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Multistep Locked-to-Sliding Transition in a Thin Lubricant Film

O. M. Braun, A. R. Bishop, J. Röder

1999
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Physical Review Letters
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Using Langevin simulations, we study dynamical transitions in a model three-layer atomic film confined between two rigid substrates moving with respect to each other. With the increase of a dc force applied to the top substrate, first the middle layer of the lubricant film transitions from locked to sliding states; this regime shows a stick-slip behavior with a relatively high effective friction. Next, the layers closest to the substrates start to slide over the substrates, as well as with
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... s well as with respect to the middle layer; the effective friction in this regime may be explained by energy losses due to the excitation of phonons in the lubricant. Finally, at high velocities the lubricant film decouples from the substrates and achieves a "flying" regime characterized by a very low friction coefficient. [S0031-9007(99)08913-9] PACS numbers: 62.20.Qp, The problem of friction between two substrates which are in moving contact is very important technologically as well as very rich physically [1] . Following the development of atomic force microscopy, studying tribology has approached the microscopic level. Besides the experimental methods, molecular dynamics (MD) with realistic potentials [2-4] may be useful to provide very detailed information on atomic motions, but such simulations are extremely time consuming. An alternate route is to use microscopic modeling which only incorporates the principal degrees of freedom, such as in simple Frenkel-Kontorova (FK) type models [5] [6] [7] [8] . The present work analyzes an intermediate complexity model consisting of three atomic layers. In a previous publication [9] this problem was considered for the commensurate film. Here we study an incommensurate case. Our three-dimensional system comprises a three atomic-layer film between two solid substrates, the top and bottom. Each substrate has N s 132 atoms of mass m s 1 organized into a 12 3 11 lattice of square symmetry with the lattice constants a sx a sy 3. The film situated between the substrates consists of N a 240 atoms of mass m a 1. In the x and y directions we use periodic boundary conditions. The atoms of the bottom substrate are fixed at their lattice sites r n ͑1 # n # N s ͒, while the top substrate moves rigidly. The positions of the top substrate atoms are therefore given by U 1 r n , where U is the vector describing the motion of the top substrate. The atoms of the film have positions denoted by u m ͑1 # m # N a ͒. Top substrate and film atoms may move in all three dimensions. All atoms interact via the 6-12 Lennard-Jones potential V ͑x͒ ͑r͒ V x ͓͑r x ͞r͒ 12 2 2͑r x ͞r͒ 6 ͔. We use different parameters V x and r x for the interaction within the film, "x a," and the interaction of the film atoms with the substrates, "x 0." This simulates a lubricant between two solids. Although we work with dimensionless quantities, the numerical values of the model parameters have been chosen such that, if energy were measured in electron volts and distances in angstroms, we would have realistic values for a typical solid. We took V 0 3 and r 0 3 for the interaction of atoms of the film with the substrates, giving a typical frequency for the system of v 0 6 q 2V 0 ͞m a r 2 0 4.9 and the corresponding characteristic period is t 0 ϵ 2p͞v 0 1.28. For the interatomic interaction within the film we took V a 1. Because V a ø V 0 , some atoms of the film will tend to stick to the top and bottom substrates, covering them with monolayers, while the others fill the space between these monolayers. Here we study the "incommensurate" lubricant film with r a 4.14. In this case the equilibrium configuration of the film corresponds to three layers, each having 80 atoms, organized into a close-packed triangular lattice slightly distorted by the substrate potentials. A typical frequency of vibrations within the layer is v a 6 p 2V a ͞m a r 2 a 2.05. To each atom of the top substrate we apply a dc force F, consisting of a driving force f along the x axis and a loading force f load 20.1 along the z direction. The Langevin equations for the system are therefore where F rand m are the random Langevin forces required to equilibrate the system to the temperature T 0.025, which corresponds to room temperature for energies measured in eV. A uniform external viscous friction, h 0.1v 0 0.49, models the energy exchange between the layer and the substrates as well as that due to other missing degrees of freedom such as electronhole excitations. The substrate acts as a thermostat and 0031-9007͞99͞82(15)͞3097(4)$15.00

doi:10.1103/physrevlett.82.3097
fatcat:b2cjhen7fbhzbci7f3kqqqk5fy