Modeling and Simulation of Carbon Nanotube Growth.

 dc.contributor.author Farmer, Brittan Alan en_US dc.date.accessioned 2015-09-30T14:22:50Z dc.date.available NO_RESTRICTION en_US dc.date.available 2015-09-30T14:22:50Z dc.date.issued 2015 en_US dc.date.submitted en_US dc.identifier.uri https://hdl.handle.net/2027.42/113397 dc.description.abstract Carbon nanotubes (CNTs) have exceptional mechanical, electronic, and thermal properties, which make them ideal for a variety of applications. Forests of CNTs have additional applications beyond individual CNTs, such as thermal interface layers and filtration membranes. In this dissertation, we present mathematical models that allow for greater understanding and control of the CNT synthesis process. We first describe an atomistic model of CNT growth, which focuses on carbon-carbon interactions and approximates the interaction of carbon atoms with the substrate and catalyst. We also describe a simplified one-dimensional atomistic model that preserves some features of the full model of CNT growth. This simple model has one global energy minimum and many competing local minima. We simulate this system and compare the non-equilibrium probability distributions with the equilibrium distribution. We calculate transition rates between the basins of different local minima, and use these in a master equation to calculate non-equilibrium distributions. To allow for further analysis, we approximate the rate matrix by a matrix with two parameters -- a slow rate and a fast rate. We present the equilibrium distribution, hitting times, and eigenvalues of this matrix and describe how they depend on the rate parameters and the number of atoms in the chain. Finally, we describe the insights this simplified model provides regarding CNT growth. We also present a mathematical model for collective chemical effects in arrays of CNT pillars, which lead to non-uniformities in pillar height. This model involves coupling a kinetic model of CNT growth with a diffusion equation for the transport of a gaseous active species. We assume this species is produced during decomposition of the feedstock gas on the catalyst and enhances the CNT growth rate by lowering the activation energy of feedstock decomposition. We simulate the effect of catalyst spacing on pillar heights and compare with experiments. We introduce a threshold on active species concentration for pillar liftoff, with which the model is able to reproduce the absence of pillars seen in widely spaced arrays in experiments. We also present strategies for creating patterns that yield more uniform pillars. en_US dc.language.iso en_US en_US dc.subject carbon nanotubes en_US dc.subject mathematical modeling en_US dc.subject molecular dynamics en_US dc.subject Markov chains en_US dc.subject chemical coupling en_US dc.title Modeling and Simulation of Carbon Nanotube Growth. en_US dc.type Thesis en_US dc.description.thesisdegreename PhD en_US dc.description.thesisdegreediscipline Applied and Interdisciplinary Mathematics en_US dc.description.thesisdegreegrantor University of Michigan, Horace H. Rackham School of Graduate Studies en_US dc.contributor.committeemember Esedoglu, Selim en_US dc.contributor.committeemember Hart, A. John en_US dc.contributor.committeemember Smereka, Peter S. en_US dc.contributor.committeemember Krasny, Robert en_US dc.contributor.committeemember Alben, Silas D. en_US dc.subject.hlbsecondlevel Mathematics en_US dc.subject.hlbtoplevel Science en_US dc.description.bitstreamurl http://deepblue.lib.umich.edu/bitstream/2027.42/113397/1/farbritt_1.pdf dc.owningcollname Dissertations and Theses (Ph.D. and Master's)
﻿

Remediation of Harmful Language

The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.

Accessibility

If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.