Monitoring of the motion

pattern of both impurities reveals that while both movealong with antimony, their angle w.r.t. HOPG varies in aregular pattern, see figures 4(b) and (c). This molecularmotion is of key importance for overcoming the averagingeffect of the incommensurability of the sliding interface, see

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Nanotechnology 22 (2011) 085704 J Brndiar et al

figure 2. Hence, the forces generated by individual dirtparticles will not cancel out but rather sum up. A roughestimate of dirt concentrations from measured forces yields≈1H2O molecule/75 nm2 and ≈1Sb4 particle/7 nm2. Thelatter estimate may seem too large to be compatible withUHV conditions. However, the high concentration of Sb4, ifindeed present, may be understood as a consequence of the‘roughness’ of the Sb–HOPG interface. These simulationsdeal with each impurity considered separately. In reality theimpurities will always interact. Simulation reveals that undersuch conditions the frictional behavior is dominated by thelargest spacer molecule which influences the gap between theSb particle and the HOPG and hence also the corrugation ofthe PES. For example combining water, a propane molecule,and a Sb4 cluster does not provide any qualitative differencecompared to a single Sb4 cluster [19]. Could the otherfrictional duality arising after exposure to ambient conditionsbe explained purely by the presence of a large number ofdirt particles? Using the same molecules as in the case ofthe normal friction branch, we arrive at the concentrations of≈1H2O molecule/7.5 nm2 and ≈1Sb4 particle/0.7 nm2. Thelatter concentration would mean that the Sb4 particles would beoverlapping. Both concentrations are clearly incompatible withUHV conditions or geometrical packing rules and, hence, anexplanation assuming modification of the Sb–HOPG interfacedue to oxidation must be called for. The results of the simplestmodel assuming the oxygen atoms to be incorporated in theSbn particle are shown in figure 4(d). While these oxygenminitips generate an appreciable corrugation of the PES of≈65 meV, their rigidity, evidenced by the absence of anyangular motion, figure 4(d), means that their effect on anincommensurate underlying substrate will cancel out.

A more plausible explanation is provided in the modelshown in figure 4(e). In accord with the above considerationof the presence of Sb4 particles as one type of impurity in theSb–HOPG interface, we consider here oxidation of the Sb4

nanoasperities to form Sb4O6-type minitips. Isolated Sb4O6

nanoparticles have been studied in the past and found to bevery stable [21]. We note that the presence of Sb4 in theinterface is not strictly required, as Sb4O6 minitips may also beformed by local oxidation of the Sbn nanoparticles without thepresence of Sb4 precursors [19, 22]. Such oxidized structuresnot only exhibit large PES corrugation of ≈130 meV but theyalso exhibit the mobility required in order to prevent the effectof formation of an incommensurate interface structure.

In summary, we have presented a joint experimentaland theoretical investigation of the frictional behavior of Sbn

nanoparticles sliding on an HOPG substrate. Depending onthe nanoparticle preparation details, i.e. in UHV or exposureto ambient conditions, the system was found to exhibit apeculiar type of double duality in its frictional behavior as afunction of the contact area. Realistic first-principles atomic-scale simulations provide valuable insights into the underlyingphysics/chemistry of the frictional behavior by yielding force

and/or dirt concentration estimates. Simulations indicate thatstructural superlubricity can account for the vanishing frictionbehavior. Ordinary mobile impurities, such as water or evenself-contaminants of the Sb4-type, can account for the normalfriction behavior. These quantitative simulations clarify alsothe notion of dirt mobility. However, the truly new insightsemerge from the simulation of high friction, after exposureto ambient conditions, where the smallest mobile frictiongenerators are identified and shown to yield friction forcescomparable to those measured experimentally. While we dealtexplicitly with the Sb–HOPG interface, the insights from oursimulations can be transferred to other systems. The behaviorof other dirt spacer particles, including their simultaneouspresence in the interface, frictional behavior resulting fromlocal oxidation effects, and comparison of antimony and goldnanoparticles will be given elsewhere [19].

Acknowledgments

Financial support from APVT (ESF-EC-0007-07) under theNanoparma ESF FANAS project is gratefully acknowledged.This research was supported in part by ERDF OP R&D, ProjectCE QUTE ITMS 26240120009, and via CE SAS QUTE(grants to JB, RT and IS).

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