A survey of interlayer interaction models for graphene and other 2D materials

TL;DR

The paper surveys interlayer van der Waals mechanical models for graphene and other 2D materials, addressing both normal adhesion and tangential friction across continuous and discrete interfaces. It integrates atomistic (DFT/MD) and continuum (FEM, CGC, SSIP) approaches, emphasizing multiscale strategies that reduce computational cost while preserving key physics such as Moiré patterns, surface reconstructions, and superlubricity. Key contributions include systematic formulations of CGC for coarse-grained contact, Fourier-based descriptions of adhesion energy for homointerfaces, GSFE frameworks for heterointerfaces, and a suite of analytical and computational friction models (PT, FK, FKT) that capture stick-slip and depinning phenomena. The work highlights how elasticity, misorientation, and scale affect interfacial behavior, offering guidance for designing vdW heterostructures with tailored tribological properties and pointing to future directions in scaling, defect effects, and thermomechanical coupling. The results hold significance for nanotribology and the engineering of layered vdW materials, where controlling adhesion and friction is crucial for reliability and performance.

Abstract

This work presents a survey of mechanical models describing van der Waals interactions between 2D materials, encompassing both continuous elastomer-like materials and discrete (crystalline) 2D materials such as graphene. These interactions give rise to a range of physical phenomena, including contact instabilities, Moiré patterns, surface reconstructions, and superlubricity. The underlying contact forces follow from the variation of an interfacial interaction potential. The presentation first discusses normal contact models, and then tangential contact models. Both atomistic and continuum approaches are considered. In addition, the influence of external loading and changes in length scale on the ground state configuration and frictional contact behavior are analyzed. A particular emphasis is placed on discussing strategies that reduce computational cost in multiscale modeling.

Figures (25)

• Figure 1: (a) Van der Waals forces between temporary charges (b) Adhesive structure of the gecko's foot (c) Some common nanomaterial structures whose adhesion has been investigated using atomic force microscopy (AFM); reprinted from wang2024colloquium with permission from American Physical Society.
• Figure 2: Description of (a) nano and (b) macro level contact. Adopted from sauer2006sauer2011challenges.
• Figure 3: (a) 1D adhesive contact model, (b) load-displacement curve. The dotted curve represents unstable solutions. Adopted from sauer2006.
• Figure 4: Interaction forces of the Coarse Grained Contact model sauer2006. (a) Closest point projection and approximation of $\mathcal{B}_\ell$ by a flat half-space, (b) body force formulation, and (c) surface force formulation. (b) and (c) reprinted from sauer2009formulation with permission from Wiley.
• Figure 5: Illustration of the SSIP approach of grill2020computational. Shown are two cross-sections at Gaussian quadrature points (GP) $\xi_{1,\text{GP}}$ and $\xi_{2,\text{GP}}$ of beams 1 and 2, characterized by their separation $\boldsymbol{x}_{1-2}$ and relative rotation $\boldsymbol{\psi}_{1-2}$. The geometric quantities of a representative pair $(\xi_{1,\text{GP}}, \xi_{2,\text{GP}})$ are depicted. Figure adapted from grill2020computational with permission from Wiley.