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benharack comments on Justifiable Erroneous Scientific Pessimism - Less Wrong Discussion
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There was a pretty solid basis for believing that 2-dimensional crystals were thermodynamically unstable and thus couldn't exist. Then in 2004 Geim and Novoselov did it (isolated graphene for the first time) and people had to re-scrutinize the theory, since it was obviously wrong somehow. It turns out that the previous theory was correct for 2D crystals of essentially infinite size, but it seems to not apply for non-infinite crystals. At least that is how it was explained to me once by a theorist on the subject.
The opening paragraph of this paper cites the relevant literature: http://cdn.intechopen.com/pdfs/40438/InTech-The_cherenkov_effect_in_graphene_like_structures.pdf
Single-layer Graphene is really really unstable and if you let it sit free, readily scrolls up and is very hard to get unstuck. In this sense, Landau's impossibility proof is entirely correct.
And that's why we don't use free-standing graphene without a frame, for just about anything. The closest we get is graphene oxide dissolved in a liquid, or extremely extremely tiny platelets that don't really deserve to be called crystals.
The pessimism about non-usefulness of graphene lay entirely in forgetting that you could put it on a backing or stretch it out (or thinking that it would lose its interesting properties if you did the former), and that was not justifiable at all.