Why is CNT considered a 1D structure despite having movement in two dimensions?

In summary, the conversation discusses the electronic structure of carbon nanotubes (CNT) in relation to the band structure of graphene. CNTs have a linear dispersion relation and exhibit quantized circumferential states due to their atomic dimensions. This suggests that there are allowed transitions between these states, leading to movement in the direction perpendicular to the axial direction of CNT. Despite this, CNTs are considered to be 1D structures because the electrons do not move in the second dimension, even though it may provide additional energy levels at certain temperatures.
  • #1
Halaaku
23
0
The electronic structure of CNT is discussed on the basis of band structure of
graphene. Graphene has a linear dispersion relation:
E = h_cut vF |k|
where k is the 2D wavevector and vF is the Fermi velocity. CNTs are
macroscopic along the axis but have a circumference of atomic dimensions, which
suggests that there will be large states in the axial direction but quantized
circumferential states. this implies that there are allowed transitions between circumferential states such that the movement is in the direction perpendicular to the axial direction of CNT. Therefore the movement is in two dimensions, yet we say CNT is a 1D structure. Why is that the case?
 
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  • #2
The second dimension does not appear as "dimension" - the electrons do not move in that direction, even if it might give additional energy levels (depending on the temperature).
 

Related to Why is CNT considered a 1D structure despite having movement in two dimensions?

1. What is a CNT?

A CNT, or carbon nanotube, is a cylindrical structure made up of carbon atoms arranged in a hexagonal lattice. It is considered a nanomaterial due to its extremely small size, typically measuring only a few nanometers in diameter.

2. Why is CNT considered a 1D structure?

CNTs are considered one-dimensional structures because they have a very high aspect ratio, meaning their length is much greater than their width. This gives them properties similar to those of a one-dimensional object, such as a nanoscale wire.

3. How are CNTs formed?

CNTs can be formed through various methods, including chemical vapor deposition, arc discharge, and laser ablation. These processes involve heating a carbon-containing material, such as a hydrocarbon gas, to high temperatures and allowing the carbon atoms to arrange themselves into a cylindrical shape.

4. What properties make CNTs unique?

CNTs have several unique properties, including their high strength and stiffness, excellent electrical and thermal conductivity, and high aspect ratio. They also have a wide range of potential applications in fields such as electronics, energy storage, and biomedical engineering.

5. Why is the 1D structure of CNTs important?

The 1D structure of CNTs gives them unique properties and makes them useful in a variety of applications. For example, their high aspect ratio allows them to be used as reinforcing materials in composite materials, while their excellent electrical and thermal conductivity make them ideal for use in electronic devices and energy storage systems.

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