We discuss the use of helical symmetry for the electronic structure of these nanotubes, and the resulting trends we observe in both band gap and strain energy versus nanotube radius, using both empirical and first-principles techniques. Hence, they are often regarded as rivals for a host of similar applications. Sign up here as a reviewer to help fast-track new submissions. where
For the continuous wave vector along the nanotube axis, we can write the energy dispersion variations for one-dimensional carbon nanotube, using the two-dimensional graphene relation (11) as [11]
In fact, carbon nanotubes come in various diameters, lengths, and functional group content which can tailor their use for specific applications. Dr. Jeong Gon Son's research team at the Photo-Electronic Hybrids Research Center at the Korea Institute of Science and Technology (KIST) developed the high-capacity, stretchable lithium-ion battery. A carbon nanotube can be thought of as a sheet of graphene (a hexagonal lattice of carbon) rolled into a cylinder. Thus using (20), can be obtained equal to 12. With considering the overlap between the two above-mentioned orbitals, we will have
The electronic band structure variations of single-walled carbon nanotubes (SWCNTs) using Huckle/tight binding approximation theory are studied. The battery was developed by fabricating a structurally stretchable electrode consisting solely of electrode materials and then assembling it with stretchable gel electrolyte and stretchable packaging. With solving (8), we obtain the total energy dispersion variations as With considering that
In Figure 4, the vectors definition of graphene plane for converting to a carbon nanotube has been shown where , , and are the chirality (circumference) vector, the chirality angle, and the translational vector, respectively. It is the 15th most abundant element in the Earth's crust, and the fourth most abundant element in the universe by mass.Carbon can be found in many forms, each of which has its own physical characteristics. Structure of Carbon Nanotubes 679 III. As shown in this figure, the band gap for the metallic nanotube is almost zero, and for the semiconductive nanotube is a nonzero value. Since an SWCNT is a rolled-up sheet of graphene, the energy band structure can be obtained simply from that of two-dimensional graphene. 2011, Article ID 471241, 6 pages, 2011. https://doi.org/10.1155/2011/471241, 1School of Electrical and Computer Engineering, Tarbiat Modares University (TMU), P.O. With considering the periodic boundary conditions on , we find that the wave vector associated with (circumference) direction is quantized [11]. With considering that and are orthogonal to each other, we have , , , and . Mod. Box 14115-194, Tehran, Iran. Graphene amplifier may tap into the "terahertz gap", Newly launched graphene-enhanced sanitary napkins enjoy great success in the US, New face masks use graphene and electrical charge to repel viruses and bacteria, MIT researchers use graphene and boron nitride to convert terahertz waves to usable energy. In this paper we have studied the basic structure of graphene and its resulted element carbon nanotube. a stack of graphene layers. Graphene’s tial is vast, and the applications include: touchscreens (for LCD or OLED displays), computer chips, batteries. However, after the initial hype, revolutions failed to happen and many gave up on CNTs. Figure 1 shows the lattice of a graphene sheet in which the two fundamental carbon atoms 1 and 2 are the basic elements of overall lattice and form a unit cell. Carbon is a non-metallic chemical element often regarded as a common element of all known life. It seems that the capacity for the production of MWNTs exceeds that of SWNTs, although there is an oversupply in the market. Each point on the periodic lattice of Figure 1 can be described by where and are two integers, and are the two unit vectors which are defined as