Available online at ScienceDirect. Procedia Engineering 79 (2014 )

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1 Available online at ScienceDirect Procedia Engineering 79 (2014 ) CTAM 2013 The 37 th National Conference on Theoretical and Applied Mechanics (37th-NCTAM) The 1 st International Conference on Mechanics (1st-ICM) Friction Coefficient Calculation and Mechanism Analysis for MoS2 Nanoparticle from Molecular Dynamics Simulation Chuin-Shan Chen a *, Hong-Jhou Cian a, Chi-Hua Yu a and Chung-Wei Huang a a Department of Civil Engineering, National Taiwan University, Taipei, Taiwan Abstract We studied friction coefficients and mechanisms of MoS2 nanoparticles from molecular dynamics simulations. A covalent bond force field of molybdenum and sulfur were implemented in LAMMPS and tri-layered capsular structured MoS2 nanoparticles subjected to different amplitudes of normal stress were performed. We found average friction coefficient predicted by molecular dynamics simulations is about 0.05, agreed well with experimental measurements. In addition, when the underlying mechanisms switched from sliding to rolling, significant reduction of friction coefficients was observed Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( The Authors. Published Elsevier Ltd. Selection and/or peer-review under responsibility of the Paper Selection Review and Committee peer-review of under CTAM responsibility of the National Tsing Hua University, Department of Power Mechanical Engineering Keywords: Nano friction; MoS 2; nanoparticles; tribology; lubrication; molecular dynamics. Nomenclature F N Normal force F T Friction (tangential) force Greek symbols Coefficient of friction 1. Introduction Nanoparticles can be used as solid lubricant to enhance the workability and efficiency of machines in motion. The inorganic fullerene-like (IF) compounds such as MoS 2 or WS 2 nanoparticles, which have a good anti-wear effect, have attracted great interests recently. Three atomic-level friction mechanisms have been reported for * Corresponding author. Tel.: ; fax: address: dchen@ntu.edu.tw Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Selection and peer-review under responsibility of the National Tsing Hua University, Department of Power Mechanical Engineering doi: /j.proeng

2 618 Chuin-Shan Chen et al. / Procedia Engineering 79 ( 2014 ) MoS 2 or WS 2 nanoparticle-based lubricant system [1]; they are sliding [2], rolling [3] and exfoliation [4]. The sliding mechanism is an apparent tribology behavior which is often observed from experiments [5]. The rolling mechanism is an inherent mechanism due to the shape nature of nanoparticles [6-9]. The exfoliation mechanism, a typical feature of IF compounds, can reduce friction by transferring the exfoliated layer to substrate and form a so-called tribofilm [1]. In this study, molecular dynamics (MD) simulation of a MoS 2 nanoparticle was used to quantitatively investigate the rolling and sliding effects on a MoS 2 nanoparticle. In the following, detailed method to perform molecular dynamics simulations was described. Tribological behaviors from the calculated results were studied. The coefficients of friction ( ) were evaluated. The influence of the sliding and rolling mechanisms on was analyzed. 2. Method Molecular dynamics simulations for tribological behaviors of individual MoS 2 nanoparticles were performed via LAMMPS [10]. In order to investigate the responses of under different normal pressures, the model composed of a top plate for applying shear rate, a sulfur substrate and a MoS 2 nanoparticle in between. Both the top plate and the substrate were composed of BCC sulfur (001) layer and BCC molybdenum (001) layer. The thicknesses of the sulfur layer and the molybdenum layer were 0.45 nm and 0.25 nm, respectively, as illustrated in Fig. 1(a). A three tri-layered capsular MoS 2 nanoparticle with 10.5 nm length and 4.4 nm in diameter was modeled. The system was controlled under a hybrid of a microcanonical NVE and canonical NVT ensembles. MD simulation was performed with a 2 femtosecond time step. The system temperature was controlled by velocity scaling to remain 300K during simulation. The Langevin thermostat [11] was applied on both the top plate and the substrate to dissipate redundant energy from the system in the NVE ensemble. (a) (b) Fig. 1. (a) An illustration of system setup and (b) visualization of system arrangement, which consists of a nanoparticle, a substrate and a top plate. Yellow and purple atoms are sulfur and molybdenum, respectively. The MoS 2 nanoparticle was subjected to different magnitudes of normal force. Friction force was computed directly from the nanoparticle as illustrated schematically in Fig. 1(b). The normal strains applied on the nanoparticle were controlled by 5%, 10% and 20%, respectively. The friction simulations were performed by sliding the top plate laterally with a sliding rate of 10 m/s. The force field reported in [12, 13] that described the covalent bond potential of Mo-S system coupled with Lennard-Jones (LJ) potential for long range van der Waals interaction was implemented in LAMMPS and used in this study.

3 Chuin-Shan Chen et al. / Procedia Engineering 79 ( 2014 ) Results and Discussion The coefficients of friction ( ) were depicted in Fig. 2. The values were evaluated directly from the ensemble average of the ratio between the normal force and the shear force acting on the MoS 2 nanoparticle. The average normal force for the cases of 5%, 10% and 20% applied normal strain were ± nn, ± nn and ± nn, respectively. The average shear force for the cases of 5%, 10% and 20% applied normal strain were ± nn, ± nn and ± nn, respectively. The average equal to was obtained by least square fitting of the mean values. Recently, Jelenc et al. [14] conducted an experimental study using atomic force microscope (AFM) on a MoS 2 nanoparticle and reported was around The predicted agreed very well with the experimental measurements. FT, nn Fig. 2. Coefficients of friction ( ) evaluated directly from the ensemble average of the ratio between the normal force and the shear force acting on the MoS 2 nanoparticle. We further investigated the influence of the sliding and rolling mechanisms on for the case of 5% strain control. Fig. 3 shows the calculated coefficients of friction ( ) through the sliding displacement of the top plate Fig. 4 shows a sequence of snapshots at (a) 1 nm, (b) 2 nm, (c) 3 nm and (d) 4 nm sliding displacements Rolling process could be visualized from red dot and green dot which denoted on the nanoparticle. Transition from the sliding to rolling process would lead to significant reduction of. Coefficient of friction,

4 620 Chuin-Shan Chen et al. / Procedia Engineering 79 ( 2014 ) Fig. 3. Calculated coefficients of friction ( ) for the case of 5% strain control. Fig. 4. Illustration of friction simulations for the case of 5% strain control. Rolling process can be visualized from red dot and green dot which denoted on the nanoparticle. The sub-figures represented the sliding displacement of the top plate at (a) 1 nm, (b) 2 nm, (c) 3 nm and (d) 4 nm, respectively. 4. Conclusions The tribological behaviors of MoS 2 nanoparticles were analyzed using molecular dynamics simulations. The coefficients of friction ( ) were evaluated directly from the ensemble average of the ratio between the normal force and the shear force acting on the MoS 2 nanoparticle. The predicted agreed very well with recent AFM measurements. Further analysis of nanoparticle motion at different sliding displacements revealed transition from the sliding to rolling process. A significant reduction of was found when the mechanism switched from typical sliding mechanism to nanoparticle-inherent rolling mechanism. Acknowledgements Computational resources were provided by the National Center for High-performance Computing and National Taiwan University. The authors would like to acknowledge funding supported by National Science Council of Taiwan (NSC E MY3, NSC E , NSC E ) and National Taiwan University (10R ). References [1] O. Tevet, P. Von-Huth, R. Popovitz-Biro, R. Rosentsveig, H.D. Wagner, R. Tenne, Friction mechanism of individual multilayered nanoparticles, Proc. Natl. Acad. Sci. U.S.A., 108 (2011) [2] A. Fischer, Well-founded selection of materials for improved wear resistance, Wear, 194 (1996) [3] J.F. Wu, W.S. Zhai, G.F. Jie, Preparation and tribological properties of WS 2 nanoparticles modified by trioctylamine, P. I. Mech. Eng. J.-J. Eng., 223 (2009) [4] L. Rapoport, O. Nepomnyashchy, I. Lapsker, A. Verdyan, Y. Soifer, R. Popovitz-Biro, R. Tenne, Friction and wear of fullerene-like WS 2 under severe contact conditions: friction of ceramic materials, Tribol. Lett.,

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