23rd International Colloquium Tribology - January 2022 437 Molecular dynamics simulation on the behavior of viscosity modifying polymers in oil Shuhei Yamamoto Mitsui chemicals, Inc., Sodegaura, Japan Corresponding author: Shuhei.Yamamoto@mitsuichemicals.com Kazunori Kamio Mitsui chemicals, Inc., Sodegaura, Japan Yoshiki Ishii Graduate School of Information Science, University of Hyogo, Kobe, Japan Deboprasad Talukdar Graduate School of Information Science, University of Hyogo, Kobe, Japan Kosar Khajeh Graduate School of Information Science, University of Hyogo, Kobe, Japan Gentaro Sawai Graduate School of Information Science, University of Hyogo, Kobe, Japan Kyosuke Kawakita Graduate School of Information Science, University of Hyogo, Kobe, Japan Eiji Tomiyama Graduate School of Information Science, University of Hyogo, Kobe, Japan Hitoshi Washizu Graduate School of Information Science, University of Hyogo, Kobe, Japan 1. Introduction Increasing global concern about the environment requires industry to develop better fuel economy tech-nologies, not only automotives but also construction machineries, agricultural machines, injection molding machines, and so on. Liquid olefin copolymer (L-OCP) is one type of viscos-ity modifying polymer, derived from ethylene and α-olefin, used for drive system lubricants due to the better shear stability based on the lower molecular weight than conventional olefin copolymer used for engine oil. Application of L-OCP to hydraulic fluids is now being studied. Recently, energy efficiency improvement of hydraulic fluid formulated with L-OCP in the field and on the bench tests are reported [1]. Secondary-flow suppression effect of L-OCP in hydraulic fluid has been proposed as a mechanism of the phenomenon [2]. In this study, two types of simulations are done to investigate the mechanism of the phenomenon from the points of view of molecular dynamics (MD) and hydro-dynamics. First one is, the all-atom MD simulation is utilized to examine the behavior and the adsorption process onto the Fe surface of two polymers, L-OCP and polyalkyl-methacrylate (PMA) in hydraulic fluid. Second one is, here we show our multi-physics numeri-cal simulation approach to investigate the dynamics of polymer solution. The numerical scheme is to provide the dynamics of suspensions of Brownian particles, coupling molecular motion treated by Langevin equa-tion and hydro-dynamics treated by lattice Boltzmann method. The motion of polymer segments are simulated under the flow in confined geometry. In order to simu-late chemical feature of realistic polymers, we modify each polymer segment as polar and non-polar particles. Point dipoles are added as the polar segments. Since the relative permittivity is very low in oil condition, the structure and dynamics of the polymer is strongly af-fected by the distribution of the polar segments. 438 23rd International Colloquium Tribology - January 2022 Molecular dynamics simulation on the behavior of viscosity modifying polymers in oil 2. Simulation Methods 2.1 MD simulation All-atom MD simulations of the adsorption process of polymers (L-OCP, PMA) in base oil are done in the following manner [3]. Simplified molecules of L-OCP, PMA, 3, 5-diethyldodecane (DED) taken from the structure of the poly α-olefin used as base oil, and schematic picture of the simulation model confined by two solid layers, placed a neutral Fe wall at the top and a charged Fe wall at the bottom is illustrated in Figure 1, 2. In this MD simulation, the partial atomic charges on the organic molecules are assigned by the MOPAC6 semi-empirical molecular orbital calculation with the Hamil-tonian: AM1, the organic molecules are dynamically treated using the Dreiding force field. By means of LAMMPS (Large-Scale Atomic/ Molecular Massively Parallel Simulator), adsorbing behaviour of each simpli-fied molecule to the charged Fe wall in 299 base oil molecules is examined at the constant temperature of 473 K for 10 ns. Figure 1: Schematic molecular structures of base oil, and L-OCP, PMA 2.2 BD (Brownian Dynamics) and LBM (Lattice Boltzmann) Coupling scheme Figure 2: Schematic picture of the MD simulation The motion of the Brownian particles (polymer segments) are tracked by the Langevin equation, whereas the Navier-Stokes equation governing the behavior of the host fluid is analyzed by using the lattice Boltz-mann method [4]. The two equations are coupled through the friction between the particle and surround-ing fluid. The friction force is proportional to the veloc-ity of a particle relative to the host fluid. The lattice Boltzmann method is employed for the flow simulation, which is compatible with massive parallel computing, and is easy to apply various types of boundary condi-tions such as the periodical shear boundary, and com-plex structure. The polymers are described as bead-spring model, i.e. each polymer segment described as a points are tied together with springs. The polymer segments have van der Waals interaction described by Lennard-Jones poten-tial. Then the interaction between functional groups are calculated by dipole-dipole interaction. 3. Results and Discussions 3.1 MD simulation Simulation results of the adsorption process onto the Fe surface of L-OCP and PMA initially placed at the bottom of liquid phase are shown in Figure 3. We observe that PMA interacts with Fe surface more frequently than L-OCP, besides the adsorbing duration of PMA is longer than that of L-OCP. After approaching the Fe surface from a terminal of molecule affected by base oil molecules’ diffusion/ aggregation, PMA tends to strongly ad- 23rd International Colloquium Tribology - January 2022 439 Molecular dynamics simulation on the behavior of viscosity modifying polymers in oil sorb onto the Fe surface due to the polar groups, while L-OCP does temporarily and easily de-sorb from the Fe surface. In addition, simulation results also imply that base oil molecules form thin layer onto the Fe surface, which has an influence on the adsorption process that L-OCP and PMA molecules’ approach the Fe surface does not always result in the adsorption. Figure 3: Snapshots of the adsorption process. 3.2 BD (Brownian Dynamics) and LBM (Lattice Boltzmann) Coupling scheme Figure 4 shows the thermal equilibrium structure of non-polar and partially polar polymers. Segment number are 128 for each polymer and the polar segments are set in every 4 segments. The stretched structure in non-polar polymer and aggregated structure in polar polymer are clearly distinguished. The steady state structure of 2 polymer (each 128 non-polar beads) under shear are shown in Figure 5. Upper boundary is sliding in each sliding velocity and the width between upper and lower boundary is 96 nm. Under very high shear (100 m/ s), each polymer is stretched and the velocity field are almost as given. In middle shear (10 m/ s), the velocity field made by the polymer motion become actual, and in low shear (1 m/ s), the velocity fields are disordered even in very low Reynolds number. This mean the effect of polymer structure strongly affect the flow dy-namics in low flow speed region. 4. Conclusion Two types of simulations were conducted to investigate the influence of viscosity modifying polymers on the secondary-flow in hydraulic fluid. These simulations revealed that the polymer structure difference affects the adsorption tendency onto the Fe surface and the flow dynamics, which may result in the secondary-flow pat-terns. Figure 4: Snapshots of polymer of non-polar (dark gray) and polar (light gray) polymers. The polar seg-ments are described by red sphere. Figure 5: Snapshots of polymers under shear calculated by BD-LBM simulation. This study provides a methodology for simulating secondary-flow suppression effect of viscosity modifying polymers, and contributes to establishment of a novel fuel economy technology for lubricants. 5. Acknowledgments The authors thank Dr. Hiroaki Yoshida for useful help. References [1] M. Moon, Lubes ‘n’ Greases, 25 (No. 10), 20 (2019) 34. [2] I.K. Karathanassis, E. Pashkovski, M. Heidari-Koochi, et al., J. Nonnewton. Fluid Mech. 275, (2020) 104221. [3] M. Konishi, H. Washizu, Trib. Intl. 149, (2020) 105568. [4] H. Yoshida, T. Kinjo, H. Washizu, Chem. Phys. Lett., 737 (2019) 136809.