Negative Friction Coefficients in Superlubric Graphite–Hexagonal Boron Nitride Heterojunctions

Negative friction coefficients, where friction is reduced upon increasing normal load, are predicted for superlubric graphite–hexagonal boron nitride heterojunctions. The origin of this counterintuitive behavior lies in the load-induced suppression of the moiré superstructure out-of-plane distortions leading to a less dissipative interfacial dynamics. Thermally induced enhancement of the out-of-plane fluctuations leads to an unusual increase of friction with temperature. The highlighted frictional mechanism is of a general nature and is expected to appear in many layered material heterojunctions.

Figure 1

(a) The model heterojunction: a graphene monolayer aligned over a four-layer thick $h\text{−}\mathrm{BN}$ substrate with rigid bottom layer. Carbon atoms are colored according to their vertical position with respect to the average basal plane of the graphene layer, where blue and red correspond to the maximum and minimum values attained, respectively. The scale bar is the same as in panel c. (b) Colored map of the average carbon-carbon distance (in units of the equilibrium bond-length) after relaxation of the graphene layer over $h\text{−}\mathrm{BN}$ at zero normal load. (c) The corresponding colored map of the out-of-plane distortions of graphene. (d) Schematics of the simulations setup: the graphene layer is attached to a rigid stage moving at fixed velocity of $v_{\text{stage}}$ along the $x$ direction. Driving forces are exerted via identical springs of elastic constant $k_{\parallel }$ acting only parallel to the substrate. No forces are exerted by the springs in the normal direction. The perpendicular position of the stage is shifted vertically for clarity of the presentation. Carbon, boron, and nitrogen atoms are represented by cyan, pink, and blue spheres, respectively.

Figure 2

Load dependence of the frictional stress obtained at zero (red) and room (black) temperature. Standard error bars are computed by block averaging.

Figure 3

Load dependence of the frictional power dissipated at zero temperature by (a) the center of mass and (b) the internal d.o.f. of all model heterojunction mobile layers.

Figure 4

Mechanism of NFCs. (a) The moiré superstructure ridge cross section at an applied pressure of 0 (black), 4 (blue), and 11 (red) GPa. The scan line (see inset) corresponds to the maximum peak-dip value of the vertical deformations of graphene along the direction of sliding $x$, expressed in units of the moiré periodicity of ${\lambda }_m\approx 14\mathrm{nm}$. The definitions of the maximum height $\mathrm{\Delta }z$ and the full-width-at-half-maximum $\mathrm{\Delta }x$ are marked by the double-headed arrows. (b) Load dependence of the characteristic peak-dip value $\mathrm{\Delta }z$ (black) and full-width-at-half-maximum $\mathrm{\Delta }x$ (red) of the moiré ridge. (c) Load dependence of the normalized power dissipated via vertical motion obtained from the simplistic model (see Supplemental Material [26], Sec. 7 for further details). (d) Vertical velocity of the carbon atom, which displays the largest velocity fluctuations during sliding under applied normal pressures of 0 (black), 4 (blue), and 11 (red) GPa, measured within the slider’s center-of-mass reference frame. Time is expressed in units of the period of the trajectory at steady state $T=a_{h-\mathrm{BN}}/v_{\text{stage}}\approx 25\mathrm{ps}$. Inset: Load dependence of the time-averaged value of $⟨{(v_{z,i}-v_{z,\text{com}})}^2⟩$, proportional to the energy dissipation, where $v_{z,i}$ is the given atom vertical velocity.