What is a chiral vector?
What is a chiral vector?
A vector connecting the centers of the two hexagons is called the chiral vector, and it determines the structure of a single-walled carbon nanotube. A chiral vector C can be specified by a chiral index (n,m) using basis vectors a1 and a2 of a graphene sheet.
What is chiral vector and chiral angle?
The chiral angle is the smallest angle between the circumference line (chiral vector) and the primitive lattice vector (zigzag direction) on the hexagonal sheet as shown in Figure 1.
What is chiral angle?
The chiral angle is defined as the angle between the chiral vector and the zigzag direction ( ). Three distinct types of CNT structures can be generated by rolling up the graphene sheet into a cylinder as shown in Fig.
What is N and M in carbon nanotubes?
Abstract. The atomic structure of a carbon nanotube can be defined by the chiral indices, (n,m), that specify its perimeter vector (chiral vector), with which the diameter and helicity are also determined.
What are chiral nanotubes?
The chiral nanotubes are formed for m ≠ n and chiral angle, 0∘ ≤ θ ≥ 30∘ [48]. CNTs with n − m = 3i (where i is an integer) have curvature induced energy band-gap typically of the order of few meV. However, carbon nanotubes for which n − m ≠ 3i, have larger energy band-gap ∼ 1 eV [49,50].
What is the structure of CNTs?
The structure of CNT consists of enrolled cylindrical graphitic sheet (called graphene) rolled up into a seamless cylinder with diameter of the order of a nanometer. It is understood that CNT is the material lying in between fullerenes and graphite as a quite new member of carbon allotropes (Tanaka et al., 1999).
How do you find a chiral angle?
The chiral angle θ, determining the degree of “twisting” of the tube, is defined as the angle (θ) between the vectors Ch and a1, which varies in the 0o ≤ |θ| ≤ 30o range.
What is chiral carbon nanotubes?
CNTs are a type of higher order fullerene and have a seamless cylindrical structure formed by the rolling of a graphene sheet. 1. The transmission electron microscope (TEM) image of a CNT and its atomic structure models are shown in Fig. 14.1.
What is a nanotube used for?
As of 2013, carbon nanotube production exceeded several thousand tons per year, used for applications in energy storage, device modelling, automotive parts, boat hulls, sporting goods, water filters, thin-film electronics, coatings, actuators and electromagnetic shields.
What are the properties of CNTs?
Carbon Nanotubes Properties
- CNTs have high thermal conductivity.
- CNTs have high electrical conductivity.
- CNTs aspect ratio.
- CNTs are very elastic ~18% elongation to failure.
- CNTs have very high tensile strength.
- CNTs are highly flexible — can be bent considerably without damage.
- CNTs have a low thermal expansion coefficient.
What is chiral symmetry and chirality in physics?
Chirality (physics) The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry .
What is the origin of chiral geometry?
The term chiral was coined by Lord Kelvin in his Baltimore lectures (given in 1884 and 1893) [2], although its usage remained ignored for nearly one century, being rediscovered by the mid-1960s to define a geometrical model devoid of certain symmetry elements, with the exception of an axis of rotation.
What is a chiral compound in biology?
Most substances relevant to biology are chiral, such as carbohydrates (sugars, starch, and cellulose), the amino acids that are the building blocks of proteins, and the nucleic acids. In living organisms, one typically finds only one of the two enantiomers of a chiral compound.
What is the difference between a chiral and non-chiral theory?
A theory that is asymmetric with respect to chiralities is called a chiral theory, while a non-chiral (i.e., parity-symmetric) theory is sometimes called a vector theory. Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories.
