Timothy S Groves

Carla S Perez-Martinez

Romain Lhermerout

Susan Perkin
email: susan.perkin@chem.ox.ac.uk

Surface Forces and Structure in a Water-in-Salt Electrolyte

Water-in-salt electrolytes are a fascinating new class of highly concentrated aqueous solutions with wide electrochemical stability windows that make them viable as aqueous battery electrolytes. However, the high ion concentration of water-in-salt electrolytes means that these systems are poorly understood when compared to more dilute electrolyte solutions. Here, we present direct surface force measurements across thin films of a water-in-salt electrolyte at several concentrations. We find that the electrolyte adopts a layered structure at charged interfaces composed of a nanostructure of hydrated cation and non-aqueous anion-rich domains. These observations will aid in the interpretation of capacitance and double layer behaviour of water-in-salt electrolytes with consequences for their use in energy storage devices.

Electrolytes are ubiquitous: they form the planet's oceans, they exist within all living cells, and they are critical to the function of many modern technologies. In the dilute regime, electrolytes are well understood by considering the established ideal Debye-Hückel

theory, 1 however as salt concentration increases and excluded volume and correlation effects become important, significant deviations from the theory are observed. [START_REF] Onsager | Theories of Concentrated Electrolytes[END_REF] Understanding the concentrated electrolyte regime is key in many areas, from the study of ion channels in biology [START_REF] Eisenberg | Interacting Ions in Biophysics: Real is not Ideal[END_REF] to designing the next generation of electrochemical energy storage devices.

Water-in-Salt (WiS) electrolytes have recently emerged as promising candidates to replace conventional organic electrolytes in state of the art lithium ion batteries. [START_REF] Suo | Water-in-salt" electrolyte enables high-voltage aqueous lithium-ion chemistries[END_REF][START_REF] Suo | Advanced High-Voltage Aqueous Lithium-Ion Battery Enabled by "Water-in-Bisalt[END_REF][START_REF] Yamada | Hydrate-melt electrolytes for high-energy-density aqueous batteries[END_REF][START_REF] Suo | Water-in-Salt" electrolytes enable green and safe Li-ion batteries for large scale electric energy storage applications[END_REF] These superconcentrated aqueous electrolytes, where the salt comprises the majority of the mass and volume of the system, are able to compete with traditional battery electrolytes owing to the vastly extended electrochemical stability windows of the aqueous system from 1.23 V in dilute electrolytes to ≈ 3 V. This is possible as the high concentration of the WiS electrolyte allows for the efficient formation of a solid electrolyte interphase at the electrode surface that prevents breakdown of the electrolyte, as well as substantially reducing the activity coefficient of the water. [START_REF] Suo | Water-in-salt" electrolyte enables high-voltage aqueous lithium-ion chemistries[END_REF][START_REF] Yamada | Hydrate-melt electrolytes for high-energy-density aqueous batteries[END_REF][START_REF] Dubouis | The role of the hydrogen evolution reaction in the solid-electrolyte interphase formation mechanism for "Water-in-Salt" electrolytes[END_REF] Much work has been focused on attempting to understand these new electrolytes, in particular on modelling the environment of WiS electrolytes, [START_REF] Vatamanu | Ramifications of Water-in-Salt Interfacial Structure at Charged Electrodes for Electrolyte Electrochemical Stability[END_REF][START_REF] Li | Capacitive Performance of Water-in-Salt Electrolytes in Supercapacitors: A Simulation Study[END_REF][11] on extending the WiS principle from lithium ion batteries to sodium, 12,13 potassium 14 and zinc [START_REF] Hu | Zn/V2O5 Aqueous Hybrid-Ion Battery with High Voltage Platform and Long Cycle Life[END_REF] ion batteries, and on broadening the electrochemical stability windows of WiS electrolytes. [START_REF] Yang | 4.0 V Aqueous Li-Ion Batteries[END_REF][START_REF] Jiang | High-Voltage Aqueous Na-Ion Battery Enabled by Inert-Cation-Assisted Water-in-Salt Electrolyte[END_REF] Despite this, the true nature of the structure of WiS electrolytes remains relatively poorly understood, as highlighted in a recent review article. [START_REF] Chen | Water-in-salt electrolytes: An interfacial perspective[END_REF] In this communication, we present measurements of the surface forces and structure of aqueous lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) in the concentrated regime in order to better understand the structure of WiS electrolytes in general and in particular at interfaces and in nanoconfinement.

Measurements were performed using a Surface Force Balance (SFB), shown schematically in Figure 1, previously described in detail [START_REF] Klein | Simple liquids confined to molecularly thin layers. I. Confinement-induced liquid-to-solid phase transitions[END_REF] and briefly summarised here. Full details of the SFB and the measurement process are given in the Supporting Information. Two back-silvered mica pieces of uniform thickness are glued, silver side down, to cylindrical glass lenses with radius R ≈ 10 mm using an epoxy resin (EPON 1004, Shell Chemicals).

The lenses are mounted vertically in the instrument in a crossed cylinder configuration as shown in Figure 1(a), with the two silver mirrors forming an interferometric cavity. White light incident on the interferometer emerges as a series of Fringes of Equal Chromatic Order (FECO), analysis of which can determine the radius of the surfaces R and the surface separation D. [START_REF] Israelachvili | Thin film studies using multiple-beam interferometry[END_REF] Distance dependent normal forces F N (D) are also determined from the FECO by measuring the deflection of a horizontal leaf spring upon which the lower lens is mounted.

Calibrations for absolute distance measurements first take place in air, then a droplet of aqueous LiTFSI is confined between the mica surfaces.

The structure and dimensions of aqueous LiTFSI are shown in Figure 1 Stern layer of immobile ions at the surface. [START_REF] Israelachvili | Measurement of forces between two mica surfaces in aqueous electrolyte solutions in the range 0-100 nm[END_REF][START_REF] Pashley | Hydration forces between mica surfaces in aqueous electrolyte solutions[END_REF] Instead, these results are more qualitatively similar i) to force profiles measured in concentrated solutions of aqueous simple salts [START_REF] Espinosa-Marzal | Hydrated-ion ordering in electrical double layers[END_REF][START_REF] Smith | The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration[END_REF] where oscillations are thought to arise from layering of hydrated cations neutralising the surface charge; ii) to force profiles measured in ionic liquids (pure salts that are liquid at or near to room temperature), [START_REF] Horn | Double-layer and solvation forces measured in a molten salt and its mixtures with water[END_REF][START_REF] Perkin | Layering and shear properties of an ionic liquid, 1ethyl-3-methylimidazolium ethylsulfate, confined to nano-films between mica surfaces[END_REF] where oscillations are thought to arise from alternating layers of cations and anions and correspond to the ion pair diameter; and iii) to measurements in This can also introduce a small difference between F (D)/R at the highest loads (smallest distances) when comparing between concentrations due to differences in contact mechanical stiffness. For this reason, we do not draw physical significance from the slight difference in closest separation between the 7.78 m and 11.64 m concentrations.

¢ o i=1 i=2 i=3 i=4 ¢ o i=1 i=2 i=3 i=4
non-polar organic liquids, polymers and liquid crystals, [START_REF] Horn | Direct measurement of structural forces between two surfaces in a nonpolar liquid[END_REF][START_REF] Horn | Molecular organization and viscosity of a thin film of molten polymer between two surfaces as probed by force measurements[END_REF][START_REF] Horn | Forces due to structure in a thin liquid crystal film[END_REF] where simple packing arguments are used to explain the layering and layer dimensions. We therefore suggest that the force profiles observed here arise from strong layering of species at the surfaces.

The dimensions and evolution with concentration of the layering wavelength, λ o , jumps between layers, ∆J i-(i-1) , and compressions within layers, ∆C i , are shown in Figure 3. Interestingly, the values of λ o are consistently larger than can be accounted for by considering hydrated cation layers (≈ 0.5 nm), [START_REF] Mason | Neutron Scattering Studies of the Hydration Structure of Li+[END_REF] or by considering a simple ionic liquid-like ordered cation-anion layer set from the ion pair diameter (≈ 0.7 nm). [START_REF] Perkin | Layering and shear properties of an ionic liquid, 1ethyl-3-methylimidazolium ethylsulfate, confined to nano-films between mica surfaces[END_REF][START_REF] Atkin | AFM and STM Studies on the Surface Interaction of [BMP]TFSA and [EMIm]TFSA Ionic Liquids with Au(111)[END_REF] Δg 2 Δg 3 Examples of all quantities are shown in Figure 2.

ΔJ 2-1 ΔJ 3-2 ΔJ 4-3 ¢ o (a) (b) (c)
The large layering dimensions suggest a self-assembled nanostructure within the liquid film. Such self assembled layers have previously been observed in SFB studies of long-chain ionic liquids [START_REF] Perkin | Self-assembly in the electrical double layer of ionic liquids[END_REF] where amphiphilic cations formed bilayers between the surfaces with layers composed of 'charge-rich' regions containing the anion and charged head group of the cation, and 'charge-poor' regions of interlocking non-polar cation tail groups.

Simplistically, lithium cations are small and charge dense, and are therefore well solvated in water, whereas TFSI anions are bulky and have delocalised charge centres, meaning they are less well solvated. We suggest that the liquid is nanostructured, consisting of a hydrated cation domain and a non-aqueous anion domain (Figure 4). The hydrated cation domain consists of lithium ions and water; the non-aqueous anion domain consists predominantly of anions with a small number of lithium ions, but with water molecules excluded. This arises because of the strongly hydrophobic nature of the anions in our electrolyte and the strongly hydrophilic lithium cations. This diverging affinity for water between cations and anions drives the charge separation in the nanostructure. These domains are templated against the SFB surfaces by the negative mica charge in a manner similar to that observed in ionic liquids. Each layer transition seen in Figure 2, with the wavelength of ≈ 1.4 nm, corresponds to the 'squeeze-out' of both a hydrated cation domain and a non-aqueous anion domain. This removal of both a cation domain and an anion domain from between the surfaces is driven by the requirement for charge neutrality between the SFB surfaces. This mechanism is analogous to the squeeze out of cations and anions as a single unit in SFB measurements of ionic liquids. [START_REF] Perkin | Self-assembly in the electrical double layer of ionic liquids[END_REF][START_REF] Perkin | Layering and shear properties of an ionic liquid, 1ethyl-3-methylimidazolium ethylsulfate, confined to nano-films between mica surfaces[END_REF] A cartoon showing a portion of the WiS film is sketched in Figure 4 with the layering dimension highlighted.

Supporting this hypothesis, a similar scale of nanostructure has been observed previously in bulk LiTFSI. Borodin et al. performed a series of spectroscopic measurements and simulations at varying concentrations up to saturation of aqueous LiTFSI. [START_REF] Borodin | Liquid Structure with Nano-Heterogeneity Promotes Cationic Transport in Concentrated Electrolytes[END_REF] They found evidence for a nanostructuring in the bulk liquid at high concentrations with a characteristic lengthscale of 1.4 nm, similar to the measured oscillatory wavelengths observed here (Figure 3 Recently, atomic force microscope (AFM) measurements were reported by Ichii et al.

involving a similar WiS electrolyte containing a mixture of LiTFSI and lithium bis(pentafluoroethylsulfonyl)imide (LiBETI). In those experiments, layering was observed with smaller structural dimensions than in our present measurements. [START_REF] Ichii | Solvation structure on water-in-salt/mica interfaces and its molality dependence investigated by atomic force microscopy[END_REF] Potential causes for these differences may lie in the different WiS electrolyte composition studied, and the impact of the AFM tip geometry and chemistry. It is also important to note that the AFM experiments output a 'resonant frequency shift' of the AFM cantilever, compared to the direct surface normal force (and therefore interaction free energy) measured in SFB. The resonant frequency shift may detect sub-layers, collectively relating to the structural units observed in SFB. For example, the measurement with AFM of an outer layer of ≈ 0.9 nm followed by an inner layer layer of ≈ 0.6 nm could together correspond to our measurement of a single wavelength of 1.4 nm (precise matching is not expected as a result of the different molecular structures present). If this is the case, then together the AFM and SFB results complement each other and lead to a deeper understanding of the WiS structure.

Although λ o varies only by a small amount over the concentration range studied, the mechanism of the squeeze-out process appears to change more substantially. As concentration is increased, the force required to overcome the repulsive energy barrier and induce a layering transition also increases. Alongside this, compression within layer i = 2 increases (Figure 3c). Whilst some part of this compression may arise within the mica layer, [START_REF] Espinosa-Marzal | Hydrated-ion ordering in electrical double layers[END_REF][START_REF] Lhermerout | The influence of mechanical deformations on surface force measurements[END_REF] under the loads and mica thicknesses considered here, mica compression is unlikely to be responsible for the full effect observed. This suggests that under the high forces required to induce a layering transition, some reversible structural reorganisation can take place within the layers to reduce their thickness before the irreversible transition takes place. Such a reorganisation could occur via a dehydration within the hydrated cation domain, or by a a compression within the non-aqueous anion domain, resulting in a more compressed layer.

The squeeze-out of this modified layer is responsible for the small jump to the final layer, ∆J 2-1 , observed at the highest concentration investigated.

The position at which the closest surface layer is first encountered varies with ion concentration. At 5 m the closest layer is observed at 2.1 nm, however at 8 m and 12 m this decreases to ≈ 0.5 nm. This variance likely corresponds to a changing mica surface charge with concentration. It is well known that potassium ions can be dissolved from mica sheets immersed in a dielectric liquid, leaving a negative charge on the surface. While the K + ions occur at such low concentration in the solution as to not affect the structure, the negative charge left on the surface can modify the ion ordering in the adjacent liquid. Potassium ion dissolution will happen to a greater extent at higher dielectric permittivities of solution, i.e. lower ion concentration, hence it is expected that the highest surface charge occurs at the lowest ion concentration studied. At the lowest concentration, the high surface charge means that the attraction between the surfaces and the adjacent layers is greater and therefore requires more force to overcome. The 2.1 nm distance observed is close to the dimensions of one oscillatory wavelength with a second hydrated cation domain, and we suggest that such a structure is held tightly enough to the surfaces to persist under the loads applied in this measurement. At the highest concentrations, the distance corresponds well to the diameter of a single hydrated cation domain that is able to neutralise the surface charges of both mica surfaces.

The insets of Figure 2 show the existence of a long range exponentially decaying monotonic force with an exponential decay length λ s . This force is similar in appearance to the screening of charge within Debye-Hückel theory, however, the concentration regime in which we observe this screening is substantially higher than can be accounted for by considering a continuum theory approach. Instead we attribute this force to the recently observed underscreening phenomenon, which has been seen in ionic liquids [START_REF] Smith | The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration[END_REF]38,[START_REF] Gebbie | Long range electrostatic forces in ionic liquids[END_REF] and concentrated solutions of simple salts. [START_REF] Smith | The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration[END_REF][START_REF] Gaddam | Electrostatic Screening Length in Concentrated Salt Solutions[END_REF] The exponential decay length of the underscreening force increases with increasing concentration from λ s = 8.3 nm at 7.78 m to λ s = 11.5 nm at 11.64 m (at 5 m the decay length is obscured by thermal drift in the experiment). These values of λ s are of the same order as those observed previously in other concentrated electrolyte systems, and the observed increase of λ s with concentration is consistent with previous reports of underscreening, [START_REF] Smith | The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration[END_REF][START_REF] Gaddam | Electrostatic Screening Length in Concentrated Salt Solutions[END_REF] however direct quantitative comparison of screening lengths is not meaningful until a theory incorporating strong assymetry of ion diameter emerges.

In summary, we have performed the first direct surface force measurements of aqueous solutions of the WiS electrolyte LiTFSI. We find that the system behaves differently to aqueous solutions of simple salts, showing well defined layers and long range screening forces similar to those observed in ionic liquids. They remain distinct from ionic liquids however, with surface forces dominated by a self-assembled nano-structure with a characteristic length scale > 1 nm, suggesting the existence of large and separated cation and anion rich domains at charged surfaces. This result has interesting implications for the nature of WiS ion transport to the electrode, and will be important in future research to improve the efficacy of WiS electrolyte based electrochemical storage devices.

Figure 1 :

 1 Figure 1: (a) Schematic of the SFB and interferometric cavity. (b) Approximate dimensions of the lithium-water primary hydration shell and TFSI anion, calculated from neutron scattering experiments 19 and Van der Waals radii. 20 (c) Phase diagram of the H 2 O -LiTFSI system adapted from a work by Ding et al. 21 with the concentrations of the experiments detailed in this work shown by yellow circles. I = L + (H 2 O) 4 LiTFSI (s) , II = L + LiTFSI (s) , where L is a liquid solution.

Figure 2 ,

 2 Figure 2, normalised by the contact spot radius R (measured in situ for each spot) to allow for quantitative comparison between different measurement spots, experiments and experimental geometries as described by the Derjaguin approximation, F N (D)/R = 2πW ll (D), where W ll (D) is the interaction free energy between two parallel plates separated by a distance D.At each concentration we observe a clear oscillatory force profile characterised by a series of repulsive walls extending to ≈ 7 nm surface separation. Retraction of the surfaces from each wall reveals an adhesive well. The force required to overcome each wall increases as surface separation decreases, similarly the force required to escape each well increases as the surface separation decreases. Forces can only be measured along the gradient of the spring constant (∼120 Nm -1 ) hence regions of the force profile between the maxima of layer i and the minimum of layer i-1 are inaccessible in our measurement and instead jumps are observed between repulsive walls and from adhesive wells. These results are substantially different from those measured in simple dilute aqueous electrolytes, where the DLVO theory holds at the lowest concentrations measured with only small deviations close to contact as the concentration is increased due to the formation of a

Figure 2 :

 2 Figure 2: Force profiles measured at three concentrations of aqueous LiTFSI, normalised by the radius of the contact spot. (a) 4.70 m. (b) 7.78 m. (c) 11.64 m. Forces measured on approach are shown in blue, and those on retraction in yellow. Layers are labelled from i = 1 at closest approach as shown in (a) and (c), compressions ∆C i within layers and jumps ∆J i-(i-1) between layers are defined in the example in (b), while oscillatory wavelength λ o is defined by linearly fitting minima positions and is shown in the example in (c) and in the Supporting Information. Small changes in the optical path can lead to an error in the absolute surface separation of up to 1 nm, so runs have been shifted relative to the first approach on the first measurement spot in each case. Beyond the oscillatory force regime there is an exponentially decaying force, shown in the insets, with decay length λ s = 8.3 nm at 7.78 m and λ s = 11.5 nm at 11.64 m. At 4.70 m, this force is obscured by thermal drift. The greater line-width in panel (b) for 7.78 m is a result of thicker mica in that experiment. This can also introduce a small difference between F (D)/R at the highest loads (smallest distances) when comparing between concentrations due to differences in contact mechanical stiffness. For this reason, we do not draw physical significance from the slight difference in closest separation between the 7.78 m and 11.64 m concentrations.

Figure 3 :

 3 Figure 3: Layering data from aqueous LiTFSI. (a). Oscillatory wavelength λ o as a function of molal concentration, defined by a linear fit of jump out positions. (b). Jump distances ∆J i-(i-1) as a function of molal concentration of sample measured on approach. (c). Compressions ∆C i within layers as a function of molal concentration as measured on approach. Examples of all quantities are shown in Figure 2.

  (a)). They attribute this to a 'solvent disproportionation', in which the liquid is sep-arated on the nanoscale into a hydrated cation-rich Li + (H 2 O) 4 domain, and a non-aqueous anion-rich Li + (TFSI -) x>1 domain. The SFB data presented here provides clear evidence for the existence of such a solvent-separated nanostructure at charged interfaces, which will have important consequences for the capacitance properties and behaviour of aqueous LiTFSI at electrode surfaces.

Figure 4 :

 4 Figure 4: A cartoon representation of ion structure over two oscillatory wavelengths. Ions are separated into hydrated cation and non-aqueous anion rich domains. The oscillatory wavelength is the sum of the breadth ot the two domains.

Table 1 :

 1 Concentrations investigated in this study in molality, molarity, and water to salt ratio. 5 m represents the lower limit of the water-in-salt regime for this system. Densities are from a work by Han.[START_REF] Han | Anionic effects on the structure and dynamics of water in superconcentrated aqueous electrolytes[END_REF]

	(b). Solutions of

Acknowledgement

This research was funded by grants from The European Research Council (under Starting Grant No. 676861, LIQUISWITCH) and The Leverhulme Trust (RPG-2015-328).

Supporting Information Available

Additional details on the methods and data collection and analysis process


Romain Lhermerout

Susan Perkin

A new methodology for a detailed investigation of quantized friction in ionic liquids †

When confined at the nanoscale between smooth surfaces, an ionic liquid forms a structured film responding to shear in a quantized way, i.e. with a friction coefficient indexed by the number of layers in the gap. So far, only a few experiments have been performed to study this phenomenon, because of the delicate nature of the measurements. We propose a new methodology to measure friction with a Surface Force Balance, based on the simultaneous application of normal and lateral motions to the surfaces, allowing for a more precise, comprehensive and rapid determination of the friction response. We report on proof-of-concept experiments with an ionic liquid confined between mica surfaces in dry or wet conditions, showing the phenomenon of quantized friction with an unprecedented resolution. First, we show that the variation of the kinetic friction force with the applied load for a given layer is not linear, but can be quantitatively described by two additive contributions that are respectively proportional to the load and to the contact area. Then, we find that humidity improves the resistance of the layers to be squeezed-out and extends the range of loads in which the liquid behaves as a superlubricant, interpreted by an enhanced dissolution of the potassium ions on the mica leading to a larger surface charge. There, we note a liquid-like friction behavior, and observe in certain conditions a clear variation of the kinetic friction force over two decades of shearing velocities, that does not obey a simple Arrhenius dynamics. 38 In this paper, we present a new methodology to measure fric-39 tion in the boundary lubrication regime with a SFB. The principle 40 consists in applying normal and lateral motions simultaneously -41 instead of alternatively-to the solid surfaces, allowing for a more 42 precise, comprehensive and rapid determination of the friction-43 load relationship. First, we validate the method by measuring the 44 J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,

Introduction

Lubrication consists in inserting a substance -generally a liquidbetween two solid surfaces in order to produce a controlled and stable friction. Its study is an old but still active field of research, because of the complexity of the phenomena at play [START_REF] Bowden | The Friction and Lubrication of 755 Solids[END_REF]2 . As most real surfaces are rough, the contact between two macroscopic bodies involve in fact many mesoscopic asperities. A first consequence is that very large pressures, shear stresses and temperatures can be reached locally to promote tribological processes like wear, phase transitions or (electro)chemical reactions, making the role of the lubricant really challenging. A second consequence is that the lubricant should act at different scales simultaneously: for thick films, friction is governed by continuum hydrodynamics and depends on the lubricant viscosity (hydrodynamic regime); for thin films, friction is determined by subtle mechanisms at the molecular scale and depends on the lubricant chemical structure and its interactions with the solid surfaces (boundary lubrication regime). Ionics liquids, which are pure salts that are liquid at ambient temperature and pressure, are promising lubri-Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, UK. E-mail: romain.lhermerout@chem.ox.ac.uk; susan.perkin@chem.ox.ac.uk † Electronic Supplementary Information (ESI) available. See DOI: 00.0000/xxxxxxxxxx/ cants thanks to their unique physico-chemical stability [START_REF] Lhermerout | [END_REF] . During 21 the last decade, many experiments with a Surface Force Appa-22 ratus/Balance (SFA/SFB) or an Atomic Force Microscope (AFM) 23 have been performed to measure the normal interactions on a 24 single asperity across an ionic liquid. They consistently showed 25 the presence of a structural force, i.e. a force profile exhibiting a 26 decaying oscillation, that has been attributed to the ordering of 27 ions in the confined film, with a structure consisting of alternat-28 ing layers of anions and cations (as sketched in Figure 1(a)) [4][5][6][7][8][9][10][11][12] .

29

Only a few studies have been conducted to measure the friction 30 response in such structured film of ionic liquid, reporting on the 31 phenomenon of "quantized friction", namely the fact that the fric-32 tion coefficient is indexed by the number of layers composing 33 the film 7,10,[13][14][15][16][17][18] . Although the presence of such exotic behavior and is known with an uncertainty of ∼ 0.01 cm (mainly caused by the fact that the separation profile between the surfaces is observed up to a maximum scale ∼ 50 nm R ∼ 1 cm). The contact radius a is measured with a precision of 0.03 µm given by the standard deviation of the signal, and an accuracy of 1 µm due to the uncertainty on the value of R, following a procedure explained in details in 23 .

The top surface can be moved normally with a stepper motor (large displacement range ∼ 10 µm, poor linearity, mechanical vibrations induced), and also normally and laterally thanks to a sectored piezoelectric tube (small displacement range ∼ 1 µm, good linearity, no measurable mechanical vibrations induced).

For a given run, the velocity v can be determined with a precision of ∼ 1%. From run to run, this velocity can typically vary by ∼ 10% for the same control parameters, because of thermal drifts. In the following, some graphs result from the superposition of several runs, that is why the indicated velocities have to be associated with an error bar of ∼ 10%. The bottom lens is mounted on two springs: a normal (resp. lateral) spring of

constant k N = 2670 ± 84 N/m (resp. k L = 379 ± 2 N/m), which
is calibrated before the experiment by measuring its deflection (resp. its resonance frequency) when adding different masses.

The normal force F N is deduced from the temporal evolution of the distance D(t) when applying a constant normal velocity v N to the top surface, using a procedure that takes into account the viscous force that is not negligible at large separations (detailed in 22 ). The lateral force F L is directly measured with a capacitance probe when applying a constant lateral velocity v L to the top surface, with a sensitivity of ∼ 10 -3 mN. In comparison to previous studies performed in our group, the normal spring is here about 20 times stiffer, in order to apply larger loads (at fixed displacement range). Together with the stepper motor, it enables the identification of the first layer consisting of a monolayer of cations (labelled i = 1, as sketched in inset of Figure 2(a)), and the assessment of the resistance of the liquid to be squeeze-out under very large pressures. Together with the sectored piezoelectric tube, it enables one to reach the first layer of ions and so to explore the whole friction-load relationship with the new methodology (procedure detailed in next subsection). This comes with a price in terms of sensitivity limit for the normal force, ∼ 10 -2 mN, which does not allow the detection of the anomalously long-range electrostatic force that has been observed with concentrated electrolytes 11,22,25,[28][29][30][31][32][33][34] .

The SFB is therefore a tool of choice to study the molecular mechanisms of friction: the two atomically-smooth surfaces are in contact on a single asperity (pure boundary lubrication regime), the apical distance D is measured with a resolution better than the molecular scale, and the geometry can be characterized insitu (radius of curvature R, contact radius a). In the literature, the measured normal force F N is generally rescaled by the radius of curvature R to compute an equivalent surface energy F N /R, considering that mechanical deformations are negligible and that the Derjaguin approximation applies [START_REF] Israelachvili | Intermolecular and Surface Forces[END_REF] . In the opposite case when the surfaces are strongly flattened, it is reasonable to assume that the total force F N is mainly due to the interaction ion the flattened region, and so to rescale it by the contact area πa 2 to compute the local pressure F N /(πa 2 ). In this study, we explore a broad range the molecules passing each other [43][44][45][46][47][48] . For the experiments re- with M the molar mass of the ionic liquid, ρ its bulk density and N A the Avogadro's number 4 ), perhaps suggesting a denser packing of ions in confinement than in the bulk. However, our value is also smaller than the previous measurements performed with the same ionic liquid, reporting a mean layer thickness of 0.80 ± 0.04 nm between two mica surfaces with a SFB 53 and 0.79 nm between a mica surface and a Si 3 N 4 tip with an AFM 54 . A possible explanation for this difference is the inherent contribution from viscosity to the force profile, in particular in vicinity to a spring instability. For the method using the distances D min i at the points of minimum force (giving a mean layer thickness of 0.64 ± 0.05 nm), viscosity tends to move the minima towards larger distances, even more than adhesion is larger (i.e.

smaller layer index i). For the method using the jump-in distances (giving a mean layer thickness of 0.64 ± 0.01 nm), viscosity tends to reduce the size of the jumps. In both cases, viscous effects possibly lead to an underestimation of the mean layer thickness. Previous studies may be less affected by viscosity, as retractions were performed by slow steps in the SFB study 53 (with similar radius of curvature), and the radius of curvature was six orders of magnitude smaller in the AFM study 54 (with a velocity less than an order of magnitude larger). Therefore, applying a stepped motion is preferable to a continuous motion in order to accurately determine the mean layer thickness.

An important aspect to interpret the structural force profiles is to identify the composition of the layers. As the period is similar to the mean ion pair diameter, it is qualitatively considered that one squeeze-out event corresponds to the squeeze-out of an electroneutral "slab" of one cation layer and one anion layer. In the case of negatively charged surfaces, the first layer (i = 1) is then assumed to be composed of a monolayer of cations (as sketched in

F max i = F max 0 exp -i λ max ζ max , ( 3
)
where the slope gives access to the ratio fit the friction-load relationship in layer i = 1 with the following empirical law:

F L,k = µ i × F N -F min i + σ c,i × π R K 2/3 F N -F min i 2/3 , (4)
where µ i , σ c,i and F min To summarize, the measured friction-load relationship can be described quantitatively with an empirical law, providing that two additive contributions are included, the first proportional the load and the second proportional to the contact area. In the previous 502 experimental studies of quantized friction across ionic liquids, the 503 friction-load relationship was found to be compatible with a lin-504 ear variation (i.e. a load-controlled friction), given the scattering 505 on the data points 13,15 . It is thanks to the new methodology that i.e friction is quantized. However, the lateral force is above the 581 sensitivity limit for three layers, instead of two for the dry case. coefficient is µ 2 = 0.035 ± 0.001, i.e. the film composed of two cations layers plus one anions layer is almost a superlubricant.

For layer i = 1 (retraction branch in faded blue), the friction coefficient is µ 3 ∼ 1.9, i.e. the film composed of a monolayer of cations is a poor lubricant. Note that retraction from layer i = 1

has been performed at a relatively large velocity, so the value of µ 1 is estimated with only a few shearing periods. Supplementary

Figure 2 shows the friction-load relationship that has been measured in a larger range of loads for layer i = 2, by approaching the surfaces by discrete steps with the stepper motor. Similarly to the dry case, a good fit can be achieved with equation 4, providing that the two contributions are included, the first proportional to the load and the second proportional to the contact area (with {µ 2 = 0.0129 ± 0.003, σ c,2 = 56 ± 2 kPa, F min 2 = -0.06 mN}).

Overall, humidity is found to strongly increase the resistance of the layers to be squeezed-out, without changing significantly their corresponding thicknesses and friction coefficients. Consequently, it leads to an extension of the range of loads in which the liquid behaves as a superlubricant. Such beneficial effect of water on the lubricating performances is extremely interesting for applications, given that ionic liquids are hygroscopic and that lubricated systems are never perfectly insulated from ambient moisture.

Kinetics aspects

In this subsection, we consider the influence of the shearing velocity on the friction force. Supplementary Figure 5 shows the friction-load relationships measured in dry conditions at v L = 652 nm/s and v L = 67.9 nm/s. No clear trend is found within the experimental errors, whether in layer i = 1 or in layer i = 2. was explored at only one shearing velocity. In layer i = 2, however, the friction clearly depends on the shearing velocity. More precisely, the kinetic friction force goes to zero at the same adhesion minimum in both cases, but with a friction coefficient that is larger with the largest shearing velocity. These observations are consistent with previous SFB experiments performed with the same ionic liquid in our group, showing that in dry conditions the kinetic friction is independent of the shearing velocity in the range v L ∈ [200; 1000] nm/s, whatever the layer considered 15 . Our findings are also comparable with previous colloidal probe AFM experiments performed with protic ionic liquids (ethylammonium nitrate (EAN), propylammonium nitrate (PAN), ethylammonium formate (EAF), etc.) between a silica sphere (R ∼ 10 µm) and a mica surface, reporting on an increase of the friction coefficient with the shearing velocity in the range v L ∈ [5000; 40000] nm/s, for some particular film compositions 13,14,16 . However, it is not clear why a dependence of the shearing velocity on the friction force is found or not, depending on the physico-chemical system and the layer considered.

To investigate this dynamics quantitatively, we have sheared the liquid under constant conditions in the normal direction, exploring two decades of lateral velocities. 653

In friction experiments between smooth surfaces, dynamics is 654 generally found to be thermally-activated, i.e. obeying an Arrhe-655 nius law of the form:

656 F = F 0 ln v v 0 . (5)
Qualitatively, such thermally-activated dynamics is associated 657 with the picture of molecules that must overcome energy barri- apolar liquids or aqueous electrolytes with a SFA 68,69 , between 665 mica surface and silicon colloid across protic ionic liquids with a 666 colloidal probe AFM 13,14,16 ). We have fitted our data with equa-

F = Av n , (7)
This model also fits reasonably our data (blue curve in

Conclusions

In this paper, we have presented proof-of-concept experiments for a new methodology to measure friction in the boundary lubrication regime with a SFB. By applying simultaneous normal and lateral motions to the surfaces, the friction-load relationship can be measured more precisely, comprehensively and rapidly. The quality achieved opens the way to more quantitative investigations to relate friction, load, contact area, adhesion and shearing velocity, while the efficiency and the versatility of the method allow for efficient probing of various physico-chemical systems. Using ionic liquids as a proof-of-concept, we have measured the phenomenon of quantized friction with an unprecedented resolution. Contrary to the existing studies in the area, we have found (i) a liquid-like friction behavior; (ii) a variation of the kinetic friction force with the applied load that is not simply linear, but can be quantitatively described by two additive contributions proportional to the load and to the contact area; (iii) a dynamics over two decades of shearing velocities that does not obey a simple Arrhenius law, appealing for more sophisticated models of friction kinetics. Furthermore, we have observed that humidity can improve the lubrication performances of ionic liquid, by increasing the resistance of the layers to be squeezed-out and so extending the range of loads in which the liquid behaves as a superlubricant.

The results presented in this study raise a number of questions, listed below, that would require dedicated experimental investi-

34 is

 34 now well-established experimentally, the fundamental mech-35 anisms responsible for it are still debated. These outstanding 36 questions motivate further detailed experimental investigations 37 of quantized friction. phosphorus pentoxide (Sigma-Aldrich, 99%), in the chamber and 77 purging the chamber with N 2 , nitrogen, for about one hour prior 78 to the calibrations. The undeformed mica thickness e mica,0 = 79 7.431 µm is determined when the surfaces are in direct contact, 80 following a procedure detailed in 23 . Secondly, measurements 81 are performed with an ionic liquid, [C 4 C 1 Pyrr][NTf 2 ], 1-butyl-82 1-methylpyrrolidinium bis[(trifluoromethane)sulfonyl]imide (Io-83 litec, 99%), which chemical structure and sizes are indicated 84 in Figure 1(b) (molar mass M = 422.41 g/mol, density ρ = 85 1.405 g/mL, refractive index n = 1.422 and dynamic viscosity 86 η = 74 mPa.s at 25 • C 24 ). This liquid is hygroscopic, and we use 87 it either in dry or wet conditions. Dry conditions are achieved by 88 drying the liquid in a Schlenck line at 60 • C and 5 × 10 -3 mbar for 89 ∼ 10 hours and by inserting it in the chamber just after, which 90 contains P 2 O 5 and is purged again with N 2 for about one hour 91 prior to the measurements. Such procedure is known to produce 92 water content typically 100 ppm 11,15,25 . Wet conditions are 93 achieved by simply letting the ionic liquid equilibrate with am-94 bient atmosphere during several days before the experiment and 95 by inserting it in the chamber, which does not contain any desic-96 cant and is filled with ambient air. In this case, the water content 97 corresponds to the thermodynamic equilibrium of the ionic liquid 98 with ambient humidity (∼ 50%). 99 White light is passed through the confined medium, interferes 100 in this optical resonator, and is then directed towards a spec-101 trometer and collected by a CCD camera. The analysis of the 102 Fringes of Equal Chromatic Order (FECO) then allows one to de-103 duce the apical distance D, the contact radius a (when the sur-104 faces are flattened) and the radius of curvature R 26 . In a sep-105 arate paper 23 , we show that the mica can be significantly com-106 pressed and that D incorporates the variations of thicknesses of 107 the mica layers and of the liquid film, i.e the materials separating 108 the two silver mirrors. For small changes of D, it is not possible 109 to disentangle the contributions coming from the mica (indenta-110 tion 2e mica,0 -2e mica = 2δ e mica , defined positive for compression 111 and negative for dilatation) and the liquid (thickness D liquid ) with 112 the FECO. In fact, we effectively measure the distance between 113 the silver mirrors D mirrors = D liquid + 2e mica , from which we sub-114 tract the undeformed mica thickness 2e mica,0 calibrated in dry at-115 mosphere, to finally obtain: 116 D = D mirrors -2e mica,0 = D liquid -2δ e mica . (1) D is measured with a precision of 0.02 nm given by the standard 117 deviation of the signal, and an accuracy of 1 nm due to light dis-118 alignment when changing the contact spot 27 . As the glue thick-119 ness is heterogeneous, the top mica surface has a different curva-120 ture than the bottom glass lens, which has to be measured every 121 time the contact spot is changed. The radius of curvature R asr n a l N a me , [ y e a r ] , [ v o l . ] , sociated to each measurement is indicated in the figure caption,

223

  ported in this paper, we ruled out these artefacts by systematically 224 checking that the normal force profile is the same with a zero and 225 non-zero lateral velocity (see Supplementary Figure1), and that 226 the friction-load relationship is the same with a zero and non-zero 227 normal velocity (see Supplementary Figure2).

228JFig. 2

 2 Fig. 2 Measurements for dry [C 4 C 1 Pyrr][NTf 2 ] (R = 0.92 cm). (a) Normal force profile when moving the top surface with the piezoelectric tube at a normal velocity v N = 0.5 nm/s and a lateral velocity v L = 652 nm/s, showing structuring with 5 distinguishable layers labeled by i. For clarity, only the full approach is shown (in red), together with retractions from layers i = 1 (in blue), i = 2 (in green), i = 3 (in orange), i = 4 (in purple), i = 5 (in yellow). Inset: proposed structure of alternating layers of cations and anions. (b) Normal force profile when approaching (in faded red) or retracting (in faded blue) the top surface with the stepper motor at v N = 10.5 nm/s. Negative distances D are reached at large loads, because the compression of mica exceeds the liquid thickness: D = D liquid -2δ e mica < 0 23 .. The curves measured on approach and retraction in layer i = 1 are not perfectly superimposed because of mechanical imperfections of the set-up (poor linearity of the stepper motor, tiny rotations of the solids, etc.). (c) Distances D min i at the points of minimum force, as a function of the layer index i, in lin-lin representation (in blue); forces F max i at the points of maximum force, as a function of the layer index i, in log-lin representation (in red). Straight lines are the corresponding linear and exponential fits (equations 2 and 3).

230

  We begin with presenting measurements of the normal interac-231 tion force. Figure2(a) shows the normal force profile obtained 232 when moving the top surface with the piezoelectric tube at a nor-233 mal velocity v N = 0.5 nm/s and a lateral velocity v L = 652 nm/s 234 across dry [C 4 C 1 Pyrr][NTf 2 ]. When the ionic liquid is confined 235 at the nanoscale, a structural force profile is observed, with five 236 distinguishable layers labeled by i. Such structural force has been 237 observed many times with ionic liquids, and attributed to the or-238 dering of ions in the film, with a structure consisting of alternating 239 layers of anions and cations (as sketched in inset) 4-12 . Because 240 of the spring instability, the surfaces experience a jump-in on ap-241 proach every time a layer is squeezed-out, and a jump-out on 242 retraction from a given layer. Therefore several runs were in fact 243 necessary for the most comprehensive exploration of the force 244 profile. Supplementary Figure 3 shows the force profiles mea-245 sured when approaching the top surface up to a given layer and 246 retracting from this layer. From run to run, the whole force pro-247 file randomly shifts laterally by a fraction of nanometer. As the 248 jump-in distances and the forces are reproducible, we consider 249 that these shifts are non physical, but result from imperfections 250 of the set-up like tiny rotations of the solids. That is why we have 251 shifted manually the force profiles such that all the approaches 252 are superimposed on the approach up to layer i = 1 (in red). Fig-253 ure 2(a) shows the resulting force profile, with for clarity only the 254 approach up to layer i = 1 (in red), and the retractions from the 255 different layers (i = 1 in blue, i = 2 in green, i = 3 in orange, i = 4 256 in purple, i = 5 in yellow).257In a separate paper23 , we show that the oscillation due to lo-258 cal variations of liquid density in the confined film is in general 259 convoluted with the mechanical response of the confining solids. 260 For the system studied here, we found that (i) mica compression 261 dominates liquid compression, i.e. the change of D within each 262 layer is mainly due to the indentation of mica; (ii) contact me-263 chanics is well described by the Derjaguin-Muller-Toporov (DMT) 264 model 19,49-52 , in particular the indentation of the solids is zero at 265 the minimum force (jump-out point) and continuously increases 266 up to the maximum force (jump-in point). For each layer i, we 267 have measured the distance D min i at the point of minimum force 268 (jump-out, as indicated in Figure 2(a) for i = 2), which does not 269 include any influence of the mica compression. The variation of 270 the distance D min i with the layer index i is shown in Figure 2(c), 271 and exhibits a good linearity. It is fitted with the relation: λ min = 0.64 ± 0.05 nm represents the mean layer 273 thickness and the intersect D min 0 = 1.6 ± 0.1 nm corresponds to the 274 position of the extrapolated layer i = 0. Another method con-275 sists in measuring the average jump-in distance, supposing an 276 unchanged mica compression and a fast viscous relaxation dur-277 ing the squeeze-out events, and providing a consistent value of 278 0.64 ± 0.01 nm for the mean layer thickness. Interestingly, this 279 value is smaller than the mean ion pair diameter of 0.79 nm (given 280 4 | 1-12 J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,

  inset of Figure 2(a)). Direct solid-solid contact is never reached, because of the strong electrostatic attraction between the cations and the negatively charged surfaces. For our experiment, one can ask whether we really reach this single layer of cations within the explored range of loads. The position of the first layer at the point of minimum force (including no indentation of the surfaces) is D min 1 = 2.2 ± 1.0 nm, a bit larger than the cation sizes (given in Figure 1(b)). However, the measurement of the absolute distance D depends on many delicate steps (alignment of the optics, calibration of the mica thickness in dry atmosphere, choice of a particular run to shift the force profiles laterally), and deducing the thickness of the monolayer from the cation sizes requires to know their conformations, making accurate comparisons difficult. For each layer i, we have measured the force F max i at the point of maximum force (jump-in, as indicated in Figure 2(a) for i = 2). The variation of the distance F max i with the layer index i is shown in Figure 2(c) in log-lin representation, and exhibits a good linearity. It is fitted with the relation:

Fig. 3 F max 0 = 4 . 8 i = 1 .

 30481 Fig. 3 Measurements for wet [C 4 C 1 Pyrr][NTf 2 ] (R = 1.45 cm), at fixed load F N = 2.79 mN, distance D = -1.05 nm (where D = D liquid -2δ e mica < 0) and contact radius a = 12.86 µm in layer i = 2. Temporal evolutions of the lateral displacement x L and lateral force F L , showing a liquid-like friction behavior. Inset: zoom on a part of the signal, delimited by a gray rectangle in the main graph. The tiny oscillation is due to the resonance of the mass-spring system at ∼ 20 Hz.

356 3 . 2

 32 Lateral force 357In this subsection, we identify the nature of the friction response, 358 by analyzing the shape of the lateral force when the liquid film 359 is sheared under constant conditions in the normal direction.

  360

Figure 3

 3 Figure3shows the temporal evolutions of the lateral displace-361

405 3 . 3 Friction-Load relationship 406 1 Fig. 4 1 = 1 = 1 =

 3340614111 Fig. 4 Measurements for dry [C 4 C 1 Pyrr][NTf 2 ] (R = 0.92 cm), when moving the top surface with the piezoelectric tube at a normal velocity v N = 0.5 nm/s and a lateral velocity v L = 652 nm/s. (a) Temporal evolution of the apical distance D on full approach. The inset shows the temporal evolution of the lateral force F L during the squeeze-out transition from layer i = 2 to layer i = 1. (b) Kinetic friction F L,k as a function of load F N on full approach (in red) then retraction from layer i = 1 (in blue). Friction is above the sensitivity limit for the layers i = 1 and i = 2 (proposed film structures in insets). Straight lines are fits with the left-hand term of equation 4, with {µ 1 = 0.210±0.003, F min 1 = -0.12±0.01 mN} and {µ 2 = 0.0064±0.0006, F min 2 = -0.062±0.008 mN}. The dotted line is a fit for layer i = 1 with the right-hand term of equation 4, with {σ c,1 = 857 ± 6 kPa, F min 1 = -0.06 mN}. The dashed line is a fit for layer i = 1 with the whole equation 4, with {µ 1 = 0.092 ± 0.004, σ c,1 = 529 ± 13 kPa, F min 1 = -0.06 mN}.

iF min 1 = 1 =F min 1 = 1 =

 1111 are respectively the friction coefficient, critical shear stress and adhesion force associated with layer i.This equation gives FL,k = 0 at F N = F min i, which is in agreement with our systematic observation that the friction force goes to zero at the jump-out point. If we suppose first that friction is purely load-controlled and we fit with the left-hand term of equation 4 only (straight line in Figure4(b)), we get {µ 1 = 0.210 ± 0.003, -0.12 ± 0.01 mN} (two free parameters). The fit is clearly not satisfactory and overestimate the adhesion force (compared to the directly measured F min -0.06 mN), because it does not describe the significant concave curvature that is observed experimentally. If we suppose on the contrary that friction is purely contact area-controlled and we fit with the right-hand term of equation 4 only (dotted line in Figure4(b)), we get {σ c,1 = 857±6 kPa, -0.06 mN} (one free parameter, the adhesion force being fixed). The fit is much better in the vicinity of the adhesion minimum, but now overestimates the concavity of the curve. In fact, the experimental data lie in between the two previous fits, and if we fit with the full equation 4 (dashed line in Figure4(b)), we obtain a very good fit with {µ 1 = 0.092 ± 0.004, σ c,1 = 529 ± 13 kPa, F min -0.06 mN} (two free parameters, the adhesion force being fixed).

506 3 . 4 [C 4 C 1

 3441 we are able to measure the friction-load relationship with an un-507 precedented resolution, and to quantitatively test the different 508 empirical laws of friction. This is crucial not only for a better 509 understanding of the physics of friction in general, but also to ex-510 tract quantities µ and σ c that are intrinsic to the physico-chemical 511 system used and not affected by the particular geometry of the ex-512 periment. Unfortunately, such high-resolution measurements are 513 not always possible, for example when friction is small or varies 514 slowly, or cannot be measured on a wide range of loads (like for 515 layer i = 2 in Figure 4(b)). However, we note that the differ-516 ent fits in layer i = 1 provide friction coefficients of same order 517 of magnitude. That is why we have decided to fit linearly the 518 friction-load relationships measured with a low resolution, as a 519 semi-quantitative evaluation of the lubrication performances. 520 Effect of humidity 521 In this subsection, we present an experiment performed with wet 522 Pyrr][NTf 2 ], illustrating the versatility and the efficiency of 523 the new methodology. The measurements, shown in Figure 5, are 524 qualitatively similar to the dry case, in the sense that we also ob-525 serve a structural force profile, a liquid-like friction behavior, and 526 a quantized friction-load relationship. But important differences 527 emerge when comparing the results quantitatively.

Figures 5 (Fig. 5 3 = 3 =Figure 5

 55335 Figures 5(a) and 5(b) show the normal force profile obtained

  580

582

  In layer i = 3 (retraction branch in orange), the friction coeffi-583 cient is µ 1 = 0.002 ± 0.001, i.e. the film composed of three cations 584 layers plus two anions layers behaves as an extremely good super-585 lubricant. In layer i = 2 (retraction branch in green), the friction r n a l N a me , [ y e a r ] , [ v o l . ] ,

Figure 5 (

 5 Figure 5(c) shows the friction-load relationships measured in wet conditions at v L = 613 nm/s and v L = 148 nm/s. In layer i = 3, no clear trend is found within the experimental errors, and layer i = 1

  Figure 6(a) shows the lateral force F L as a function of the lateral displacement x L when shearing wet [C 4 C 1 Pyrr][NTf 2 ] at different velocities v L ∈ 641 {32; 128; 639; 1918; 3197} nm/s (with same displacement range), 642 at fixed load F N = 2.79 mN, distance D = -1.05 nm (where 643 D = D liquid -2δ e mica < 0) and contact radius a = 12.86 µm in 644 layer i = 2. A liquid-like friction behavior is obtained for all 645 the friction loops, but with a kinetic friction force that increases 646 monotonically with the the shearing velocity. Finally, Figure 6(b) 647 shows the kinetic friction force F L,k as a function of the lateral ve-648 locity v L , in lin-log representation (Supplementary Figures 6(a) 649 and 6(b) show the same data, respectively in lin-lin and log-log 650 representations). The dynamics is strongly non-linear, and is in-651 terpreted with different models of friction kinetics in the follow-652 ing.

658

  ers in order to pass each other, with the external force inducing 659 a potential biais and with the temperature allowing for the cross-660 ing of non-zero barriers. It has been observed for dry friction 661 (between Langmuir-Blodgett films with a SFA 66 , between a NaCl 662 surface and a silicon tip with an AFM 67 ), as well as for lubricated 663 friction in the boundary regime (between mica surfaces across 664

667 tion 5 ( 679 F = F c -∆F ln v c v 2/ 3 . ( 6 )Fig. 6

 5679366 Fig. 6 Measurements for wet [C 4 C 1 Pyrr][NTf 2 ] (R = 1.45 cm), at fixed load F N = 2.79 mN, distance D = -1.05 nm (where D = D liquid -2δ e mica < 0) and contact radius a = 12.86 µm in layer i = 2. (a) Lateral force F L as a function of lateral displacement x L , for different lateral velocities v L ∈ {32; 128; 639; 1918; 3197} nm/s respectively in blue, purple, red, orange and yellow. The bumps on the signals, particularly visible for the blue curve, are due to external vibrations that are not totally suppressed by the damping elements of the SFB. (b) Kinetic friction F L,k as a function of lateral velocity v L , in lin-log representation. The red curve is a fit with equation 5 giving {F 0 = (23 ± 4) • 10 -3 mN, v 0 = 18 ± 10 nm/s}. The green curve is a fit with equation 6 giving {F c = 0.13 ± 0.02 mN, v c = (3.4 ± 1.5) • 10 3 nm/s, ∆F = (36 ± 7) • 10 -3 mN}. The blue curve is a fit with equation 7 giving n = 0.30 ± 0.02.

Fig- ure 6

 6 (b)), with an exponent n = 0.30 ± 0.02 close to the reported value of 1/3. Therefore, these measurements of the friction force over two decades of shearing velocities allow us to unambiguously reject a description of the friction kinetics by an Arrhenius law, but not to discriminate between the modified Arrhenius law and the empirical power-law.

.2 New Methodology for friction measurement 184

	180
	181	of situations from no deformation to strong deformations, that is
	182	why we have chosen to simply use the force F without any rescal-
		ing in the plots.
	185	So far, friction measurements with the SFA/SFB or the AFM were
	186	performed by applying normal and lateral motions alternatively:
	187	the surfaces were approached/retracted at a given distance un-
	188	der a given load, then the liquid was sheared, and so on 13,15 .
	189	The principle of the new methodology consists in applying nor-
	190	mal and lateral motions simultaneously to the surfaces: if the
	191	approach/retraction rate is much smaller than the shearing rate
	192	(typically v N ∼ 1 nm/s	v L ∼ 100 nm/s), the distance and the
	193	load can be considered as constant within one shearing period.
	194	Such procedure has been already used by Hoth et al. 10 with a
	195	AFM but without analyzing the data to deduce the friction-load
	196	relationship, and by Crespo et al. 35 and us 36 with a SFA but not
	197	in the context of a structured liquid film.
	198	Simply imposing a continuous instead of stepped motion in the
	199	normal direction potentially offers significant advantages. (i) The
	200	measurements are more precise (i.e. less scattered), because less
	201	time is left for the system to drift between points (inevitable long-
	202	term drifts due to thermal expansion and creep of the mechanical
	203	parts), which is necessary to investigate quantitatively the rela-
	204	tionship between friction, load and contact area, and to finely test
	205	proposed models. (ii) The method allows for a more comprehen-
	206	sive exploration of friction-load relationship, in particular in the
	207	vicinity of spring instabilities (jump-out on retraction, jump-in on
	208	approach), which is crucial to elucidate the role of adhesion on
	209	friction, and to better understand the film dynamics during the
	210	squeeze-out transition. (iii) The whole friction phenomenology
	211	can be acquired more rapidly (in typically ∼ 1 h instead of ∼ 10 h
	212	to probe all the layers of a structured film), which is convenient to
	213	efficiently probe various physico-chemical systems and to assess
	214	the reproducibility of the measurements.
	215	However, a careful implementation of the technique is re-
	216	quired to avoid possible artefacts. First, the liquid structure it-
	217	self can be affected by the shearing motion, a phenomenon that
	218	has been qualitatively interpreted as a combing of long-chain
	219	molecules 37-42 . Secondly, the friction force can be reduced by
	220	mechanical vibrations (potentially induced by the simultaneous
	221	normal motion), which qualitatively act as an effective temper-
	222	ature that helps to overcome the energy barrier associated with

183 2

Acknowledgements 748 S.P. and R.L. are supported by The Leverhulme Trust (RPG-

gations. This scenario could be tested by combining X-ray scattering 744 and friction measurements in a modified SFA/SFB [START_REF] Golan | Is-837 raelachvili[END_REF]82,83 .

Conflicts of interest


Romain Lhermerout

Christophe Diederichs

Sapna Sinha

Kyriakos Porfyrakis

Susan Perkin
email: susan.perkin@chem.ox.ac.uk

Are Buckminsterfullerenes Molecular Ball Bearings?

Buckminsterfullerenes (C 60 ) are near-spherical molecules which freely rotate at room temperature in the solid state and when dissolved in solution. An intriguing question arises as to whether C 60 molecules can act as molecular ball bearings, i.e. preventing direct contact between two solid surfaces whilst simultaneously dissipating shear stress through fast rotation. To explore this, we performed measurements of friction across a solution of C 60 in the boundary lubrication regime. High resolution shear and normal force measurements between mica sheets separated by the C 60 solution were made using a Surface Force Balance to provide a single-asperity contact and sub-nanometer resolution in lm thickness. We nd that, even at small volume fraction, C 60 forms a solid-like amorphous boundary lm sustaining high normal load, suggesting that this system undergoes a glass transition under connement. The C 60 lm gives rise to a low friction coecient up to moderate applied loads, and we discuss the possible relevance of the ball bearing eect at the molecular scale.

Introduction

force during shearing cycles evolves as the applied load is increased. At higher loads a clear yield spike followed by smooth sliding is observed; from this the kinetic friction F L,k is deduced.

in magnitude and varies directly with the applied shearing amplitude; the saw-tooth shape is the signature that the surfaces are rigidly coupled, i.e with no relative motion throughout the cycle. Because of the strong adhesion between the surfaces, friction is controlled by adhesion 36 and is so high that the yield point of the contact is not reached within the range of lateral force explored. Thus we nd that the yield force of the contact must be higher than 110 µN in this case. In experiments with higher shearing amplitudes, we found that the yield force was in fact higher than 330 µN; corresponding to a lower limit for the contact shear stress of σ L ∼ 26 MPa. During retraction, a damped oscillation at the resonance frequency of ∼ 25 Hz is obtained when the surfaces jump-out, and then no lateral force is detected, consistently with the behavior on approach. In sum, we nd that tetralin alone cannot support any applied load, and so squeezes out of a contact whennite load is applied, giving rise to high friction in accordance with direct mica-mica contact.

1 ferent

 1 Human activity has always required the motion of objects, from the building of edices in prehistorical ages to the harvesting of energy 29 with wind turbines in present times. The ques-30 tion of whether logs were used as rollers to 31 move megaliths has been debated, 1 nonetheless 32 it is clear that the idea of using wheels to re-33 place sliding by rolling was early found to be 34 an ecient way to reduce energy dissipation 35 during motion, i.e. friction. While formulat-36 ing the rst fundamental laws of solid friction, 37 Da Vinci conceived of many ingenious machines 38 involving rotary parts where the friction is lim-39 ited to the axis. 2 Ball bearings, consisting of 40 balls running along a groove (e.g. in an axle 41 assembly), are designed to reduce the friction 42 further by transforming sliding into rolling. It 43 is also known, since ancient times, often complicated by processes act-55 ing over multiple length-scales and timescales 56 simultaneously. For example a uid may lu-57 bricate motion as a thick lm (hydrodynamic 58 regime) or in molecular connement between 59 close asperities (boundary regime), either at dif-60 regions of a rough contact or under different shearing conditions. Buckminsterfullerene (C 60 ) is a molecule of almost ideal spherical shape 7 (structure in Fig- ure 1(a)). In its pure form under ambient conditions C 60 forms a solid in which the molecules are able to rotate freely; inspection of the temperature dependence of the heat capacity shows that the energy associated with rotation of C 60 in the crystal is smaller than the ambient thermal energy. 8 This interesting property, com- bined with relative chemical stability, led to the early proposal that C 60 could act as an eective boundary lubricant: it might be expected that even when conned between two surfaces it could rotate to dissipate stress, the molecules eectively performing as molecular ball bearings. Direct observations have shown that spherical nanoparticles can rotate between sheared surfaces, in a manner which is reminiscent of the rolling without slipping motion of macroscopic ball bearings. 9 By analogy to the macroscopic mechanism of ball bearings, a molecular ball bearing system should sustain normal load (i.e. keeping the shearing solid surfaces apart) yet without hindering molecular rotations (which serve to dissipate shear stress and so reduce friction). Although this provides a useful motivating concept to consider the eect of rotations in modifying friction at the nanoscale, we note that the macroscopic mechanism of ball bearings does not map perfectly onto molecular systems under ambient conditions: the molecular rotation rate will typically be much higher than the imposed shear under ambient conditions. To dierentiate between these two situations, we call the molecular mechanism the molecular ball bearing effect. In this work we measure and appraise whether C60 might satisfy these criteria. Previous studies have investigated lubrication by C 60 or fullerene-like molecules in dif- ferent ways. On one hand, they have been used as a solid lubricant in dry conditions (from simply dispersed powder to carefully sublimated thin lm), but they didn't provide particularly exceptional frictional properties. 1014 C 60 have been used as wheels for single- molecule nanocars, and the displacement of such nanocars was found to be indeed due to 110 the rotation of the C 60 on the Au-(111) sur- 111 face at ∼ 200 • C.

3 amately 5 C∼ 2 ∼ 5 Figure 2 :

 35252 Figure 1: (a) Chemical structures and sizes of buckminsterfullerene (C 60 ) and tetralin. (b) Schematic of the SFB experiment, that allows to determine the interaction and friction forces between two mica surfaces separated by a liquid lm of controlled thickness. (c) Normal force F N rescaled by the radius of curvature R of the surfaces as a function of the separation D obtained at approach velocities v N ∼ 1 nm/s, for tetralin (approach in brown, pull-o force measured on retraction indicated by the black arrow) and the solution of C60 in tetralin (approach in purple, retraction in black).

Figure 3 :∼ 1

 31 Figure 3: (a) Kinetic friction F L,k as a function of load F N . Friction in pure tetralin was above the range limit of the experiment, as indicated by the shaded bar, whereas the solution of C 60 in tetralin gave rise to measurable friction (in purple). The two stars correspond to the lateral force traces shown in insets of Figure 2(b), and the red lines are the linear ts used to deduce the local friction coecient µ. (b) Normal (red) and kinetic friction (blue) force proles, for the solution of C 60 in tetralin. (c) Schematic representation of the system in connement: the C 60 molecules are randomly packed, steric interactions lead to a signicant repulsion between the solid surfaces, but fast rearrangements induce a relatively small shearing resistance.

  transition as C 60 molecules be- 451 ing kinetically trapped between the surfaces 452 and having no time to order. We never ob-453 served a structural force over the explored spots 454 on the surfaces, experiments and velocities be-455 tween ∼ 1 nm/s and ∼ 12 nm/s. This is most 456 likely to be due to the dierent solvent and 457 concentration chosen: Campbell et al. used 458 a concentration of 0.095 mg/mL correspond-459 ing to a molar fraction of ∼ 0.001% or ∼ 3% 460 of the saturation limit in toluene (2.8 mg/mL 461 at 25 • C 22 ), whereas here we use a concentra-462 tion of 5.60 mg/mL corresponding to a molar 463 fraction of ∼ 0.1% or ∼ 35% of the saturation 464 limit in tetralin (16 mg/mL at 25 • C 22 ). In our 465 case, the C 60 molecules in the bulk are much 466 more concentrated and close to the agglomera-467 tion limit, and the order/disorder kinetic tran-468 sition may have been shifted to approach ve-469 locities much smaller than 1 nm/s. Combining 470 the observations of no structural force and of 471 a solid-like friction response, we conclude that 472 under the experimental conditions used the C 60 473 must form a disordered/amorphous solid, i.e. a 474 glass, where the molecules are randomly packed 475 in the gap (as illustrated in Figure 3(c)). The 476 situation is thus related to the dicult probthen tempting to interpret our mea- 481 sured kinetic friction-load curve as a kind of 482 Angell plot, that conventionally represents how 483 the logarithm of the viscosity increases with the 484 inverse temperature (for molecular liquids) or 485 with the packing fraction (for colloidal liquids) 486 when approaching the glass transition. 49,50 Fol- 487 lowing this scenario, it would be the increase 488 of the C 60 packing fraction with the load (as 489 shown by the compression of the lm) that leads 490 to a dramatic slowing down of the dynamics, 491 i.e. of the rearrangement timescale of the glassy 492 lm in the gap, as measured by the increase of 493 the friction force. 494 Role of rotation. One can nally ask 495 whether the rotation of C 60 contributes to the 496 frictional behavior. As shown by a 2D molecu-497 lar dynamics simulation of lubrication by cir-498 cular molecules, a high concentration in the 499 gap can lead to jamming, which hinders the 500 molecular rotation because the two sides of two 501 molecules in contact would have to rotate in opposite directions.51 So if the rotation of C 60 plays a role in our system, it is likely to happen at small loads, for which we indeed measured a small friction coecient. Because of the relatively strong adhesion of the C 60 on mica (De- bye interaction), the lateral motion is probably distributed in the middle of the gap and not at the lm/mica interfaces. The small resistance to ow in the gap indicates that energy is dissipated eciently in the lm; the mechanism for this could originate from (at least) three modes. First, there is only small adhesion between C 60 molecules (London interaction).

18 Second,

 18 there is room and time for rearrangements, since C 60 molecules are randomly packed with vacancies, at a packing fraction far enough from the glass transition. Third, the C 60 may rotate freely in the thin disordered lm, like they do in the bulk crystal, and this free rotation could contribute to a dissipation mechanism leading to low friction. In other words, a molecular ball bearing eect may be occurring and be partly responsible for the low friction regime. Conclusions To summarize our ndings, C 60 performs as an excellent boundary lubricant additive in our system; ∼ 0.1% of C 60 is sucient to form a strong boundary lm that reduces wear by preventing direct contact between the sliding surfaces and gives rise to a small friction coecient at moderate loads. A key ingredient leading to this useful outcome is that C 60 has a nite sol- ubility and tends to solidify when the concentration exceeds the saturation point locally in conned contacts thus preventing squeeze-out of the lm. The fact that the C 60 appears to form a disordered solid, evidenced by no regular oscillatory structural force despite solid-like mechanical response, indicates that the convex friction-load relationship may be the manifestation of a glass transition under connement. The friction coecient at moderate loads is remarkably small, and so it is hypothesised that the molecular rotations intrinsic to C 60 the molecular ball bearing eect may be impor-548 tant for reducing shear stress. 549 Future investigations should involve a sys-550 tematic study of the eect of the concentra-551 tion on kinetic trapping and on friction re-552 sponse. To clarify the role of molecular rota-

Acknowledgement S.P. and R.L. are supported The Leverhulme Trust (RPG-2015-328) and the ERC (under Starting Grant No. 676861, LIQUISWITCH). R.L. is supported by the EPA Cephalosporin Junior Research Fellowship and Linacre College (University of Oxford). S.P. is grateful for research leave enabled by the Philip Leverhulme Prize.