The real space finite element Hartree-Fock method and the thermo-mechanical properties of carbon nanotubes

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\rMicroscopy (AFM);van der Waals (vdW) Interaction;Dispersibility;Collapse and Inflation Propagation;Thermal Footprint;Non-Equilibrium Green’s Function (NEGF) Method

Alizadegan, Rouhollah

关键词: 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\rMicroscopy (AFM);    van der Waals (vdW) Interaction;    Dispersibility;    Collapse and Inflation Propagation;    Thermal Footprint;    Non-Equilibrium Green’s Function (NEGF) Method;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/29489/Alizadegan_Rouholla.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis consists of two parts. The first part aims to explore the application ofthe popular method of the finite element method (FEM) in the electronic structuretheory. The finite element method is a very general numerical technique in mathematicsfor solving partial differential equations (PDEs) and it has been widely applied incomputational mechanics and engineering in general, but it has not been extensivelyused in science for electronic structure calculations. Currently most electronic structurecalculations rely on well-established and fast basis-set alternatives. However, there areserious shortcomings with the standard global basis-set methods such as basis saturationand ill-conditioning of the matrices as the basis-set size is increased. In this dissertationwe exploit new strategies that rely on the divide-and-conquer (DC) as well as theenriched/generalized FEM (GFEM) and face-based smoothed FEM (FS-FEM) methodsto solve the electronic structure problems. The linear-scaling DC partitioning schemehas been used to scale up the method for larger systems with facile parallelizationamong many processors utilizing locality assumptions. GFEM and FS-FEM techniqueshave been proposed to deal with the inner core singularity and to improve the quality ofthe solutions without considerable added computational cost. While these results arehighly encouraging, still more research needs to be conducted in order to be able todecisively determine the best method of tackling the numerical solution of the electronic structure of atoms and molecules. Based on these preliminary results, it is anticipatedthat 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 othercarbon-based materials such as graphene in science and technology has been constantlyon the rise in the past two decades for example as wires, switches, transistors or othernano-electro-mechanical systems (NEMS) and nanostructures. Here, several of the morefundamental mechanical, chemical, heat transport and thermal properties of the CNTsfor these applications and for microscopy purposes (in particular, atomic forcemicroscopy or AFM) have been computationally as well as experimentally studied.Properties such as stability and collapse propagation in CNTs, dispersibility and thermalcoupling to the substrate have been the focus of attention. The origins of the difficulty ofthe dispersion of CNT solutions have been explained and quantitative suggestions havebeen made to solve this problem. The thermal footprint of CNTs on SiO2 substrate hasbeen extracted to predict the thermal conductance from CNT to SiO2. AFM tip-CNTinteractions have been thoroughly investigated and recommendations for the correctinterpretation of AFM images of individual CNTs have been given. Energetics ofcollapse and inflation of CNTs on SiO2 have been studied and upper-bound estimates forthe collapse/inflation propagation speeds have been obtained. These studies providesome computational tools and rather in-depth theoretical insight into the mechanisms atplay at the nano-scale and should lead to a better understanding for the design andanalysis of future carbon-based nanodevices and nanostructures.