From quantum to continuum mechanics in the delamination of atomically-thin layers from substrates

Paul Hauseux,Alexandre Tkatchenko,Katerine Saleme Ruiz,Stéphane P. A. Bordas,Alberto Ambrosetti,Thanh-Tung Nguyen

doi:10.1038/s41467-020-15480-w

Paul Hauseux, Alexandre Tkatchenko + Show 4 more

Open Access

https://doi.org/10.1038/s41467-020-15480-w

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Abstract

Anomalous proximity effects have been observed in adhesive systems ranging from proteins, bacteria, and gecko feet suspended over semiconductor surfaces to interfaces between graphene and different substrate materials. In the latter case, long-range forces are evidenced by measurements of non-vanishing stress that extends up to micrometer separations between graphene and the substrate. State-of-the-art models to describe adhesive properties are unable to explain these experimental observations, instead underestimating the measured stress distance range by 2–3 orders of magnitude. Here, we develop an analytical and numerical variational approach that combines continuum mechanics and elasticity with quantum many-body treatment of van der Waals dispersion interactions. A full relaxation of the coupled adsorbate/substrate geometry leads us to conclude that wavelike atomic deformation is largely responsible for the observed long-range proximity effect. The correct description of this seemingly general phenomenon for thin deformable membranes requires a direct coupling between quantum and continuum mechanics.

Highlights

Anomalous proximity effects have been observed in adhesive systems ranging from proteins, bacteria, and gecko feet suspended over semiconductor surfaces to interfaces between graphene and different substrate materials
The results show that the adhesive strength rapidly decays to zero when the crack opening exceeds ~35 Å, meaning that the interaction range is slightly larger than those obtained in the literature[16,18], but remains three orders of magnitude smaller when compared with experimental observations
We developed a coupled quantum/continuum model to calculate adhesive traction-separation laws for arbitrary nanomaterials via variational optimization, combining elastic theory of interatomic bonds with full inclusion of quantum-mechanical many-body vdW interactions

Summary

Introduction

Anomalous proximity effects have been observed in adhesive systems ranging from proteins, bacteria, and gecko feet suspended over semiconductor surfaces to interfaces between graphene and different substrate materials. The estimated force per unit surface area during delamination plateaus only at a distance of ~1 μm This result is in stark contradiction to all models of intermolecular interactions known to the authors, which predict an effective interaction range on the order of 2–10 nm, i.e. two to three orders of magnitude smaller than measured experimentally. It seems that even the fundamental nature and strength of the adhesive interactions between 2D materials and their substrates remain poorly understood. Density-functional calculations with vdW corrections in ref. 16 obtain an interaction distance range of 1 nm

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