Non-equilibrium molecular dynamics

simulations of organic friction modifiers

James Ewen

PhD Student

Tribology Group (Shell UTC)

Imperial College London

Session 8B • Bronze 2

Lubrication Fundamentals

STLE Annual Meeting

19th May 2016

Contents

1. Introduction:

a) Molecular Dynamics (MD) in tribology

b) Organic Friction Modifiers

c) Research objectives

2. Methodology:

a) Simulation procedure

b) Force-Fields

3. Results:

a) Preliminary squeeze out simulations

b) Film structure

c) Friction coefficient

d) AA vs. UA

4. Conclusions

1. Introductiona) Molecular Dynamics (MD) in tribology

• Classical MD is the ‘cheapest’ atomic

scale simulation method

• But no reactivity information

(electrons not treated explicitly)

• In tribology, MD gives unique insight into:

» Nanoscale structure of lubricant and

additive molecule systems

» Complex friction behaviour

» Important tribological phenomena

(e.g. shear thinning, stick-slip)

Fig 1: Computational Simulation Methods - adapted from:

Kermode et al., Multiscale Simulation Methods in

Molecular Sciences, NIC Series, Vol 42, 215-228 (2009)

Length Scale

0.1nm 1nm 10nm >1μm

Tim

e S

ca

leS

tatic

1p

s1

ns

1μ

s1

ms

1 10 102 103 104 105 106 107 ∞

Continuum

(e.g. CFD)

QMC

DFT

Coarse

Graining

Atomistic

MD

QM/MM

Number of Atoms

• Boundary Lubrication (low sliding

speed/high pressure) high friction

• OFM polar head groups adsorb onto

surface

• Form monolayer – interchain Van Der

Waals forces between fatty tails

• Incompressible and prevents solid-solid

contact reduces friction

Polar Head Group

Fatty Tail

Fig 3. Schematic of action of model organic friction modifiers

Stachowiak & Batchelor, Engineering Tribology, Elsevier Inc.,

2005

Hardy Model

Fig 2. Generalised Stribeck Curve

1. Introductiona) Organic Friction Modifiers (OFMs)

• Confined NEMD simulations of OFMs

• Gain unique insight into:

Nanoscale film structure

Friction reduction mechanism

Relative performance of different OFMs

• Comparative studies, different:

Tail groups (Z-unsaturation)

Head groups (acid, amide, glyceride)

Surface coverages

Conditions – sliding velocity, pressure

Force-fields – AA vs. UA

1. Introductiona) Research objectives

55 A

• Surface (100) α-Fe2O3 (hematite) – harmonic potential (Berro 2010)

• Surface-OFM, Surface-Lubricant – Lennard-Jones and Coulombic potentials

• Lubricant and OFM molecules – (L-)OPLS All-Atom (Jorgensen 1996, Price

2001, Siu 2012)

OFM Film

OFM Film

Hexadecane

Fig 4. (a) NEMD system set up, (b) OFM molecules simulated

2. Methodologya) Simulation procedure

Three OFM coverages: 4.32, 2.88, 1.44 nm-2

(max = 4.55 nm-2)

Vtotal = Vstretch + Vbend + Vtorsion + VVDW + Vqq

Fig 5. Potentials included in classical empirically parameterised Force-Field

𝑉𝑉𝐷𝑊(𝑟𝑖𝑗 ) = 4𝜀𝑖𝑗 𝜎𝑖𝑗

𝑟𝑖𝑗

12

− 𝜎𝑖𝑗

𝑟𝑖𝑗

6

Fig 6. a) All-Atom and b) United-Atom force-field representation of n-hexadecane

𝑉𝑞𝑞 𝑟𝑖𝑗 =𝑞𝑖𝑞𝑗

4𝜋𝜀𝑟𝑟𝑖𝑗2

2. Methodologya) Force-Fields

• Vacuum added in x-y plane to allow hexadecane to be

squeezed out (Sivebaek 2003)

• Decreasing wall separation converges at equilibrium value

• Equilibrium wall separation increases with OFM coverage

• Equilibrium amount of hexadecane remaining inside

contact volume independent on OFM coverage (two layers)

Fig 7. Variation in; (a) wall separation, (b) number of hexadecane molecules inside contact, with time

3. Resultsa) Preliminary squeeze out simulations

Estimate

hexadecane

layer

thickness at

0.5 GPa

SA Medium (2.88 nm-2)

• High coverage solid-like films with well-separated confined hexadecane layer

• Medium coverage amorphous films which are significantly interdigitated

• Molecular tilt partially aligns with the sliding direction

• NEMD can gain unique insight into structure and friction of OFM the films

SA High (4.32 nm-2) 0.5 GPa, 10m/s

3. Resultsb) Film structure - NEMD videos

• Higher coverage lower tilt angle

• Tilt angle relatively independent of

head and tail group type

• Good agreement with SFA and in-situ

AFM experiments (Campen 2015)

• Higher coverage larger z-CoM

• Saturated and unsaturated tail-groups

similar z-extension

• GMS & GMO larger z-extension –

most significant at high coverage

Fig 8. Variation in; (a) zCoM, (b) tilt angle, with OFM coverage

3. Resultsb) Film structure – OFM zCoM and tilt angle

4.32 nm-2 2.88 nm-2 1.44 nm-2

• Layering of additive

and lubricant in z

• More interdigitation of

lubricant into OFM film

at lower coverage

• More interdigitation of

lubricant into OFM film

in acids than

glycerides

• Glyceride films slightly

thicker than acid

• Good agreement with

SFA and in-situ AFM

• Z-unsaturated tail

group similar structureFig 9. Atomic Mass Density Profiles for: (a) GMS/GMO (b) SA/OA

3. Resultsb) Film structure – atomic mass density profiles

• Higher coverage more solid-like film

(increased long-range order)

• Glyceride (green) more solid-like than acid (orange)

• Intermolecular hydrogen bonding (3 vs 1 HB per OFM)

• Explanation for lower interdigitation for glycerides films

4.32 nm-2 2.88 nm-2 1.44 nm-2

C

CTT

C

CTT

Fig 10. RDF for SA and GMS at high, medium and low coverage

3. Resultsb) Film structure – RDF and intermolecular hydrogen bonding

• High coverage: OFM molecules move with wall, clear slip planes between

OFM-hexadecane and hexadecane-hexadecane layers

• Medium coverage: slip plane less clear – viscous friction in interdigitated region

• Low coverage: more Couette-like velocity profile – similar to confined pure

hexadecane (Savio 2013)

4.32 nm-2 2.88 nm-2 1.44 nm-2

Fig 11. Velocity profile for SA at high, medium and low coverage

3. Resultsb) Film structure – Velocity Profiles

‘Liquid’‘Amorphous’‘Solid’

• High coverage: low friction – formation of solid-like film, interdigitation low,

facilitates slip plane between layers

• Medium coverage: high friction – interdigitation high, rearrangement slow

• Low coverage: intermediate friction – films more interdigitated, rearrangement fast

• Friction coefficient: OA ≈ SA > OAm ≈ SAm ≈ GMO > GMS (Campen 2012)

0.5 GPa, 10m/s 4.32 nm-2 2.88 nm-2 1.44 nm-2

Fig 12. Variation in friction coefficient with coverage

3. Resultsc) Friction coefficient – effect of OFM coverage

(Yoshizawa 1992)

• Friction increases linearly with logarithm of sliding velocity

• Predicted by shear-induced thermal activation theory (Briscoe 1982, He 2001)

• Observed experimentally for boundary friction of OFM films (Campen 2012)

• Medium coverage friction greater dependence on sliding velocity

• Experimental behaviour: saturated (high coverage) vs. Z-unsaturated (low coverage)

Fig 13. Variation in friction coefficient with sliding velocity at high, medium and low coverage

4.32 nm-2 2.88 nm-2 1.44 nm-2

3. Resultsc) Friction coefficient – effect of sliding velocity

3. Resultsd) AA vs. UA

• Compare SA film structure and friction results for AA vs. UA force-fields:

1. (L-)OPLS All-Atom (Jorgensen 1996, Price 2001, Siu 2012)

2. TraPPE United-Atom (Martin 1998, Clifford 2006)

• UA order of magnitude cheaper – lower sliding velocities accessible

• But UA known to under-predict viscosity of long-chain alkanes (Allen 1997)

Viscosity?

Film Structure?

Film Phase?

Friction?

• UA accurately represents OFM film

structure, however:

• UA much lower friction coefficient

than AA

• AA friction-coverage behaviour

agrees with experiment

(Yoshizawa 1993)

• UA friction-coverage behaviour

opposite of experimental trend

• For UA, interdigitation much less

critical to friction

• AA model necessary for accurate

simulations of OFM friction

Fig 14. Variation in SA friction coefficient with coverage – UA vs AA

3. Resultsd) AA vs. UA – effect of OFM coverage

• UA much lower friction coefficient at all speeds and coverages

• Larger difference between AA and UA at medium coverage - more interdigitation

• UA also captures logarithmic trend, but values well below experiments…

4.32 nm-2 2.88 nm-2

Fig 15. Variation in friction coefficient with sliding velocity – UA vs AA

3. Resultsd) AA vs. UA – effect of sliding velocity

1E+01 1E+021E-001E-01

(1ms-1) (10ms-1)

Experimental (Campen 2012)

• Experimental friction coefficients agree much better with AA simulations

• Further suggests that AA models necessary for OFM simulations

Stearic acid AAStearic acid UA

Fig 15. Variation in friction coefficient with logarithm of sliding velocity – UA vs AA LHS experimental (Campen 2012), RHS high coverage NEMD results

NEMD (high coverage)

3. Resultsd) AA vs. UA – experimental comparisons

• Constructed model to compare various

OFMs under different conditions

• Film structure varies significantly

depending on OFM type and coverage

• Substantial reduction in friction at high

coverage - slip plane

• Z-unsaturated OFMs equally low CoF to

saturated ones – experimental

differences due to lower coverage

• GMS outperforms other OFMs at all

coverages (H-bonding)

• Friction coefficient increases with

logarithm of sliding velocity

• AA force-fields critical to accurately

model OFM friction behaviour

4. Conclusions

Ewen, J., Gattinoni, C., Morgan, N.,

Spikes, H., Dini, D. Non-equilibrium

molecular dynamics simulations of

organic friction modifiers adsorbed on

iron oxide surfaces, Langmuir, 2016

Research funded by the EPSRC and Shell (CASE)

Many thanks to: Dr. D. Dini, Prof. H. Spikes, Prof. D. Heyes, Dr. C. Gattinoni

(Imperial), Dr. N. Morgan (Shell) and the computational chemistry group at Shell India

Private Markets Limited

All systems were constructed using the MAPS platform by Scienomics Inc.,

simulations were run in LAMMPS and visualisations were created using VMD.

Acknowledgements

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