I just did a back-of-the-envelope calculation to work out what size of sphere containing a vacuum would give the same average density as helium at room temperature, if the sphere is made of graphene, the new one-size-does-everything-you-can-imagine wonder material.
Why? Well, the Yanks have just prototyped a big airship and it uses helium for buoyancy. http://www.dailymail.co.uk/sciencetech/article-2257201/The-astonishing-Aeroscraft–new-type-rigid-airship-thats-set-revolutionise-haulage-tourism–warfare.html
Helium weighs 0.164kg per cubic meter. Graphene sheet weighs only 0.77mg per square meter. Mind you, the data source was Wikipedia so don’t start a business based on this without checking! If you could make a sphere out of a single layer of graphene, and have a vacuum inside (graphene is allegedly impervious to gas) it would become less dense than helium at sizes above 0.014mm. Wow! That’s very small. I expected ping pong ball sizes when I started and knew that would never work because large thin spheres would be likely to collapse. 14 micron spheres are too small to see with the naked eye, not much bigger than skin cells, maybe they would work OK.
Confession time now. I have no idea whether a single layer of graphene is absolutely impervious to gas, it says so on some websites but it says a lot of things on some websites that are total nonsense.
The obvious downside even if it could work is that graphene is still very expensive, but everything is when is starts off. Imagine how much you could sell a plastic cup for to an Egyptian Pharaoh.
Helium is an endangered resource. We use it for party balloons and then it goes into the atmosphere and from there leaks into space. It is hard to replace, at least for the next few decades. If we could use common elements like carbon as a substitute that would be good news. Getting the cost of production down is just engineering and people are good at that when there is an incentive.
So in the future, maybe we could fill party balloons and blimps with graphene foam. You could make huge airships happily with it, that don’t need helium of hydrogen.
Tiny particles that size readily behave as a fluid and can easily be pumped. You could make lighter-than-air building materials for ultra-tall skyscrapers, launch platforms, floating Avatar-style sky islands and so on.
You could also make small clusters of them to carry tiny payloads for espionage or terrorism. Floating invisibly tiny particles of clever electronics around has good and bad uses. You could distribute explosives with floating particles that congeal into whatever shape you want on whatever target you want using self-organisation and liberal use of EM fields. I don’t even have that sort of stuff on Halo. I’d better stop now before I start laughing evilly and muttering about taking over the world.
Carbon foam can be adjusted to be soft and malleable or hard and rigid. It can be used to make balloons for transporting freight or people, just like airships, and for some of the same military uses. Foam balloons will show a multitude of uses.