Dependence of the Vibrational Frequencies of a Graphene Sheet on the Ratio of Its Sides and the Number of Vacancy Defects

The vibration behavior of a single-layer graphene sheet has been studied by the molecular dynamics method. The dependence of the vibrational frequencies of the graphene sheet on its size and the concentration of vacancy defects has been obtained. It has been found that the dependence of the type of vibrational modes and their number on the aspect ratio of the graphene sheet is very different for large and small samples. It has been shown that ripples appear in narrow graphene sheets (nanoribbons), reducing the vibrational frequencies. In the case of nanoribbons with an aspect ratio x/y ≥ 3.5, the influence of ripples becomes significant and leads not only to a decrease in the vibrational frequencies, but also to the disappearance of the fundamental vibrational modes.