Modeling and Simulation of Carbon Nanotube Growth.

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.