On the importance of timescales in the atomistic modelling of friction

Danny Perez1, Yalin Dong2, Ashlie Martini3

1Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA

2The University of Akron, Akron, Ohio, 44325, USA

3University of California at Merced, Merced, California, 95343, USA

Friction is an inherently multiscale phenomenon where both characteristic length- and

time-scales span many orders of magnitude. This fact makes the direct investigation of

friction through atomistic simulation methodologies, such as molecular dynamics (MD),

very challenging, especially as far as timescales as concerned. Indeed, conventional MD

on leadership class computers can simulate trillion of atoms. While this is still short of

completely embracing the mesoscale, it is probably sufficient to simulate the regions

where atomic resolution is necessary. In contrast, conventional MD can only generate

individual trajectories for times of the order of microseconds, even for small systems

containing only thousands atoms.

Over the last few years, we demonstrated that the physics of friction at scanning velocities

constrained by MD timescales could differ considerably from that prevailing at

experimentally relevant FFM velocities [1], severely limiting the direct correspondence to

experiments. We demonstrated two strategies that can be used to bridge that gap: first,

using Accelerated Molecular Dynamics (AMD) techniques [2] that aim at directly

extending the timescales amenable to MD simulations, and second, by parameterizing rate

theory models directly from atomistic simulations [3]. I will introduce and discuss these

two approaches and demonstrate their ability to address the timescale issue. I will

conclude by highlighting the remaining challenges that needs to be addressed in order to

simultaneously tackle both the length- and time-scale issues in their full generality.

[1] Qunyang Li, Yalin Dong, Danny Perez, Ashlie Martini, Robert W Carpick, Speed

dependence of atomic stick-slip friction in optimally matched experiments and molecular

dynamics simulations, Physical Review Letters 106, 126101 (2011)

[2] Danny Perez, Blas P. Uberuaga, Yunsic Shim, Jacques G. Amar, Arthur F. Voter,

Accelerated molecular dynamics methods: introduction and recent developments, Annual

Reports in Computational Chemistry 5, 79 (2009)

[3] Danny Perez, Yalin Dong, Ashlie Martini, Arthur F. Voter, Rate theory description of

atomic stick-slip friction, Physical Review B 81, 245415 (2010)

Atomic scale modelling of third body formation and wear in hard carbon materials

Michael Moseler

Fraunhofer Institute for Mechanics of Materials IWM, Wöhlerstr. 11, 79108 Freiburg Germany

Physics Department, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany

Despite the fact that diamond and diamond-like carbon (DLC) [1] coatings are used in an

increasing number of applications, not much is known about the atomic scale processes that cause

the wear of these films. For instance, the microscopic mechanisms that occur in DLC films in

tribological applications [2,3] or the polishing of diamonds are still poorly understood [4].

Molecular dynamics is ideally suited to gain a deeper understanding of the underlying wear

processes. In this talk a variety of atomistic simulations employing a novel Brenner bond order

potential [5,6] that has been corrected for a faithful description of bond breaking processes are

reported. For diamond polishing, the occurrence of soft polishing direction can be related to the

generation of thick amorphous soft layers [7] that are not stable with respect to mechanical

plowing or oxidative etching by ambient air [8]. The velocity of the diamond/amorphous-carbon

interface depends crucially on the diamond surface orientation with the highest speed found for

(110) surfaces that are rubbed in the (001) direction, while the lowest interface speed was

observed for the diamond (111) surface. These finding are in perfect agreement with a 600 years

old experimental knowledge of diamond polishers. The anisotropy of the wear is rationalized

within a rate model based on a yield criterion for single bonds at the crystalline/amorphous

interface [7]. Wear in hydrogen-free DLC films follows a similar route [9]. Both theory and

experiment demonstrate the formation of a soft amorphous carbon (a-C) layer with increased sp2

content, which grows faster than an a-C tribolayer found on selfmated diamond sliding under

similar conditions. The faster sp3 sp

2 transition in ta-C is explained by easy breaking of

prestressed bonds in a finite, nanoscale ta-C region, whereas diamond amorphization occurs at an

atomically sharp interface. A detailed analysis of the underlying rehybridization mechanism

reveals that the sp3 sp

2 transition is triggered by plasticity in the adjacent a-C. Rehybridization

therefore occurs in a region that has not yet experienced plastic yield. The resulting soft a-C

tribolayer is interpreted as a precursor to the experimentally observed wear that proceeds by

removing the a-C from the sliding interfaces by plowing or etching [8]. The talk will close with

new results on wear of lubricated rough ta-C surfaces and wear of diamond in contact with iron

surfaces.

[1] M. Moseler, P. Gumbsch, C. Casiraghi, A. Ferrari, J. Robertson, Science 309, 1545 (2005)

[2] L.Pastewka, S. Moser, M. Moseler, B. Blug, S. Meier, T. Hollstein, P. Gumbsch, Int. J. Mat.

Res., 10, 1136 (2008)

[3] L.Pastewka, S.Moser, M.Moseler, Tribo. Lett. 39, 49 (2010)

[4] J.Hird and J.Fields, Proc. R. Soc. Lond. 460, 3547 (2004)

[5] L.Pastewka, M.Mrovec, M.Moseler, P.Gumbsch, MRS Bulletin 37, 493 (2012)

[6] L. Pastewka, P. Pou, R. Perez, P. Gumbsch, M. Moseler, Phys. Rev. B (R) 78, 161402 (2008)

[7] Lars Pastewka, Stefan Moser, Peter Gumbsch, Michael Moseler, Nature Mat. 10, 34 (2011)

[8] Gianpietro Moras, Lars Pastewka, Johan Schnagl, Peter Gumbsch, Michael Moseler, J. Phys.

Chem. A 115, 24653 (2011)

[9] Tim Kunze, Matthias Posselt, Sibylle Gemming, Gotthard Seifert, Andrew R. Konicek,

Robert W. Carpick, Lars Pastewka and Michael Moseler, Tribo. Lett. 53 119 (2014)

Tight-Binding Quantum Chemical Molecular Dynamics Study on Tribo-Chemical

Reaction of Diamond-Like Carbon under Water Lubrication

Shandan Bai1, Yasunori Niiyama

2, Yoshihiko Kobayashi

1, Seiichiro Sato

1,

Yuji Higuchi1, Nobuki Ozawa

1, Koshi Adachi

1, Shigeyuki Mori

2, Kazue Kurihara

3, 4,

Jean Michel Martin5, Momoji Kubo

1

1

Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan 2

New Industry Creation Hatchery Center, Tohoku University, Sendai 980-8579, Japan 3

Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 4

Institute of Multidisciplinary Research for Advanced Materials, Tohoku University,

Sendai 980-8577, Japan 5

Laboratoire de Tribologie et Dynamique des Systemes, Ecole Centrale de Lyon, 69134

Ecully Cedex, France

[Introduction] Much attention has been paid to Diamond-Like Carbon (DLC) coatings,

which have low friction and anti-wear tribological performances. The friction coefficient

of the DLC films drastically changes under the water lubrication, since some

tribo-chemical reactions occur during sliding. The details of the chemical reaction are

difficult to be revealed only by chemical

analyses. In this study, we use the computational

method to reveal the chemical reaction at an

atomic scale.

[Method] In order to understand tribo-chemical

reactions of DLC films under water lubrication,

we apply our tight-binding quantum chemical

molecular dynamics method [1]. Figure 1 shows

the model of DLC film under water lubrication.

[Results and Discussion] Figure 2 shows the

snapshots of dynamic behaviors of upper DLC

substrate. Figure 2 (a) shows the initial state of

upper DLC substrate. At 0.235 ps, the C-H bond

is formed between the water molecule and upper

substrate of DLC, and then the H atom is

terminated at the surface as shown in Figure 2

(c). We also observe the C-OH bond formation

between the water molecule and upper DLC

substrate at 0.015 and 0.840 ps, as shown in

Figure 2 (b) and (d). Then, the DLC surface

becomes progressively terminated by H/OH.

These results show that the water molecule

dissociates into H and OH, which terminated the

surface of DLC during friction.

[1] K. Hayashi, M. Kubo et al, J. Phys. Chem. C.

115, 22981 (2011).

Figure 1: Model of DLC under water lubrication.

Figure 2: Snapshots of dynamic behaviors (a) initial state, (b) OH termination at 0.015 ps, (c) H termination at 0.235 ps, and (d) OH termination at 0.840 ps.

Fx

Fz

Sliding

Fixed

Carbon

Hydrogen

Oxygen

Pressure

OH termination

OH termination

H termination

0.000 ps 0.015 ps

0.840 ps

(a)

(c)

(b)

(d)

0.235 ps

Tribochemical interactions between DLC coatings and hydrocarbon gases

Komlavi Dzidula KOSHIGAN1, Julien FONTAINE

1,

Christophe HEAU2, Christophe DONNET

3, Florence GARRELIE

3

1Laboratoire de Tribologie et Dynamique des Systèmes, UMR5513 CNRS / Ecole

Centrale de Lyon, 69134 Ecully cedex, France 2IREIS, HEF Group, 42162 Andrézieux-Bouthéon, France

3Laboratoire Hubert Curien, UMR 5516 CNRS / Université Jean Monnet, Saint-Etienne,

France

Diamond-Like Carbon coatings are increasingly popular in tribological applications, not

only as solid lubricants, but also in combination with lubricant additives for boundary-

lubricated conditions. Modern automotive engines are indeed relying on these materials

both for wear protection and for friction reduction of severe contacts. Nevertheless, the

solid lubrication processes of Diamond-Like Carbon coatings are not fully elucidated:

these coatings are usually as hard or harder than most metallic substrates and

counterfaces, and yet provide low friction coefficient as soft solid lubricants do. Clearly,

surface phenomena are paramount in these peculiar solid lubrication processes, especially

tribochemical interactions. Furthermore, wear rates of different DLC coatings in base oil

– without lubricant additives – are not necessarily related to the coating hardness,

emphasizing the critical role of tribochemistry.

In this study, 3 different DLC have been compared: a hydrogen-free DLC obtained by

Pulsed Laser Deposition, and two hydrogenated DLC obtained by Plasma-Enhanced

Chemical Vapor Deposition, with respectively 20 at.% and 36 at.% of hydrogen. It is

noteworthy that sp2 content in all these films is expected to be larger than 50%. The effect

of hydrocarbon molecules has been evaluated with an environmentally controlled

tribometer, allowing to perform experiments from ultra-high vacuum to atmospheric

pressure. Linear reciprocating sliding experiments have been conducted with both pin and

flat coated with the same DLC coating. Three hydrocarbon gases have been considered,

at the same pressure of 10 kPa: C2H6, C2H4 and C2H2.

These experiments reveal that the friction coefficient is significantly affected not only by

the hydrogen content of the DLC coating, but also by the nature of the hydrocarbon

molecule. Furthermore, both wear and tribofilm build-up could be observed on the pin

wear scars, but in amounts that strongly rely on both coating and hydrocarbon gas nature.

The role of tribochemical interactions, and especially the contributions of both hydrogen

and sp2 carbon, will thus be discussed in light of these experiments.

Smoothed Particle Hydrodynamics Simulations of Abrasive Flow Machining

Claas Bierwisch, Christian Nutto, Hanna Lagger, Michael Moseler

MikroTribologie Centrum µTC, Fraunhofer IWM, Wöhlerstr. 11, 79108 Freiburg,

Germany

Manufacturing techniques of complex geometries often rely on the precise finishing of

surfaces in order to achieve their designated performance. Obtaining the necessary

surface roughness and a sufficiently high material removal rate in finishing processes of

hard-to-access surfaces remains a great challenge. An example process is abrasive flow

machining (AFM), where abrasive suspensions are forced to flow along internal

geometries resulting in an abrasive wear on the work piece. In spite of the huge range of

applications for this process, the difficulties to adjust the parameters correctly for each

work piece geometry prevents its utilization in a greater variety of industrial applications.

We numerically study the process of abrasive flow machining at the scale where the

actual interaction between the abrasive grains of the applied suspension and the work

piece occurs. We present the development of smoothed particle hydrodynamics (SPH)

models for this purpose. Rheological properties of the carrier fluid are included by using

the viscoelastic model of Phan-Thien and Tanner [1]. Abrasive grains are modeled as

perfectly rigid bodies. Material removal from the ductile work piece is described by the

Johnson-Cook flow stress model in combination with a strain-based failure model [2].

The predictive power of the numerical simulations is demonstrated by comparison with

experimental studies.

We study the influence of various parameters such as grain shape, fluid viscoelasticity,

and work piece temperature on the material removal (Fig. 1). Based on these analyses

design rules for abrasive suspensions are discussed.

[1] N. Phan-Thien, R.I. Tanner, J. Non-Newtonian Fluid Mech. , 353-365 (1977).

[2] G.R. Johnson, W.H. Cook, 7th

Int. Symposium on Ballistics, 541-547 (1983).

Figure 1: Simulation snapshots of an abrasive grain (dark grey) in a viscoelastic carrier fluid (blue) which removes material from a ductile work piece (light grey).

Multiscale-Multiphysics Approach to Polyelectrolyte Brush Friction

Hitoshi Washizu1,2

, Tomoyuki Kinjo1,2

, Hiroaki Yoshida1,2

1 Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan

2Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University,

Katsura, Kyoto 615-8520, Japan

The final goal of controlling frictions in automotive tribology may be dependent on the

control of forces in the ion atmosphere that surrounds the charged particles or polymers

in solution [1]. Not only the static but also the dynamic behavior of the ions in the ion

environment is different [2]. Synovial joints are a typical biomimetic system of tribology,

which is governed by this force, and the tribological properties of polyelectrolyte brushes

have been widely examined as model systems [3].

The Monte Carlo Brownian Dynamics method [4] was used to simulate the nature of

polyelectrolyte brushes. For the basic understanding, the effect of linear charge density

on the polyions, added salt, and surface charge on

the structure of polyelectrolyte brushes was studied

[5]. In order to discuss the friction behaviors in these

systems, improvements in the simulator were then

needed to include the effect of the solvent in multi-

scale environments (Fig. 1). First, the solvent model

was made to include the solvation effect of polymers

and counter- and co-ions. In the framework of

dissipative particle dynamics, the polarizability of a

set of solvent molecules was described as oscillators

[6]. The solvent flow was then included by

calculating the Brownian particles by Langevin

dynamics and the solvent flows by the Lattice

Boltzmann method [7]. In this method, the dynamics of a huge amount of small ions were

enabled by treating each Brownian particle as a point described by a Stokes-source.

These methods essentially treat ions as particles. In order to treat macroscopic

phenomena, a multiphysical simulator based on continuum equations of ion solvent flow

and electric fields was created. The distributions of small ions are treated by the Nernst-

Planck equations to determine transitional and nonbulk ion distribution [8]. Whereas

these methods are under investigation, the friction of a very complicated tribo-system,

which is governed by long-range Coulomb interactions, should be considered before

long.

[1] J. Klein, Friction 1, 1 (2013).

[2] H. Washizu, K. Kikuchi, J. Phys. Chem. B, 110, 2855 (2006).

[3] M. Kobayashi, M. Terada, A. Takahara, Faraday Disc., 156, 403412 (2012).

[4] K. Kikuchi, et al. Chem. Phys. Lett., 185, 335 (1991).

[5] H. Washizu, T. Kinjo, H. Yoshida, Friction 2, (2014) (in print).

[6] T. Kinjo, H. Yoshida, H. Washizu, J. Jpn. Soc. Phys. Sppl. (in print).

[7] H. Yoshida, T. Kinjo, H. Washizu, Proc. 3rd Intl. Conf. Mol. Sim. (2013).

[8] H. Yoshida, T. Kinjo, H. Washizu, Proc. 3rd Euro. Conf. Microfluidics (2012).

Figure 1: Molecular simulations for ionic systems..

Instabilities at Frictional Interfaces: Creep Patches, Nucleation and Rupture Fronts

Yohai Bar-Sinai1, Robert Spatschek

2, Efim A. Brener

1,3, Eran Bouchbinder

1

1Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel

2Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany 3Peter Grünberg Institut, Forschungszentrum Jülich, D-52425 Jülich, Germany

The strength and stability of frictional interfaces, ranging from tribological systems to

earthquake faults, are intimately related to the underlying spatially-extended dynamics.

Recent experimental discoveries have revealed rich spatio-temporal dynamics that

precede the onset of sliding motion, and occur well below the nominal static friction

coefficient. In this talk we will highlight novel features of frictional constitutive laws

– most notably a transition from velocity-weakening friction at small slip velocities to

velocity-strengthening friction at higher velocities – and theoretically explore their

implications on the stability and failure of spatially-extended frictional interfaces. We

provide a comprehensive theoretical account, both analytic and numeric, of spatio-

temporal interfacial dynamics in a realistic rate-and-state friction model. Slowly

extending, loading-rate dependent, creep patches undergo a linear instability at a critical

nucleation size, which is nearly independent of interfacial history, initial stress conditions

and the frictional behavior at high velocities. Nonlinear propagating rupture fronts – the

outcome of instability – depend sensitively on the stress state and velocity-strengthening

friction. The rupture fronts are related to steady state fronts solutions and span a wide

range of propagation velocities, in some cases much smaller than elastic wave speeds,

possibly related to the recently much-debated phenomenon of “slow rupture”. This work

provides theoretical tools to aid the understanding of the onset of frictional motion and

precursory dynamics within a general continuum-mechanics framework.

Effects of atomic-scale geometry on rough contact

Tristan Sharp, Lars Pastewka, Mark O. Robbins

Johns Hopkins University

Continuum models show that surface roughness can control the contact area, friction, and

wear between two contacting solids. Intriguingly, the smallest resolved surface features in

the continuum model can play the largest role, but continuum descriptions break down at

small scales. Here, we use molecular dynamics simulations to illuminate how atomic

scale features on surfaces affect contact properties. Beginning from the established case

of continuum linear elasticity that gives a linear relationship between real contact area

and load, we systematically introduce atomic-scale physics to determine the affects on

normal contact. Replacing an ideal linear isotropic elastic medium with a harmonic

atomic lattice produces only small changes in the mechanical response. For more realistic

interactions, plasticity increases the contact area when the surface is sufficiently rough.

The atomic steps present on crystal surfaces lead to increased plasticity and change the

small scale structure of contacts. Depending on the tendency for the material to yield, the

presence of steps can increase or decrease the area of very high pressure, but steps always

decrease the area of very low pressures. The large scale structure of the contact is the

same for all cases.

Rate-dependent contact mechanics of polymer composites

Sam Krop, Han. E.H. Meijer, Lambert C.A. van Breemen

Eindhoven University of Technology, Mechanical Engineering, Polymer Technology,

5600MB Eindhoven, The Netherlands

Polymers play an increasingly important role in tribological applications. This is a

challenging subject because of the complex contact conditions involving many variables.

Therefore, simplification to a well-defined contact situation is needed: the single-asperity

sliding friction test. With this test, a wide range of surface mechanical properties is

analysed in a controlled manner. In a previous study a hybrid experimental-numerical

approach was employed which revealed the subtle interplay between the constant

polymer-indenter adhesion and the velocity/rate-dependent deformation of the polymer

during a single-asperity sliding friction test [1]. Understanding and quantifying the

polymers’ intrinsic mechanical response [2] proved to be key.

In practice, however, most polymers are filled. These fillers are added for many different

reasons: e.g. to improve mechanical properties, to change the appearance through

colorants, or even to reduce costs by adding a cheaper material in the polymer matrix.

These additives have an effect on both the intrinsic mechanical response, and the

adhesive interaction with the indenter tip. Consequently, the frictional response of the

polymer changes completely.

To characterize the effect of filler particles experimentally, our model materials, i.e.

polycarbonate and epoxy, are filled with either hard (TiO2) or soft (MBS) particles. An

identical experimental-numerical approach is used to investigate the response of these

model systems. The effect of adding fillers to the polymer matrix is revealed by scratch

tests; finite-element simulations reveal the interplay between composite-indenter

adhesion and the composites’ response to deformation. Adding either soft or hard fillers

only results in a change in magnitude of intrinsic mechanical properties like modulus and

yield stress. A similar effect is seen for the response in friction; the dependence on

scratch velocity does not change, whereas the penetration into the composite changes

with filler type and amount.

[1] Van Breemen et al., Wear 2012, 274-275, 238-247

[2] Van Breemen et al., J. Mech. Phys. Solids 2011, 59(10), 2191-2207