Model of graphene nanobubble: combining classical density functional and elasticity theories

TL;DR

This paper introduces a combined classical density functional and elasticity theory model for graphene nanobubbles, enabling analysis of their shape and internal structure, with validation against experimental and simulation data.

Contribution

It presents a novel integrated model that accounts for inhomogeneous enclosed substances and the deformable graphene wall, extending understanding of nanobubble behavior.

Findings

Constant height-to-radius ratio observed, matching experiments.

Model accurately predicts nanobubble shape and internal structure.

Applicable to various nonrigid confinement systems.

Abstract

A graphene nanobubble consists of a graphene sheet, an atomically flat substrate and a substance enclosed between them. Unlike conventional confinement with rigid walls and a fixed volume, the graphene nanobubble has one stretchable wall, which is the graphene sheet, and its volume can be adjusted by changing the shape. In this study, we developed a model of a graphene nanobubble based on classical density functional theory and the elastic theory of membranes. The proposed model takes into account the inhomogeneity of the enclosed substance, the nonrigidity of the wall and the alternating volume. As an example application, we utilize the developed model to investigate fluid argon inside graphene nanobubbles at room temperature. We observed a constant height-to-radius ratio over the whole range of radii considered, which is in agreement with the results from experiments and molecular dynamics simulations. The developed model provides a theoretical tool to study both the inner structure of the confined substance and the shape of the graphene nanobubble. The model can be easily extended to other types of nonrigid confinement.