High-pressure lubricity at the meso- and nanoscale

3.8 MB·English

by  A. Vanossi

High-pressure lubricity at the meso- and nanoscale
A. Vanossi1,2, A. Benassi3, N. Varini4,5, and E. Tosatti2,1,6
1 CNR-IOM Democritos National Simulation Center, Via Bonomea 265, 34136 Trieste, Italy
2 International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
3 Empa, Materials Science and Technology, U¨berlandstrasse 129, 8600 Du¨bendorf, Switzerland
4 Research & Development, Curtin University, GPO Box U 1987, Perth, Western Australia 6845
5 iVEC, 26 Dick Perry Ave, Kensington WA 6151, Australia
6 International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34014 Trieste, Italy
(Dated: January 14, 2013)
The increase of sliding friction upon increasing load is a classic in the macroscopic world. Here
wediscussthepossibilitythatfrictionrisemightsometimesturnintoadropwhen,atthemesoscale
3
andnanoscale,aconfinedlubricantfilmseparatingcrystallineslidersundergoesstronglayeringand
1
solidification. Under pressure, transitions from N → N −1 layers may imply a change of lateral
0
periodicity of the crystallized lubricant sufficient to alter the matching of crystal structures, influ-
2
encingtheensuingfrictionjump. Apressure-inducedfrictiondropmayoccurasthesheargradient
n maximum switches from the lubricant middle, marked by strong stick-slip with or without shear
a melting,tothecrystallineslider-lubricantinterface,characterizedbysmoothsuperlubricsliding. We
J
present high pressure sliding simulations to display examples of frictional drops, suggesting their

1 possible relevance to the local behavior in boundary lubrication.
1
PACSnumbers: 68.35.Af,68.08.De,62.10.+s,62.20.Qp
]
i
c
s INTRODUCTION L V(P)
l- V(0)1.0 (e)
r
t
m Confinedlubricantsundershearandhighpressuredis-
play, both experimentally [1–3] and theoretically [4–9], 0.87
.
t intriguing nano- and meso-scale tribological phenomena.
a
m The intervening lubricant film between two sliding solid
surfaces generally changes from liquid (with hydrody- (a) 0.75
- 2 20
d namic lubrication), to solid or nearly solid at high pres- P
n
sure when the film is only a few monolayers thick. Both
o
experiments and simulations find that in this regime the
c
[ film develops a solid-like layered structure, supporting

static friction, and a strong stick-slip frictional behavior.
1
The stick-slip is often believed to be associated either
v (b) (c) (d)
3 with a lubricant melting-freezing mechanism, where the
0 film disorders and melts at slip and solidifies during the FIG. 1: (Color online) Sketch of the three-dimensional fric-
4 stickphase(see[8]andreferencestherein),orelsewitha tionalmodel(a)andsnapshotsofthreedifferentslidingstates:
2 layer-on-layer shear (a shear band) within the film bulk (b) 8-layer crystalline lubricant (sticking), (c) 8-layer melted
. lubricant (slipping), (d) 7-layer (relayered) crystalline lubri-
1 or at the film-wall interface [10–12]. Moreover, as lubri-
0 cant layers get successively squeezed out under increas- cant,withasuperlubricfilm-wallinterface. Thegrey-redcol-
3 oredscalehighlightsparticlekineticenergies,fromlowtohigh
ing pressure, each N → N −1 (“relayering”) transition
1 values. (e) Bulk lubricant equation of state (sketch) with
: generally corresponds to an upward friction jump [2, 5]. jumps indicating pressure-induced relayering transitions un-
v Virtually everywhere in sliding friction, including the der confinement.
i
X smoothest boundary lubricated systems, friction grows
with load. The question which we raise here is whether,
r
a andunderwhichcircumstances,thatfrictionjumpcould ularsqueezoutsimulations[15]indicatingcrystallinepar-
bedownwardratherthanupwardatrelayering. Therela- allel ordering of the narrowly confined lubricant, and its
tivesurfacestructurepropertiesattheinterfacebetween dependence on the load. That detail is important for
sliders and confined film may play the key role. Under thecaseofcrystallinesliders, foringeneralthefrictional
pressurethecrystal-likelubricantorderingperpendicular forces will depend on the relative geometry and com-
totheinterfacewilltypicallybeaccompaniedbyordering mensurability at the slider-lubricant interfaces, in a way
paralleltotheinterface[13,14]. However,littleisknown which is not immediately predictable, in particular not
about possible two-dimensional (2D) parallel crystalline automatically monotonic with pressure. To explore the
order,andevenlessaboutitschangesuponhighpressure variety of possibilities, we decided to abandon the open
relayering. Thereissomeevidence,forexampleinmolec- geometry where lubricant squeezout takes place, surely
2
much faster with sliding than without [16, 17], and we plate and the confined lubricant particles are
simulatedinsteadlubricatedslidingfrictionundersealed
conditions, with constant particle number and no squee- MR¨ =−(cid:88)nt (cid:88)n d U (|r −rt|)−k(X −v t)ˆi
zout. Sealedconditionsmightbelocallyrealizedinsome top drt WL j i top 0
i=1j=1 i
real cases, but we use them here essentially as a theo-
n
retical device. Our results show that in agreement with −(cid:88)mη(R˙ −r˙ )−Lkˆ+Fran, (1)
top i
pressure-induced N → N −1 relayering of the solidified
i=1
confined lubricant film, the parallel lubricant periodicity
alsochanges;andasaresultthelubricatedslidingfriction
may indeed switch from stick-slip, accompanied by bulk (cid:88)n d (cid:88)nt d
m¨r =− U (|r −r |)− U (|r −rt|)
shearwithorwithoutmelting-freezing,tosmoothsliding i dr LL i j dr WL i j
i i
j(cid:54)=i j=1
regimes typical of incommensurate interfaces exhibiting
superlubric dry friction. In that case the friction coeffi- +(cid:88)nb d U (|r −rb|)−mηr˙ −mη(r˙ −R˙ )+fran,
cient correspondinglyshowsa strong, if counterintuitive, dri WL i j i i top i
j=1
non-monotonic behavior as afunction ofincreasing load.
(2)
where r , rt, and rb are the lubricant, top and bottom
i j j
MODEL plate particle coordinates, respectively, m is the lubri-
cant particle mass, M = n m that of the top plate,
t
Our model system comprises two parallel, rigid, pe- andˆi and kˆ are unit vectors along x and z respectively.
riodically corrugated plates confining between them a During simulated sliding, the shear-induced Joule heat
small number of lubricant layers, with planar periodic is removed by means of a viscous damping proportional
boundary conditions (PBC), with n, n and n defining to the relative velocity between the top plate and the
t b
the total numbers of particles in the lubricant, top, and lubricant, η being the friction coefficient. Importantly
bottomplatesrespectively. Wewillpresentmoleculardy- here, as detailed later, notwithstanding this rather arbi-
namics(MD)simulationresultsandadetailedstatistical trarychoiceofdissipation,pickinganotherthermostating
dataanalysismostlyfor2Dsystems,wherethetwoplates procedure only influences details, but it does not change
consist of one-dimensional line-like confining substrates the phenomenology essence. The temperature T is con-
with PBC applied only along the sliding x-direction. We trolled by an ordinary Langevin thermostat, with a ran-
also simulated, not as extensively, more realistic (and dom force obeying the fluctuation-dissipation theorem,
computationallymoreexpensive)three-dimensional(3D) i.e. (cid:104)fran(t)(cid:105)=0 and (cid:104)fran(t)fran(t(cid:48))(cid:105)=4ηK Tδ δ(t−
i i j B ij
systems such as that depicted in Fig. 1(a) observing t(cid:48)), K being the Boltzmann constant. For the top
B
an essentially identical behavior (details in supplemen- plate Fran = −(cid:80)n fran so that (cid:104)Fran(t)(cid:105) = 0 and
i=1 i
tal material). The bottom plate is assumed to be rigid (cid:104)Fran(t)Fran(t(cid:48))(cid:105)=n4ηK Tδ(t−t(cid:48)).
B
and immobile while the top sliding plate, whose cen- LJ units are used throughout the paper. The equa-
ter of mass coordinate is defined in two dimensions by tions of motion are integrated using a modified Velocity-
R ≡ (X ,Z ), is connected to an external spring Verletalgorithmwithasufficientlysmalltimestep(∆t=
top top top
of stiffness k driven horizontally along x at constant ve- 0.005). Slidingsimulationsareperformedattemperature
locity v . A downward vertical load force L is applied to K T = 0.1. The external driving velocity is v = 0.1,
0 B 0
the top plate center of mass, F = L/n being the load the spring constant k/n = 0.1, the damping coefficient
N t t
per top slider particle. The corresponding friction force η = 0.2 (underdamped regime), and the lubricant par-
(per top particle) is directly measured by the instanta- ticle mass m = 1. Typical system sizes comprise from
neousspringelongationF =k(X −v t)/n . Thewall- hundredsuptoafewthousandsparticles. Statisticalval-
top 0 t
lubricant(WL)andthelubricant-lubricant(LL)interac- ues of the considered physical quantities are obtained by
tionsaremodeledbyLennard-Jones(LJ)potentialsU averaging over sufficiently long time intervals in steady
LL
and U , choosing an amplitude ratio (cid:15) /(cid:15) smaller state regimes.
WL LL WL
than1(typicallyweused0.2), sothatthelubricantwets
the substrate, favoring epitaxial ordering in the solid
phase, such as would generally be the case for example RESULTS
for an octamethylcyclotetrasolixane (OMCTS) lubricant
film between crystalline sliders. We assume σ =1 as Load-induced drop of friction
WW
our reference length and define σ ≡(σ +σ )/2.
WL WW LL
Acting on the LJ interparticle distance ratio σ /σ WestartoffwithafilmofN =8solidlubricantlayers,
LL WL
we can explore the effect of wall-lubricant interface com- zero load, and zero sliding speed. Choosing our temper-
mensurabilitychangesonthetribologicalresponseofthe ature above the melting point, the lubricant film first
confined system. The equations of motion for the top melts. FromthispointweincreasebystepstheloadF ,
N
3
1.0 (a)
0.8
0.6
0.4
0.2
0.0
10.0
9.0
Z
8.0
(b)
7.0
0.2 0.5 1.0 2.0 5.0 10.0 20.0
N
(c) 1.2 (d)
0.05
0.8
0.04
0.4
0.03 0.0
0.0 1.0 2.0 5 10 15 20 25 30 35
N N
FIG. 2: (Color online) (a): average friction force versus adi- time
abatically increasing (circles) and decreasing (squares) ver-
tical load, for the lubricant-slider 2D commensurate system
FIG.3: (Coloronline)Upperpanels: frictionforceasafunc-
(σ /σ =1). A hysteresis loop appears at the relayering
LL WL tionoftimeforthethreedifferentincreasingloads(F =1.6,
N
transitions of the lubricant. The numbers 1,2 and 3 refer to
3.0 and 3.5) highlighted in Fig. 2 (a), for the 2D commensu-
three different values of load highlighted in Fig. 3. (b): load
rate system (σ /σ = 1). At F = 3.5 (panel 3) the
LL WL N
dependence of the lubricant film thickness, measured by the
lubricantfilmhasalreadyundergonetherelayeringtransition
top wall vertical coordinate, (cid:104)Z (cid:105). (c)-(d): average friction
top from 8 to 7 layers. Lower panels: corresponding top plate
force, same as (a) now for 2D lubricant-slider incommensu-
and layer-averaged lubricant velocities, color-coded along z
rate system (σ /σ ≈ 1.11475). The 8 → 7 relayering
LL WL according to the inset sketch. At the relayering transition
transition here takes place at smaller load, still leading to a
slidingswitchesfromthelubricantmiddle(panels1,2),shear
friction drop.
melting with an almost laminar flow, to the hard solid wall-
lubricant interface (panel 3).
thus exerting a pressure P; at first the lubricant recrys-
tallizes with N = 8 layers. Increasing further the pres- lowpressurestate. Thatinterfacebecomesincommensu-
sure, the compressed confined lubricant roughly follows rateasrelayeringjumpstakeplaceunderpressure. When
(with a kinetics that is fast here given the small system successivelythetopplatedrivingspeedv israisedabove
0
size) the Lennard-Jones equation of state, as sketched in zero, and sliding takes place, the frictional force, and in
Fig. 1(e). Specifically, the averaged perpendicular inter- fact the overall sliding habit, displays a strong depen-
particle spacing diminishes gradually, as highlighted by dence upon pressure. While friction naturally increases
the corresponding gentle decrease of Z in Fig. 2(b), withload,therearelargejumpsateachrelayering,where
top
up to the occurrence of a relayering transition. As indi- frictionnowdrops,runningagainstconventionalwisdom.
cated, the finite system size determines a series of crit-
ical pressures P , P , etc, where relayer- Figures 2(a) and (b) show the non-monotonic pres-
N→N−1 N−1→N−2
ing takes place, first from 8 to 7 layers, then from 7 to sure behavior of the average friction force (cid:104)F(cid:105), and the
6, etc, corresponding to significant downward jumps of corresponding average effective film thickness (top wall
interparticle spacing and to a sudden change of the mu- vertical coordinate) (cid:104)Z (cid:105), for adiabatically increasing
top
tualparallelcommensurabilitybetweenlubricantfilmand (circles) and decreasing (squares) load F , and an ini-
N
sliders. The interparticle space shrinking taking place in tially commensurate sliding interface (σ /σ = 1).
LL WL
alldirections,ateachrelayeringthemutualcommensura- At small load, with N = 8 solid lubricant layers, the
bilitybetweenlubricantfilmandslidersundergoesasud- sliding is smooth and friction is relatively low. With
denchange. Atthisstaticlevel,ourchoice σWW =1and increasing load, the smooth sliding regime is gradually
σLL
therelativelystrongplate-lubricantinteraction,makethe (although not uneventfully, as will be described later)
plate-lubricant interface initially commensurate in the replaced by stick-slip. Here friction is much higher, cor-
4
responding(forthischoiceoftheinteractionLparameters)
toshearinducedmelting-freezing[5–8]originatinginside
the lubricant, as visually highlighted in snapshots (b)
and (c) of Fig. 1. At a critical load P , however, the
8→7
lubricant, unable to support the excessive pressure, un-
dergoesrelayeringaccompaniedbyanabrupt,andtribo-
logically crucial, change of parallel lubricant crystalline
periodicity accompanying the drop of perpendicular in-
terlubricant spacing. In the denser relayered state, two
things happen. First, the shear induced melting is now
more difficult. Second, and most important, the inter- N
faces change their mutual commensurability. Thus the
relayering causes the shear gradient maximum to switch FIG. 4: (Color online) 3D lubricant-wall system geometry:
(a) average friction force versus adiabatically increasing ver-
from the bulk lubricant middle to the plate-lubricant
tical load, showing a large frictional drop at the 8→7 relay-
solid interface (Fig. 1, snapshot (d) and movies in the
ering transition; (b) z-resolved profile (layer-by-layer) of the
SupplementalMaterial)wherebystick-slipisreplacedby
lubricant velocity x-component.
“superlubric” [18, 19] smooth sliding, with a dramatic

frictiondecrease. Uponfurtherincreaseofload,thestick-
slip dynamics returns, this time without lubricant melt-
u n if o r m d a m p in g
ing, until P and the next relayering take place. Cy- 1 .6
7→6
z - d e p e n d e n t d a m p in g
cling adiabatically the pressure up and down opens up
1 .4
hysteretic frictional cycles close to relayering transitions
(Fig. 2(a) and (b)).
1 .2
> 1 .0
Robustness of friction drop F
<
0 .8
This observed frictional drop phenomenon might ap-
0 .6
pear at first strictly determined by our special choice of
parameters, and thus not robust; we found that it is not
0 .4
so.
AvariationoftheLJparameterratioσ /σ makes 0 .2
LL WL
the initial low pressure lubricant-wall interface incom- 0 5 1 0 1 5 2 0 2 5 3 0 3 5
mensurate, yet still leading to clear non-monotonic fric- F
tion and downward jumps, as shown in Figure 2 (c) and N
(d).
FIG. 5: (Color online) Average friction force versus adia-
The same qualitative result is also obtained changing
batically increasing vertical load for two distinct dissipation
the total number of confined lubricant particles, and by schemes: (circles) a constant and heavy damping (η = 2.0,
moving to a more realistic 3D model. In Fig. 4, the blue i.e.,10timeslargerthanthatusedfortheresultsreportedin
datapointsshowanalmostlaminarlubricantflowofthe Fig. 2) on all lubricant particles; (squares) a damping expo-
confined film corresponding to a high dissipative stick- nentially decaying with distance away from both substrates
(see Ref. [8]).
skip regime of motion. The red points highlight the slid-
ing switch, after pressure-induced relayering, from the
bulk lubricant middle to the incommensurate top wall-
film interface, realizing an almost frictionless (superlu- tance away from both sliders [8]) only influences details
bric) dynamical regime (movies in Supplemental Mate- here,withoutchangingtheessence: thepressure-induced
rial). switches of the maximal shear zone from the lubricant
Nonequilibrium molecular-dynamics simulations in middle to the slider-lubricant interface, entailing a fric-
sliding friction, are also hampered by arbitrariness and tional drop, is robust and occurs with all thermostating
uncertainties in the way Joule heat is removed; in order procedures tried.
to attain a frictional steady state, a realistic energy dis- Another relevant point strengthening the results’ gen-
sipation is generally impossible to simulate reliably, due erality deals with the unimportance of whether dissipa-
to size and time limitations [20, 21]. However, as shown tivestick-slipshearingthroughthemiddleofthesolidlu-
by the average friction force trend in Fig. 5, increasing bricant film will be accompanied by melting-freezing, or
Langevin damping or else adopting a different thermo- willjustconstituteaninterlayershearband. Experimen-
statscheme(adampingexponentiallydecayingwithdis- tally(e.g.,insurfaceforceapparatusmeasurements),one
5
cannot directly observe the film dynamics and both sce- 1 .0 (a )
narioseasilyachievableinMDsimulations(dependingon 0 .9
the model parameters, geometry and driving conditions) (t) 0 .8
0 .7
represent interesting perspectives. However the physics F
0 .6
which we describe is not bound to one or the other. The
(b )
1 0 2 6 0
switch of shear from center to interface which we pro-
pose and demonstrate in a particularly simple model, top11 00 22 24 00 z - d e p e n d e n t d a m p in g
describes a more general phenomenon, that occurs in X
F = 2 .5
our simulations, where forces are rather generic, in ei- 1 0 2 0 0 N
ther cases. 9 .8 (c )
9 .7
The time dependent dynamical frictional forces in p 9 .6
to 9 .5
Fig.3show,atloadsFN markedas1,2,3inFig.2(a),an Z 9 .4
increasingly strong stick-slip followed by a drop back to 9 .3
smooth sliding corresponding to a harder solid lubricant 1 8 0 0 2 0 0 0 2 2 0 0 2 4 0 0 2 6 0 0
withadifferentparallelcommensurabilityattherelayer- t i m e
ing transition. As highlighted by the color-coded lubri-
FIG. 6: Stick-slip dynamics in the presence of a damping
cant speed along z (lower panels 1,2, Fig. 3), the shear
exponentially decaying with distance away from both sub-
flow profile is almost laminar inside the film, starting off
strates, at a vertical load F = 2.5 just before the 8 to 7
N
as a shear band at the center of the film. At relayering
relayeringtransition: (a)frictionalforcepattern;(b)topwall
(e.g.,8→7layers),bulksheardisappears,andthespeed horizontal X-coordinate; (c) top wall vertical Z-coordinate.
gradient switches entirely to the (now incommensurate, Here we do not observe a density decrease in mid-lubricant
andsuperlubric)slider-lubricantinterface(lowerpanel3, slips, that now leave the film mostly crystalline and do not
Fig. 3). Upon further increase of load, superlubric slid- lead to shear-induced melting.
ingpersistsonlyuptoathresholdpressure. Here,despite
incommensurability, static friction and stick-slip sliding
1 .5 (a )
reappear, with friction again rising with pressure. Un- 1 .4
like low pressures, high pressure melting-freezing is sup- t) 1 .3
( 1 .2
pressed, and stick-slip is ruled by inertia [8]. At each F 1 .1
successive relayering transition (eg. from 7 → 6 lay- 1 .0
ers), friction may, in principle, jumps down (as shown in (b )
2 5 6 0 0
Fig. 2(a) and (d)) or up depending, respectively, on the
2 5 5 9 0
p
realization of a more favorable or unfavorable interface to2 5 5 8 0 z -d e p e n d e n t d a m p in g
incommensurability due to lubricant reordering parallel X F = 2 5
2 5 5 7 0 N
to the confining surfaces.
7 .8 8 (c )
For the choice of the interaction parameters in Fig. 2, 7 .8 4
whenmeltingtakesplace,thelubricantdensitydecreases. top 7 .8 0
Wedoobservethatdensitydropintheformofasmallex- Z 7 .7 6
7 .7 2
pansion of the film thickness in mid-lubricant slips (that
5 5 6 0 0 5 5 7 0 0 5 5 8 0 0 5 5 9 0 0 5 6 0 0 0
lead to shear-induced melting), clearly resulting in cor-
t i m e
respondingverticaljumpsofthetopconfiningsubstrate.
In contrast, the stick-slip dynamics in the presence of
FIG. 7: Stick-slip dynamics as in Fig. 6 but at a vertical
a damping exponentially decaying with distance away load F = 25 approaching the 7 to 6 relayering transition.
N
from both substrates (square-point curve in Fig. 5) does Here,apartfromthesubstrate-distancedependentdissipation
not display melting-freezing induced by sliding, with the scheme, the shear induced lubricant melting during slips is
top wall vertical Z -coordinate just fluctuating weakly hampered by the strong confining pressure.
top
aroundameanvalueandwithoutanyobservabledensity
decrease in mid-lubricant slips (panel (c) in Figs. 6 and
7). derstandthat,wecalculatedthestaticfrictionasfollows.
Starting from a set of configurations of the film whose
loads are above the 8 to 7 relayering transition, we first
Superlubric sliding under pressure removed the external driving and equilibrated the sys-
tem under the action of increasing loads. For each con-
This pressure induced switch from superlubricity to figuration, we evaluated the static friction threshold by
static friction with stick-slip sliding deserves special at- drivingthetopwallexternalspringataverysmallveloc-
tention, because it takes place continuously and within ity(i.e.,100timessmallerthanthatpreviouslyadopted)
the same incommensurate state of the lubricant. To un- and measuring the height of the peak preceding the first
6
CONCLUSIONS
n0.4 1.0 4.8
Frictio00..23 stick-slip FN 234...000 567...000 catIendssulimdimngaruyndweersheaavleedecxopnldoriteido,nsb,ythseimpuoslasitbinilgitylutbhrait-
cs atic 0.1 4.5 8.0 frictional jumps associated with N → N −1 relayering
mi St0.0 superlubric transitions might be downward rather than upward as
na 2 4 6 8 commonly observed. We find that downward jumps may
y FN occur due to two factors: (i) high friction with internal
d
p shear, easier at low pressure and low density,could dis-
o
Xt
appear after relayering, when density is higher; (ii) the
change of interface commensurability entails possible su-
perlubricity at higher pressure. In experiments so far,
the friction drop just described is likely removed by lu-
bricant squeezout, and routes should be considered to
overcome that. Despite a clear difficulty in realizing
0 500 1000 1500 2000
sealed sliding configurations in ordinary materials and
time
sliding geometries, these two elements stand as results
of general importance, given the relevance of any ele-
FIG. 8: (Color online) Time-evolution of the top plate coor-
ments that could control, and especially decrease, fric-
dinateX for2Dincommensurateslidingwithσ /σ ≈
top LL WL tion. Under the more common open boundary condi-
1.11475) (same as in Fig. 2(c)), for increasing load just after
tionsofboundarylubrication,whererelayeringalsotakes
theoccurrenceofthe8→7relayeringtransition. Curvesare
offset vertically for clarity. The inset highlights the Aubry- place, one still could, depending on conditions and ma-
likeload-inducedonsetofthestaticfrictionforthetopplate, terials, realize one or both points above. In realistic in-
marking the transition from superlubric sliding to stick-slip. homogeneous conditions, moreover, lubricant “puddles”
might become sealed under pressure [23], and their sud-
den yielding could be important for the local sliding dy-
slip. Figure 8 shows a clear onset of static friction near namics. Finally, future developments of artificial sliding
F = 4.7, taking place without any change in the in- colloidal systems [25, 26] might permit soon the realiza-
N
commensurate slider-lubricant registry. This represents tion of sealed sliding, and the verification of our results,
an example of the well-known “Aubry transition” [22] in including, in addition to the downward jumps, pressure
one-dimensional systems, where the increasing interac- induced Aubry transitions.
tionbetweenaharmonicslidingchainandanincommen- ThisworkispartoftheSwissNationalScienceFounda-
surate periodic potential gives rise to dynamic pinning tion SINERGIA Project CRSII2 136287\1. The authors
with the onset of static friction. The sliding trajectories gratefully acknowledge D. Vanossi for computational re-
(Fig. 8) correspondingly switch from smooth sliding to sources; and N. Manini and O.M. Braun for discussions.
stick-slip of strength increasing with load.
Possible experimental realization [1] R. G. Horn and J. N. Israelachvili, J. Chem. Phys. 75,
1400 (1981).
[2] H.YoshizawaandJ.N.Israelachvili,J.Phys.Chem.97,
First let us consider estimates for OMCTS, a reason- 11300 (1993).
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LJparametersforOMCTSasprovidedbyH.Matsubara [4] J. P. Gao, W. D. Luedtke, and U. Landman, Phys. Rev.
et al. [24], the critical pressure for the 8 → 7 relayering Let. 79, 705 (1997).
[5] J. P. Gao, W. D. Luedtke, and U. Landman, J. Phys.
isabout6−7Kbar. Thatseemstoohighcomparedwith
Chem. B 102, 5033 (1998).
ordinary squeezing loads in surface force apparatus, al-
[6] P. A. Thompson and M. O. Robbins, Science 250, 792
thoughlocaltrappingofsealedlubricant“puddles”might
(1990).
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Mesoscopic systems appear more promising. For ex- Applications (Springer, Berlin, 2000).
[8] O. M. Braun and A. G. Naumovets, Surf. Sci. Rep. 60,
ample,colloidscanbeconfinedinlayers,crystallizeddue
79 (2006).
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[9] A. Vanossi, N. Manini, M. Urbakh, S. Zapperi,
to slide against laser generated periodic potentials [25–
and E. Tosatti(2011), Rev. Mod. Phys., in press;
27]. Theymightthereforerepresentagoodtrialcasefor arXiv:1112.3234v3 [cond-mat.mes-hall].
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