Sep 15, 2017 - Jean Michel Martin,. ⥠and Momoji Kubo*,â . â . Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Senda...
Oct 24, 2014 - Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208 ..... their MP2 counterparts for water clusters with sizes up to n = 4.
Jul 31, 2009 - from the burner head, in situ mass spectrometry yield- ing indirect ..... B3000Kg3_7. 6/70. 1/70. 0/69. 22.39. 74. 168. 0.168. B3000Kg3_8. 6/70. 1/70 .... C6H8, C6H4, C6H5, C4H6, C4H4, and H2 were identified also in another ...
Sep 15, 2017 - New Industry Creation Hatchery Center, Tohoku University, 6-6-10 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan. §. Department of ...
Jul 31, 2009 - flames at temperatures up to 2000 °C.36. While the combustion synthesis offers ad- vantages for large-scale operation, it is sen- sitive to ...
Published on Web 05/26/2004 ... globally best solutions when using the GCM for property evaluation. ... provides the subroutine Model Builder,15,16 which gen-.
The use of the Electronegativity Equalization Method (EEM) is presented for high performance calculation of molecular electrostatic descriptors, giving quite ...
May 5, 2015 - extremely interesting to note that an octagon formation was found, which was presumably surrounded by alternate permutation of pentagons ...
Oct 24, 2014 - His research area includes molecular scalar fields, software development and parallel computing, information entropy, electron density in momentum ... He joined as a Ph.D. student under the supervision of Professor Shridhar R. Gadre in
Shridhar R. Gadre was born in May 1950 in Akola (Maharashtra), India. He received his Ph.D. under the supervision of Professor Palliakaranai T. Narasimhan ...
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Article
Tight-binding Quantum Chemical Molecular Dynamics Study on the Friction and Wear Processes of Diamondlike Carbon Coatings: Effect of Tensile Stress Yang Wang, Jingxiang Xu, Yusuke Ootani, Shandan Bai, Yuji Higuchi, Nobuki Ozawa, Koshi Adachi, Jean-Michel Martin, and Momoji Kubo ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b07551 • Publication Date (Web): 15 Sep 2017 Downloaded from http://pubs.acs.org on September 17, 2017
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Tight-binding Quantum Chemical Molecular Dynamics Study on the Friction and Wear Processes of Diamond-like Carbon Coatings: Effect of Tensile Stress Yang Wang a, Jingxiang Xu a, Yusuke Ootani a, Shandan Bai b, Yuji Higuchi a, Nobuki Ozawa a, Koshi Adachi c, Jean Michel Martin d, and Momoji Kubo a,* a
Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-
8577, Japan b
New Industry Creation Hatchery Center, Tohoku University, 6-6-10 Aoba, Aramaki, Aoba-ku,
Sendai 980-8579, Japan c
Department of Mechanical System Engineering, Graduate School of Engineering, Tohoku
University, 6-6-01 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan d
Laboratory of Tribology and System Dynamics, Ecole Central de Lyon, 36 Avenue Guy de
Diamond-like carbon (DLC) coatings have attracted much attention as an excellent solid lubricant due to their low-friction properties. However, wear is still a problem for the durability of DLC coatings. Tensile stress on the surface of DLC coatings has an important effect on the wear behavior during friction. To improve the tribological properties of DLC coatings, we investigate the friction process and wear mechanism under various tensile stresses by using our tight-binding quantum chemical molecular dynamics method. We observe the formation of C-C bonds between two DLC substrates under high tensile stress during friction, leading to a high friction coefficient. Furthermore, under high tensile stress, C-C bond dissociation in the DLC substrates is observed during friction, indicating the atomic-level wear. These dissociations of CC bonds are caused by the transfer of surface hydrogen atoms during friction. This work provides atomic-scale insights into the friction process and wear mechanism of DLC coatings during friction under tensile stress.
1. INTRODUCTION Diamond-like carbon (DLC) has an amorphous structure containing sp3- and sp2hybridized carbon atoms. DLC shows excellent properties, including low friction, high hardness, good chemical inertness, and good bio-compatibility1. There are various industrial and biomedical applications of DLC. In recent years, DLC has been used as a solid lubricant on the surface of the sliding materials due to its excellent low-friction properties.1,2 Various types of DLC have been studied widely to improve the tribological properties of DLC coatings further. The ratio of sp3- to sp2-hybridized carbon atoms and the hydrogen content play important roles in the low-friction behaviors of DLC coatings.1–4 The rearrangement from diamond-like to graphitic-like structure of the hydrogen-free DLC coatings at high temperatures during friction results in a low friction coefficient of around 0.03 in the air.3 Fontaine et al.4 reported that DLC coatings with a high concentration of hydrogen exhibit super-low friction coefficients of less than 0.01 at room temperature in an ultra-high vacuum. The super-low friction coefficient is due to the hydrogen terminations on the DLC surface. These hydrogen terminations are reported to reduce the adhesion and inhibit the formation of interfacial bonds across the sliding surfaces.5–8 These studies have demonstrated the excellent lubricity of DLC due to the surface passivation and formation of graphite-like structure. However, wear of DLC coatings during friction is still a problem for their durability. Chemical reactions, such as the formation of graphite-like structure, increase the wear rate at high temperatures although it results in a low friction coefficient.9 Furthermore, the wear rate is decreased by the carbonaceous transfer layer on the counterpart of the coating that is formed by the chemical adhesion between DLC and its counterpart.10 Thus, the wear is strongly affected by
the chemical reactions at the friction interface such as the formation of graphite-like structure and transfer layers. In addition, the stress also has a significant effect on their wear during friction. There are two kinds of stresses on DLC coatings: residual stress in the coatings and tensile stress on the surface of the coatings. The residual stress originates in the deposition process and the tensile stress is produced due to the inhomogeneous contact. Kodali et al.11 investigated the effects of the residual and tensile stresses on the tribological properties of DLC coatings. They found that the tensile stress on the surface directly causes the fractures that are the initial stage of the wear,12 whereas the residual stress only has a small effect on the propagation of these fractures. The tensile stress, rather than the residual stress, is suggested to play the key role on the wear. It is necessary to understand the friction process and wear mechanism induced by tensile stress to improve the tribological properties of DLC coatings. However, the friction process and wear mechanism are still unclear because the in situ observation of the chemical reaction dynamics during friction and wear is difficult experimentally. Therefore, an atomistic simulation is necessary to fully understand the chemical reaction dynamics, their effects on the friction process, and the wear mechanism of DLC coatings under tensile stress during friction. Classical molecular dynamics (MD) has been widely used to study the friction and wear process at an atomic scale.13–17 The effects of hydrogen14 and film thickness16 on the tribological behavior of DLC coatings were revealed. Harrison et al. successfully studied the atomic-level wear of diamond due to the abstraction of hydrogen terminations.17 Vahdat et al. studied the atomic-scale wear of DLC by combining the experiment, theory and classical MD simulations, and showed that the wear of DLC is a result of the bond dissociation processes.18 Some recent classical MD methods, such as the bond order based force filed such as REBO II19,20 and ReaxFF21, can describe bond formation and dissociation during chemical reactions very well.
Moseler et al. successfully investigated the graphitization process of tetrahedral amorphous (taC, a type of DLC) during friction by using the REBO II.15 In addition to the well description of the bond formation and dissociation, an analysis based on the electronic state would be preferred to understand the interfacial chemical reactions more deeply and to investigate the bond formation and dissociation more clearly and accurately. The first-principles calculation method is suitable for handling the electronic state analysis during chemical reactions. Static first-principles calculations have been used to reveal the effects of hydrogen and nitrogen molecules in the environment on the tribological behaviors of diamond.22 Zilibotti et al. studied the effects of surface passivation by various gas molecules such as O2 and H2O on the adhesion and shear strength of diamond surface.23 Furthermore, the effect of Si dopants on the hydrophilicity of diamond surface is investigated by the first-principles calculations.24 To understand the chemical reactions fully, it is also important to study the chemical reaction dynamics. The chemical reaction dynamics between water and the diamond surface during friction were investigated by first-principles MD simulations.25,26 However, the computational cost of first-principles MD calculations on the models that are large enough for friction and wear simulations is very huge. For decreasing the computational cost, we developed the tight-binding quantum chemical molecular dynamics (TB-QCMD) simulator.8 The TB-QCMD simulation is much faster than the conventional first-principles MD simulation due to the tight-binding approximation. For example, for a system containing about 400 atoms, 100 steps calculation by using 4 cores of the Intel Xeon CPU only needs about one minute. We have investigated various chemical reaction dynamics of DLC coatings during friction with our TB-QCMD simulator.8,27–29 However, we have not investigated the effect of tensile stress on the chemical reaction dynamics of DLC coatings during friction. To improve the tribological properties of DLC coatings, it is essential to
investigate the chemical reaction dynamics at the friction interface under tensile stress and their effects on the friction process and wear mechanism of DLC coatings. In this study, we examine the friction process and wear mechanism of DLC coatings under various tensile stresses by using our TB-QCMD simulator. We use the ta-C model with hydrogen terminations only on the surface to typically study the effect of tensile stress on the friction and wear processes. The hydrogen atoms in the DLC bulk will be considered in our future work. The chemical reaction dynamics at the friction interface under tensile stress during the friction process are investigated, and their effects on the friction process and wear mechanism of DLC coatings are discussed.
2. SIMULATION METHOD We use our software package, Colors,8 based on the TB-QCMD method to investigate the friction process and wear mechanism of DLC coatings at an atomic scale under various tensile stresses. In the TB-QCMD method, the following electronic Hamiltonian is used.30 = −
(1)
= + r ≠ s
(2)
= 1 + + 1 − Δ + Δ exp− + − +
(3)
Δ =
(4)
!! " ## !! $ ##
Here, is the diagonal element in the Hamiltonian matrix, defined as the negative of the first ionization potential, . is the off-diagonal elements of the Hamiltonian matrix. is the offdiagonal elements of the overlap integral matrix which is calculated by using the single-zeta Slater-type orbitals. In formula (3), and are parameters, is the distance between two atoms to which the th and %th atomic orbitals belong, and is the radius of the atomic orbital, which is determined by the method reported by Calzaferri et al.31 The total electronic energy
&'(') of the system is obtained from the eigenvalue, *+ , of the electronic Hamiltonian matrix and the repulsive energy, &', ,30 as &'(') = ∑.)) + *+ + ∑031 &', / 01 2 &', / 01 2 = /40 + 41 2 exp 5
67 $68 "78 97 $98
(5) :
(6)
where ; is the index of molecular orbitals and 01 is the distance between the
0 and 40 are parameters that are related to the size and stiffness of the
0 , and 40 for the hydrocarbon system in our previous paper.28 These parameters reproduce the bond lengths and binding energies of C-C, CH, and H-H bonds. Furthermore, we compare our TB-QCMD calculation results to the DFT calculations as shown in the Supporting Information. The TB-QCMD calculation results agree with the DFT calculations, showing the reasonable accuracy.
Figure 1. Friction simulation model of the DLC substrates.
We construct a DLC model to perform the friction simulations. First, a diamond bulk model is heated to 4000 K under NVT ensemble conditions for 2 ps. During heating, the
diamond adopts an amorphous structure. The amorphous carbon is cooled to 300 K within 9.4 ps. Next, the DLC bulk model is relaxed at 300 K under the NPT ensemble conditions with a standard atmosphere for 2 ps to eliminate the internal stress. The DLC bulk model is cleaved and the C-C bonds across the cleave surface disappear. The disappearance of C-C bonds leave the dangling bonds on the surface carbon atoms. Then, the hydrogen atoms are used to passivate theses dangling bonds. Figure 1 shows the friction simulation model of the hydrogen-terminated DLC substrates. Two DLC substrates are packed together in the same simulation box. The cell size is 10.75 × 10.93 × 60 Å and the thickness of each DLC substrate is 7.72 Å. The friction simulation model contains 288 carbon atoms and 90 hydrogen atoms. In the friction simulation, the bottom layer atoms of the lower substrate are fixed and the top layer atoms of the upper substrate are forcibly slid in the x-direction at 100 m/s. A normal pressure of 3 GPa is applied to the top layer atoms of the upper substrate. The simulation temperature is kept at 300 K with the velocity scaling method.32 The Verlet algorithm33,34 is used to calculate the motion of atoms under the periodic boundary condition. The MD time step is 0.2 fs and the total friction simulation time is 40 ps. To perform the friction simulations of DLC/DLC under different tensile stresses, we stretch the DLC substrate along the x-direction (Figure 2a). Figure 2b shows the stress-strain curve of the DLC substrate. The volume of the DLC substrate is used to calculate the total stress along the x-direction. An almost linear relationship between the tensile stress and tensile strain is obtained as shown in Figure 2b. The Young’s modulus of the DLC model is about 244 GPa, showing good agreement with the experimental values of 200–400 GPa35. Figure 2c shows the total number of complete C-C bonds in DLC substrates as a function of tensile strain. The total number of C-C bonds decreases when the tensile strain is higher than 0.04. This indicates that some of the C-C bonds are dissociated and the DLC is deteriorated by the high
tensile strain of 0.05 and 0.06. Therefore, the friction simulations are performed on the DLC models before the tensile strain of 0.04, because the DLC substrates are not deteriorated under these tensile strains. The friction coefficient, ?, is calculated as ?=
"@A @B
(7)
where CD and CE are the total forces along the x- and z-directions, respectively, acting on the atoms, which are forcibly slid. The instantaneous friction coefficient is obtained by using the forces, which are averaged every 2000 steps to decrease the dispersion of the friction coefficient, and the average friction coefficient is calculated by averaging the forces over the whole friction simulation from 0 to 40 ps. In the structure analysis, the atomic bond populations given by Mulliken population analysis36,37 are calculated to identify the chemical bond during the simulation. The atomic bond population between Xth and Yth atoms, FGH , is obtained as follows: FGH = 4 ∑∈G ∑∈H ∑.)) 1 J1 J1
(8)
where the J1 is the element of the molecular orbital (MO) coefficient matrix. The Xth and Yth atoms are considered to bond when the FGH is higher than a cutoff value of 0.2. The Csp3- and Csp2-hybridized carbon atoms are identified by the coordination number of each carbon atom.
Figure 2. DLC model under tensile stress. (a) Stretching of DLC, (b) tensile stress-strain curve, and (c) total number of C-C bonds as a function of tensile strain.
3. RESULTS AND DISCUSSION We investigate the sliding behaviors of the DLC substrates at tensile strains of 0.00, 0.02, and 0.04 to understand the tribological behaviors under each tensile strain. Figures 3a–c show snapshots of the DLC substrates at tensile strains of 0.00, 0.02, and 0.04 during sliding, respectively. At a tensile strain of 0.00 (Figure 3a), smooth sliding is observed during the whole friction simulation. At a strain of 0.02 (Figure 3b), a C-C bond between the upper and lower DLC substrates (interfacial C-C bond) forms at 14.16 ps and dissociates at 20.80 ps owing to the
sliding of the two DLC substrates. At a tensile strain of 0.04 (Figure 3c), an interfacial C-C bond forms at 8.08 ps and a second interfacial C-C bond forms at 17.46 ps. Then, the interfacial bonds form and dissociate repeatedly during sliding. At 40 ps, many interfacial C-C bonds are observed. At a tensile strain of 0.04, the number of interfacial C-C bonds is larger than that at a tensile strain of 0.02. Thus, the high tensile strain of DLC coatings leads to the formation of interfacial C-C bonds. The number of interfacial C-C bonds during sliding at each tensile strain is investigated to understand the effect of tensile strain on the formation of interfacial C-C bonds quantitatively. Figure 4a shows the time evolution of the number of interfacial C-C bonds in each simulation. At a tensile strain of 0.00, no interfacial C-C bonds form during sliding (Figure 3a); thus, the number of interfacial C-C bonds is always zero (Figure 4a). At a tensile strain of 0.02, there is one interfacial C-C bond from about 14 to 21 ps (Figure 3b). At a tensile strain of 0.04, the number of interfacial C-C bonds increases slightly from about 8 ps and rapidly from about 18 to 25 ps. After 25 ps, the number of interfacial C-C bonds does not increase (Figure 4a). These interfacial C-C bonds connect the two DLC substrates together. Then, a shearing process of the interfacial C-C bonds is observed. We investigate the friction coefficient during sliding at each tensile strain to reveal the effect of tensile strain on the frictional behaviors of DLC/DLC. Figure 4b shows the time evolution of the instantaneous friction coefficients in each simulation. At a tensile strain of 0.00, the instantaneous friction coefficient oscillates around an average friction coefficient of 0.02. This low friction is due to the repulsion caused by hydrogen termination on the surfaces of both DLC substrates.8,38 The experimental friction coefficient of DLC/DLC with hydrogen termination is 0.01 to 0.05.39 Another classical MD simulation reported the friction coefficient of hydrogen-terminated DLC/DLC as 0.035.40 Thus, the friction coefficient of hydrogen-terminated DLC/DLC in our simulation agrees with previous experimental and
classical MD simulation results. At a tensile strain of 0.02, the instantaneous friction coefficient also oscillates around the average friction coefficient of 0.10, which is higher than that at a tensile strain of 0.00. The higher friction coefficient is due to the interfacial C-C bond that exists from 14.16 to 20.80 ps (Figure 4a). At a tensile strain of 0.04, the instantaneous friction coefficient increases slowly from about 8 to 18 ps and rapidly from about 18 to 25 ps, and then does not increase after 25 ps. Finally, a high average friction coefficient of 0.76 is obtained. These results show that the friction coefficient increases with the number of interfacial C-C bonds. Therefore, the increasing tensile strain of the DLC substrates increases the number of interfacial C-C bonds formed during sliding, which increases the friction coefficient of DLC/DLC.
Figure 4. Time evolution of the (a) number of interfacial C-C bonds which is investigated based on the atomic bond population and (b) instantaneous friction coefficients of DLC substrates at each tensile strain. The blue, red, and black lines represent the results for the DLC substrates at tensile strains of 0.00, 0.02, and 0.04, respectively.
Next, we investigate the interfacial chemical reaction dynamics at tensile strains of 0.02 and 0.04. Figure 5a shows the typical pathway of the interfacial C-C bond formation at a tensile strain of 0.04. Initially, at 7.04 ps a carbon atom (C2) in the upper substrate approaches hydrogen atom H2, which terminates C3 in the lower substrate. A bond between C2 and one of its neighbors (C1) dissociates because the C1-C2 bond is elongated by the tensile stress and easy to dissociate. During the C1-C2 bond dissociation, a hydrogen atom (H1) that initially terminated C2 is transferred from C2 to C1. To clearly understand the causality between the dissociation of C1-C2 bond and the transfer of H1, we investigate the time evolution of the bond lengths for C1C2, H1-C1, and H1-C2 as shown in Figure 5c. The bond length of C1-C2 bond increases at about
7.0 ps, and the bond length of H1-C1 bond decreases at the same time. This provides the evidence that hydrogen transfer of H1 and C1-C2 bond dissociation occur simultaneously during friction. Subsequently, H2 is transferred from C3 to C2 at 7.74 ps and an interfacial C2-C3 bond forms at 8.08 ps. In this reaction, an interfacial C-C bond forms with the C-C bond dissociation on the DLC surface and transfer of hydrogen atom occurs. We also observe another chemical reaction at the interface, in which a C-C bond in the DLC substrate is dissociated by hydrogen transfer. This reaction is mainly observed at a tensile strain of 0.04. Figure 5b shows the typical pathway for the C-C bond dissociation in the DLC substrates induced by the hydrogen transfer at a tensile strain of 0.04. A hydrogen atom (H3) initially terminates a carbon atom (C4) in the DLC substrate. The C4-H3 bond dissociates during sliding, H3 moves to the nearby C5-C6 bond separating C5 and C6. The C5-C6 bond dissociates at 33.32 ps, and the C5-H3 bond dissociates at 33.58 ps. We investigate the time evolution of the bond length for C5-C6, H3-C5, and H3-C6 to show the causality between the transfer of H3 and dissociation of C5-C6 as shown in Figure 5d. The distances of both H3-C5 and H3-C6 decreases at about 33.23 ps, indicating that H3 begins to approach C5-C6 bond. On the other hand, the bond length of C5-C6 increases at about 23.32 ps and the subsequently C5-C6 bond is dissociated. Transfer of H3 is about 0.09 ps earlier than the C5-C6 bond dissociation. This is regarded as the evidence that the hydrogen transfer of H3 causes the dissociation of C5-C6 bond. Finally, the unsaturated carbon atoms of C4 and C5 react with other nearby atoms or convert to Csp2-hybridized carbon atoms. In this reaction, hydrogen transfer causes the C-C bond dissociation in the DLC substrates, indicating the atomiclevel wear41,42 of DLC.
Figure 5. Typical chemical reactions of DLC substrates at a tensile strain of 0.04. (a) Interfacial C-C bond formation on the DLC surfaces and (b) C-C bond dissociation in the DLC substrates induced by hydrogen transfer, (c) and (d) are the time evolution of bond lengths in (a) and (b), respectively.
Next, the effect of the tensile strain on the structural change in the DLC substrates is evaluated quantitatively. We investigate the number of complete C-C bonds in the simulation model. Figure 6a shows the change in the number of complete C-C bonds during sliding. At a tensile strain of 0.00, the number of complete C-C bonds does not change because there are no chemical reactions at the friction interface during the simulation. At a tensile strain of 0.02, there is little change in the number of complete C-C bonds. At a tensile strain of 0.04, the number of complete C-C bonds decreases from about 15 ps, indicating the continuous atomic-level wear of the DLC substrate. Furthermore, we investigate the graphitization (rearrangement from Csp3- to Csp2-hybridized carbon atoms) of the DLC substrates during friction. Figure 6b shows the time evolution of the number of Csp2-hybridized carbon atoms. At tensile strains of 0.00 and 0.02, the increase in the number of Csp2-hybridized carbon atoms is small. At a tensile strain of 0.04, the number of Csp2-hybridized carbon atoms increases from about 15 ps. The increase in the number of Csp2-hybridized carbon atoms and the decrease in the number of entire C-C bonds begin at almost the same time (about 15 ps). These results show that the graphitization of the DLC substrates occurs with the C-C bond dissociation induced by the hydrogen transfer (Figure 5b). Furthermore, we investigate the change in the stress of the DLC substrates along the sliding direction (x-direction). Figure 6c shows the time evolution of the stress along the sliding direction. At tensile strains of 0.00 and 0.02, the stress along the sliding direction does not change. At a tensile strain of 0.04, the stress along the sliding direction decreases at about 15 ps. This decrease in the stress occurs simultaneously with the decrease in the number of entire C-C bonds in Figure 6a. The decrease in the stress along the sliding direction is due to the structural
relaxation of DLC after the continuous C-C bond dissociation in the DLC substrates at about 15 ps.
Figure 6. Time evolution of the (a) number of complete C-C bonds, (b) number of Csp2hybridized carbon atoms, and (c) stress along the sliding direction of the DLC substrates. The number of C-C bonds and Csp2-hybridized carbon atoms are investigated based on the atomic bond population. The blue, red, and black lines show the results for the DLC substrates at tensile strains of 0.00, 0.02, and 0.04, respectively.
As mentioned above, hydrogen transfer plays an important role in the C-C bond dissociation in the DLC substrates (Figure 5b). We investigate the mean square displacement (MSD) of the hydrogen atoms from 0 ps along the y- (Figure 7a) and z-directions (Figure 7b) to quantitatively evaluate the degree of hydrogen transfer along the DLC surface and into the DLC substrates, respectively. At a tensile strain of 0.00, the MSD values along the y- and z-directions do not change with the simulation time, indicating no hydrogen transfer occurs during sliding. This is because no chemical reactions between the DLC substrates occur during sliding. At a tensile strain of 0.02, the MSD value along the y-direction increases slightly, indicating that the hydrogen transfer occurs along the DLC surface during the formation of the interfacial C-C bonds (Figure 5a). The MSD value along the z-direction changes little, indicating that the hydrogen atoms do not move toward the inside of the DLC substrates. The transfer of hydrogen atoms only occurs along the DLC surface at a tensile strain of 0.02 during sliding. At a tensile strain of 0.04, the MSD value along the y-direction increases slowly before around 23 ps and sharply after 23 ps. The MSD value along the z-direction also increases with the simulation time, which is not observed at tensile strains of 0.00 and 0.02. This indicates that the hydrogen atoms are not only transferred along the surface, but also toward the inside of the DLC substrates during the dissociation of the C-C bonds in the DLC substrate (Figure 5b). In the C-C dissociation process induced by hydrogen transfer (Figure 5b), H3 is transferred from the surface (C4) to the inside of the DLC substrate (C6), leading to the C5-C6 bond dissociation in the DLC substrate. At the tensile strain of 0.04, a lot of interfacial C-C bonds between two DLC substrates are formed during friction. The two DLC substrates are connected together by these interfacial bonds, leading to the high friction. Then, during the shearing process of the interfacial bonds, high external energy is applied on the system to overcome the high friction force. The external
energy induces various interfacial chemical reactions. This is because the external energy helps these reactions overcome their energy barriers. Thus, driven by the external energy, a part of the hydrogen terminations on the surface are dissociated during friction. These dissociated hydrogen atoms are able to transfer both along the DLC surface and into the DLC substrates, contributing to the increase in the MSD along y- and z-directions. An experimental study reported the diffusion of hydrogen atoms during the wear process of DLC coatings,43 which is consistent with our simulation results. In our simulation, hydrogen transfer leads to the continuous dissociation of C-C bonds in the DLC substrates, indicating the atomic-level wear event of DLC. The accumulation of these atomic-level wear events is considered to finally result in the wear of DLC coatings in experiment.18 Our TB-QCMD simulation clarifies the effect of tensile stress on the friction process and the wear mechanism of DLC coatings. The tensile stress of DLC coatings results in the high friction coefficient of DLC coatings due to the formation of interfacial C-C bonds. The atomiclevel wear of DLC is related to the hydrogen transfer under high tensile stress driven by the surface shear deformation when a lot of interfacial C-C bonds are formed, and these atomic-level wear events are considered to finally cause the wear of DLC coatings in experiment. This study provides atomic-scale insights into the friction process and the wear mechanism of DLC coatings under tensile stress.
Figure 7. MSD values of the hydrogen atoms in the DLC substrates along the (a) y- and (b) zdirections. The blue, red, and black lines show the results for the DLC substrates at tensile strains of 0.00, 0.02, and 0.04, respectively.
4. CONCLUSION In this work, we elucidate the friction process and wear mechanism of DLC coatings under tensile stress by using our TB-QCMD method. In DLC substrates without tensile stress, smooth sliding behavior is observed, and a low friction coefficient of around 0.02 is obtained. In DLC substrates under tensile stress, interfacial C-C bonds form during friction, and the number of the interfacial C-C bonds increases with the increasing tensile stress. The interfacial C-C bonds contribute to the high-friction behavior of the DLC substrates. Therefore, the tensile stress leads to the increase in the friction coefficient of the DLC substrates. Furthermore, at high tensile stress, hydrogen atoms are transferred both along the DLC surface and toward the inside of the
substrate during friction. This hydrogen transfer causes C-C bond dissociation in the DLC substrates, indicating the atomic-level wear of DLC. The accumulation of these atomic-level wear events is considered to finally result in the wear of DLC coatings in experiment. Our simulation results provide atomic-scale insights into the chemical reactions at the friction interface and their effects on the friction process and wear mechanism of DLC coatings under tensile stress.
SUPPORTING INFORMATION Comparison of reaction energies of dangling bonds calculated by the TB-QCMD and DFT; Energy curves in TB-QCMD and DFT; Time evolution of the number of interfacial C-C bonds at tensile strain of 0.06; Friction coefficient at tensile strain of 0.06; MSD of hydrogen atoms at tensile strain of 0.06.
ACKNOWLEDGMENTS This research was supported by JST CREST, JSPS Grant-in-Aid for Scientific Research (A) (Grant No. 26249011), MEXT as “Exploratory Challenge on Post-K computer” (Challenge of Basic Science-Exploring Extremes through Multi-Physics and Multi-Scale Simulations), and MEXT and Reconstruction Agency as “Tohoku Innovative Materials Technology Initiatives for Reconstruction (TIMT)”. This work was also supported by Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Innovative Combustion Technology” (Funding agency: JST).
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