StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...
Free

Tight Binding Method for Carbon Nanotubes - Essay Example

Cite this document
Summary
The paper "Tight Binding Method for Carbon Nanotubes" discusses that generally, while conventional metals have a smooth density of states, these nanotubes are characterized by a number of singularities, where each peak corresponds to a single quantum subband…
Download full paper File format: .doc, available for editing
GRAB THE BEST PAPER96% of users find it useful
Tight Binding Method for Carbon Nanotubes
Read Text Preview

Extract of sample "Tight Binding Method for Carbon Nanotubes"

Page 12 October, 2006 Tight Binding Method For Carbon Nanotubes Discovery of nanotubes in the year 1991 by S. Iijima, opened a completely new field in the science of carbon related materials, especially carbon nanotubes, single-wall and multiwall structures. Nanotubes are cylindrical structures based on the hexagonal lattice of carbon atoms that forms crystalline graphite. They can be thought of as a sheet of graphite rolled into a cylinder. Nanotubes are of three types armchair, zigzag and chiral nanotubes. Besides having a single cylindrical wall (SWNTs), nanotubes can have multiple walls (MWNTs).Single-wall nanotubes can be either conducting or semi-conducting, depending on their structure. Carbon nanotubes are long, thin cylinders of carbon and have a very broad range of electronic, thermal, and structural properties that change depending on the different kinds of nanotube. The chiral vector of the nanotube, B'= nR1 + mR2 where R1 and R2 are unit vectors in the two-dimensional hexagonal lattice, and n and m are integers. Another important parameter is the chiral angle, which is the angle between Band R1. Chiral angle , = arc tan (3m/[2n + m]) and Diameter D = a3 (n2 + nm + m2)/ p ,Where, ac is the distance between neighboring carbon atoms in the flat sheet. The different values of n and m lead to different types of nanotube. They are armchair, zigzag and chiral nanotubes. Armchair nanotubes are Page 2 formed when n = m and the chiral angle is 30. Zigzag nanotubes are formed when either n =0 or m==0 and the chiral angle is 0. Other nanotubes, with chiral angles between 0 and 30, are known as chiral nanotubes. The properties of nanotubes are determined by their diameter and chiral angle, both of which depend on n and m. The electronic characteristics of the nanotubes have been done by numerical band structure, the structure of the chemical bonds. is given by the local spatial structure of the orbital. The electronic structure of the nanotube fragments are calculated by SCF-MO-LCAOVmethods. In this method, only valence electrons are taken into account and the three- and four-center integrals are omitted and the repulsion of lone electron pairs can be explained. The SCF convergence criterion was 10-8for total-energy changes and 10-5 for charge-density changes between two subsequent cycles. Band structure calculations of [n, 0] (n = 6, 7, 8, 9)tubes were performed using the tight-binding Hamiltonian, with a universal set of first and second nearest-neighbor hopping integrals that reproduce various carbon structures, including graphite. The 2s, 2px, 2py, 2pz, and s* orbital of each carbon atom are used as the basis set for expressing the tight binding model. The Hamiltonian matrix elements and related parameters are obtained by adjusting the model to fit photoemission band-structure data. The (6, 0) carbon tube seems to have the lowest diameter and are thermodynamically unstable. The bonds at the ends of the nanotube fragments get saturated by hydrogen atoms. The structural unit of the tube is the distorted carbon hexagon. All c-c bonds were assumed to be of the same length: 1.4 . Page 3 The distance between third-neighbor carbon atoms along the tube circumference is 2.39 . The point group symmetry of the (6, 0) nanotube fragment is determined by the number N of carbon hexagons along the tube axis. There is a difference between heat of formation of the nanotube fragments, caused by the boundary atoms affect, strongly at the central part of the nanotube fragment. In the above Figure, the dispersion curves of the (n, 0) tubes with n = 6... 11 are shown. This tube family splits into three groups. The (3n, 0) tubes have vanishing energy gaps. The gap increases in (3n + 1, 0) and in (3n + 2, 0) tubes. Consequently, (6, 0) and (9, 0) tubes will likely show metallic conductivity, similar to graph. In graphite, orbital are represented in carbon nanotubes, the radial orbital are analogous to the lone orbital of graphite .This changes the character of the frontier orbital of carbon nanotubes in comparison with those of graphite, and in particular for nanotubes the changed s-hybridization resulted in the different the reactivity of inner and outer surfaces of single tubes. The charge-density distribution of frontier orbital in Page 4 (n, 0) nanotube fragments shifted from the inside to the outside of the tube. , resulting in nonzero electric field in the radial direction .These dispersion relations show how the electronic energy in three types of nanotube varies with wave vector. Each curve corresponds to a single quantum sub band. Fermi level is at E = 0: states of lower energy are fully occupied, while higher energy states are completely empty. In an armchair (5,5) nanotube (left) and a zigzag (9, 0) nanotube (middle), an infinitesimally small amount of energy is needed to excite an electron into an empty excited state, and such nanotubes are metallic. For a zigzag (10, 0) nanotube (right) there is a finite band gap between the occupied and empty states, so this nanotube is a semiconductor. A small increase in diameter has a major impact on the conduction properties of carbon nanotubes. The density of electronic states as a function of energy has been calculated for a variety of nanotubes. As an example, consider the density of states for metallic Page 5 (8, 8), (9, 9), (10, 10) and (11, 11) armchair nanotubes .The graph below shows energy on X-axis and Density on Y- axis. While conventional metals have a smooth density of states, these nanotubes are characterized by a number of singularities, where each peak corresponds to a single quantum sub band. .At the Fermi Energy, the highest occupied energy level, the density of states is finite for a metallic tube and zero for a semi-conducting tube. As energy is increased, sharp peaks in the density of states, called Van Hove singularities, appear and specific energy levels, where, E is the energy difference between occupied and unoccupied states, especially near the peaks. In addition, the electronic mean free path exhibits a downscaling law with a lower dependence on the coverage density of grafted molecules than for conventional substitutional doping or homogeneous disorder. Page 6 Works cited Bulusheva L G, Okotrub A V, Romanov D A and Tomanek D Electronic. "Structure of (n, 0) Zigzag Carbon Nanotubes: Cluster and Crystal." pa.msu.edu. 12November1997. 10October2006 [http://www.pa.msu.edu/cmp/csc/eprint/DT114.pdf]. "Carbon nanotubes." physicsweb.org .01January 1998.11 October 2006 [http://physicsweb.org/articles/world/11/1/9/1#further]. "Carbon nanotube science and technology."A Carbon Nanotube page: personal.rdg.ac.uk 11 October 2006 [http://www.personal.rdg.ac.uk/scsharip/tubes.htm]. "Discrete Variational Method for the Energy-Band Problem with General Crystal Potentials."APS Physics. Physical Review Online Archieve.01 May 1970. 10 October 2006[http://prola.aps.org/abstract/PRB/v2/i8/p2887_1]. "Tight-binding modeling of materials." iop.org: Electronic Journals. 28 April 1997. 10 October 2006 [http://www.iop.org/EJ/abstract/0034-4885/60/12/001] ] SaitoR, DresselhausG, and DresselhausM S . "Physical Properties of Carbon Nanotubes" World Scientific Publishing Company Read More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Tight Binding method for carbon nanotubes Essay”, n.d.)
Tight Binding method for carbon nanotubes Essay. Retrieved from https://studentshare.org/miscellaneous/1529021-tight-binding-method-for-carbon-nanotubes
(Tight Binding Method for Carbon Nanotubes Essay)
Tight Binding Method for Carbon Nanotubes Essay. https://studentshare.org/miscellaneous/1529021-tight-binding-method-for-carbon-nanotubes.
“Tight Binding Method for Carbon Nanotubes Essay”, n.d. https://studentshare.org/miscellaneous/1529021-tight-binding-method-for-carbon-nanotubes.
  • Cited: 0 times

CHECK THESE SAMPLES OF Tight Binding Method for Carbon Nanotubes

Liquid Gated Biosensor

The paper "Liquid Gated Biosensor" states that food-borne illnesses may be widespread and pose growing health problems.... The problems are with conventional pathogens which are detected using methods that have speed and sensitivity such as Conductometric biosensor.... ... ... ... Nanotechnology advances are opening development for biosensors on micron-size features that are suitable for the detection of molecules in biological sciences....
14 Pages (3500 words) Research Paper

Nanotechnology and water purification

Today, millions of people are losing their lives because of contaminated water.... According to WHO (World Health Organization), “1.... billion people around.... ... ... e world lacked access to “improved water supply” and more than 2.... billion, or roughly 40 percent of the world's population lacked access to “improved sanitation” in 2000....
14 Pages (3500 words) Essay

The Benefits and Consequences of Utilising Nanotechnology Within a Society

The paper "The Benefits and Consequences of Utilising Nanotechnology Within a Society" affirms that nanotechnology maintains many positive advantages for society in areas of medicine, consumer product manufacture, and the energy industry, and improve the durability and strength of certain composite materials....
19 Pages (4750 words) Research Paper

The Perspective of Using Carbon Nanotube in Everyday Life

The review 'The Perspective of Using carbon Nanotube in Everyday Life' speaks about the greater practicality of this technology than other revolutionary scientific research and discusses whether it can, for example, become a safe and practical material for wrinkles and not soiled clothes.... carbon Nanotube (CNT) is an application of nanotechnology which has the potential of revolutionizing the way we carry out different types of works, the way medical fraternity treats patients, the functioning of disaster management teams etc....
32 Pages (8000 words) Literature review

Nitrogen-Containing Carbon Nanotubes for Solar Cells

This research 'Nitrogen-Containing carbon nanotubes for Solar Cells' provides a deep insight into the less expensive alternatives for the present Silicon crystalline PV cells.... carbon nanotubes' benefits, their electrical and optical properties amounted to great opportunities for its commercial use.... carbon nanotubes were found to be excellent in terms of mechanical properties.... In a study conducted by the Japan Science and Technology Agency, single-walled carbon nanotubes (SWNTs) were made to work with n-type Si in a solar cell....
31 Pages (7750 words) Dissertation

Developing Membranes with Water

This literature review "Developing Membranes with Water" discusses chitosan membrane that is defined as a plasma membrane perturbing compound that consists of ß-1, 4 linear chains-linked glucosamine residues that become positively charged at acidic pHs and it is used as an antimicrobial compound....
13 Pages (3250 words) Literature review

Risks in Different Nanotech Applications

They have also included carbon nanotubes and gold nanoparticles in the detection of proteins that indicate the presence of oral cancer.... It is being developed as a method of detecting cancer cells in the bloodstream using nanoparticles called nanoflares.... There is also a development of a method of detecting brain cancer using magnetic nanoparticles together with nuclear magnetic resonance (NMR) technology....
51 Pages (12750 words) Literature review

Scanning Probe Microscopy

This assignment "Scanning Probe Microscopy" describes tasks from Physik tests.... This paper outlines key aspects of scanning probe, the main advantage of TERS, a range of excitation wavelengths.... advantages and disadvantages of methods.... ... ... ... The above plot shows the interatomic force versus distance curve an AFM tip experiences as it approaches a surface....
17 Pages (4250 words) Assignment
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Contact Us