R&D Review of Toyota CRDL, Vol.44 No.2 (2013) 1-10

1Special Feature: Powertrain and Environment
Review

Molecular Dynamics Analysis of Elastohydrodynamic Lubrication Oil Film
Hitoshi Washizu, Shuzo Sanda and Toshihide Ohmori
Report received on May 9, 2013This paper reviews the recent research regarding the non-equilibrium all-atom
molecular dynamics studies of the traction properties of hydrocarbon fluids under elastohydrodynamic
lubrication. The effect of the oil film thickness, shear rate and pressure were studied. The dynamic
mechanisms of the momentum transfer on layers of fluid molecules are analyzed focusing on theintermolecular interactions and intramolecular interactions. Characteristic molecular mechanisms are
obtained for the high traction molecules of cyclohexane and dumbbell-like molecules (dicyclohexyl,
dicyclohexylmethyl and santotrac 50). In the dumbbell-like molecules, alicyclic rings, which distributeacross the low ordered molecular layers, behave as a stiff bulky mass, and momentum transfers to the endof the molecular axis. The traction mechanisms of hydrocarbon fluids are also determined during the courseof the analysis. The method would be applied to design composite fluid molecules of high-performance
traction oil.
Molecular Dynamics, Traction Fluid, Elastohydrodynamic Lubrication, Hydrocarbon,
Momentum Transfer

In this paper, we brieﬂy describe the history ofmolecular dynamics (MD) simulations applied totribology, and introduce some examples of research
regarding the analysis of molecular mechanisms ofelastohydrodynamic oil films.
MD is a numerical simulation method incomputational chemistry or physics which describes
the motion of atoms under classical approximation bysolving Newtonian equations of motion.(1) Figure 1
shows the time development of a number of scientificarticles, which contain the keyword “Tribology” or“Lubrication” and “Molecular dynamics” in the title
or in the abstract, which are found in the Web of
Science database by Thomson Reuters.
The MD studies which focus to “Tribology” or“Lubrication” started in the 1990s and made rapid
progress in the late 1990s. We hereafter call thesestudies “Tribo Molecular Dynamics”.
Before the beginning of the Tribo MD, many studies
corresponding to this topic have been done. The originof the MD method can be traced back to a calculationof dynamics of hard sphere particles by Alder andWainwright in the late 1950s.(2) At the beginning,© Toyota Central R&D Labs., Inc. 2013subjects of the simulations were mainly the phasetransitions of solids and liquids, then the authors founda long time tail in the velocity autocorrelation
functions.(3) The correlation functions are related to theviscosity. The results have indicated the necessity ofsufficiently long time calculations of the motion of theatoms with the correlation of neighboring atoms inorder to obtain transport coefficients in the statisticalmechanics such as the diffusion coefficients or
viscosity coefficients for realistic atoms or molecules.

250
Number of papers

1. Introduction: Tribo Molecular Dynamics

200
150
100
50
0
-1990

1991-1995 1996-2000 2001-2005 2006-2010

Years

Fig. 1

Number of scientific articles concerning themolecular dynamics in tribology.
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R&D Review of Toyota CRDL, Vol.44 No.2 (2013) 1-10

The simulations of the bulk viscous liquids became
one of the main subjects in non equilibrium molecular
dynamics simulations and were described in two books
written by Allen & Tildesley(4) and Evans & Morriss(5)in 1987 and 1990, respectively.
The understanding of the molecular origin of thebulk viscosity of liquids is important but it is notenough. This is because tribology is surface science.
Simulations of equilibrium structures of liquid
molecules absorbed on the surface began to be studied
around 1980.(6,7) The fluidity of the absorbed
molecules were studied. Analysis from the viewpointof viscosity was discussed by Bitsanis et al. in 1987.(8)They studied the dynamics of sphere-shaped LennardJones particles confined between two parallel walls,
and discussed the relation between the equilibrium
structure and the viscosity including the effect of theboundary slip under a framework of the linear response
theory.
A MD simulation of liquid molecules, which wereconstructed by 20 linearly connected sphere particles
i.e., which had intramolecular degrees of freedom
confined between two parallel walls and adopted shear
by moving the walls was done by Thompson et al. in
1992.(9) This work can be regarded as the completionof the foundation of the Tribo MD.
The friction coefficients can be considered as a typeof transport coefficient.(10) It can then be related to theenergy dissipation due to the thermal vibration such as
molecular motions under a weak external field. In
other words, the molecular origin of frictions is related
to the dissipation of the molecular motion energy
responses to the external field produced by the sliding
motion. The energy dissipation process can be
described by classical molecular dynamics
simulations.(11,12) Adopting this idea to the analysis of
MD simulations, the friction force changes by the
specific molecular vibration mode within a huge
relaxation mode of the molecular motion. In this paper,
we review studies of non-equilibrium MD simulationsof a traction fluid in a confined geometry, and analyze
the energy dissipation processes due to this concept.
Friction behavior of confined molecular layers differs
when the molecules are governed by the main chain
motion in the chain molecules, or the ring ﬂap motion
is incorporated in the ring molecules. In thesesimulations, the heat generated during the friction
process is extracted by a heat bath, which is used tomaintain the system at a fixed temperature.
If we cannot neglect the chemical reactions, the© Toyota Central R&D Labs., Inc. 2013

friction dynamics can be analyzed by the non-classicalor modified MD simulation. For example, thedynamics of an organic or inorganic film, which is
chemically absorbed on the surface, the energy
dissipates by the formation and disappearance of achemical bond due to the friction. In order toinvestigate the mechanism of low friction of a DLC(diamond-like carbon coating) surface, the REBO
(Reacting Empirical Bond Order) method, which isextended classical MD including bond exchanges due
to a chemical reaction,(13) or a tight-binding quantum
MD method(14) is used. If there are no chemical
reactions, and no molecular internal degree of freedom,
then the energy dissipation is due to lattice vibrationin the solid.(15-17)
If we need to consider not only the atomistic motion,
but also a structure change of some large molecules or
ﬂakes consisting of a large number of atoms, a coarsegrain molecular simulation is proper for the analysis.
Recently, the ultra low mechanisms of solid layered
graphites have been solved by coarse-grained
molecular simulation, which is normally used to modelsoft materials such as polymers or liquid crystals.(18)
Each graphene sheet consisting of some hundreds toten thousand atoms are modeled as a single coarsegrain sheet. The friction of layered materials isunderstood in the framework of the thermal escapemotion of a transferred pile of graphene sheets. Energy
dissipation is related to the dynamics of the structualchanges of the coarse-grain sheets.
Although the extra simulational methods arepresented to treat quantum mechanics or coarse-grain
dynamics, the classical all-atom MD are effective
method to analyze the tribological process. The
analysis of traction fluids is one of the examples.
2. Traction Fluids and Elastohydrodynamic
Lubrication
For fluids used in a traction drive type continuously
variable transmission (CVT), its traction properties
largely depend on the structure of the fluid
molecules.(19,20) In order to minimize and to achieve ahigher CVT capacity, improved fuel economy andprotect the environment, the molecular design on amolecular level of high traction coefficients is effective
for the developments.
The lubrication condition of a working traction fluid
is under elastohydrodynamic lubrication (EHL).(21,22)
On the other hand, the molecular mechanism of the
http://www.tytlabs.com/review/R&D Review of Toyota CRDL, Vol.44 No.2 (2013) 1-10transmission of force in a highly-loaded fluid layer is
not clearly known. Hence, the non-equilibrium MD
simulations of a traction fluid in a confined geometry
were investigated.(23-25) The methods and some results
are shown in the following sections. First, the fluidlayer is confined between two solid plates under highpressure. The traction simulations are performed byapplying a relative sliding motion to the solid layer.
The mechanism of the traction due to the structure of
the fluid molecules is finally analyzed.
Because of the large difference in the oil film
thickness and shear viscosity, the simulations do notdirectly model the experiments.(23-27) In mostexperiments, the film thicknesses are over 0.1 μm andthe shear rates are below 106 s−1. The film thickness
regime in the simulations is far too thinner and theshear rate regime is far too higher than that in theexperiments. Although recent hybrid simulations of the
MD and computational fluid dynamics show thepossibility of simulation under realistic shear rates andfilm thicknesses,(28) a simple method described in thenext section is useful for survey.
The traction force of a fluid, which has the samedefinition as friction force, has its origin in thetranslational momentum transfer across the fluid layer.
The traction force is generated by the momentum
transfer between molecules from the viewpoint of the
MD scale. At first, the external force, which is applied
to the solid layer by a constant sliding movement
velocity and normal constant pressure, transfers to thefluid molecules in the vicinity of the solid layer by anintermolecular interaction. The affected molecules
deform their shape by an intramolecular interaction.
The force transfers again to another molecule by anintermolecular interaction, and finally the force
transfers to the other side of the solid layer as a traction
force. The heat produced during this process dissipatesto the bulk in each process. This process of momentum
transfer should be treated as a statistical mechanicalprocess, which is carefully extracted from the hugethermal noise. In order to solve this difficult problem,
non-equilibrium MD simulations, which can treat alarge number of fluid molecules up to a several
hundred nm film thickness, are made using a
supercomputer. The dynamics of several hydrocarbon
fluids including industrial lubricant under shear andhigh pressure are then simulated. These test fluids havetheir own characteristic structures, and their traction
coefficients were measured experimentally andcompared to one another. The relation between the© Toyota Central R&D Labs., Inc. 20133

obtained traction coefficients μ and molecular structure
were then analyzed by focusing on the inter- andintramolecular interactions. The molecular mechanismof the traction phenomena in a fluid layer was thenpresented.
3. Molecular Dynamics Simulation
Figure 2 shows a schematic view of the Tribo MD.
The all-atom modeled fluid molecules are dynamicallytreated using the AMBER force field.(29) The force
field is described as a set of functions of two to fourbody interactions within each organic molecule ofwhich the parameters are determined from ab initio
molecular orbital calculations. On the x and y axes, theperiodic boundary condition is adapted to thesimulation cell, where x is the sliding direction and yis the direction of the fluid thickness.
The temperatures are controlled at 350 K using the
Nosé-Höver formalism,(30) in which all the molecules
are connected to a heat bath. While this model of a heatbath has been shown to affect the rheology of confined
fluids at shear rates above γ& = 0.2 (in reduced
Lennard-Jones units), the low shear rates here, amaximum of γ& (ε / mR 2 )1/ 2 ≈ 0.004 , suggest that such
artifacts should be negligible.(31,32)
Each simulation step corresponds to 0.5 fs and thetime integral due to the motion of the atoms is
calculated by the rRESPA (Reversible Reference
System Propagator Algorithm) method based on thevelocity Verlet method for a time integral.(33)
pzz

v0

z
v0

y
pzz

Fig. 2x

Schematic view of Tribo Molecular Dynamics
simulation.
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The solid plate is modeled as an atom layer with alattice of 100 × 100 × 3 in the x, y, z directions and thelattice parameter is 2.87 due to the structure of analpha-ferrous crystal. The fluid-solid interface faces
the (100) surface, and the vibrations of each atom aresuppressed.
The solid-fluid interaction is defined as a no-slipping
condition by a sufficiently large interaction. This isbecause, under the EHL condition for a realistic
submicron oil film thickness, the fluid-fluid interaction
will be the origin of the traction appearance. The
Lennard-Jones well depth parameter is then set to12.14 kcal /mol. Under this condition, no slipping isobserved.
Constant shear states under constant pressure andconstant velocity are obtained in the following manner.
First, a set of fluid molecules without a solid layer isarranged in a lattice configuration. The molecules arethen relaxed by the MD simulation under the periodic
boundary condition in the (x, y, z) direction at theconstant temperature of 350 K until a thermal
equilibrium is obtained. Next, the sets of thermal
equilibrium fluids are arranged in the z direction
between two solid layers. Fluid molecules arecompressed by the MD simulation under the periodic
boundary condition for the x, y direction by adopting
the constant pressure of 1 GPa on the plates. The shear
in the x direction is then applied by a relative sliding
motion on the solid layers by the constant velocity. A
judgment of the constant shear state is made by tracing
the traction coefficients μ defined byμ = ∑ Ffluid ( x ) / Fext , · · · · · · · · · · · · · · · · · (1)where Ffluid(x) is the x component of the pressure on
the plate from the plate-fluid interaction.
The traction coefficients μ increases first after thesliding starts, and then saturates to some fixed value
and oscillates around this value at 50 ps from the
beginning of the sliding, which corresponds to a
constant shear state. The time average of μ is
calculated from the average of μ within 5 ns of theconstant shear state.
4. Molecular Structure and Traction Mechanism

the traction coefficient μ are first studied. To determine
the condition that can qualitatively simulate theexperiments, the dependence of μ on the film thickness
was calculated. Figure 3 shows the time average of the
traction coefficient μ of n-hexane in the steady state in
the film thickness range z0 = 1.0 to 10.0 nm and in theshear rate range of γ& = 1.0 × 107 to 1.0 × 109 s−1.
Although the calculated traction coefficients show
higher value than the experimental ones over the entire
simulation range, μ decreased for both with thedecreasing shear rates and increasing film thickness.
This tendency provides a qualitative agreement withthe experiments. In an ultrathin film less than 2.5 nm,
a large stick-slip-like motion caused by slip between
the molecular layers is observed, which suggests thata film thickness of at least 5.0 nm is needed.
4. 2 The Effect of External Pressure and Phase
Transition
The effect of the external pressure pzz is studied by
the large time scale simulations of 50 ns for each pzz.
In Fig. 4., the dependence of the traction coefficient μ
on the external pressure is plotted. The number ofn-hexane molecules is fixed to 576 that corresponds tothe film thickness of 10 nm at 1.0 GPa. The limiting
shear stress transition of the traction coefficients isobserved around 0.5 GPa to 1.0 GPa that corresponds
to the phase transition from the viscoelastic region to
the plastic-elastic region which was experimentally
determined by Evans et al.(22)
Molecular mechanisms of the phase transition arethen analyzed by the radial distribution functions andthe velocity profiles.(1) From the analysis, the transition
is not only related to the arrangement of the molecules.
The plasticity is also related to the suppression of the
ﬂuctuations in the molecular motion.

© Toyota Central R&D Labs., Inc. 2013

0.25
0.2
0.15
0.1
0.05
0

4. 1 Dependence of Traction Coefficient on Film
Thickness and Shear Rate
The effects of the film thickness and shear rates on.
γ = 1.0 ×109 / s
5.0 ×108 / s
1.0 ×108 / s
5.0 ×107 / s
1.0 ×107 / s

0.3
Traction coefficient μ

40Fig. 32

4
68
Film thickness z 0 , nm

10Film thickness and shear rate dependence on μ.
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4. 3 Comparision of Experiments for Hydrocarbon
FluidsThe MD simulations of 10 hydrocarbon fluids,
which are composed of 6 to 18 carbon atoms, were
examined as test fluids, their traction coefficients μalso measured by the disk on ball experiments andwere compared to one another. The fluid molecules are
A: n-Hexane, B: n-Hexadecane (chain molecule),
C: Benzene (single ring aromatic molecule),
D: Cyclohexane (single ring alicyclic molecule),
E: tert-Butylcyclohexane, F: Methylcyclohexane,
G: 1,4-Dimethylcyclohexane (single ring alicyclic
molecule with side chain), H: Dicyclohexyl (dumbbelllike molecule made by two bound alicyclic molecules),
I: Dicyclohexylmethyl (dumbbell-like molecule),
J: Santotrac 50 (dumbbell like molecule, industrial
traction lubricant).
In each simulation, the film thickness was fixed at
6.7 nm by fitting the number of fluid molecules. The
sliding velocity was fixed to 1.0 m/s. Figure 5 shows
a comparison between the MD simulation andexperiments. The simulated values of μ are always
larger than the experimental values. This is because thefilm thickness on the simulation is too small comparedto the experimental condition of a submicron
thickness. Even if the absolute values are different, theorder of μ according to the molecular structure is
reproduced by the simulation.
The result supports the selection of the force fieldparameter, a sufficiently low shear rate, which can beachieved by the all atom MD simulations, asufficiently large fluid thickness, which contains thebulk fluid layer region in the center of the film, an a

0.14

5

plate-fluid interaction in which the macroscopic
interfacial slip is suppressed, which are correct and thesimulation qualitatively reproduces the traction
phenomena.
In both the MD simulation and experiment, the orderof the traction coefficient depends not on the molecularweight, but the structure of the molecules, and seems
to show the following tendencies.
1. Single ring alicyclic molecules show a large traction
coefficient μ compared to the chain or aromatic
molecules.
2. μ decreases with the substitution of a side chain.
3. If the side chain is an alicyclic residue itself(dumbbell-like molecule), μ does not decrease, but
becomes larger than that for the mono-alicyclic
molecule.
4. 4 Structure of Oil Film
In order to investigate the order of the structure of
the molecular layer, the molecular density profiles
were plotted in Fig. 6. The molecular density is
calculated from the density of the center of the massin each molecule. The horizontal axis corresponds tothe average film thickness, and the vertical axis
corresponds to the average molecular density.
In the single alicyclic molecule D, the periodicallylayered structure is clearly constructed. That is, fromthe viewpoint of the structure of the fluid film, in
molecule D, the molecules are well layered. On theother hand, the layered structure is not clear in chain
molecules A and B, and the dumbbell-like molecules
H, I and J. Therefore, each molecule is bridging thelayers of molecules and the distribution is disordered.
We now discuss the relation between the order of themolecular layer and the mechanism of the momentum

0.12
0.1

0.3

0.08

0.25

μ

μ (Simulation)

C

0.06
0.04
0.02
0
0

Fig. 4

0.5

1

1.5

2 2.5 3p zz / GPa

3.5

4

External pressure dependence on film thickness
and traction coefficients. n-hexane: 576 molecules,
Sliding velocity: 1 m/s.

© Toyota Central R&D Labs., Inc. 2013

F

H

C

I

0.15

C
C

J

0.1
G
C

C

C C C
C

B

0.05
0

Fig. 5

D

C C
C

0.2

0

4.5

E

A
C

C

0.02

0.04
0.06
μ (Experiment)

0.08

0.1

Comparison of experiments (Film thickness z0 =8
6.7 nm, shear rate γ& = 1.5 × 10 / s).
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6transfer in the fluid layer from the viewpoint of the MD
scheme. In order to transmit the momentum from one
atom to another, using a bonded interaction like acovalent bond has an advantage over using thenonbonded interaction like the van der Waals(Lennard-Jones) force. Therefore, if the molecularlayers are disordered and each fluid molecule
distributes across the layer, molecules would generatea high traction force in the entire system. Based on thishypothesis, the tendency of μ of B > A in the chainlike molecules, and of E, H, I, J > F, G in the alicyclic
molecules, are able to be understood. The tendency
that μ of molecule D is larger than that of A and E,
however, cannot be explained from this point of view.
To analyze the condition of each molecule in thefluid layer, the orientation factor()

Φ = 3 cos 2 θ − 1 / 2 , · · · · · · · · · · · · · · · · (2)is employed for the aromatic and alicyclic molecules.
Here, θ is the angle between the normal to the plane of

the hexagonal ring of benzene and alicyclic products,
and the z axis (direction of the film thickness), and is
the average of all molecules. Φ = 1: is completelyoriented and Φ = 0: is completely random.
The average orientation factor of each fluid moleculeis shown in Fig. 7. When compared to molecule D, theorientation factor of molecule C is smaller. This isbecause in molecule D, the arrangement of thehexagonal rings face each other is stable, whereas, inmolecule C, the T-shape conformation becomes much
more stable than when facing each other.(34,35)
Comparing the alicyclic molecules, the orientation
factor decreases with the substitution of a side chain.
The very low orientation factor values in molecules H,
I and J reﬂect that in this molecule, the order of themolecular layer is low and the hexagonal rings are
distributed across the layers, thus the hexagonal rings
are hard to orient in the direction of the film thickness.
4. 5 Intramolecular Interaction
The translational momentum transferred to the fluid
molecule produces an internal distortion on themolecule by an intramolecular interaction. Figure 8
shows the intramolecular interaction energy of thebond, bond angle, torsion (dihedral) angle of the 10
fluid molecules. Each intramolecular interaction

ρ /ρ 0

A
B
C
D
C
C C

E

0.25

F
G

Orientation Factor

C
C
C

0.15

C

H
I
J

C
C

0.2
C

C
C C

0.1

C

C

C

0.05

C

C C C
C

- 0. 5

Fig. 60z / z00

0 .5

CFig. 7

Molecular density profiles.

A

B

C

D

E

F

G

D

E

F

G

H

I

J

Orientation factor of hexagonal rings.

H

Bond

I

J

E / E m ax
1. 0

0. 8
0. 6

Ang le0. 4

To rsion

0. 2
0. 0

Fig. 8© Toyota Central R&D Labs., Inc. 2013

Intramolecular energy on carbon atoms.
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the hexagonal rings facing together within the highlyordered and oriented molecular layer.

energy is normalized by dividing the energy by the
maximum energy Emax for all molecules of the bond,bond angle and torsion angle, respectively. Emax forthe bond and bond angle interaction is found inmolecule J, and Emax for the torsion interaction isfound in molecule D. In chain molecule A, all theinteraction energies of the bond, bond angle andtorsion angle, have their peaks in the center of themolecule. The interaction energy in the aromatic
molecule C is smaller than that of the alicyclic
molecules which means that the distortion is low. In
the alicyclic molecules, a large distortion is observedin the joint part of the substituted group. For any
intramolecular interaction energy, the value ofmolecules A is quite low as is the distortion.
Comparing molecule D and the dumbbell-likemolecules H, I and J, in molecules H, I and J, all theinteraction energies are high in the joint part of the two
alicyclic rings, so the distortion on the joint is theprincipal intramolecular interaction. On the other hand,
the torsion angle energy is low in molecule D. This
result suggests that the role of the hexagonal ring in
the traction effect is different between molecule D andthe dumbbell-like molecules H, I and J.
The hexagonal rings in the alicyclic molecules havea stable chair conformation, the boat conformation isunstable, and the chair conformation has axial andequatorial conformations which undergo rapidlychanges of the so-called ring-ﬂip.(36)
For the stable chair conformation, the distance of apair of carbon atoms on the opposite side is always
greater than 2.7. We then defined the unstabilities of
the alicyclic group as the ratio of the number of
unstable rings divided by the number of whole rings,
and plotted it in Fig. 9. Substitution on an alicyclic ringcauses suppression of the mobility of the ring. The
order of the unstability corresponds to the order of thedihedral angle energy shown in Fig. 8.
Therefore, the mechanism for the high traction
shown in molecule D, in contrast to the substituted
molecules E, F and G, is due to the ring-ﬂip motion of

A

B

C

D

7

4. 6 Intermolecular Interaction
According to the ﬂuctuation dissipation theorem,(10)shear viscosity is related to the correlation function of
the momentum of the molecules generated in theabsence of a shear field.(37) The mechanism of
momentum transfer in the molecular layer is able to beanalyzed by correlation functions. At every 25 ps, we
numerically sorted the carbon atoms in increasingorder of the distance from acarbon atom i, thencorrelation of the atom and the ith atom in the sorted
list is calculated using the following equationpx px (n) = ∑ i pix (t ) pnx (t ) / N , · · · · · · · · (3)twhere, pix(t), and pnx(t) are the components of the
momentum of atom i, n in time t, N is the total numberof carbon atoms in the simulation cell, and < > is thetime average. The partial correlation coefficient C(k)is defined as the integral of the pair correlation
functions px px(n) with respect to n and subdivided theintegral into the topologically different carbon atoms
k on each fluid molecule, as shown in Fig. 10. All the

Unstability , %

100
C

80

C
C

60
40

C

20

C

C

C
C C

C C C
C

C

0
D

F

G

F

G

H

I

J

Unstabilities of an alicyclic group.

Fig. 9

E

E

H

I

J

C ( k ) tota lmax(a) minC ( k )Xmax(b) minFig. 10 Pair correlation coefficients.
© Toyota Central R&D Labs., Inc. 2013

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R&D Review of Toyota CRDL, Vol.44 No.2 (2013) 1-10

values of C(k) in Fig. 10 (a) are normalized by the
maximum value of the 10 hydrocarbon fluids, C(k)total.
Comparing chain molecule A and the dumbbell
molecules H, I and J, a small deviation in molecule A
is found whereas a large value in both ends of themolecule is found in molecules H, I and J which means
the molecular motion works together with the othermolecule at both ends of the molecules.
Comparing the momentum transfer among thealicyclic molecules, in contrast of the case that inmolecules H, I and J, for the momentum transfer onboth ends, the maximum values are observed in thecenter of molecules and the momentum transfer is low
at both ends in the case of F and G. The bicephalous
properties (the center part of the momentum transfer
is divided into two parts in the molecule) are found inmolecule E, and this tendency becomes clear inmolecules H, I and J. The pseudo bicephalous
properties shown in molecule B should be attributed
to the decreasing number of surrounding molecules in
the middle of the long chain.
4. 7 Molecular Mechanism of Traction
Based on the above results and analysis, we propose
the origin of traction in the fluid layer as follows:
1. If the order of the molecular layer is low(disordered), fluid molecules distribute across thelayers, and the fluid shows a high traction.
Therefore, the tendency of μ in chain molecules B> A, alicyclic molecules E, H, I, J > F, G can be
explained from this point of view.
2. The reason that within the alicyclic molecules,
molecule D shows a high traction coefficient μ thanthe others, is due to the ring-ﬂip motion of thehexagonal rings facing together within the highlyordered and oriented molecular layer.
3. The high traction coefficients of the dumbbell likemolecules H, I and J compared to E, F and G occur
because the fluid molecules in which the hexagonalrings distribute across the disordered molecularlayer transmit the momentum at both ends of themolecule in the bulk. The reason why molecule E,
which is close to the bicephalous property ofmolecule H, shows a higher traction coefficient, andmolecule B, which does not have the bulk part ofthat in F and G, shows a lower traction coefficientthan H can also be understood.
4. The reason why the traction coefficient of thealicyclic molecule D has a higher value than the© Toyota Central R&D Labs., Inc. 2013

aromatic molecule C is due to its origin in thepresence of the ring-ﬂip motion, the same as 2.
5. Conclusions
The simulations of the all-atom molecular dynamics
were performed to analyze the molecular mechanismof the EHL oil film. From the analysis of the film
thickness, the results suggest that the MD simulations
provide reliable results for the films thicker than 5 nm
to explain the behavior of groups of molecules in
actual phenomena. The phase condition of the oil film
under 1 GPa is in the elastic-plastic region which was
confirmed from the existence of the limiting shear
stress. During the course of the MD simulation of
traction fluids, the order of the traction coefficients of
10 hydrocarbon fluid molecules using disk on ballexperiments are reproduced. The mechanisms of the
traction are analyzed from the viewpoint of the relation
between the translational momentum transfer acrossthe fluid layer and inter- and intramolecularinteractions. In the dumbbell-like molecules, alicyclic
rings, which distribute across the low orderedmolecular layers, behave as a stiff bulky mass, and themomentum transfers to the end of the molecular axis.
The origin of the traction generated in the fluid layers
is clarified.
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(2) Alder, B. J. and Wainwright, T. E., J. Chem. Phys,
Vol. 31, No. 2 (1959), pp. 459-466.
(3) Alder, B. J. and Wainwright, T. E., Phys. Rev. A,
Vol. 1, No. 1 (1970), pp. 18-21.
(4) Allen, M. P. and Tildesley, D. J., Computer
Simulation of Liquids (1987), Oxford.
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© Toyota Central R&D Labs., Inc. 20139(37) McQuarrie, D. A., Statistical Mechanics (2000),
p. 512., University Science Books.
Fig. 1
Reprinted from Proceedings of JAST Tribology
Conference (in Japanese) (2012), pp. 47-48, Washizu, H.,
Boundary Lubrication viewd from Molecular Dynamics,© 2012 Japanese Society of Tribologists.
Fig. 3
Reprinted from Journal of Japanese Society of Tribologists(in Japanese), Vol. 51, No. 12 (2006), pp. 885-891,
Washizu, H., Sanda, S., Ohmori, T. and Suzuki, A.,
Analysis of Traction Properties of Fluids Using Molecular
Dynamics Simulayions (Part 1), © 2006 Japanese Societyof Tribologists.
Fig. 4
Reprinted from Journal of the Japan Fluid Power System
Society (in Japanese), Vol. 38, No. 5 (2007), pp. 253-257,
Washizu H., Sanda, S. and Ohmori, T., Traction Properties
of EHL Oil Film, © 2007 JFPS, with permission from theJapan Fluid Power System Society.
Figs. 5-10
Reprinted from Proceedings of CVT-HYBRID 2007
Yokohama, 20074569 (2007), pp. 159-164, Washizu, H.,
Sanda, S., Hyodo, S., Ohmori, T., Nishino, N. and Suzuki,
A., Analysis of Traction Properties of Fluids Using
Molecular Dynamics Simulations, © 2007 Society ofAutomotive Engineers of Japan.
Sections 3 and 4.3-4.7
Partially reprinted from Proceedings of CVT-HYBRID
2007 Yokohama, 20074569 (2007), pp. 159-164, © 2007
JSAE, with permission from Society of Automotive
Engineers of Japan.
Sections 3, 4.2-4.7 and 5
Partially reprinted and modified from Lubrication Science,Vol. 22, No. 8 (2010), pp. 323-340, Washizu, H. andOhmori, T., Molecular Dynamics Simulations of
Elastohydrodynamic Lubrication Oil Film, © 2010 John
Wiley and Sons, Ltd., with permission from John Wileyand Sons, Ltd.

Hitoshi Washizu
Research Field:- Physical Chemistry of Surfaces
Academic Degree: Ph.D.
Academic Societies:- American Chemical Society- Materials Research Society- Japanese Society of Tribologists
Award:- Award for Young Tribologists, Japanese Society of
Tribologists, 2004

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10

R&D Review of Toyota CRDL, Vol.44 No.2 (2013) 1-10

Shuzou Sanda
Research Field:- Tribology of Automotive Power Train
Components
Academic Degree: Dr.Eng.
Academic Societies:- Japanese Society of Tribologists- The Japan Society of Mechanical Engineers- Society of Automotive Engineers of Japan
Award:- Best Paper Award, Society of Automotive Engineersof Japan, 1995
Toshihide Ohmori
Research Field:- Tribology
Academic Degree: Dr.Eng.
Academic Societies:- Japanese Society of Tribologists- Society of Automotive Engineers of Japan
Awards:- Best Paper Award, Japanese Society of Lubrication,
1991- R&D 100 Award, 1991
- Award of Tokai Chemical Industry Association, 1996
- Best Paper Award, Society of Automotive Engineersof Japan, 2012
- Tribo-Technology Award, Japanese Society of
Tribologists, 2012

© Toyota Central R&D Labs., Inc. 2013

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