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Difficulty: Very hardBiotechnology and Nanotechnology

In nanotechnology, Single-Walled Carbon Nanotubes (SWCNTs) exhibit uniform metallic conductivity across all structural configurations, irrespective of their chiral indices (n,m)(n, m), due to unconstrained π\pi-electron delocalization along their cylindrical lattice.

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Answer

The statement is False. The electrical conductivity of Single-Walled Carbon Nanotubes (SWCNTs) depends on their chiral indices (n,m)(n, m), making them either metallic or semiconducting.
The statement is false because the conductivity of SWCNTs is dictated by their chirality indices (n,m)(n, m). Only nanotubes satisfying the relation where (n−m)(n - m) is a multiple of 33 demonstrate metallic conductivity, whereas all other chiral arrangements produce semiconducting behavior.

Step-by-Step Solution

1
Analyze the structural synthesis of Single-Walled Carbon Nanotubes (SWCNTs).
SWCNTs can be conceptualized as a single-atom-thick graphene sheet rolled into a seamless cylinder along a specific chiral vector (n,m)(n, m).
The vector direction determines the circumferential alignment of carbon hexagons relative to the tube axis.
2
Evaluate the 1D quantum confinement effects on electronic band structures.
Rolling graphene imposes periodic boundary conditions along the circumference, quantizing wave vectors into 1D sub-bands.
Depending on whether these sub-bands pass through the Dirac points of graphene, the nanotube becomes metallic or semiconducting.
3
Apply the mathematical criterion for conductivity classification.
SWCNTs are metallic if (n−m)(n - m) is divisible by 33; otherwise, they exhibit a bandgap and function as semiconductors (comprising roughly two-thirds of all synthesized SWCNTs).
This structural dependence refutes the claim that all SWCNTs possess metallic conductivity regardless of chiral indices.

Key Concept

Chirality and Electronic Transport in Carbon Nanotubes
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Topics

Biotechnology and Nanotechnology

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