Simulation of frictional behavior of Sb nanoparticles on HOPG: Frictional duality and biduality

Antimony nanoparticles deposited under UHV conditions on HOPG are experimentally found to exhibit frictional behavior characterized by the presence of three clearly separated frictional branches featuring double dual behavior of dependence of the frictional force on the contact area. We present extensive density functional simulations, augmented to accommodate van der Waals interactions, in order to shed light on the dual frictional behavior. The simulations include incommensurable interface, wide range of spacer molecules and clusters, such as H${}_2$O, O${}_2$, propane, Sb${}_4$ spacer clusters, mobile oxidized nanoasperities as well as multiple friction generators arising from combination of spacer particles. These simulations not only provide deep insights into all the frictional branches experimentally observed but they also provide realistic incarnations of the previous simplified models. In addition, they also yield explanation of experimental results that lie well beyond the scope of the existing theoretical models.

Figure 1

Experimental results for antimony nanoparticles of varying contact area sliding over an HOPG substrate, exhibiting double duality of frictional behavior with three different frictional regimes.[7, 8, 9] Data points from nanoparticles prepared under UHV conditions are shown by filled marks, data points after exposure to air are shown by circles. From bottom to top: (a) vanishing friction branch (red/grey points), (b) nonvanishing friction branch (black squares, grey circles), and (c) friction branch corresponding to exposure to air for several days (blue/dark grey circles). The dashed line indicates the position of a $30\times {10}^3$ nm${}^2$ particle used as a reference for comparison of experiment and simulation. Adapted from Refs.7, 8, 9.

Figure 2

Schematic illustration of the scenarios corresponding to immobile (black lines) and mobile (orange/grey lines) spacers for two particles moving on a model potential energy surface. The upper panels show the respective energy profiles with the average shown in green/grey thick lines.

Figure 3

Schematics of the simulation setup illustrated on Sb${}_4$ nanoparticle on HOPG. Two different partitions between “chemically active” and van der Waals regions tested are shown on left and right, with the scheme on the right used in the production simulations.

Figure 4

Comparison of incommensurable (upper panel) and commensurable (lower panel) Sb-HOPG interfaces. Shown in each panel are structural models (antimony in violet/dark grey, carbon in grey) and variation of energy during sliding of the interface. The upper arrows indicate the sliding direction of the interface.

Figure 5

Electronic charge redistribution in the O${}_2$ molecule upon insertion into the Sb-HOPG interface. Note the population of two strongly antibonding ${\pi }^{☆}$ molecular orbitals (yellow/light grey-blue/dark grey and green/light grey-red/dark grey).

Figure 6

Oxygen atom incorporated into Sb-HOPG interface. Left panel: PES (green/grey triangles) and angles characterizing spacer particle motions (black dots) upon sliding the interface. Right panel: geometry of the interface (HOPG shown as small grey hexagons and antimony as large violet/dark grey hexagons) with an oxygen atom. Motion of the spacer atom is depicted by the $\overrightarrow{AB}$,${\overrightarrow{cd}}_{\parallel }$ angle (in degrees) with ${}_{\parallel }$ denoting projection into the HOPG plane. The upper arrow indicates the sliding direction of the interface.

Figure 7

Water molecule incorporated into Sb-HOPG interface. Color/grey-scale coding of the PES and molecular mobility characterized by the $\overrightarrow{AB}$,$\overrightarrow{cd}$ angles as in Fig. 6. Bottom two panels show induced electronic charge upon insertion of water into the interface for geometries corresponding to minimum (left), and maximum energy (right). Yellow/light grey color corresponds to charge pile up, blue/dark grey color to charge depletion.

Figure 8

Propane spacer molecule incorporated into the Sb-HOPG interface. Color/grey-scale coding of the PES, molecular mobility, and charge densities as in Fig. 6. Bottom two panels show induced electronic charge upon insertion of propane into the interface. Red color corresponds to charge pile up, blue color to charge depletion. Left and right correspond to two different views of geometry corresponding to minimum energy.

Figure 9

Sb${}_4$ spacer cluster incorporated into the Sb-HOPG interface.

Figure 10

Sb${}_4$O${}_6$ spacer cluster incorporated into Sb-HOPG interface.

Figure 11

Sb${}_4$O${}_6$ spacer cluster formed by local oxidation of antimony surface incorporated into Sb-HOPG interface. Note that the Sb${}_4$O${}_6$ minitip is dug deeper in the surface. Horizontal line indicates rotation of the antimony cell with respect to HOPG.

Figure 12

Two water molecules incorporated into Sb-HOPG interface at sites where an in-phase amplification of their effect is to be expected, see Fig 2. Left panel: PES for two H${}_2$O spacers molecules (green/grey triangles), red/grey and black dots depict the PESs of the first and second water molecule considered separately. Blue/grey crosses show the exact sum of PESs of the two water molecules considered separately. Right panel: configurations sampled from the simulation at points 1, 2, and 3, shown in the left panel.

Figure 13

Two water molecules incorporated into Sb-HOPG interface at sites where an out-of-phase combination of their effect is to be expected, see Fig 2. Meaning of left and right panels as in Fig. 12.

Figure 14

Two Sb${}_4$O${}_6$ spacer clusters corresponding to local oxidation of antimony surface incorporated into the Sb-HOPG interface at sites where an out-of-phase combination of their effects is to be expected, see Fig 2.

Figure 15

Sb${}_4$, H${}_2$O, and propane spacer particles simultaneously incorporated into the Sb-HOPG interface. Black and green/grey triangles: total corrugation of the PES before and after reconstruction of the spacer particles took place; orange/light grey circles: PES without water molecule; blue/dark grey squares: PES without propane molecule.

Figure 16

Total energy variation of Sb${}_4$ cluster on HOPG determining the diffusion barrier as a function of the optimization step number.

Figure 17

PES for sliding Sb${}_4$ cluster on HOPG revealing the energy separation between vdW and chemical components; for details see the text. The insets show two configurations sampled from the simulation with electronic charge densities on the HOPG plane determining the chemical bonding element. The sliding direction is evident from the insets.

Figure 18

Variation of total energy as a function of the number of HOPG layers included in the simulation for Sb${}_4$ cluster (left panel) and Sb${}_4$O${}_6$ oxidized asperity (right panel) sliding on HOPG substrate represented by a single layer (black triangles) and by four layers (red/grey circles).