Geometrical Effect Explains Graphene Membrane Stiffening at Finite Vacancy Concentrations

TL;DR

This paper explains how vacancies in graphene cause swelling and morphological changes that lead to an unexpected increase in stiffness, combining analytical and simulation approaches to clarify experimental observations.

Contribution

It introduces a membrane model and simulations demonstrating that vacancy-induced swelling can cause stiffening in graphene, challenging traditional views on defect effects.

Findings

Vacancies cause graphene to swell and alter its morphology.

Swelling combined with in-plane softening explains defect-induced stiffening.

The model aligns with experimental and simulation results.

Abstract

The presence of defects such as vacancies in solids has prominent effects on their mechanical properties. It not only modifies the stiffness and strength of materials, but also changes their morphologies. The latter effect is extremely significant for low- dimensional materials such as graphene. We show in this work that graphene swells while point defects such as vacancies are created at finite concentrations. The distorted geometry resulted from this areal expansion, in combination with the in-plane softening effect, predicts an unusual defect concentration dependence of stiffness measured for supported graphene membrane in nanoindentation tests, which explains the defect- induced stiffening phenomenon reported recently. The mechanism is elucidated through an analytical membrane model as well as numerical simulations at atomistic and continuum levels. In addition to elucidate the counter-intuitive observations in experiments and computer simulations, our findings also highlight the role of defect- modulated morphology engineering that can be quite effective in designing nanoscale material and structural applications.