Interlayer coupling and strain localization in small-twist-angle graphene flakes

Moiré superlattice effects on interfacial mechanical behavior: A concise review

“…(blue line in Figure 4C), where w is determined by the shape of the slider and the twist angle. [110] Similarly, when the slider is circular, the relationship between the sliding friction force (F ) and the twist angle (θ) and size (R) can be derived as, [77,120]…”

“…Typical results for regular polygonal (square) graphene flakes sliding along the armchair direction of graphene substrate are shown in Figure 4C, which can be predicted by: [ 110 ] $$${F}_{{\rm{s}},\text{sqr}}(L,\theta )\approx \left|\frac{4\sqrt{3}{a}_{m}^{2}{U}_{0}}{9{\rm{\pi }}{a}_{{\rm{s}}}\sin \theta }\sin \left(\frac{2{\rm{\pi }}L\cos \frac{\theta }{2}}{\sqrt{3}{a}_{{\rm{m}}}}\right)\sin \left(\frac{2{\rm{\pi }}L\sin \frac{\theta }{2}}{\sqrt{3}{a}_{{\rm{m}}}}\right)\right|,$$$and the envelope of the friction (Equation []) can be described by $${F}_{s}^{\text{env}}\propto |\sin {wL}|\,$$(blue line in Figure 4C), where $$w$$ is determined by the shape of the slider and the twist angle. [ 110 ] Similarly, when the slider is circular, the relationship between the sliding friction force ($$F$$) and the twist angle ($$\theta $$) and size ($$R$$) can be derived as, [ 77,120 ] …”

Structural Superlubricity of Two-Dimensional Materials: Mechanisms, Properties, Influencing Factors, and Applications

“…The microscopic nature of self-retraction motion observed in 2D materials like graphite was explored, and the elastic deformation of the sliding interface becomes more pronounced with increasing contact size. A finite element method based on the continuum medium model was utilized to analyze the interlayer deformation and in-plane deformation of twisted graphene sheets on a rigid graphene substrate [99]. The potential energy in the small-angle large-size elastically twisted bilayer graphene (tBLG) interlayer was significantly reduced by elastic structural relaxation and localized strains.…”

“…The elastic effect was a result of the principle that local lattice mismatch caused a change in the stacking of interlayer atoms, leading to the formation of local AB-stacked (commensurate) domains and AA-stacked domains. When the layers slid relative to each other, shear strain was generated along the boundary between the two domain walls, forming a localized strain soliton, which is also called saddle point (SP) stacking [81,99,100]. An elastic model for MD simulations was utilized to examine the impact of surface elasticity on the superlubricity phenomenon of multilayer graphite flakes in contact with a graphite substrate of 120 nm × 120 nm [81].…”

“…The relationship between elastic strain energy and interlayer potential energy through the shape of the moiré superlattice was investigated by Morovati et al [99]. Specifically, the length of the moiré stripes indicates the magnitude of elastic strain energy, while the size of AA-stacked domains versus AB-stacked domains within the moiré cell reflects the magnitude of the interlayer potential energy [99]. The shape of the moiré superlattice between bilayer graphene layers is quantitatively characterized by constructing a statistical method for lattice mismatch intervals [96].…”