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Graphene is one of the strongest materials in the world. It's a two-dimensional structure (insofar the overall extension in three dimensions is concerned):

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A pencil contains graphite, which is a stacking of graphene layers. The layers are held together by single-electron bindings between carbon atoms while the bindings involved in producing the layer itself are two-electron bindings that are much stronger. Two layers can slide over each other. But why is it so easy to break a pencil? Supposedly graphene can hold a (micro) bullet (see here).

So why wouldn't stacked graphene (like in my pencil) be able to withstand a real bullet? Why can't my pencil resist the applied force when I try to break it (or pull it apart but this will require a bigger force)? Is it because the whole structure of graphite in my pencil is composed of smaller pieces of graphite? Is it because the force I apply is bigger than the total of the two-electron bondings holding all layers of graphene together? Is it because in breaking something a leverage effect is introduced? Or what?

Maybe I should rephrase my question. Is it easy to break a collection macroscopic sized graphene layers, hold together by relatively small bindings (as compared to the bonding required to keep the C-atoms of the layer together)? Say the layers have the same area (in form and size) as that of the (length) cross-section of the black inside of the pencil, and the layers are stacked to a height that is the same as the diameter of the black inside. I can imagine that if I had a piece of diamond of that form, the piece would break easy. But why?

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The bonds between graphene layers in a graphite crystal are incredibly weak. You can peel a layer of graphene off of the surface using scotch tape. Internal stresses in a macroscopic crystal can easily break it apart by separating neighboring layers. If you get your hands on naturally-occurring graphite, you will find it to be quite flaky.

That being said, this is of tangential relevance to your question because pencils do not contain single-crystal graphite. Instead, modern pencils typically contain a mixture of powdered graphite and clay which can be molded into the appropriate size and shape before being baked to harden them.

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  • $\begingroup$ What if the pencil graphite consists of complete pencil-sized graphene layers? Will you not have to pull the layers themselves apart? All the layers? Or will all the layers be just slid over each other (which is something different as breaking)? $\endgroup$ Commented May 27, 2021 at 18:44
  • $\begingroup$ @DescheleSchilder A sheet of graphene is effectively 2D, so I’m not sure what a pencil sized sheet of graphene means. Do you mean a pencil sized single single crystal of graphite, consisting of many layers of graphene? $\endgroup$
    – J. Murray
    Commented May 27, 2021 at 18:49
  • $\begingroup$ Yes. I mean when the area of the graphene structure is the same as that of the cross-section (in length) of the pencil (more or less). Many weakly bonded complete layers (so not many small pieces of graphene). I'm assuming the layers to be parallel to the pencil's length direction (which need not be the case if many pieces are involved). $\endgroup$ Commented May 27, 2021 at 18:57
  • $\begingroup$ It must be our dog who is asking me to walk with her...:-) $\endgroup$ Commented May 27, 2021 at 19:27
  • $\begingroup$ @DescheleSchilder Can you be more specific with what you mean by "breaking"? Graphite flakes apart relatively easy because of the weak binding between layers, and individual sheets of graphene are very strong for their thickness but not difficult to break with your hands, but it sounds like you have something else in mind? $\endgroup$
    – J. Murray
    Commented May 27, 2021 at 23:53

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