Simulation Of Carbon Nanotube Growth
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 nano-particles 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
TABLE OF CONTENTS--vi
1.1.0 Aims and Objectives--5
2.1.0 Geometry of a Graphene Sheet--6
2.2.0 Geometry of an SWCNT-8
2.3.0 Classical Molecular Dynamics (MD) Simulation Method-14
2.3.1 Computation of Forces-15
2.3.2 Equations of Motion--16
2.4.0 Ab initio Molecular Dynamics Simulation Methods-17
2.4.1 Ab initio Born-Oppenheimer Molecular Dynamics (BOMD)-24
4.1.0 Classical MD Simulation--31
4.2.0 Ab initio Optimization--32
4.2.1 Determination of the Equilibrium Lattice Constant and Bulk Modulus-32
4.2.2 Results of the Murnaghan Fit for Carbon-33
4.2.3 Results of the Murnaghan Fit for Carbon-34
4.2.4 Variable Cell Calculation--35
4.4.0 Conclusion and Recommendation--38
4.5.1 LAMMPS codes for the Classical Molecular Dynamics--39
4.5.2 Quantum Espresso input for the geometry and variable cell optimization--40
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
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 . (a) (b) (c)
Fig.1.1. The outlines of three types of nanotube: (a) a (10,0) zigzag nanotube; (b) a (5,5) armchair nanotube; (c) a (7,3) general chiral nanotube.(Rafil, 2008)
The angle usually can range from 0-30o. This rolling up of the graphene sheet is represented by a pair of indices (n1,n2) where n1 and n2 denotes the number of unit vectors along the direction of the honey comb crystal lattice of graphene .For n2 =0 the nanotube is said to be zigzag with chiral angle=0, for n1=n2 it is armchair with chiral angle=30o, otherwise it is chiral.
One can also show  that the bandgap of the CNT is a function of |n2-n1| and, hence, the indices (n1,n2) determine whether the CNT is metallic or semiconducting.
Their discovery by Sumio Lijima of NEC in 1991has come to be a giant leap in Science and Technology and has since then been envisioned as a step to revolutionizing nanotechnology.
This is true considering their many unique properties ranging from being 100 times stronger than stainless steel and six times lighter, hard as diamond but thermal capacity twice that of pure diamond, current-carrying capacity of 1000 times higher than that of copper, and thermally stable up to 4000K .
Their wide range of applications are also astonishing in the sense that it opens the possibility of weaving them into clothes that are bullet proof and stab-proof, further miniaturization of electronic devices, production of paper batteries, production of solar cells of improved efficiencies, treatment of cancerous cells e.t.c.
So far, there have been many growth techniques employed in the production of nanotubes. They include laser ablation, arc discharge, high pressure carbon monoxide disproportionate (Hipco) and chemical vapor deposition (CVD). Of all these, CVD approach has proven more promising for large scale production, and the ease to directly grow the CNT on any given substrate .
The CVD approach involves using a substrate containing particles of metallic catalyst usually cobalt, iron, nickel or their combination .
There are diverse opinions about the mechanism of CNT growth, but the most accepted one is described by Kumar . A hydrocarbon is passed through a chamber containing transition metal nanoparticles at a very high temperature. Meyyapan reported that CNT growth does not occur below 550 degree Celsius . The hydrocarbon (usually methane) is broken down and a carbon deposit is created while the hydrogen escapes. The carbon deposit diffuses into the metal nanoparticles catalyst. It nucleates within it and latter precipitates out a cylindrical network with no dangling bond and energetically stable. This is the CNT and in other instances gives carbon nano-fibres (CNFs). The process is sustained due to the thermal gradient inside the metal nanoparticles. There are two modes of growth namely, base growth (when the metallic catalyst is lifted by the growing carbon nano-structures) and tip growth (when the metallic catalyst remains at the bottom of the CNT), these he said depends on the energy gained as a result of adding carbon atoms from the carbon metal catalyst solution to the graphene sheets forming the carbon nano-structures . However, Kumar reported that when the catalyst-substrate interaction is weak, the carbon diffuses down through the metal; the CNT precipitates out at the metal bottom thereby pushing the metal catalyst off the substrate. The growth continues as long as the metal’s top is open for carbon diffusion but stops when the surface is completely covered with the excess carbon which stops the catalytic activities. When the catalyst-substrate interaction is strong, carbon diffuses into the metal catalyst, but this time the CNT precipitation fails to push the metal particles up so that the CNT emerge out from the metal apex.
Fig1.2. Widely-accepted growth mechanisms for CNTs: (a) tip-growth model, (b) base-growth model (Banerjee et al, 2008)
Despite the huge advancement made so far in the production of CNT, yet there is no known mechanism for controlling the chirality of CNT during the growth process whether it will be semiconducting or metallic. Factors or parameters that influence a specific growth still needed to be understood. Is the mechanism sensitive to metal catalyst, catalyst size, carbon precursor, the substrate type, temperature, pressure e.t.c? These and many more are questions awaiting answers about CNT growth.
Stephanie et. al.  proposed an idea for the chirality-selective growth of nanotubes by controlling the type of caps that form on the catalyst at the nucleation stage by ab-initio calculation. The work of Raty et. al.  (see fig2) further demonstrated convincingly the possibility of achieving the growth mechanism by ab-initio simulation.
It is therefore in the interest of this work to attempt answering some of the questions above through both classical Molecular Dynamics (MD) and ab-initio simulation similar to that of Raty et. al. but by employing other necessary means to understand the nanotube growth mechanism.
Fig1.3. Schematic representation of the basic steps of SWCNT growth on a Fe catalyst, as observed in ab initio simulations. (I) Diffusion of single C atoms (red spheres) on the surface of the catalyst. (ii) Formation of a sp2 graphene sheet floating on the catalyst surface with edge atoms covalently bonded to the metal. (iii) Root incorporation of diffusing single Catoms. [Raty et. al., 2005]
1.1.0 AIMS AND OBJECTIVES
The aim of this work is to understand the mechanism by which certain chirality occur in carbon nanotube growth processes.
The objectives are
1). Perform molecular dynamics simulation using empirical force fields (with LAMMPS codes) of carbon on nanoparticles of Fe
2). Carry out Born-Oppeinheimer MD simulations and geometry optimization of carbon atoms on
iron nano-clusters. Here, the program used will be Quantum Espresso.