Graphene bubbles on a substrate : Universal shape and van der Waals pressure

TL;DR

This study investigates the shape, size, and internal pressure of bubbles formed by 2D materials like graphene on substrates, revealing universal scaling laws and high-pressure conditions that could influence trapped substances.

Contribution

The paper provides a combined theoretical and experimental analysis of bubble morphology and pressure in 2D material heterostructures, demonstrating universal shape scaling and high internal pressures.

Findings

Bubbles exhibit universal aspect ratio scaling.

Internal pressure increases as bubble size decreases.

Pressures can reach tens of MPa, up to 1 GPa in small bubbles.

Abstract

Trapped substances between a 2D crystal, such as graphene, and an atomically flat substrate, for example, hexagonal boron nitride, give rise to the formation of bubbles. We show that the size, shape and internal pressure inside these bubbles are determined by the competition between van der Waals attraction of a 2D crystal to the substrate and the elastic energy needed to deform the atomically thin layer. This presents opportunities to use bubbles to study the elasticity of 2D materials as well as the conditions of confinement, yet none of these have been explored so far, either theoretically or experimentally. We have created a variety of bubbles formed by monolayers of graphene, hBN and MoS2 mechanically exfoliated onto hBN, graphite and MoS2 substrates. Their shapes, analyzed using atomic force microscopy, are found to exhibit universal scaling with well-defined aspect ratios, in agreement with theoretical analysis based on general properties of membranes. We also measured the pressure induced by the confinement, which increased with decreasing bubble's size and reached tens on MPa inside submicron bubbles. This agrees with our theory estimates and suggests that for bubbles with radii < 10 nm hydrostatic pressures can reach close to 1 GPa, which may modify the properties of a trapped material.