Orders of Magnitude Changes in the Friction of an Ionic Liquid on

Subscriber access provided by READING UNIV

Article

Orders of Magnitude Changes in the Friction of an Ionic Liquid on Carbonaceous Surfaces Nicolas Voeltzel, Nicolas Fillot, Philippe Vergne, and Laurent Joly J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10173 • Publication Date (Web): 04 Jan 2018 Downloaded from http://pubs.acs.org on January 4, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Orders of Magnitude Changes in the Friction of an Ionic Liquid on Carbonaceous Surfaces Nicolas Voeltzel1,2), Nicolas Fillot1), Philippe Vergne1) and Laurent Joly2),*

1) Univ Lyon, INSA Lyon, CNRS, LaMCoS - UMR5259, F-69621 Villeurbanne, France 2) Univ Lyon, Université Lyon1, CNRS, ILM - UMR5306, F-69622 Villeurbanne, France *Corresponding author: Laurent Joly, [email protected]

Abstract The fast development of ionic liquids as new lubricants and carbon-based coatings as performant tribological surfaces calls for the characterization of their frictional and interfacial hydrodynamic behavior. Here we use molecular dynamics simulations to explore the response under shear of an ionic liquid confined between various carbon-based surfaces, and an iron oxide surface for comparison. We show that extremely low fluid friction and giant hydrodynamic slippage can be obtained on graphite and to a lesser extent on diamond, but that friction on amorphous carbon surfaces is comparable to that on iron oxide. We relate these differences to the atom-scale roughness of the surfaces. In particular, although amorphous carbon surfaces are apolar, their nanometric roughness is enough to generate a fluid friction comparable to that of the extremely smooth but polar iron oxide surface. We also show that at high shear rates, seemingly small differences in viscosity and interfacial friction can result in a significant change of the slip length. We finally discuss on the consequences of the ultralow fluid friction that we observed on the macroscopic behavior of lubricated contacts.

Introduction Room temperature ionic liquids (RTILs), often simply referred to as ionic liquids (ILs), are a potential new class of lubricant likely to operate on an extended range of pressure and temperature. They feature high thermal stability, non-flammability, very low volatility, and pressure-viscosity and temperature-viscosity dependences that matches the needs of lubricants1–7. Moreover, lower friction and wear can take place with IL-lubricated systems compared with standard oil lubrication1,8. Those improvements could stem from the polar nature of ILs. When in contact with polar surfaces, as it is the case when confined between commonly 1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 24

used oxidized steel surfaces9, they can form a protective tribolayer adsorbed on the shearing surfaces that help to prevent solid-solid contact8,10,11. With the continuous improvement of surface finishing processes, the film thickness in lubricated contacts has gradually decreased down to the size of a few molecules at some locations12,13. In this context, the interfacial friction between the liquid lubricant and the solid surface, often referred to as the fluid friction, is a key component of the dynamics of such systems14. In particular, a low fluid friction can lead to hydrodynamic slip between the lubricant and the surfaces, which will strongly affect the behavior of the lubricated contact15. For instance, if the slip condition is different on the shearing surfaces of an elastohydrodynamic (EHD) contact, the film thickness will be greatly impacted and can either increase and prevent solid-solid contact or drop toward the apparition of a local film breakdown that would damage the system16. Among the promising materials for tribological applications, diamond like carbon (DLC) coatings exhibit very low friction and high wear resistance17,18, and might provide low fluid friction19 as compared to standard oxidized steel surfaces. Recently, IL-lubricated contacts with DLC coatings were experimentally investigated. With DLC-coated surfaces, lower friction and wear were noticed using IL lubricants rather than with standard ones (PAO, MAC, Zdol or PFPE)20–22. With IL-lubricated contacts, experimental studies also confirmed the higher performances of DLC-steel surfaces compared to steel-steel ones23,24 or even to other coatings depending on the considered IL25. Beyond experimental studies, molecular dynamics (MD) simulations offer a powerful complementary means to explore various situations of lubricated contacts at the nanoscale and to understand the mechanisms governing the changes in the lubrication properties. Hence, several works were conducted using MD to explore some aspects of the lubrication capability of ILs confined between DLC or graphite materials26–32. Some investigated the structuration of ILs at the solid/liquid interface27,28. Pushing forward, Mendonça and coworkers characterized the friction of a nanoconfined IL between two amorphous carbon surfaces for different normal loads and speeds30. Hence, a first overview of the lubrication capability of DLC+IL systems is already pictured but some investigations on the mechanisms underlying their enhanced tribological performance are still needed in order to optimize them. Moreover, a comprehensive analysis of their interaction with different surfaces is also missing to quantify the improvements and to speed up their use in real systems. In that context, the current study aims at characterizing the influence of the surface nature on the response under shear of the liquid/solid interface, and more globally of the whole contact. An ionic liquid modeled by an all-atom force-field33 is nanoconfined between five different materials and sheared over a large velocity range. After describing the systems and methods, we first present friction results which we relate to slip and interfacial fluid friction of the IL at the confining surfaces. We then discuss the influence of the atomic 2 ACS Paragon Plus Environment

Page 3 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


roughness on the liquid-solid interfaces and the role of temperature. Finally, we develop a simple model to understand the hydrodynamic slip results, and we come back on the consequences of slip on the macroscopic behavior of contacts lubricated by ILs.

Systems and methods MD simulations were performed with the open source LAMMPS code34. Newton’s equations of motion were integrated using the reversible RESPA algorithm35, which solves the equations over different time steps to optimize computational times. The time step was set to 0.5 fs for intramolecular interactions and to 2 fs for intermolecular interactions. Langevin thermostats36 controlled the temperature of both surfaces and the temperature of the confined ionic liquid was free to fluctuate. The confining pressure was imposed uniformly on two external atomic layers of the solid walls, not in contact with the fluid (highlighted in blue in Figure 1).

FIGURE 1: SIMULATION DOMAIN OF 188 IL PAIRS BETWEEN TWO FEO SURFACES WITH PERIODIC BOUNDARIES ALONG THE X AND Y DIRECTIONS

Among the large number of existing IL pairs, those based on imidazolium cations perform well as lubricants37,38. In particular, they are very good candidates for extreme lubrication regimes thanks to their high thermal stability, and their tunable viscosity that can be adapted to a large range of loads2. Concomitantly, the hydrophobicity of bis(trifluoromethylsulfonyl)imide anions is an important asset to compose a lubricant as it limits oxydation1. ILs based on these anions also have excellent pressure-viscosity coefficient and viscosity index7,39. In this work, we therefore considered the 1,3-dimethylimidazolium bis(trifluoromethylsufonyl)imide (abbreviated in [mmIm+][NTf2-]) ionic liquid. 3 ACS Paragon Plus Environment


Page 4 of 24

Because the rheological behavior of a fluid strongly depends on its molecules geometry, we chose an allatom force field. Canongia Lopes et al. built an all-atom force field from quantum mechanics calculations to model a large ensemble of imidazolium-based ionic liquids40,41. Nevertheless some transport properties are not properly described by the initial force field for all the IL pairs42, so we implemented a standard charge scaling procedure42,43 to calibrate it so that the density, the diffusion coefficient and the viscosity of the [mmIm+][NTf2-] ionic liquid were accurately predicted. All the information on the ionic liquid force field is available in the electronic supplementary information provided with a previous paper33. To explore the properties of different DLC structures as confining and shearing surfaces, we first studied the extreme cases of the two crystalline allotropes of carbon: graphite (sp2 carbons only) and diamond (sp3 carbons only). In both cases, ideally flat surfaces were simulated (Figure 2).

a)

b)

c)

d)

FIGURE 2 REPRESENTATION OF THE SIMULATED CARBON-BASED SURFACES: A) DIAMOND B) GRAPHITE C) SMOOTH AMORPHOUS CARBON D) ROUGH AMORPHOUS CARBON. ATOMS ARE SHOWN WITH VAN DER WAALS SPHERES FOR DIAMOND AND AMORPHOUS CARBON, WHILE ONLY COVALENT BONDS ARE SHOWN FOR GRAPHITE, TO HIGHLIGHT THE DIFFERENT GRAPHENE LAYERS.

We also considered amorphous carbon (a-C) surfaces as a model of DLC coating. A 3-dimensional periodic volume of molten carbon was cooled and stabilized to nearly the solidification temperature (≈ 4000 K). From this state, two surfaces with different roughness where generated (Figure 2): the system was cooled down to 3000 K (rough a-C) and 2000 K (smooth a-C) at a cooling speed of 0.2 K/ps and blocs were cut out in the volume with two free surfaces along the z direction where carbon atoms were free to relax, while keeping periodic boundary conditions in the x and y directions. Depending on the bloc temperature, the topography of the surfaces changes: at 2000 K, the system is fully solid so that the surface structure does not rearrange 4 ACS Paragon Plus Environment

Page 5 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


much, while at 3000 K carbon atoms at the surface can relax more easily and the surface roughness increases. Once stabilized, both surfaces quenched down to ambient temperature before being integrated into shearing simulations. We used the Tersoff force field44 to represent the carbon-carbon interactions for diamond and amorphous carbon materials. For graphite we used a hybrid force field, combining a Tersoff force field44 to model interactions within graphene layers, and a Lennard-Jones (LJ) potential to model interactions between graphene layers. For this last material, the Tersoff force field coefficients were taken from Lindsay work45 and the LJ ones from the AMBER force field. Finally, for all surfaces, LJ interaction potentials also from the AMBER force field were implemented between the carbon and the ionic liquid atoms. Therefore, pi-pi interactions, which are a priori relevant for the [mmIm+][NTf2-] ionic liquid on graphite, are not described explicitly. While this is a common approximation of most empirical force fields, this may affect the quantitative results presented in the following. Note however that LJ interactions in the AMBER force field will also favor pi-pi stacking between the rings of the graphite surfaces and the cations, reproducing at least qualitatively the effect of pi-pi interactions. In addition to carbon-based materials, an iron oxide (FeO) surface was also considered for comparison. Iron oxide is representative of the top layers of (oxidized) steel surfaces commonly found in lubricated contacts9. Composed equally of negative oxygen atoms and positive iron ones, FeO surfaces feature electrostatic interactions with the lubricant in contact but are globally uncharged. The integration of FeO in MD simulations was based on a force field introduced by Cygan et al.46 and adapted in a previous paper33. Finally, LJ coefficients of atoms of different types were calculated by means of Lorentz-Berthelot mixing rules. We confined 188 ionic liquid pairs between two surfaces of diamond, graphite, 2 types of a-C (Figure 2), or FeO (Figure 1). Periodic boundary conditions were set in the two directions parallel to the surfaces, x and y. In order to depict as accurately as possible a realistic tribological contact, the confining pressure 𝑃conf was fixed to 500 MPa and the wall temperature to 350 K (Figure 1). The resulting film was roughly 3-nm thick. Shearing was introduced in the system through a relative motion between the two surfaces: velocities of ± 𝑈/2 were imposed to the same surface atom layers on which pressure was applied. We ran a parametric study with sliding velocities 𝑈 ranging from 0.2 to 320 m/s, with an exact range depending on the nature of the surfaces. These conditions, which can occur in the central region of lubricated contacts, are representative of a particular lubrication regime taking place between elastohydrodynamic and molecular lubrication. Based on a film thickness criterion, Luo et al.47 referred to it as the Thin Film Lubrication (TFL) regime while Chaomleffel et al.48 proposed the expression Very Thin Film (VTF) lubrication: its domain was determined from specific values of dimensionless parameters used in lubrication. The speed domain covered by the simulations is

5 ACS Paragon Plus Environment


consistent with the values nowadays found in lubricated components. Overall this range is explored at the laboratory scale with tribometers, although very high speeds are difficult to replicate and study.

Results We first focus on the coefficient of friction 𝜇 of the nano-lubricated contact, defined as the ratio between the shear stress 𝜏 and the confining pressure 𝑃conf : 𝜇 = 𝜏/𝑃conf . The simulations bring out large disparities for 𝜇 according to the nature of the confining surfaces (Figure 3). On the one hand, 𝜇 is extremely low for graphite surfaces: from 0.00033 (at 0.5 m/s) to 0.0063 (at 160 m/s). It is also low with diamond: from 0.0094 (at 0.2 m/s) to 0.056 (at 160 m/s). On the other hand, 𝜇 is higher and remarkably close for the two amorphous carbon surfaces and the iron oxide one, of the order of 0.1. Overall, large differences are obtained with the same fluid as lubricant, highlighting the major role of the surfaces in lubrication at this scale. Rough a-C Smooth a-C FeO Diamond Graphite

1

0,1

µ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 24

0,01

0,001

0,0001 0,1

1

10

100

1000

U (m/s) FIGURE 3: COEFFICIENTS OF FRICTION OBTAINED WITH A CONFINING PRESSURE OF 500 MPA AND A WALL TEMPERATURE OF 350 K FOR FIVE DIFFERENT SURFACES: IRON OXIDE, DIAMOND, GRAPHITE AND TWO AMORPHOUS CARBON COATINGS. We now explore the mechanisms underlying these massive differences in 𝜇, and show in particular the critical role of liquid-solid interfaces. Indeed, the velocity difference between the confining surfaces can be accommodated by two mechanisms in the nano-lubricated contact: first, the liquid film can be sheared, resulting in a shear stress 𝜏 controlled by the effective shear rate in the liquid 𝛾̇ eff and the viscosity 𝜂: 𝜏 = 𝜂 𝛾̇ eff . But at the nanoscale, low liquid-solid friction can result in a velocity jump at the liquid-solid 6 ACS Paragon Plus Environment

Page 7 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


interface. This velocity jump is described by the partial slip boundary condition first introduced by Navier49,50, which relates the slip velocity (i.e., the jump of tangential velocity at the interface) 𝑣slip to the effective shear rate in the liquid close to the wall, 𝛾̇ eff : 𝐿s =

𝑣slip 𝛾̇ eff

(1)

where 𝐿s is the so-called slip length, illustrated in Figure 4. Denoting ∆𝑣 = 2 𝑣slip the total velocity difference assimilated by slippage at both surfaces and using Eq. (1), one can express the fraction of the shearing velocity assimilated by slippage, ∆𝑣⁄𝑈 , as a function of the ratio between the fluid thickness H and the slip length 𝐿s : ∆𝑣 2 = 𝑈 2 + 𝐻⁄𝐿

(2) 𝑠

According to this expression, the shearing is assimilated at the interfaces, i.e. ∆𝑣 ~ 𝑈, when 𝐿𝑠 ≫ 𝐻 and in return, the fluid assimilates the shearing, i.e. ∆𝑣 ≪ 𝑈, when 𝐿𝑠 ≪ 𝐻, see Figure 4.

𝐿𝑆 𝑈/2

𝑣slip 𝛾̇ 𝑒𝑓𝑓

𝑧

−𝑈/2 − 𝐻/2

0

𝐻/2

FIGURE 4: SCHEMATIC DEFINITION OF THE SLIP LENGTH. THE CHARACTERISTIC VELOCITY PROFILE IS DRAWN IN BLUE. Back to our numerical results, high velocity slips of the ionic liquid on the surfaces were detected. The order of magnitude of those slips varied significantly with the surface nature and could explain the large disparities for 𝜇. Note that the above theoretical description assumes a linear velocity profile over the entire liquid film, with a constant shear rate. Since mechanical equilibrium imposes that the shear stress is constant throughout the system, this corresponds to a constant (local) viscosity – defined as the ratio between the shear stress and the local shear rate. However, in the nanometric vicinity of walls, liquids generally form layers, and their dynamics is generally slowed down. Both liquid layering27,28,51,52,30,53,54 and slowdown of the dynamics55–57 have indeed been observed in systems similar to ours. Here, we also observed liquid layering for all surfaces 7 ACS Paragon Plus Environment


Page 8 of 24

– see the supporting information (SI) for more details. We nonetheless measured linear velocity profiles throughout the whole liquid film on the three atomically smooth surfaces (graphite, diamond and FeO), corresponding to a constant viscosity profile (see the SI). In the range of shearing velocities considered in this work, this is consistent with previous results on a similar system58. The observed constant viscosity could arise because viscosity can depend non-locally on the density59, which can smooth out the effect of layering. We also would like to emphasize that a constant viscosity is compatible with a slowdown of the dynamics, since this slowdown is not simply related to a change in viscosity. For instance, continuum descriptions of diffusion assuming a homogeneous viscosity predict a decrease of the diffusion coefficient in the vicinity of walls60. For the a-C surfaces, we observed a small decrease of the shear rate close to the walls, corresponding to an increase of the local effective viscosity (see the SI). This effect of roughness has been reported previously on similar systems61 and can be understood as the roughness will increase momentum transfer between the wall and the liquid. When the velocity profile was not linear over the entire film, we used the linear part in the middle of the film to measure the effective shear rate 𝛾̇ eff , and we extrapolated this linear part of the velocity profile up to the walls in order to define the slip velocity 𝑣slip . The details of the velocity profiles within the interfacial region are therefore encompassed in the effective hydrodynamic boundary condition (partial slip boundary condition, or fluid friction). The slip length variations with the shearing velocity are plotted in Figure 5 for the five surfaces. Slip lengths vary over five orders of magnitude with the considered surfaces, graphite being confirmed as the most slippery material. Moreover, the slip length of iron oxide and a-C surfaces saturates above a limit shearing speed. This can be compared with previous numerical results on simple fluids obtained in less severe thermodynamic conditions, where some studies have shown a divergence of the slip length62, while other studies also observed a saturation when using thermostated walls63,64. According to Eq. (2), distinct regimes take place for the different surfaces depending on how the slip length and the film thickness (of the order of 3 nm) compare. Graphite leads to a surface-controlled regime with a complete assimilation of the shearing at the solid-liquid interface and no shear of the fluid since 𝐿𝑠 ≫ 𝐻. Close to this configuration, diamond induces an assimilation of the shearing at the interfaces starting from 57 % at low speed (0.2 m/s) to more than 90 % at higher shear velocities (above 3 m/s). Interfacial slip with iron oxide follows the same trend but remains in a more mixed regime: from 16 % of assimilation of the shear at a 2 m/s shearing speed to a maximum of 62% at higher velocity. While similar coefficients of friction 𝜇 are featured by a-C and FeO surfaces, the slip length is lower for both a-C surfaces than for the iron oxide one. We will interpret this counterintuitive feature in the discussion section. Finally, the low slip results in a mainly fluid-sheared regime for amorphous carbon surfaces.


Page 9 of 24

10000

Graphite

1000

Diamond FeO

100

Smooth a-C

Ls (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Rough a-C Equation 6

10

1

0,1 0,1

1

10

100

U (m/s)

1000

FIGURE 5: SLIP LENGTH VARIATION WITH THE SHEARING VELOCITY COMPUTED FOR FIVE SHEARING SURFACES. DASHED LINES REPRESENT THE PREDICTIONS OF EQ. (6) FOR THE SLIP LENGTH IN THE POWER-LAW REGION, USING PARAMETERS OF TABLE 2 FOR FEO, SMOOTH A-C AND ROUGH A-C SURFACES (SEE THE DISCUSSION SECTION).

To understand both the strong differences in slip length and the saturation of the slip length on some surfaces, further analysis of the interface behavior is needed. For that purpose, the interfacial fluid friction coefficient (FFC), denoted 𝜆 and defined as the ratio between the shear stress and the interfacial velocity slip, 𝜆 = 𝜏/𝑣slip , is studied. Indeed, liquid-solid slip results from a competition between viscous shear in the liquid and fluid friction at the interface, and the slip length is accordingly controlled by the ratio between the shear viscosity 𝜂 and the FFC 𝜆 33: 𝐿𝑠 = 𝜂/𝜆

(3)

Therefore, for a given fluid viscosity, the slip length and the FFC are directly related. The evolution of 𝜆 with the slip velocity is presented in Figure 6. The ideal surface of graphite (flat, non-polar) shows the lowest interfacial fluid friction coefficient while the polar (but smooth) surface of iron oxide and the uneven (but non-polar) surfaces of a-C give rise to larger FFC. Each variation can be fitted by a negative power law with an exponent varying from -0.54 for the graphite to ca. -0.94 for both a-C surfaces. The different 𝜇 values obtained with the five surfaces (Figure 3), can be related to differences in λ: the lower λ, the lower 𝜇 and to equivalent values of λ for iron oxide and a-C surfaces correspond equal values of 𝜇. Nonetheless, it looks like the variation of the FFC alone cannot explain the saturation of the slip length previously noted nor the difference of slip between iron oxide and a-C materials. We will analyze these features in the following discussion section. 9 ACS Paragon Plus Environment


100

Rough a-C Smooth a-C FeO Diamond Graphite

10

1

λ (mPa.s/Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 24

0,1

0,01

0,001

0,01

0,10

1,00

10,00

100,00

vslip (m/s) FIGURE 6: FLUID FRICTION VERSUS INTERFACIAL SLIP VELOCITY OF FIVE DIFFERENT SURFACES: IRON OXIDE, DIAMOND, GRAPHITE AND TWO AMORPHOUS CARBON

Discussion Now that the dynamic behavior occurring at the fluid/solid interface has been detailed, its origins will be identified.

Influence of surface geometry and composition The effects of the interfacial friction were computed for 5 distinct materials. The observed differences stem from the atoms composing the surface and from their geometrical arrangement15,65,66. To estimate the influence of both factors, we characterize in this section the corrugation of the solid surfaces, independently of the fluid. Indeed, the ionic liquid we considered is made of molecular ions, with different types of atoms of different interaction properties and partial charges. Consequently, we chose to probe the surface corrugation with a generic uncharged atom. We computed two parameters ℎroughness and 𝐹corr (Table 1) that describe respectively the geometrical roughness and the force corrugation. The geometrical roughness was defined as follows: a plan of 200 by 200 probing atoms was set parallel to the tested surface and relaxed in the direction orthogonal to the surface. The probing atoms interact with the surface atoms through a LJ potential. The LJ parameters are the same for every probing atom: a default 10 ACS Paragon Plus Environment

Page 11 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


energy ε of 1 kcal/mol and a size σ of 3.93 Å, characteristic of the fluid atoms. The parameter ℎroughness is then estimated with the following expression: 𝑁

ℎroughness

1 = √ ∑(ℎ(𝑥, 𝑦) − ℎ)² 𝑁

(4)

𝑖=1

The force corrugation is estimated by scanning the energy landscape of the tested surface, as previously described by Savio et al.15. For both ℎroughness and 𝐹corr , the LJ potential alone is considered in the computations. Coulombic interactions of the iron oxide surfaces are not taken into account given that the probing atoms are non-polar ones. In the following analysis, the FFC of the different cases are compared at a given interfacial velocity slip of 5 m/s. To do so, we interpolated the data plotted in Figure 6.

Graphite

Diamond

FeO

Smooth a-C

Rough a-C

ℎroughness (Å)

0.0115

0.0534

0.0705

0.571

0.820

𝐹corr (kcal/mol/Å)

0.135

0.548

1.71

2.27

0.0171

0.294

2.10

2.15

 (mPa.s/ Å) for 𝑣slip (m/s) = 5 m/s

0.350 (non-polar) 1.59

TABLE 1: GEOMETRICAL ROUGHNESS AND FORCE CORRUGATION PARAMETERS FOR THE FIVE SURFACES. For carbon-based materials, a direct correlation exists between the surface characteristics (roughness and corrugation) and the interfacial fluid friction with the ionic liquid. As an example, to a geometrical roughness of 0.0115 Å and a force corrugation of 0.135 kcal/mol/Å for graphite corresponds a FFC of 0.0171 mPa.s/Å. Comparatively, a FFC of 2.15 mPa.s/Å is attributed to the rough a-C surface, for a geometric roughness of 0.820 Å and a force corrugation of 2.27 kcal/mol/Å. More generally, at low friction, λ is very sensitive to the increase of roughness: between graphite and diamond, both ℎroughness and 𝐹corr are increased by a factor ≈ 5 and the FFC is multiplied by ≈ 20. At higher friction, λ is less sensitive: while there is a difference in roughness of ca. 30% between the a-C surfaces, λ only varies by 3%. This behavior is consistent with the results obtained by Savio and coworkers, who studied the interactions of alkanes with surfaces of various natures15. In particular, as soon as a nanoroughness is present at the surfaces, slip is greatly reduced14,67. With iron oxide, the friction is high (3.06 mPa.s/Å at a 5 m/s interface velocity slip), whereas the measured corrugation and roughness are close to the values obtained for diamond. As the Coulombic interactions are not considered in the calculation of the surface parameters, this suggests a strong influence of the surface polarity on friction in the presence of a polar fluid (such as an ionic liquid), which is reflected by a substantial increase of the



Page 12 of 24

force corrugation. This is also consistent with experimental observations that point out the locking of counterions of IL on mica surfaces (charged surface)68. Over the past 20 years, a number of experimental and MD studies claimed the existence of a quasi-universal relationship between the slip length and the wetting properties of the liquid/solid couple69,70, although some recent studies have shown that the wetting properties alone can fail to predict the slip length71,72. For the present work, comparable wetting properties are expected for all the carbon-based surfaces, and yet they display extremely different interfacial fiction coefficients (up to more than 2 orders of magnitude).

Role of the temperature In the two following subsections, we will provide some insight on the possible origin of the differences in slip length observed between a-C and FeO surfaces, while these surfaces show an apparently similar FFC. One could first wonder about the role of temperature: as detailed in a previous study33, temperature can play a major and complex role directly impacting the fluid viscosity and consequently, the slip length. When sheared by an adhesive surface, the fluid accommodates the shear. As a consequence, elevation of the lubricant temperature and shear thinning occur, drastically reducing its viscosity at high shear rates. When sheared by a more slippery surface, the effective shear rate in the liquid is smaller, so that the fluid is less heated. However, the generated energy might dissipate less as the liquid/solid interfacial thermal resistance, 𝑅𝑡ℎ , is generally higher with low friction surfaces73, although this is not systematic74. Hence, the properties of the surface material have a clear impact on the temperature, but which is complex to foresee as the effects of thermal interfacial resistance and fluid shearing compete. To assess the thermal properties of the studied surfaces we compare, for the different surfaces, the relation between the rise of the fluid temperature and the heat produced in the lubricated contact. In Figure 7, for each surface the evolution of the fluid average temperature is plotted as a function of 𝑄, the power produced per unit area of a contact nanopatch in each simulation. As the surfaces are the only frontiers with the lubricant, 𝑄 also corresponds to the total heat flux through both surfaces. Therefore, if the temperature was homogeneous in the fluid film, the slope of the data obtained for a given type of surface (Figure 7) would correspond to half the interfacial thermal resistance of the liquid-solid interfaces, and generally larger slopes will correspond to larger thermal resistances.


Page 13 of 24

650

Rough a-C Smooth a-C

600

FeO Diamond

550

Tmean

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


500

450

400

350

0

5

10

15

20

Q (nW/nm²) FIGURE 7. AVERAGE TEMPERATURE OF THE FLUID WITH RESPECT TO THE PRODUCED HEAT Q AND THE SURFACE NATURE. For graphite surfaces, since the effective shearing of the fluid is extremely low, both the generated heat and the temperature increase are negligible, and it is not possible to estimate the slope. For the other systems, the interfacial thermal resistance of the different surfaces increases consistently with the decrease of their FFC observed in Figure 6. This is in line with previous observations stating that the thermal resistance 𝑅𝑡ℎ is generally higher with surfaces featuring a lower friction73. However, it can be noticed that, even though a-C and FeO have close 𝜆 values, FeO surfaces exhibit a higher thermal resistance (corresponding to a larger slope in Figure 7) than a-C ones. This can tentatively be explained by the greater effective contact area of the rough a-C surfaces. Nevertheless, the difference of temperature rise has a moderate influence on the viscosity (see Figure 8): the viscosity variations between FeO and a-C simulations with the shear rate remain equivalent, and only the quick elevation of temperature with diamond surfaces (due to their very high thermal resistance) induces an anticipated drop of the viscosity at medium shear rates. Since the slip length can be computed as the ratio between the viscosity and the FFC, Eq. (3), and both the viscosity versus shear rate (Figure 8) and the FFC versus slip velocity (Figure 6) appear very similar for iron oxide and a-C surfaces, one could expect the slip length to be also close. In the next subsection, we will investigate why this is not the case, as the slip length computed with FeO systems is up to 5 times the one computed with a-C ones (Figure 5).



1000

150

t (MPa)

100

100

η (mPa.s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 24

50 1E+8

10

1 1E+5

1E+9

.

1E+10

γeff (s-1)

1E+11

Rough a-C Smooth a-C FeO Diamond Graphite

1E+6

1E+7

1E+8

. γeff (s-1)

1E+9

1E+10

1E+11

FIGURE 8. VISCOSITY WITH RESPECT TO THE EFFECTIVE SHEAR RATE FOR THE DIFFERENT SURFACES. INSET: BULK SHEAR STRESS (𝝉 = 𝜼 𝜸̇ 𝐞𝐟𝐟 ) VERSUS EFFECTIVE SHEAR RATE FOR FEO, SMOOTH A-C AND ROUGH A-C SURFACES; A PLATEAU IS OBSERVED AT THE HIGHEST 𝜸̇ 𝐞𝐟𝐟 VALUES, CORRESPONDING TO A VISCOSITY SCALING LIKE 𝜸̇ 𝐞𝐟𝐟

−𝟏

(SEE SECTION “PREDICTING THE SLIP

LENGTH”).

Predicting the slip length in a strongly sheared lubricated contact For the FeO surface and the two a-C surfaces, both viscosity and FFC can be fitted by power laws at large shearing velocities, see Figure 8 and Figure 6. We used the following expressions: 𝜂 = 𝜂0 (𝛾̇ eff ∗ /𝛾̇ eff )𝛼 , and 𝜆 = 𝜆0 (𝑣slip ∗ /𝑣slip )𝛽 , arbitrarily fixing 𝛾̇ eff ∗ = 1 s −1 and 𝑣slip ∗ = 1 m/s. Looking in detail at the 𝜂 versus 𝛾̇ eff and 𝜆 versus 𝑣slip data, we note in all cases a change of slope for the last few points at the highest shearing velocities, with both 𝛼 and 𝛽 reaching 1. This corresponds to a significant change in the rheological behavior, specifically to a plateau of the shear stress, both for the viscosity: 𝜏 = 𝜂 𝛾̇ eff = 𝜂0 (𝛾̇ eff ∗ )𝛼 𝛾̇ eff1−𝛼 = 𝜂0 𝛾̇ eff ∗ (see inset of Figure 8), and for the FFC: 𝜏 = 𝜆 𝑣slip = 𝜆0 (𝑣slip ∗ )𝛽 𝑣slip1−𝛽 = 𝜆0 𝑣slip ∗ (see Figure 9). Since in the steady-state the shear stress must be the same in the bulk and at the liquid-solid interfaces, this imposes a relation between the a priori independent bulk viscous behavior and interfacial fluid friction: 𝜂0 𝛾̇ eff ∗ = 𝜆0 𝑣slip ∗. Also, since the slip length is defined as the ratio between the slip velocity and the effective shear rate, it becomes undetermined when 𝛼 = 𝛽 = 1. We leave a detailed investigation of the mechanisms underlying this special regime at extreme shearing velocities for future work, and here we exclude the corresponding points from the fit. We report the fitting parameters for the different surfaces in Table 2. 14 ACS Paragon Plus Environment

Page 15 of 24

𝜂0 (mPa.s)

𝛼

𝜆0 (mPa.s/m)

𝛽

𝐻 (nm)

FeO

4.74 x 109

0.8687

7.19 x 1010

0.9195

2.9

Smooth a-C

1.37 x 1010

0.9106

9.51 x 1010

0.9360

3.4

Rough a-C

1.18 x 1010

0.9046

9.87 x 1010

0.9368

3.5

TABLE 2 : FITTING PARAMETERS FOR THE VISCOSITY AND INTERFACIAL FLUID FRICTION COEFFICIENT FOR IRON OXIDE AND THE TWO AMORPHOUS CARBON SURFACES (A-C). FILM THICKNESSES ARE ALSO REPORTED IN THE RIGHT COLUMN.

Rough a-C

150

Smooth a-C FeO Power-law fit

t (MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50 0,10

1,00

10,00

100,00

vslip (m/s)

Figure 9: Interfacial shear stress (𝜏 = 𝜆 𝑣slip ) versus slip velocity for three surfaces: iron oxide and two amorphous carbon. The dashed lines represent the power law fits from which the parameters in Table 2 are extracted. A plateau is observed at the highest 𝑣slip values, corresponding to 𝜆 scaling like 𝑣slip −1 (see section “Predicting the slip length”). One can then implement the power laws in Eq. (3) relating the slip length to the viscosity and FFC: 𝐿s =

𝜂 𝜂0 (𝛾̇ eff ∗ /𝛾̇ eff )𝛼 = 𝜆 𝜆0 (𝑣slip ∗ /𝑣slip )𝛽

(5)

Finally, one can express both 𝛾̇ eff and 𝑣slip as a function of the shearing velocity 𝑈, the film thickness 𝐻 and 1

the slip length 𝐿s : 𝛾̇ eff = 𝐿 × 𝑈/(2 + 𝐻/𝐿s ) and 𝑣slip = 𝑈/(2 + 𝐻/𝐿s ). By replacing these expressions in s

Eq. (5), one finally gets: 15 ACS Paragon Plus Environment


𝐿s

1−𝛼

Page 16 of 24

𝐻 𝛽−𝛼 𝜂0 (𝛾̇ eff ∗ )𝛼 × (2 + ) = × 𝑈𝛽−𝛼 𝐿s 𝜆0 (𝑣slip ∗ )𝛽

(6)

Unless both 𝛼 and 𝛽 are equal to 1, this non-linear equation can be solved to obtain the evolution of the slip length 𝐿s with the shearing velocity 𝑈 for a given film thickness. One can also obtain approximate solutions when 𝐿s ≫ 𝐻 (assuming 𝛼 ≠ 1):

𝐿s ≈ {

2

𝛼−𝛽

1 ∗ 𝛼 1−𝛼

𝜂0 (𝛾̇ eff ) 𝛽

𝜆0 (𝑣slip ∗ )

}

𝛽−𝛼

× 𝑈 1−𝛼

(7)

Or when 𝐿s ≪ 𝐻 (assuming 𝛽 ≠ 1):

𝐿s ≈ {

𝐻

𝛼−𝛽

1 ∗ 𝛼 1−𝛽

𝜂0 (𝛾̇ eff ) 𝛽

𝜆0 (𝑣slip ∗ )

}

𝛽−𝛼

× 𝑈 1−𝛽

(8)

In both cases, the slip length follows a simple scaling law as a function of the shearing velocity, where the prefactor can strongly vary with small differences in viscosity or fluid friction when 𝛼 or 𝛽 are close to 1, because the exponents

1 1−𝛼

or

1 1−𝛽

can then become very large. A similarly strong dependency can be

expected in the general case described by Eq. (6), explaining the large differences observed between FeO and a-C surfaces, while they display similar viscosity and fluid friction. In practice, Eq. (6) with the parameters of Table 2 reproduces quite well the slip lengths measured for FeO and a-C surfaces, see dashed lines in Figure 5. Note that in each simulated configuration, the number of molecules is the same but the film thickness features little variations depending on the shearing velocity and the domain dimensions. Indeed, in order to guarantee the exact periodicity of the system, small variations of the domain dimensions in the periodic directions are necessary and induce slight disparities of the contact thickness 𝐻. Hence, at the same shearing velocity, the film thickness in simulations with FeO surfaces is roughly 15 % smaller than in ones with a-C surfaces (see Table 2). Nevertheless, we checked that changes in 𝐻 of such amplitude had a negligible effect on the prediction of the slip length via Eq. (6).

Consequence of high slip at the macroscale The order of magnitude of the slip length for the graphite goes from 0.5 to 5 μm. Considering the average film thickness in a roller bearing is usually in the range 0.02-0.2 μm, Eq. (2) tells us that a contact of this size implying at least one perfect graphite surface would be exclusively driven by the surface and the fluid would be very little sheared. Diamond slip length rises up to 0.1 μm at high shearing velocities so slip would still be significant for contacts with diamond-surfaces separated by standard film thicknesses. For iron oxide and a16 ACS Paragon Plus Environment

Page 17 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


C surfaces, the slip length is comprised between 0.0001 and 0.003 μm and becomes negligible compared with regular film thickness. In the corresponding regime, the shearing is mainly absorbed by the viscous fluid. Nonetheless, thanks to the progress made in surface conception and with the use of less viscous lubricants, the film thickness might decrease significantly in the future75,76. In any case, even in present lubricated systems surfaces roughness can introduce local spots with film thickness under 10 nanometers. Knowing the slip capability of the fluid/surface interface is relevant in those cases to predict the occurrence of a local film breakdown.

Conclusions Trough molecular dynamics simulations, we investigated the response under shear of an ionic liquid confined between four different carbon-based materials and iron oxide. It was first noticed that graphite surfaces present an ultralow fluid friction that leads to giant hydrodynamic slip. At the scale of the simulated lubricated contact, the shearing is almost entirely absorbed by interfacial slip, and an ultralow coefficient of friction is measured. Friction induced by diamond is relatively low too, so the shear is absorbed by both the liquid-solid interface and the viscous fluid. Finally, friction exhibited by both amorphous carbon surfaces is very close to the one of the iron oxide and limits the amplitude of hydrodynamic slip at the interface. The interfacial fluid friction was compared to the geometrical roughness and force corrugation of each surface. Friction increases with both parameters, but it is much more sensitive at lower values so once roughness exists, the slip capability is not strongly affected by its amplitude. The polarity of the iron oxide was also found to significantly increase friction even if the surface was globally uncharged. Despite their comparable interfacial fluid friction coefficient, FeO surfaces were found to slip more than amorphous carbon ones. After discussing the possible influence of the different thermal properties of these surfaces, we showed that for large shearing – where both the viscosity and the fluid friction coefficient have entered the non-linear response regime, small differences in the viscous or interfacial friction behavior could result in large differences of slip length. From this knowledge, the contact behavior could be controlled by better-informed design of the fluid and surfaces of the contact. In particular, the ultralow fluid friction induced by graphite materials could substantially improve the contact lubricity. For instance, if a graphitic coating of higher interfacial fluid friction was affixed on the entraining surface, it would enhance the hydrodynamic lift16 of a lubricated contact and ensure the upkeep of the full film regime, thus guaranteeing the low global friction and wear of the system.



Page 18 of 24

Acknowledgements The authors are grateful to the SKF company for financial support through the Research Chair ‘‘Lubricated Interfaces for the future’’ hosted by the INSA de Lyon Foundation. L.J. is supported by the Institut Universitaire de France. Guillermo E. Morales-Espejel is acknowledged for his much appreciated expertise on lubrication systems. The authors also thank the Fédération Lyonnaise de Modélisation et Sciences Numériques (FLMSN) for providing computing resources via the P2CHPD facility.

Supporting Information Available Examples of density and velocity profiles for the five different confining surfaces considered in this work.

References (1)

Zhou, F.; Liang, Y.; Liu, W. Ionic Liquid Lubricants: Designed Chemistry for Engineering Applications. Chem. Soc. Rev. 2009, 38, 2590–2599.

(2)

Minami, I. Ionic Liquids in Tribology. Molecules 2009, 14, 2286–2305.

(3)

Bermúdez, M.-D.; Jiménez, A.-E.; Sanes, J.; Carrión, F.-J. Ionic Liquids as Advanced Lubricant Fluids. Molecules 2009, 14, 2888–2908.

(4)

Maginn, E. J. Molecular Simulation of Ionic Liquids Current Status and Future Opportunities. J. Phys. Condens. Matter 2009, 21, 17.

(5)

Palacio, M.; Bhushan, B. A Review of Ionic Liquids for Green Molecular Lubrication in Nanotechnology. Tribol. Lett. 2010, 40, 247–268.

(6)

Dold, C.; Amann, T.; Kailer, A. Influence of Structural Variations on Imidazolium-Based Ionic Liquids. Lubr. Sci. 2013, 25, 251–268.

(7)

Fernández, J.; Paredes, X.; Gaciño, F. M.; Comuñas, M. J. P.; Pensado, A. S. Pressure-Viscosity Behaviour and Film Thickness in Elastohydrodynamic Regime of Lubrication of Ionic Liquids and Other Base Oils. Lubr. Sci. 2013, 26, 449–462.

(8)

Somers, A. E.; Howlett, P. C.; MacFarlane, D. R.; Forsyth, M. A Review of Ionic Liquid Lubricants. Lubricants 2013, 1, 3–21.

(9)

Gräfen, H.; Horn, E.-M.; Schlecker, H.; Schindler, H. Corrosion. In Ullmann’s Encyclopedia of Industrial Chemistry; Wiley-VCH Verlag GmbH & Co. KGaA, 2000. 18 ACS Paragon Plus Environment

Page 19 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(10)


Liu, X.; Zhou, F.; Liang, Y.; Liu, W. Tribological Performance of Phosphonium Based Ionic Liquids for an Aluminum-on-Steel System and Opinions on Lubrication Mechanism. Wear 2006, 261, 1174–1179.

(11)

Weng, L.; Liu, X.; Liang, Y.; Xue, Q. Effect of Tetraalkylphosphonium Based Ionic Liquids as Lubricants on the Tribological Performance of a Steel-on-Steel System. Tribol. Lett. 2007, 26, 11–17.

(12)

Dowson, D. History of Tribology; Longman: London, 1979.

(13)

Vergne, P.; Fillot, N.; Bouscharain, N.; Devaux, N.; Morales-Espejel, G. An Experimental and Modeling Assessment of the HCFC-R123 Refrigerant Capabilities for Lubricating Rolling EHD Circular Contacts. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 2015, 229, 950–961.

(14)

Savio, D.; Fillot, N.; Vergne, P. A Molecular Dynamics Study of the Transition from Ultra-Thin Film Lubrication Toward Local Film Breakdown. Tribol. Lett. 2013, 50, 207–220.

(15)

Savio, D.; Fillot, N.; Vergne, P.; Zaccheddu, M. A Model for Wall Slip Prediction of Confined N-Alkanes: Effect of Wall-Fluid Interaction Versus Fluid Resistance. Tribol. Lett. 2012, 46, 11–22.

(16)

Savio, D.; Fillot, N.; Vergne, P.; Hetzler, H.; Seeman, W.; Morales Espejel, G. E. A Multiscale Study on the Wall Slip Effect in a Ceramic–Steel Contact With Nanometer-Thick Lubricant Film by a Nano-toElastohydrodynamic Lubrication Approach. J. Tribol. 2015, 137, 31502.

(17)

Robertson, J. Properties of Diamond-like Carbon. Surf. Coatings Technol. 1992, 50, 185–203.

(18)

Robertson, J. Diamond-like Amorphous Carbon. Mater. Sci. Eng. R Reports 2002, 37, 129–281.

(19)

Kannam, S. K.; Todd, B. D.; Hansen, J. S.; Daivis, P. J. How Fast Does Water Flow in Carbon Nanotubes? J. Chem. Phys. 2013, 138, 94701.

(20)

Feng, X.; Xia, Y. Tribological Properties of Ti-Doped DLC Coatings under Ionic Liquids Lubricated Conditions. Appl. Surf. Sci. 2012, 258, 2433–2438.

(21)

González, R.; Hernández Battez, A.; Blanco, D.; Viesca, J. L.; Fernández-González, A. Lubrication of TiN, CrN

and

DLC

PVD

Coatings

with

1-Butyl-1-Methylpyrrolidinium

Tris(pentafluoroethyl)trifluorophosphate. Tribol. Lett. 2010, 40, 269–277. (22)

Wang, L.; Liu, X. Tribological Behavior of DLC/IL Solid-Liquid Lubricating Coatings in a High-Vacuum Condition with Alternating High and Low Temperatures. Wear 2013, 304, 13–19.

(23)

Liu, X.; Wang, L.; Xue, Q. DLC-Based Solid-Liquid Synergetic Lubricating Coatings for Improving Tribological Behavior of Boundary Lubricated Surfaces under High Vacuum Condition. Wear 2011, 271, 889–898. 19 ACS Paragon Plus Environment


(24)

Page 20 of 24

Liu, X.; Pu, J.; Wang, L.; Xue, Q. Novel DLC/ionic Liquid/graphene Nanocomposite Coatings towards High-Vacuum Related Space Applications. J. Mater. Chem. A 2013, 1, 3797–3809.

(25)

Kondo, Y.; Koyama, T.; Tsuboi, R.; Nakano, M.; Miyake, K.; Sasaki, S. Tribological Performance of Halogen-Free Ionic Liquids as Lubricants of Hard Coatings and Ceramics. Tribol. Lett. 2013, 51, 243– 249.

(26)

Okada, Y.; Ito, T.; Minamikawa, T.; Kamisuki, H.; Higai, S.; Shiratsuyu, K. Molecular Dynamics Study of Ionic Liquids in Graphite Nanopores. Electrochemistry 2013, 81, 808–810.

(27)

Wang, S.; Li, S.; Cao, Z.; Yan, T. Molecular Dynamic Simulations of Ionic Liquids at Graphite Surface. J. Phys. Chem. C 2010, 114, 990–995.

(28)

Maolin, S.; Fuchun, Z.; Guozhong, W.; Haiping, F.; Chunlei, W.; Shimou, C.; Yi, Z.; Jun, H. Ordering Layers of [bmim][PF6] Ionic Liquid on Graphite Surfaces: Molecular Dynamics Simulation. J. Chem. Phys. 2008, 128, 134504.

(29)

Liu, X.; Wang, Y.; Li, S.; Yan, T. Effects of Anion on the Electric Double Layer of Imidazolium-Based Ionic Liquids on Graphite Electrode by Molecular Dynamics Simulation. Electrochim. Acta 2015, 184, 164– 170.

(30)

Mendonça, A. C. F.; Fomin, Y. D.; Malfreyt, P.; Pádua, A. A. H. Novel Ionic Lubricants for Amorphous Carbon Surfaces: Molecular Modeling of the Structure and Friction. Soft Matter 2013, 9, 10606.

(31)

Gong, X.; Li, L. Nanometer-Thick Ionic Liquids as Boundary Lubricants. Adv. Eng. Mater. 2017, 1700617.

(32)

Gkagkas, K.; Ponnuchamy, V.; Dašić, M.; Stanković, I. Molecular Dynamics Investigation of a Model Ionic Liquid Lubricant for Automotive Applications. Tribol. Int. 2017, 113, 83–91.

(33)

Voeltzel, N.; Giuliani, A.; Fillot, N.; Vergne, P.; Joly, L. Nanolubrication by Ionic Liquids: Molecular Dynamics Simulations Reveal an Anomalous Effective Rheology. Phys. Chem. Chem. Phys. 2015, 17, 23226–23235.

(34)

Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1–19.

(35)

Tuckerman, M.; Berne, B. J.; Martyna, G. J. Reversible Multiple Time Scale Molecular Dynamics. J. Chem. Phys. 1992, 97, 1990–2001.

(36)

Schneider, T.; Stoll, E. Molecular-Dynamics Study of a Three-Dimensional One-Component Model for Distortive Phase Transitions. Phys. Rev. B 1978, 17, 1302–1322. 20 ACS Paragon Plus Environment

Page 21 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(37)


Mu, Z.; Liu, W.; Zhang, S.; Zhou, F. Functional Room-Temperature Ionic Liquids as Lubricants for an Aluminum-on-Steel System. Chem. Lett. 2004, 33, 524–525.

(38)

Mu, Z.; Zhou, F.; Zhang, S.; Liang, Y.; Liu, W. Effect of the Functional Groups in Ionic Liquid Molecules on the Friction and Wear Behavior of Aluminum Alloy in Lubricated Aluminum-on-Steel Contact. Tribol. Int. 2005, 38, 725–731.

(39)

Pensado, A. S.; Comuñas, M. J. P.; Fernández, J. The Pressure-Viscosity Coefficient of Several Ionic Liquids. Tribol. Lett. 2008, 31, 107–118.

(40)

Lopes, J. C.; Pádua, A. Molecular Force Field for Ionic Liquids Composed of Triflate or Bistriflylimide Anions. J. Phys. Chem. B 2004, 108, 16893–16898.

(41)

Canongia Lopes, J.; Deschamps, J.; Padua, A. Modeling Ionic Liquids Using a Systematic All-Atom Force Field. J. Phys. Chem. B 2004, 108, 2038–2047.

(42)

Salanne, M. Simulations of Room Temperature Ionic Liquids: From Polarizable to Coarse-Grained Force Fields. Phys. Chem. Chem. Phys. 2015, 17, 14270–14279.

(43)

Schroder, C. Comparing Reduced Partial Charge Models with Polarizable Simulations of Ionic Liquids. Phys. Chem. Chem. Phys. 2012, 14, 3089–3102.

(44)

Tersoff, J. New Empirical Approach for the Structure and Energy of Covalent Systems. Phys. Rev. B 1988, 37, 6991–7000.

(45)

Lindsay, L.; Broido, D. A. Optimized Tersoff and Brenner Empirical Potential Parameters for Lattice Dynamics and Phonon Thermal Transport in Carbon Nanotubes and Graphene. Phys. Rev. B 2010, 81, 205441.

(46)

Cygan, R. T.; Liang, J.; Kalinichev, A. G. Molecular Models of Hydroxide, Oxyhydroxide, and Clay Phases and the Development of a General Force Field. J. Phys. Chem. B 2004, 108, 1255–1266.

(47)

Luo, J.; Wen, S.; Huang, P. Thin Film Lubrication. Part I. Study on the Transition between EHL and Thin Film Lubrication Using a Relative Optical Interference Intensity Technique. Wear 1996, 194, 107–115.

(48)

Chaomleffel, J. P.; Dalmaz, G.; Vergne, P. Experimental Results and Analytical Film Thickness Predictions in EHD Rolling Point Contacts. Tribol. Int. 2007, 40, 1543–1552.

(49)

Bocquet, L.; Barrat, J.-L. Flow Boundary Conditions from Nano- to Micro-Scales. Soft Matter 2007, 3, 685–693.

(50)

Navier, C. Mémoire Sur Les Lois Du Mouvement Des Fluides. Mem. Acad. Sci. Inst. Fr 1823, 6, 389. 21 ACS Paragon Plus Environment


(51)

Page 22 of 24

Atkin, R.; Warr, G. G. Structure in Confined Room-Temperature Ionic Liquids. J. Phys. Chem. C 2007, 111, 5162–5168.

(52)

Kislenko, S. A.; Samoylov, I. S.; Amirov, R. H. Molecular Dynamics Simulation of the Electrochemical Interface between a Graphite Surface and the Ionic Liquid [BMIM][PF6]. Phys. Chem. Chem. Phys. 2009, 11, 5584.

(53)

Merlet, C.; Rotenberg, B.; Madden, P. A.; Salanne, M. Computer Simulations of Ionic Liquids at Electrochemical Interfaces. Phys. Chem. Chem. Phys. 2013, 15, 15781.

(54)

Cooper, P. K.; Wear, C. J.; Li, H.; Atkin, R. Ionic Liquid Lubrication of Stainless Steel: Friction Is Inversely Correlated

with

Interfacial

Liquid

Nanostructure.

ACS

Sustain.

Chem.

Eng.

2017,

acssuschemeng.7b03262. (55)

Singh, R.; Monk, J.; Hung, F. R. Heterogeneity in the Dynamics of the Ionic Liquid [BMIM + ][PF 6 – ] Confined in a Slit Nanopore. J. Phys. Chem. C 2011, 115, 16544–16554.

(56)

Singh, R.; Rajput, N. N.; He, X.; Monk, J.; Hung, F. R. Molecular Dynamics Simulations of the Ionic Liquid [EMIM+][TFMSI−] Confined inside Rutile (110) Slit Nanopores. Phys. Chem. Chem. Phys. 2013, 15, 16090.

(57)

Pean, C.; Daffos, B.; Rotenberg, B.; Levitz, P.; Haefele, M.; Taberna, P.-L.; Simon, P.; Salanne, M. Confinement, Desolvation, And Electrosorption Effects on the Diffusion of Ions in Nanoporous Carbon Electrodes. J. Am. Chem. Soc. 2015, 137, 12627–12632.

(58)

Castejón, H. J.; Wynn, T. J.; Marcin, Z. M. Wetting and Tribological Properties of Ionic Liquids. J. Phys. Chem. B 2014, 118, 3661–3668.

(59)

Hoang, H.; Galliero, G. Shear Viscosity of Inhomogeneous Fluids. J. Chem. Phys. 2012, 136, 124902.

(60)

Saugey, A.; Joly, L.; Ybert, C.; Barrat, J. L.; Bocquet, L. Diffusion in Pores and Its Dependence on Boundary Conditions. J. Phys. Condens. Matter 2005, 17, S4075–S4090.

(61)

Ewen, J. P.; Echeverri Restrepo, S.; Morgan, N.; Dini, D. Nonequilibrium Molecular Dynamics Simulations of Stearic Acid Adsorbed on Iron Surfaces with Nanoscale Roughness. Tribol. Int. 2017, 107, 264–273.

(62)

Thompson, P. P. A.; Troian, S. S. M. A General Boundary Condition for Liquid Flow at Solid Surfaces. Nature 1997, 389, 360–362.

(63)

Martini, A.; Hsu, H. Y.; Patankar, N. A.; Lichter, S. Slip at High Shear Rates. Phys. Rev. Lett. 2008, 100, 206001. 22 ACS Paragon Plus Environment

Page 23 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(64)


Martini, A.; Roxin, A.; Snurr, R. Q.; Wang, Q.; Lichter, S. Molecular Mechanisms of Liquid Slip. J. Fluid Mech. 2008, 600, 257–269.

(65)

Falk, K.; Sedlmeier, F.; Joly, L.; Netz, R. R.; Bocquet, L. Ultralow Liquid/solid Friction in Carbon Nanotubes: Comprehensive Theory for Alcohols, Alkanes, OMCTS, and Water. Langmuir 2012, 28, 14261–14272.

(66)

Falk, K.; Sedlmeier, F.; Joly, L.; Netz, R. R.; Bocquet, L. Molecular Origin of Fast Water Transport in Carbon Nanotube Membranes: Superlubricity versus Curvature Dependent Friction. Nano Lett. 2010, 10, 4067–4073.

(67)

Mendonça, A. C. F.; Pádua, A. A. H.; Malfreyt, P. Nonequilibrium Molecular Simulations of New Ionic Lubricants at Metallic Surfaces: Prediction of the Friction. J. Chem. Theory Comput. 2013, 9, 1600– 1610.

(68)

Jitvisate, M.; Seddon, J. R. T. Local Structure and Flow Properties of Ionic Liquids on Charged and Inert Substrates. J. Phys. Chem. C 2016, 120, 4860–4865.

(69)

Hoang, H.; Galliero, G. Local Viscosity of a Fluid Confined in a Narrow Pore. Phys. Rev. E 2012, 86, 21202.

(70)

Huang, D. M.; Sendner, C.; Horinek, D.; Netz, R. R.; Bocquet, L. Water Slippage versus Contact Angle: A Quasiuniversal Relationship. Phys. Rev. Lett. 2008, 101, 226101.

(71)

Ho, T. A.; Papavassiliou, D. V; Lee, L. L.; Striolo, A. Liquid Water Can Slip on a Hydrophilic Surface. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 16170–16175.

(72)

Tocci, G.; Joly, L.; Michaelides, A. Friction of Water on Graphene and Hexagonal Boron Nitride from Ab Initio Methods: Very Different Slippage despite Very Similar Interface Structures. Nano Lett. 2014, 14, 6872–6877.

(73)

Barrat, J.-L.; Chiaruttini, F. Kapitza Resistance at the Liquid Solid Interface. Mol. Phys. 2003, 101, 1605– 1610.

(74)

Ramos-Alvarado, B.; Kumar, S.; Peterson, G. P. Solid-Liquid Thermal Transport and Its Relationship with Wettability and the Interfacial Liquid Structure. J. Phys. Chem. Lett. 2016, 7, 3497–3501.

(75)

Lugt, P. M.; Severt, R. W. M.; Fogelström, J.; Tripp, J. H. Influence of Surface Topography on Friction, Film Breakdown and Running-in in the Mixed Lubrication Regime. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 2001, 215, 519–533.

(76)

Habchi, W.; Vergne, P.; Eyheramendy, D.; Morales-Espejel, G. E. Numerical Investigation of the Use of 23 ACS Paragon Plus Environment


Page 24 of 24

Machinery Low-Viscosity Working Fluids as Lubricants in Elastohydrodynamic Lubricated Point Contacts. Proc. IMechE Part J J. Eng. Tribol. 2011, 225, 465–477.

TOC image


Orders of Magnitude Changes in the Friction of an Ionic Liquid on

Recommend Documents