Charge density of carbon nanotubes and graphene

[Nod]

Hi everyone!
I'm trying to solve the following problem: given the charge densities of carbon nanotubes and graphene, the charge density difference of 2 systems must be found. So I need to unfold in some way the nanotube and compare it charge density with the graphene's one. But how this unfolding process should be done? I mean, the nanotube has different distances between the carbons than the graphene, should it be so also once I map it on the plane? Or is it fine to just map it as a graphene structure and find some way of describing the charge density in an adequate manner? And which way would be adequate?
Thanks for any ideas, because I'm out of any.

 

[TeethWhitener]

I suppose it depends on what you're after, but maybe just compare the 2-carbon unit cell of graphene to an analogous 2-carbon "unit cell" of nanotubes. Otherwise, you'll have to worry about boundary conditions and such.

 

[Nod]

The boundary conditions are already applied to the nanotubes. I was given a hint that I need to open up the nanotube and "map" it: just like the mapping of the round Earth is made on a flat surface. But even in this case I saw that there are manu ways of doing it. Should I preserve the distances? Or modify the charge density? The charge densities for both cases are given as values on the grid points.

 

[TeethWhitener]

Is this for homework? I think your answer consists in combining:

The charge densities for both cases are given as values on the grid points.

and

"map" it

Does each case have different numbers of grid points?