[Physics] How to determine the (n,m) dimensions of a carbon nanotube

nanoscience

I've been reading about nanotubes lately, and I keep seeing the $ (n,m) $ notation. How does this describe a nanotube's structure? How do I determine which is $n$ and which is $m$ ?

I'm familiar with matrix notation referring to rows and columns, but I couldn't connect it with the nanotube structure which is, albeit predictable, not quite like a row-column grid.

Best Answer

In the picure below, you can see how the row-column grid correspond to the graphene structure.

Graphene structure

To have a (n,m) nanotube, you "just" have to roll your graphene sheet so that the (0,0) hexagon coincides with the (n,m) hexagon. Of course, it is much easier said than done !

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