Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene
We present classical molecular dynamics calculations of the behavior of copper and gold nanoparticles on a graphene sheet, sheared with a constant applied force Fa. The force Fs acting on the particle from the substrate depends on the material of the nanoparticles (Au or Cu), and exhibits a sawtooth...
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nasplib_isofts_kiev_ua-123456789-1208322025-02-09T23:15:43Z Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene Атомiстичне моделювання тертя Cu та Au наночастинок адсорбованих на графенi Khomenko, A.V. Prodanov, N.V. Persson, B.N.J. We present classical molecular dynamics calculations of the behavior of copper and gold nanoparticles on a graphene sheet, sheared with a constant applied force Fa. The force Fs acting on the particle from the substrate depends on the material of the nanoparticles (Au or Cu), and exhibits a sawtooth dependency on time, which we attribute to local commensurability between the metal nanoparticle surface atomic positions with the graphene lattice. The time-averaged value of Fs (the friction force) acting on Au nanoparticles increases linearly with the contact area, having slopes close to the experimentally observable ones. A qualitative model is proposed to explain the observed results. Представлено розрахунки на основi класичної молекулярної динамiки поведiнки мiдних i золотих наночастинок на шарi графену, що зсуваються з постiйною прикладеною силою Fa. Сила Fs, що дiє на частинку з боку пiдкладки, залежить вiд матерiалу наночастинок (Au або Cu) i демонструє пилкоподiбну залежнiсть вiд часу, яка обумовлена локальною сумiрнiстю мiж положеннями атомiв поверхнi металевих наночастинок та ґратки графену. Середнє за часом значення Fs (сила тертя), що дiє на Au наночастинки, збiльшується лiнiйно з площею контакту з нахилами близькими до експериментально спостережуваних. Запропоновано якiсну модель для пояснення результатiв, що спостерiгаються. A.V.K. and N.V.P. thank the Ministry of Education and Science, Youth and Sports of Ukraine (MESYSU) for supporting this work by the grant “Modelling the friction of metal nanoparticles and boundary liquid films which interact with atomically flat surfaces” (No. 0112U001380). A.V.K. acknowledges a grant from MESYSU for a research visit to the Forschungszentrum Jülich (Germany). 2013 Article Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene / A.V. Khomenko, N.V. Prodanov, B.N.J. Persson // Condensed Matter Physics. — 2013. — Т. 16, № 3. — С. 33401:1-8. — Бібліогр.: 24 назв. — англ. 1607-324X PACS: 46.55.+d, 62.20.Qp, 81.40.Pq, 68.35.Af, 68.37.Ps, 61.72.Hh DOI:10.5488/CMP.16.33401 arXiv:1302.6432 https://nasplib.isofts.kiev.ua/handle/123456789/120832 en Condensed Matter Physics application/pdf Інститут фізики конденсованих систем НАН України |
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We present classical molecular dynamics calculations of the behavior of copper and gold nanoparticles on a graphene sheet, sheared with a constant applied force Fa. The force Fs acting on the particle from the substrate depends on the material of the nanoparticles (Au or Cu), and exhibits a sawtooth dependency on time, which we attribute to local commensurability between the metal nanoparticle surface atomic positions with the graphene lattice. The time-averaged value of Fs (the friction force) acting on Au nanoparticles increases linearly with the contact area, having slopes close to the experimentally observable ones. A qualitative model is proposed to explain the observed results. |
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Khomenko, A.V. Prodanov, N.V. Persson, B.N.J. |
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Khomenko, A.V. Prodanov, N.V. Persson, B.N.J. Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene Condensed Matter Physics |
| author_facet |
Khomenko, A.V. Prodanov, N.V. Persson, B.N.J. |
| author_sort |
Khomenko, A.V. |
| title |
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene |
| title_short |
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene |
| title_full |
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene |
| title_fullStr |
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene |
| title_full_unstemmed |
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene |
| title_sort |
atomistic modelling of friction of cu and au nanoparticles adsorbed on graphene |
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Інститут фізики конденсованих систем НАН України |
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2013 |
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https://nasplib.isofts.kiev.ua/handle/123456789/120832 |
| citation_txt |
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene / A.V. Khomenko, N.V. Prodanov, B.N.J. Persson // Condensed Matter Physics. — 2013. — Т. 16, № 3. — С. 33401:1-8. — Бібліогр.: 24 назв. — англ. |
| series |
Condensed Matter Physics |
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2025-12-01T15:49:52Z |
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2025-12-01T15:49:52Z |
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1850321607812186112 |
| fulltext |
Condensed Matter Physics, 2013, Vol. 16, No 3, 33401: 1–8
DOI: 10.5488/CMP.16.33401
http://www.icmp.lviv.ua/journal
Atomistic modelling of friction of Cu and Au
nanoparticles adsorbed on graphene
A.V. Khomenko1,2, N.V. Prodanov1,3,4, B.N.J. Persson2
1 Department of Complex Systems Modeling, Sumy State University, 2 Rimskii-Korsakov St., 40007 Sumy, Ukraine
2 Peter Grünberg Institut-1, Forschungszentrum-Jülich, 52425 Jülich, Germany
3 Jülich Supercomputing Center, Institute for Advanced Simulation, Forschungszentrum-Jülich,
52425 Jülich, Germany
4 Department of Materials Science and Engineering, Universität des Saarlandes, 66123 Saarbrücken, Germany
Received April 27, 2013, in final form May 29, 2013
We present classical molecular dynamics calculations of the behavior of copper and gold nanoparticles on a
graphene sheet, sheared with a constant applied force Fa. The force Fs acting on the particle from the substrate
depends on the material of the nanoparticles (Au or Cu), and exhibits a sawtooth dependency on time, which we
attribute to local commensurability between the metal nanoparticle surface atomic positions with the graphene
lattice. The time-averaged value of Fs (the friction force) acting on Au nanoparticles increases linearly with the
contact area, having slopes close to the experimentally observable ones. A qualitative model is proposed to
explain the observed results.
Key words: nanotribology, molecular dynamics, nanoparticle, friction force, atomic force microscopy,
graphene
PACS: 46.55.+d, 62.20.Qp, 81.40.Pq, 68.35.Af, 68.37.Ps, 61.72.Hh
1. Introduction
The atomic force microscope (AFM) and surface force apparatus have greatly expanded the possibil-
ities to investigate tribological properties of nanoscale objects [1]. In particular, the AFM has been used
to study the frictional interaction between nanoparticles (NPs) on atomically flat substrates. These repre-
sent very well defined experiments where both the size and shape of the nanoparticles and the nature of
the substrate can be studied with atomic resolution both before and after sliding the particles [2].
A series of experiments concerned with the shear of NPs have been carried out recently [1–5]. The
measurements suggest that the friction force acting on antimony NPs deposited on highly oriented py-
rolytic graphite (HOPG) depends linearly on the contact area of the NP. Another interesting result is the
discovery that some nanoislands with the contact area up to 9 ·104 nm2 show very low friction forces,
while other similar NPs exhibit much larger friction forces.
In spite of some theoretical efforts presented in literature [2, 6], no definitive explanation of the ex-
perimental results has been proposed so far. Classical molecular dynamics (MD) simulations of silver
and nickel NPs adsorbed on graphene and sheared with constant external force Fa were presented in
reference [7], where it was shown that the friction force acting on the nanoislands changes linearly with
the contact area. The friction force is quite sensitive to the material the NP is made of. In particular, the
results suggest that Ni NPs on graphene experience higher friction than the Ag NPs. Moreover, a saw-
tooth form of the substrate shear force Fs acting on the nanoparticle, versus the lateral component of
the center of mass position, was found for Ni while the corresponding curves for Ag NPs turned out to
be rather irregular. Such a behavior was attributed to the local commensurability of the counterface of
Ni NPs due to the close match of the nearest-neighbor distance in metal and the lattice constant of the
graphene substrate.
© A.V. Khomenko, N.V. Prodanov, B.N.J. Persson, 2013 33401-1
http://dx.doi.org/10.5488/CMP.16.33401
http://www.icmp.lviv.ua/journal
A.V. Khomenko, N.V. Prodanov, B.N.J. Persson
In reference [7] only two metals were considered and additional investigations are required to test
how general the previous computational results are and to prepare the foundations for a quantitative
theory. With this aim we perform classical MD simulations described in this paper. We pursue two main
goals. First, we want to confirm the results related to the effect of the material of NPs on their tribological
behavior. It is clear that short-range order of atoms can play a significant role in determining the friction
force [7]. If the distance a between nearest-neighbors in metal is close to the graphene lattice constant of
0.246 nm [8], then local commensurability of atoms is possible leading to a sawtooth type dependence of
the force Fs acting on the NP from the substrate (graphene). The time-average 〈Fs(t)〉 = Ff of the (lateral)
substrate force is the friction force. The commensurability can happen for Ni, where a = 0.249 nm [9].
On the other hand, for metals with larger values of a, commensurability should not occur and this was
observed for Ag with a = 0.289 nm [7]. To confirm this hypothesis we consider here two other metals: Cu
with a = 0.256 nm and Au with a = 0.289 nm [9].
The paper is organized as follows. Section 2 describes the atomistic model. Results of the calculations
and the discussion are given in section 3. Brief conclusions are presented in section 4.
2. Model
A detailed description of the model can be found in reference [7]. Here, we provide only a general
sketch and the details which are specific to the current calculations. The substrate is a graphene sheet
parallel to the x y -plane, with zigzag and armchair edges along the x- and y -directions, respectively (see
figure 1; all snapshots in this work were produced with VMD software [10]). Boundary carbon atoms
along the perimeter of the graphene layer are held rigid in order to provide a fixed position of the layer.
Copper and gold nanoislands containing from 5000 up to 30000 atoms are considered. Depending on the
size of the nanoparticle, the x × y dimensions of the graphene sheet varied from about 19.68×17.04 nm
to 36.40×31.52 nm. The total number of atoms in the calculations varies from 17800 to 73808.
Interactions between carbon atoms in graphene are described by the harmonic potential [11]. Embed-
ded atommethod (EAM) potential is employed for forces between metal atoms [12]. For the metal-carbon
interaction the pairwise 6-12 Lennard-Jones (LJ) potential is used [7, 11]. The simulation code is imple-
mented using the NVIDIA CUDA platform [13, 14] which allowed us to carry out the computations on a
single graphics processing unit (GPU) NVIDIA GeForce GTX 460. Algorithms for GPU based on the neigh-
borlist technique [15, 16] from reference [14] with our own algorithm for binning atoms into cells are
employed. The equations of motion are integrated using the leapfrog method [15, 16] with a time step ∆t
= 0.2 fs.
3. Results and discussion
NPs are obtained using the procedure similar to the dewetting of thin metallic films by thermal treat-
ments [17] and described in reference [7]. Briefly, a rectangular slab of metal atoms is placed on the
graphene sheet and the simulation starts. The metal atoms assemble into a more compact structure,
Figure 1. (Color online) Snapshots of the formed nanoparticle containing 22000 Cu atoms: perspective (a)
and top (b) views.
33401-2
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene
which is more energetically favorable than the rectangular slab. At an appropriate time moment the
system is cooled down in order to get a hemispherical shape of the NP and to prevent it from forming a
ball. During this preparation stage a single Berendsen thermostat [15] is applied to both metal and car-
bon atoms. After the equilibrium has been reached, the external force Fa is applied along the x-direction
(zigzag edge of graphene), and the NP starts to move in this direction. This force is distributed uniformly
on all metal atoms with the x < XCM, where XCM is the NP center of mass position along the x-direction.
Starting from this moment the thermostat decouples from the metal atoms and acts only on the graphene
in order to diminish the effect of the temperature control on the dynamics of the system. We perform
several series of calculations with different values of the applied force Fa acting on the NPs of the same
size. Where it is not stated explicitly, the Fa acting on Cu NPs consisting of 5000 and 29000 atoms is equal
to 2.31 nN and 15.29 nN, respectively. For Au NP consisting of 10000 and 25000 atoms Fa is 5.07 nN and
13.05 nN, respectively. We note that in our MD calculations the NPs are accelerating since in general the
applied force Fa is not equal to the substrate force Fs.
0 200000 400000 600000
0
200
400
600
800
1000
0
100
200
300
400
0
4
8
4
8
12
16
20
244
8
12
16
20
24
28
-4
0
4
8
0
2
4
6
T
(K
)
V
X
(m
/s
)
time (0.2 fs)
X
C
M
(n
m
)
L
y
(n
m
)
L
x
(n
m
)
F
s
(n
N
)
F
a
(n
N
)
Figure 2. (Color online) Time dependencies of the sys-
tem temperature T , lateral position XCM and veloc-
ity VX of the center of mass of the NP, total applied
force Fa, substrate force Fs, and lateral dimensions Lx
and L y obtained for Cu nanoisland containing 19000
atoms.
Figure 2 shows the time dependency of the
quantities measured during the simulation of
a copper NP containing 19000 atoms. Note that
once the motion of the NP is initiated, the val-
ues of VX and XCM increase nearly linearly
and quadratically with time, respectively. This
is possible only if the friction force acting on the
NP is independent of the sliding velocity (in the
studied velocity range) so that and Fa−Ff is time
independent. However, the substrate force Fs(t)
acting on the NP is not constant, but exhibits a
sawtooth shape with increasing frequency (in
time) as the particle moves faster, which indi-
cates an atomistic stick-slip motion of the NP.
Wenote that usingMD simulations (or any other
exact numerical simulation method) one can-
not study the low NP sliding velocities (of order
∼ µm/s) prevailing in the AFM measurements,
but the numerical results presented below in-
dicate a very weak velocity dependency in the
studied velocity interval.
To examine the sliding dynamics inmore de-
tail, in figure 3 we show Fs vs XCM for several
Cu and Au NPs. While for the majority of Cu NPs
a sawtooth dependence of the substrate force is
observed and Fs peaks are more or less regular,
the Fs vs XCM curves for Au havemore irregular
form. The distances between the peaks for Cu
are close to the value of the lattice constant of
graphene. Note that Fs takes both positive and
negative values. Thus, the force acting on the NP
from the graphene changes its direction during
the sliding of the NP. On average, the amplitude
of the peaks for Cu is larger than for Au. The substrate force for the Cu nanoparticle exhibits fluctuations
with a periodicity close to the lattice constant as expected for a nearly commensurate contact. For the Au
nanoparticles, the substrate force fluctuates much more rapidly with the displacement coordinate XCM,
which is expected for a nearly incommensurate (or high-order commensurate) interface [18].
Figure 4 presents the dependence of the substrate force Fs on the center of mass coordinate, for two
different Au NPs with different applied forces Fa. Note that the curves exhibit “fine structure” for all sizes
of the NPs, i.e., the peaks are split into high-frequency subpeaks, and that the stick-slip oscillations are
reduced or disappear for the largest XCM corresponding to the largest sliding velocities. To explain such a
33401-3
A.V. Khomenko, N.V. Prodanov, B.N.J. Persson
behavior one can assume that only at sufficiently low speeds the atoms on the surface of NPs can adjust to
the potential energy landscape of the graphene layer. In this way, local atomic commensurability patches
can form at the interface, resulting in atomic-scale oscillations in the substrate force acting on the NP.
0 20 40 60
-2
-1
0
1
2
F
s
(n
N
)
XCM (0.1 nm)
(a)
0 20 40 60
-2
-1
0
1
2
F
s
(n
N
)
XCM (0.1 nm)
(b)
0 20 40 60
-2
-1
0
1
2
F
s
(n
N
)
XCM (0.1 nm)
(c)
0 20 40 60
-3
-2
-1
0
1
2
F
s
(n
N
)
XCM (0.1 nm)
(d)
Figure 3. (Color online) Substrate force versus the lateral position of the center of mass of the nanoparti-
cles: Cu with 5000 (a) and 29000 atoms (b), Au with 10000 (c) and 25000 (d).
0 10 20 30 40
-2
-1
0
1
2
F
s
(n
N
)
XCM (0.1 nm)
(a)
0 20 40 60
-3
-2
-1
0
1
2
F
s
(n
N
)
XCM (0.1 nm)
(b)
Figure 4. (Color online) Substrate force versus the lateral position of the center of mass of the Au nanois-
lands at low applied force: 10000 atoms (Fa = 0.74 nN) (a) and 25000 atoms (Fa = 2.08 nN) (b).
33401-4
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene
By contrast, at a high sliding speed, the interfacial atoms of the NP do not have enough time to adjust to
the corrugated substrate potential, and no local commensurate regions or patches can form. This can be
the reason for the irregular form of the substrate force dependencies for Au NPs at high sliding velocities.
20 40 60 80
0
0.2
0.4
0.6
Au higher applied force
Au lower applied force
F
f
(n
N
)
A (nm2)
Figure 5. (Color online) Friction force versus contact
area of Au nanoparticles for different applied forces
and hence different sliding velocities.
Figure 5 shows the dependence of the friction
force Ff = 〈Fs〉 on the contact area of the NPs. The
geometry of the NPs is used in order to calculate
the contact area. The shape of the NP in the x y -
plane is approximated by an ellipse whose area
is computed using the lateral dimensions of the
particle. It is noteworthy that the change in the
applied force does not significantly alter the av-
erage value of the friction force, i.e., the friction
force is nearly velocity independent in the con-
sidered velocity interval. The slopes of the linear
fits to the friction force data for Au NPs are 2.29
and 2.03 pN/nm2 at a higher and lower Fa, re-
spectively. They exceed the values of 1.21 pN/nm2
obtained in MD simulations for silver [7] and
1.04 pN/nm2 from the experiments [3, 5]. How-
ever, the experiments are performed at much
lower sliding velocities than in the MD simula-
tions, and the fact that the slope for the lower ap-
plied force is slightly smaller than for the higher
force is consistent with a smaller slope at the AFM sliding velocities. Poor statistics did not allow us to
reliably determine the slopes for copper NPs. We note that if the NP atomic positions at the interface
were strictly incommensurate with the graphene lattice, one would expect a friction force roughly pro-
portional to the linear size of the NP contact area. The fact that the friction force is proportional to the
contact area is consistent with a model where in the contact region the metal atoms form commensurate
patches separated by domain walls.
We note that thermally activated processes will become more important as the sliding velocity de-
creases. Thermal activation will tend to reduce the friction by allowing a jump over energy barriers
before the driving force has pulled the system to the top of the barriers. Thermal activation may be
very important at low velocities (∼ 1 µm/s) typically involved in AFM measurements. However, no exact
atomistic calculation (as the present MD simulations), can reach velocities as low as those typically used
0 2 4 6 8 10
0
10
20
30
before cooling
after cooling
bulk crystal
g
(r
)
r (0.1 nm)
Au
(a)
0 2 4 6 8
0
10
20
30
40
before cooling
after cooling
bulk crystal
g
(r
)
r (0.1 nm)
Cu
(b)
Figure 6. (Color online) Radial distribution function obtained at different timemoments for the Au (a) and
Cu (b) nanoparticles containing 29000 atoms. Plots for the bulk state are obtained using the same EAM
potential.
33401-5
A.V. Khomenko, N.V. Prodanov, B.N.J. Persson
in most AFM measurements. Nevertheless, most practical applications in tribology involve much higher
velocities similar to those in many MD simulations.
The structure of NPs can be analyzed using a radial distribution function (RDF) measured at different
time moments, and from snapshots of the contact surface. Typical RDFs are shown in figure 6. As can
be seen, RDF has a completely blurred shape after the formation of the NP for both metals, indicating a
disordered structure of the NPs. After the cooling phase some ordering occurs which manifests in the for-
mation of the first peak corresponding to the distance between the nearest neighbors of about 0.256 nm
and 0.289 nm for Cu and Au, respectively. Additional smaller peaks also appear in the figure. However,
they are very diffusive compared to the ideal bulk crystal. This suggests that nanoislands have an amor-
phous or polycrystalline bulk structure, at least when prepared following our preparation procedure.
The structure of the NPs does not change significantly during their sliding. Visual inspection of figure 7
indicates that contact surfaces of both Cu and AuNPs are not perfectly ordered but exhibit commensurate
domains separated by domain walls.
The results obtained above can be summarized as follows:
• a sawtooth substrate force is observed mainly for metals with the lattice constant a close to the
lattice constant of graphene. In our simulations it is Cu and Ni [7];
• at low sliding velocities the sawtooth substrate force appears also for metals with larger discrep-
ancy between their value of a and the graphene lattice constant. In our case this is true for Au;
• RDFs indicate the absence of the long-range order in the bulk for all the metals prepared using our
cooling procedure;
• visual inspection of the surfaces (see figure 7) confirms the fact that there is no long-range order of
the surface atoms of the NP. However, ordered domains of atoms can be identified on the surface
of NPs.
To explain the results of our computer simulations, we propose a “patch” model. It is based on the
assumption of local commensurability of some regions of the interface. As was mentioned above, there
Figure 7. (Color online) Side (a, c) and bottom (b, d) views of Cu (a, b) and Au (c, d) nanoparticles containing
25000 atoms. Clusters of surface atoms with local order are outlined by red contours.
33401-6
Atomistic modelling of friction of Cu and Au nanoparticles adsorbed on graphene
are domains with a local atomic order on the surface of a NP (see figure 7). The domains can form com-
mensurable regions (“ordered patches”) at the metal-carbon interface due to some matching of metal
atoms with the graphene lattice. The commensurate regions will effectively increase the amplitude of
the corrugated substrate potential experienced by the nanoparticles, and thus the friction will increase.
Such domains are formed more easily when the lattice constants of the NPs and the substrate are similar,
as well as for elastically [18] or plastically softer materials. We suggest that atomic stick-slip processes
involving the “ordered patches” should make the major contribution to the net friction force of nanois-
lands [7, 19, 20]. In general, the patches are randomly distributed over the interface and are separated
by domain walls. They are quite dynamic during the motion of a NP. Every patch can be considered as
a locked atom and may be the reason for the atomic-scale oscillations in the friction force. To observe a
sawtooth shape of Fs and a higher net friction force Ff = 〈Fs〉, all the patches should act coherently. This
situation is more probable for Cu due to the proximity of its value of a to the graphene lattice constant.
Such an amplification can also occur for Au and for other metals with larger a, as was observed in the
current work, when the velocity of the NP is low. In this case the surface atoms have time to relax into
the substrate potential energy landscape and form pinned “patches”. The extent to which such pinned
domains can form depends not only on the lattice constants but also on the elastic or plastic properties of
the solids and on the strength of the corrugated substrate potential [21–24].
4. Conclusions
We have performed classical MD simulations of friction of Cu and Au NPs adsorbed on graphene,
and sheared with a constant external force. The results obtained in this work confirm the earlier conclu-
sion [7] on a significant role of the short-range order of atoms located on the surface of the NP. Ordered
domains of atoms can be the source of the local match of the rubbing surfaces leading to a sawtooth type
dependence of the substrate force on the coordinate of the NP’s center of mass. It is shown that for Cu,
especially for small NPs, sawtooth substrate force is clearly manifested. For Au, which has larger a com-
pared to Cu, sawtooth substrate force can be observed only at a small sliding speed. The Fs(t) exhibits
“fine structure”, i. e., larger peaks are split into a set of high-frequency peaks.
As in the previous work [7], the dependence of friction force on the contact area of Au NPs is linear
both at higher and lower Fa. The functional form of these dependencies is not affected by changing the
value of the applied force, indicating a weak velocity dependency, which is consistent with the experi-
mental results [1–3, 5].
A “patch” model is proposed in order to explain the observed behavior. The application of the model
to different systems will be presented elsewhere.
Acknowledgements
A.V.K. and N.V.P. thank the Ministry of Education and Science, Youth and Sports of Ukraine (MESYSU)
for supporting this work by the grant “Modelling the friction of metal nanoparticles and boundary liquid
films which interact with atomically flat surfaces” (No. 0112U001380). A.V.K. acknowledges a grant from
MESYSU for a research visit to the Forschungszentrum Jülich (Germany).
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Атомiстичне моделювання тертя Cu та Au наночастинок
адсорбованих на графенi
О.В. Хоменко1,2, М.В. Проданов1,3,4, Б.Н.Й. Перссон2
1 Кафедра моделювання складних систем, Сумський державний унiверситет,
вул. Римського-Корсакова, 2, 40007 Суми, Україна
2 Iнститут Петера Грюнберга-1, Дослiдницький центр Юлiха, 52425 Юлiх, Нiмеччина
3 Суперкомп’ютерний центр Юлiха, Iнститут передових обчислень, Дослiдницький центр Юлiха,
52425 Юлiх, Нiмеччина
4 Кафедра фундаментального та прикладного матерiалознавства, Унiверситет Зарланду,
66123 Зарбрюкен, Нiмеччина
Представлено розрахунки на основi класичної молекулярної динамiки поведiнки мiдних i золотих на-
ночастинок на шарi графену, що зсуваються з постiйною прикладеною силою Fa. Сила Fs, що дiє на
частинку з боку пiдкладки, залежить вiд матерiалу наночастинок (Au або Cu) i демонструє пилкоподiбну
залежнiсть вiд часу, яка обумовлена локальною сумiрнiстю мiж положеннями атомiв поверхнi металевих
наночастинок та ґратки графену. Середнє за часом значення Fs (сила тертя), що дiє на Au наночастинки,
збiльшується лiнiйно з площею контакту з нахилами близькими до експериментально спостережуваних.
Запропоновано якiсну модель для пояснення результатiв, що спостерiгаються.
Ключовi слова: нанотрибологiя, молекулярна динамiка, наночастинка, сила тертя, атомно-силова
мiкроскопiя, графен
33401-8
http://dx.doi.org/10.1103/PhysRevB.82.035401
http://dx.doi.org/10.1088/0957-4484/22/8/085704
http://dx.doi.org/10.1021/jp108981e
http://dx.doi.org/10.1103/RevModPhys.81.109
http://dx.doi.org/10.1016/0263-7855(96)00018-5
http://dx.doi.org/10.1103/PhysRevB.54.2138
http://dx.doi.org/10.1016/S1359-6454(01)00287-7
http://dx.doi.org/10.1080/08927020701744295
http://dx.doi.org/10.1016/j.jcp.2008.01.047
http://dx.doi.org/10.1021/jp908427r
http://dx.doi.org/10.1088/0953-8984/18/17/004
http://dx.doi.org/10.5488/CMP.11.4.615
http://dx.doi.org/10.3367/UFNe.0179.200901b.0035
http://dx.doi.org/10.1016/j.carbon.2009.11.046
http://dx.doi.org/10.1016/j.susc.2010.01.024
http://dx.doi.org/10.1103/PhysRevLett.104.074302
http://dx.doi.org/10.1209/0295-5075/91/66008
Introduction
Model
Results and discussion
Conclusions
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