Simulation of Carbon Nanotube Growth.
Abstract
The basic understanding of the underlying techniques of growing Carbon Nanotubes (CNTs) with a specific chirality is still obscure and needs to be understood so as to properly harness its potentials.
Using both Classical Molecular Dynamics (MD) simulation with empirical force fields and a geometry optimization based on ab initio forces, we show that the dynamics involved in the growth of CNT on iron nanoparicles is non linear but complex.
For a good geometry, the growth depends on the deposition rate of the carbon atoms on the iron nanoparticles. Observations show that defects in the CNT first appear in the cap formed and then propagate through the wall of the growing tube.
Partial results from ab initio show the formation of a cap which is a precursor of an armchair type CNT.
Table Of Contents
TITLE PAGE……………………………. i
APPROVAL PAGE……………………….. ii
DEDICATION…………………………… iii
ACKNOWLEDGEMENT………………… iv
ABSTRACT…………………………. v
TABLE OF CONTENTS………………… vi
CHAPTER ONE
1.0.0 Introduction…………………. 1
1.1.0 Aims and Objectives……………. 5
CHAPTER TWO
2.0.0 Theory……………………… 6
2.1.0 Geometry of a Graphene Sheet……………….. 6
2.2.0 Geometry of an SWCNT………………………………. 8
- Classical Molecular Dynamics (MD) Simulation Method……….. 14
- Computation of Forces…………………………….. 15
- Equations of Motion……………………………………. 16
- Ab initio Molecular Dynamics Simulation Methods……………………. 17
- Ab initio Born-Oppenheimer Molecular Dynamics (BOMD)……………….. 24
CHAPTER THREE
3.0.0 Methodology…………….. 26
CHAPTER FOUR
4.0.0 Results…………………….. 30
4.1.0 Classical MD Simulation………… 31
- Ab initio Optimization…………….. 32
- Determination of the Equilibrium Lattice Constant and Bulk Modulus…………… 32
- Results of the Murnaghan Fit for Carbon……………….. 33
- Results of the Murnaghan Fit for Carbon……………… 34
- Variable Cell Calculation……………….. 35
4.3.0 Discussion…………… 37
4.4.0 Conclusion and Recommendation…………… 38
- Appendix……………………….. 39
- LAMMPS codes for the Classical Molecular Dynamics………………….. 39
- Quantum Espresso input for the geometry and variable cell optimization………… 40
4.6.0 References……………………. 42
Introduction
Background of Study
Carbon nanotubes (CNT) occur as allotropes of carbon, others being diamond, graphite and fullerenes. Their walls are formed by an atom thick sheet of graphite(called graphene) rolled into cylinders.
The diameters are in the order of nanometer and the length in micrometers. In recent times, nanotubes of length-to-diameter ratio of 132,000,000:1 have been constructed.
This big ratio leads to a huge and unusual electrical transport. The bonds present are sp2 which is much similar to those of graphite and the tubes align themselves together by a van der Waals forces (pi-stacking).
When the graphite sheets are rolled up in a discrete(chiral) angle and a given radius with respect to a plane perpendicular to the tubes long axis, a CNT of specific chirality (either metallic or semiconducting) is formed depending on the combination of the rolling angle and the radius.
References
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