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-everthing-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 metre. Graphene sheet weighs only 0.77mg per square metre. 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.
Timeguide - The future before it comes over the horizon 
I had thoughts in the same direction time ago, and i had a concern about geometry.
Since the backyball would be built of hexagons and pentagons, like C60 or C240, is it possible to build a regular structure backyball approximately the size you calculated?
I could not find on the internet a geometry discussion of the possible spheres that can be built.
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Well some papers have reported it’s impermiable to gases especially hydrogen and helium. Maybe you have this the wrong way around. Use graphene spheres to trap H2 or He at 1 atm pressure. Turn them into conventional balloons. You could then fill a balloon with a foam that’s lighter than air. Since H2 and CH4 are often used in the manufacture of graphene, there’s hydrogen around. The question is whether you can make a graphene sphere whilst trapping 1 atm of H2 within. Maybe a spherical chamber with some H2 and CH4 could be heated to form the bubble.
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Or if graphene spheres were impermeable to only O2, N2, H2O, the big molecules, but permeable to H2 and He2 – this would still work. If the spheres were either empty of full of lighter than air molecules they’d be practically the same buoyancy.
Building platforms for low earth orbit launch from graphene foam would be a great way to get us cheaply into space. A stairway to heaven – made from graphene.
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Unfortunately graphene is like the finest silk cloth. It folds and wrinkles very easily. Any vacuum filled graphene bubble would collapse upon itself. graphene’s strength lies in its resistance to stretching.
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Some very useful comments, thanks to all. It certainly needs more work. Maybe using an internal structure with a outer graphene cover would work to make bigger spheres that wouldn’t collapse but still retain the lightness.
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I am shooting myself in the foot by saying this but here goes. Wrap graphene around a layer of ice. Seal the ice in by laser welding the edges of the graphene. Drill holes through the graphene and insert carbon nanotubes. Anneal the ends of the nanotubes to the top and bottom graphene layers. You now have ‘worm holes” through the ice. Melt the ice. It is said that water passes right through graphene. Do the melting in a vacuum. What is left is a vacuum sponge. If the volume of the vacuum times the volume density of air is greater than the surface area of the graphene times the area density of graphene then the sponge will fly. The question becomes: how many columns (worm holes) per unit area are needed to resist atmospheric press? How long can a nanotube be and not buckle under atmospheric pressure?
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The advantage of vacuum is that you can easily vary the lift by pumping air in or out.
I see an airship composed of many balls from 1 meter to 10 meter diameter, contained but separated.
Enough so one or two or more could spring a leak, and the ship could still fly.
MC
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I love the idea as I do High Altitude Ballooning, and I’ve pondered this before as well. But there’s also the potential polution problem to consider as well. Small, microscopic peices of foam would float unabaited into the atmosphereand begin forming their own structures up there, not unlike the plastic sea in the Pacific. These graphene clouds could could become a significant problem, and the effects should be considered. As graphene is slightly darker than clear, would these clouds absorb heat? Would they radiate that heat or keep it from the lower atmosphere? Would they signifigantly block light and reduce the efficiency of solar cells and plant photosynthisis? If the clouds fall, what is the effect of breathing microscopic fractured foam? Might turn out not to be a signifigant problem but it should be researched
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Good point. If the balloons were somehow to break up it would cause problems. Theoretically they shouldn’t, but so far there is little knowledge of the behavior of graphene when exposed to very long periods of UV and other radiation. Many environmental problems have occurred in the past because of unexpected effects, so it should be studied in some depth before such structures are permitted in the wild. It would be very hard to find and collect fragments after the fact.
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There is a general misunderstanding about graphene. Claims are that it is 200 times stronger than steel. BUT that is for stretching, not compression. Graphene is like silk. It folds very easily. A vacuum sphere of graphene is unstable with respect to slight perturbations of its surface. It would quickly collapse. What is needed is a scaffolding of carbon nano rods. But then what is the compression strength of a rod? If the rod is too long it also will bend and fold under perturbations. I believe the graphene foams have air in them. They would need to be produced in vacuum but then the size of the individual vacancies would dictate the stability of the structure. Not a simple problem.
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I am aware that it is only really strong under tension, but firstly, in the foam, the bubbles would only need to be 14 microns across, which makes a huge difference to the distortion factors and secondly they would all be in contact with each other to make a large mass, so the forces would be distributed very differently compared to a single sphere of graphene on its own. When you pack circles, you often end up with a hexagonal structure, and with spheres, you get many surfaced 3d structures such as dodecahedrons. I’m not saying it will work, just that it might, and it needs more research to work out the optimal conditions. Maybe that will end up being low pressure gas inside rather than a vacuum. I haven’t done that research, just posited an idea so far. Not a simple problem, no, and one I don’t have either the ability or resources to research properly. In other ideas such as using graphene in building design, I’ve always gone with mixing nanotubes and graphene to get both compression and tension strenghts. One such structure biometically copies trees with tubes of graphene mimicking phloem and xylem, holding together compression-resistant nanotubes.
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They say if you can think of it someone else has lol I had an idea back in 2013 to create a vacuum spearer from sheets of carbon nanotubes assembled inside a vacuum chamber. I imaged them to be about the size of a marble so if one did break the there would be millions for redundancy. I thought you could build aircraft like a quadcopter but with bladless fans and the hull would be lined with these vacuum spheres by the millions to offset the weight making it almost if not totally weightless (I never worked out the math on that) but I figured the craft would be powered by tesla battery’s which aren’t light. I figured someday I’d be rich enough to building it. I’m still waiting on that to happen.
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There have been a few ultralight material designs since then but not using small spheres as far as I know, but give it time. I’d like to see huge floating platforms using such foams that can be used for space launches.
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