Carbon Nanotubes Under Pressure

Abstract

Graphene has been investigated intensively since its discovery in 2004, for its unique mechanical and electrical properties. Strain modi es these properties to meet speci c scienti c or technological needs. Therefore, the strain determination and monitoring are of critical application importance and contribute to the characterization and understanding of this remarkable material. However, in many cases strain cannot be directly and precisely measured. Strain is therefore related to easily-detected phonon frequency. To be speci c, researchers attribute the frequency shift of graphene in-plane vibrational mode E2g (the graphite-mode) entirely to the in-plane strain and quantify this relation via the Gr uneisen parameter and shear deformation potential. Di erent values of these parameters however have been reported by various experiments and calculations. The discrepancy comes from considering the in-plane strain contribution alone and whether this error is acceptable depends on the accuracy required in the speci c scienti c or technological problem. Chapter 2 presents our work to quantify other contributions to the graphite-mode shift under strain, namely the compression of the -electrons into the sp2 network. Calculations will use density functional theory, generalised gradient approximation for the exchangecorrelation potential, with the van der Waals interaction add-on. Carbon nanotubes can be considered as rolled-up graphene sheet. Similar to graphene, strain modi es their properties and can be determined and monitored by the graphite-mode frequency. The tube structure gives additional mechanical stability for application and meanwhile, complication in the relationship between frequency and applied strain. The thick wall tube model explains the e ect of tube diameter on this relation (Chapter 3) while more recent experiment shows the graphite-mode frequencies of tubes of similar diameter but di erent chiralities shift very di erently under pressure (Chapter 4), which is beyond current understanding. The signi cant bundling e ect is reported but not fully understood either (Chapter 5). Chapter 6 presents our attempt to describe the collapse of tubes with the atomistic re ned elastic ring model.