Carbon Nanotubes are so light that they float in airpic.twitter.com/AlHWeap8cm
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I mean, I just find it surprising that a solid could somehow manage to be less dense than air. Wood is porous enough that it can float in water, yes, but air is just so thin that it seems rather unintuitive that a solid could possibly float in it...

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Yes! counterintuitive. Aerogel is a low density solid that is mostly air, so it can NOT be lighter than air. i infer It requires a very specific geometry and scale for the voids to be "large" wrto density but "small" enough wrto O2, N2 so they won't wander into the voids.
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Carbon Nanotubes have a "tensile strength" σ of about 60 Giga-Pascals
weighs about 20,000 Newtons
Most nanotubes are constructed with a cross sectional area of about 1nm²

My question is how could this occur in a solid material...