“Brave new world”

Although the title refers to the famous novel of Aldous Huxley, but this really is a brave new world.

In his lecture Tashiaki Enoki (“The Role of Edge Geometry and Chemical Structure in the Electronic Structure of Nanographene”, Nano Today 2013) described the physical and chemical effects of bisecting on graphene. He also told the differences of cutting graphene in zig-zag (Fig. 1.) and armchair (Fig. 2.) directions.

But these are only two theoretical limits.

There is a third one also existing! This is shown in Fig 3A. At this type, all along the cut there are carbon atoms having two free valence electrons.

In reality, a cut would only go in these directions if all graphene layers could be aligned in the same direction, and if all layers could be cut precisely in said directions

This, however is a martinet requirement.

A real cut is like the one on Figure 3b and Figure 3c.

The following equation describes it:

C = xA + (1-x)Z
where c – cut, A – armchair, Z – zig – zag,  x – armchair coefficient.
x = 1,
then cut goes armchair, if
x = 0,
then cut goes in zig-zag direction

The question is, what are the properties of a such cut graphene?

Are they proportional with the value of “C” (Fig 4a), do they follow step function (Fig 4b), maybe S-curve (Fig 4c), or maybe a function having extremes (Fig 4d) or something else?


There are possibly going to be ones like these, and others too.

And so it occurs that there is a much more complex situation than described in the lecture.

And this still is an idealized version.

In reality, the different layers are cut differently. This complicates things further.

In case there is not only one layer (MLG), but there are two (BLG) or more (FLG), then on one chip only there can appear different cuts.

And there can be different cuts on just one layer.

This way, if we consider two cuts, it could be A-A cut (Fig 5a), A-Z cut (Fig 5b), Z-Z cut (Fig 5c), 1 – 1 cut (Fig 5d), 1-A cut (FIG 5e), 1 – Z cut (Fig 5f),  semi-general, of which one side is “A” (Fig 5g) or “Z” (Fig 5h),  or “1” (Fig 5i), and general, where none of the sides are either “A” or “Z” or “1”(Fig 5j).

Let’s make the direction which connects the two cuts the width direction of the graphene layer, and the one perpendicular the direction of length.

In case there forms a nano sized length after the cuts, then the layer is a nanographene.

In case the width becomes nano sized, then a planar graphene nano ribbon is generated.

Let’s introduce the concept of minimal graphene nano ribbon.

Minimal graphene nano ribbon  is a nano ribbon in which in the width direction there is only a Kekulé sextett.

These could be A-A minimal graphene nano wire, A-Z minimal graphene nano wire, Z-Z minimal graphene nano wire, 1 – 1 minimal graphene nano wire, 1-A minimal graphene nano wire, 1 – Z minimal graphene nano wire, semi-general, of which one side is “A” or “Z”, or “1” and general, where none of the sides are either “A” or “Z” or “1”.

Finally, there can be such minimal graphene ribbon, which is a minimal graphene nano ribbon.

It is possible to form various geometric shapes with more than two cuts.

Is there a proper way of cutting layers at all?

So is there a solution at all?

One is, if we can achieve aligning all layers parallel and cutting them in the same direction. This is unlikely to happen.

The other one is, if such libraries as those made about chemical bonds are completed, but these could contain the different properties belonging to “C” values. We define the  implemented cuts’ directions and from the measured directions, and from the information found in the libraries, we assign the real property values.

Either of these comes into being, there is a huge group of new matters going to evolve, surely with many valuable and plannable properties.

So this really is a brave new world!

Endre Simonyi