Quantifying Superlubricity of Bilayer Graphene from the Mobility of Interface Dislocations

Van der Waals (vdW) heterostructures subjected to interlayer twists or heterostrains demonstrate structural superlubricity, leading to their potential use as superlubricants in micro- and nanoelectromechanical devices. However, quantifying superlubricity across the vast four-dimensional heterodeformation space using experiments or atomic scale simulations is a challenging task. In this work, we develop two multiscale models to predict the interface friction drag coefficient of an arbitrarily heterodeformed bilayer graphene (BG) system─an atomistically informed dynamic Frenkel-Kontorova (DFK) model and a discrete dislocation (DD) model. The DFK and DD models are motivated by molecular dynamics simulations of friction in heterodeformed BG. In particular, we note that interface dislocations formed during structural relaxation translate in unison when a heterodeformed BG is subjected to shear traction, leading us to the hypothesis that the kinetic properties of interface dislocations determine the friction drag coefficient of the interface. The constitutive law of the DFK model comprises the generalized stacking fault energy of the AB stacking, a scalar displacement drag coefficient, and the elastic properties of graphene, which are all obtained from atomistic simulations. Simulations of the DFK model confirm our hypothesis, since a single choice of the displacement drag coefficient, fitted to the kinetic property of an individual dislocation in an atomistic simulation, predicts interface friction in any heterodeformed BG. In addition, we develop a DD model to derive an analytical expression for the friction coefficient of heterodeformed BG. While the DD model is analytically tractable and numerically more efficient, the drag at dislocation junctions must be explicitly incorporated into the model. By bridging the gap between dislocation kinetics at the microscale and interface friction at the macroscale, the DFK and DD models enable a high-throughput investigation of strain-engineered vdW heterostructures.