First-principles comparative study on the interlayer adhesion and shear strength of transition-metal dichalcogenides and graphene

Due to their layered structure, graphene and transition-metal dichalcogenides (TMDs) are easily sheared along the basal planes. Despite a growing attention towards their use as solid lubricants, so far no head-to-head comparison has been carried out. By means of ab initio modeling of a bilayer sliding motion, we show that graphene is characterized by a shallower potential energy landscape while more similarities are attained when considering the sliding forces; we propose that the calculated interfacial ideal shear strengths afford the most accurate information on the intrinsic sliding capability of layered materials. We also investigate the effect of an applied uniaxial load: in graphene, this introduces a limited increase in the sliding barrier while in TMDs it has a substantially different impact on the possible polytypes. The polytype presenting a parallel orientation of the layers ($R0$) bears more similarities to graphene while that with antiparallel orientation ($R180$) shows deep changes in the potential energy landscape and consequently a sharper increase of its sliding barrier.

Figure 1

Geometry of graphene (left) and $R180-{\mathrm{MoS}}_2$ (right) bilayers in their most stable configurations. Upper row: top views, with the unit cells marked with red solid lines [panels (a) and (c)]. Lower row: corresponding lateral views [panels (b) and (d)]. In panel (a), dark and light gray correspond to the different graphene planes. In panels (c) and (d), Mo atoms are represented in gray and S atoms in yellow.

Figure 2

Variation of the work of separation at different bilayer configurations for each analyzed system. Each profile is associated with a bilayer sliding along the $y$ direction marked with red dots in Fig. 1. Circles correspond to the ab initio data; lines are guides for the eyes only.

Figure 3

Two-dimensional maps of the potential energy surface for the sliding motion of bilayers of graphene (a), ${\mathrm{MoS}}_2$ (b), ${\mathrm{MoSe}}_2$ (c), and ${\mathrm{MoTe}}_2$ (d). The length scale is reported in the top left corner of panel (a); the orientation in the bottom right corner of panel (d). Units and color code are reported in the column on the right. In each panel MEP paths are indicated as white lines.

Figure 4

Top panel: profiles of the work of separation for graphene (black line) and ${\mathrm{MoS}}_2$ (red line) bilayers sliding along their minimum energy path (MEP). Bottom panel: the corresponding variation of the forces associated associated with the motion, normalized to the cell area. Their maximum (absolute) value corresponds to the ${\tau }_{\text{MEP}}$ value reported in Table 1.

Figure 5

Top panel: enthalpy increase with load for the absolute minima (Min1) of graphene (black line) and TMDs (red lines) bilayers. Bottom panel: differential enthalpy behavior for selected structures on the sliding path of graphene (dashed lines) and $R180-{\mathrm{MoS}}_2$ (solid lines) with increasing load, compared to Min1 (black baseline). For graphene, Min2 is equivalent to Min1.

Figure 6

Enthalpy variation upon load for the sliding barrier associated with the MEP paths of graphene (black line) and ${\mathrm{MoS}}_2$ (red lines; solid for $R0$, dashed for $R180$), calculated at each value of the load as the difference between the saddle point and the most stable minimum structure. As in Fig. 5, the star marks the point where in $R180$ Min2 becomes more stable than Min1.