Multiscale simulation of thin-film lubrication: Free-energy-corrected coarse graining

The quasicontinuum method was previously extended to the nonzero temperature conditions by implementing a free-energy correction on non-nodal atoms in coarse-grained solid systems to avoid the dynamical constraint, [Diestler, Wu, and Zeng, J. Chem. Phys. 121, 9279 (2004)]. In this paper, we combine the extended quasicontinuum method and an atomistic simulation to treat the monolayer film lubrication with elastic (nonrigid) substrates. It is shown that the multiscale method with the coarse-graining local elements in the merging regions between the atomistic and continuous descriptions of the substrates can reasonably predict the shear stress profile, the mean separation curve, and the transverse stress profile in the fully atomistic simulation for the tribological system. Moreover, when the nonlocal elements are placed in the merging regions, the inhomogeneous solid atoms in the near regions covered by the cut-off circles of the nonlocal elements replace the homogeneous ones at the equilibrium configuration for the free-energy correction on the non-nodal atoms. The treatment can cause an unphysical sliding between the near and far regions of the upper substrate. It is shown that if the free-energy correction on the non-nodal atoms in the coarse-grained merging regions is removed, the multiscale method can still well reproduce the shear stress profile, the mean separation curve, and the transverse stress profile obtained from the fully atomistic simulation for the system.

Figure 1

Schematic diagram of idealized two-dimensional tribological system with periodic boundary conditions in $x$ direction at temperature $T=0$ K and register $\alpha =0$. (a) Fully atomistic description; (b) coarse graining of far regions of substrates with local elements (a cut-off circle is embedded itself in a representative element); (c) coarse graining of far regions of substrates with nonlocal elements (a cut-off circle of a representative element is surrounded by several nearby elements). The fluid atoms are marked by solid circles, the solid atoms in the substrates are marked by hollow squares, and the wall atoms are marked by hollow triangles.

Figure 2

Forward shearing process of the tribological system at temperature $T=0.05$ simulated by the free-energy-corrected HACG method for the nonlocal elements. (a) snapshot diagrams at the quasistatic states $\alpha =0.95$, 1.00, and 1.05; (b) shear-stress profiles ($T_{yx}$ vs register $\alpha$) for fully atomistic profile $T_{yx}\left(\alpha \right)$ (solid line) and free-energy-corrected HACG $T_{yx,cf}\left(\alpha \right)$ (dark gray filled squares).

Figure 3

(a) Shear-stress profile ($T_{yx}$ vs register $\alpha$) (b) mean separation between walls $\langle L_y\rangle$ vs register $\alpha$ (c) transverse-stress profile $(T_{xx}$ vs register $\alpha$) for model contact with monolayer film at temperature $T=0.1$. Local or nonlocal elements are placed in the coarse-grained substrates. Fully atomistic profile $T_{yx}\left(\alpha \right)$ (forward, by solid line; reverse, by dashed line); dynamically constrained HACG $T_{yx,c}\left(\alpha \right)$ calculated with the local or nonlocal elements (forward, by black/dark gray filled circles; reverse, by white/light gray filled circles); free-energy-corrected HACG $T_{yx,cf}\left(\alpha \right)$ calculated with the local or nonlocal elements (forward, by black/dark gray filled squares; reverse, by white/light gray filled squares).

Figure 4

Same as Fig. 3, except $T=0.05$.