Interfacial Charge Density and Its Connection to Adhesion and Frictional Forces

We derive a connection between the intrinsic tribological properties and the electronic properties of a solid interface. In particular, we show that the adhesion and frictional forces are dictated by the electronic charge redistribution occurring due to the relative displacements of the two surfaces in contact. We define a figure of merit to quantify such a charge redistribution and show that simple functional relations hold for a wide series of interactions including metallic, covalent, and physical bonds. This suggests unconventional ways of measuring friction by recording the evolution of the interfacial electronic charge during sliding. Finally, we explain that the key mechanism to reduce adhesive friction is to inhibit the charge flow at the interface and provide examples of this mechanism in common lubricant additives.

Figure 1

Calculation of ${\rho }_{\mathrm{diff}}$ using Fe(110) surfaces as an example. The total charge density $\rho$ is visualized in a black-brown-white color scheme on a log10 scale. ${\rho }_{\mathrm{diff}}$ is visualized in a color scheme from blue (depletion) to red (accumulation) of charge. Line plots are planar averages of ${\rho }_{\mathrm{diff}}$ and $\rho$, respectively, on a scale of ${10}^{-3}$ electrons per ${\AA }^3$.

Figure 2

Charge density differences ${\rho }_{\mathrm{diff}}$ of (a) Gr, (b) Fe, (c) C, (d) Fe-S, (e) Fe-Gr, and (f) C-H, and their connection to adhesion values. Scales differ from plot to plot. The effects of partial and full passivation of Fe(110) and diamond(111) on ${\rho }_{\mathrm{diff}}$ and $W_{\mathrm{sep}}$ are shown. ${\rho }_{\text{redist}}$ values are shown as well and indicated by gray shaded areas. Units are the same as in Fig. 1.

Figure 3

Adhesion energy versus charge redistribution ${\rho }_{\text{redist}}$ for (a) VDW bonded materials, (b) simple and noble metals (squares) and non-noble transition metals (circles), and (c) covalently bonded materials. C(Pan) specifies the Pandey reconstruction.

Figure 4

PES corrugation $\mathrm{\Delta }V$ versus adhesion energy $|E_{\mathrm{adh}}|$. The main figure enlarges the region where most data are located, while the inset shows all data. The black line fits all data with a power law, and their Pearson correlation coefficient is 0.95. Symbols and colors are the same as in Fig. 3.

Figure 5

Total charge profiles for (a) Gr, (b) Fe, (c) C, and (d) Cu interfaces. Solid black lines are for the minimum configurations; dashed red lines are for the maxima. Charge is normalized to the respective value at the center of the interface in the minimum configuration.

Figure 6

Potential energy surface of Cu(100) interface (a). Total charge densities at the interface for the minimum (b), a intermediate position (c), and the maximum (d), which are marked on the sliding path shown by the arrow in (a). Interaction potentials for minimum and maximum configurations are shown in (e).