The real space finite element Hartree-Fock method and the thermo-mechanical properties of carbon nanotubes
This thesis consists of two parts. The first part aims to explore the application of the popular method of the finite element method (FEM) in the electronic structure theory. The finite element method is a very general numerical technique in mathematics for solving partial differential equations (PDEs) and it has been widely applied in computational mechanics and engineering in general, but it has not been extensively used in science for electronic structure calculations. Currently most electronic structure calculations rely on well-established and fast basis-set alternatives. However, there are serious shortcomings with the standard global basis-set methods such as basis saturation and ill-conditioning of the matrices as the basis-set size is increased. In this dissertation we exploit new strategies that rely on the divide-and-conquer (DC) as well as the enriched/generalized FEM (GFEM) and face-based smoothed FEM (FS-FEM) methods to solve the electronic structure problems. The linear-scaling DC partitioning scheme has been used to scale up the method for larger systems with facile parallelization among many processors utilizing locality assumptions. GFEM and FS-FEM techniques have been proposed to deal with the inner core singularity and to improve the quality of the solutions without considerable added computational cost. While these results are highly encouraging, still more research needs to be conducted in order to be able to decisively determine the best method of tackling the numerical solution of the electronic structure of atoms and molecules. Based on these preliminary results, it is anticipated that yet more elegant hybrid techniques may exist. In the second part of the thesis, special attention has been paid to carbon nanotubes (CNTs) and their thermo-electro-mechanical properties. Application of CNTs and other carbon-based materials such as graphene in science and technology has been constantly on the rise in the past two decades for example as wires, switches, transistors or other nano-electro-mechanical systems (NEMS) and nanostructures. Here, several of the more fundamental mechanical, chemical, heat transport and thermal properties of the CNTs for these applications and for microscopy purposes (in particular, atomic force microscopy or AFM) have been computationally as well as experimentally studied. Properties such as stability and collapse propagation in CNTs, dispersibility and thermal coupling to the substrate have been the focus of attention. The origins of the difficulty of the dispersion of CNT solutions have been explained and quantitative suggestions have been made to solve this problem. The thermal footprint of CNTs on SiO2 substrate has been extracted to predict the thermal conductance from CNT to SiO2. AFM tip-CNT interactions have been thoroughly investigated and recommendations for the correct interpretation of AFM images of individual CNTs have been given. Energetics of collapse and inflation of CNTs on SiO2 have been studied and upper-bound estimates for the collapse/inflation propagation speeds have been obtained. These studies provide some computational tools and rather in-depth theoretical insight into the mechanisms at play at the nano-scale and should lead to a better understanding for the design and analysis of future carbon-based nanodevices and nanostructures.
Electronic Structure, Hartree-Fock Method, Finite Element Method (FEM), Divide-and-Conquer Method, Generalized Finite Element Method (GFEM), Enrichment Functions, Face-based Smoothed FEM (FS-FEM), Carbon Nanotube (CNT), Atomic Force Microscopy (AFM), van der Waals (vdW) Interaction, Dispersibility, Collapse and Inflation Propagation, Thermal Footprint, Non-Equilibrium Green’s Function (NEGF) Method
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign