Modal analysis for determining the size-and temperature-dependent bending rigidity of graphene

TL;DR

This study introduces a modal analysis method to estimate the effective bending rigidity of graphene membranes from Brownian motion spectra, accounting for temperature and size effects caused by thermal ripples.

Contribution

It presents a novel approach combining molecular dynamics and continuum mechanics to determine temperature-dependent bending rigidity of 2D materials.

Findings

Effective bending rigidity varies with temperature and size.

The method accurately captures the influence of thermal ripples.

Framework applicable to other 2D nano-structures.

Abstract

The bending rigidity of two-dimensional (2D) materials is a key parameter for understanding the mechanics of 2D NEMS devices. The apparent bending rigidity of graphene membranes at macroscopic scale differs from theoretical predictions at micro-scale. This difference is believed to originate from thermally induced dynamic ripples in the atomically thin membrane. In this paper, we perform modal analysis to estimate the effective macroscopic bending rigidity of graphene membranes from the frequency spectrum of their Brownian motion. Our method is based on fitting the resonance frequencies obtained from the Brownian motion in molecular dynamics simulations, to those obtained from a continuum mechanics model, with bending rigidity and pretension as the fit parameters. In this way, the effective bending rigidity of the membrane and its temperature and size dependence, are extracted, while including the effects of dynamic ripples and thermal fluctuations. The proposed method provides a framework for estimating the macroscopic mechanical properties at high frequencies in other two-dimensional nano-structures at finite temperatures.