Hydrodynamic Modeling of Dielectric Response in Graphene and Carbon Nanotubes
This thesis studies two important carbon structures, graphene and carbon nanotubes, with the purpose of understanding how their three-dimensional electron density distribution affects the way fast ions interact with them. <br /><br /> A brief introduction to research in pure carbon structures is made. We then use different models to calculate the equilibrium electron density distribution in graphene and carbon nanotubes. <br /><br /> In the second part of the thesis we investigate fast ions moving parallel to a graphene sheet and experiencing forces due to the dynamic polarization of carbon valence electrons. Using the three-dimensional electron density distribution of graphene, we calculate the force directly opposing the ion's motion (stopping force), as well as the force which bends the ion's trajectory towards the sheet (image force). It is our purpose to compare these results with those based on a two-dimensional hydrodynamic model of graphene, which approximates the electron distribution of graphene by a charged fluid confined to the two-dimensional plane of the sheet. <br /><br /> The results obtained for interactions of ions with a single graphene sheet should be useful for a further analysis of ion channeling through carbon nanostructures.