Is there material to make balloons or balls that can then be (almost) vacuumed and become lighter than air, while at the same time being strong enough to prevent them from imploding?

Answer

As far as I know, these vacuum zeppelins are currently only theoretically possible. Archimedes’ Law says that it is possible in principle, but the material-technical challenges are such that it cannot be carried out with conventional materials. Wikipedia also has an article about it:
http://en.wikipedia.org/wiki/Vacuum_airship. The wikipedia article concludes that diamond is 5 times too weak (under certain assumptions) to run the vacuum zeppelin.

The forces at play are very great. I think a good example to illustrate this is the imploding barrel, which you can view at https://www.youtube.com/watch?v=nNXuk2RdULY. This vessel is initially filled with water vapour. By cooling the vessel afterwards, this water vapor will condense. It is made impossible for the air to fill up the vacated space (the opening is in a bottom of water in the pool), and in the vessel we get something close to a vacuum. Due to its cylindrical shape and additional stiffening ribs, the vessel is reasonably resistant to external pressure. Yet it implodes violently. We can roughly calculate the forces. We have 1 atmosphere of air pressure on the outside. This corresponds to 101325 Pa. Pa (Pascal) is the unit of pressure, and can also be written as N per m2 (Newton per square meter). Newton is the unit of force. For a physicist it is not entirely relevant, but we can also convert that Newton to kilogram-force for easier interpretation. For this we know that 9.81N = 1 kilogram force. All the above together gives us that the force per surface (= pressure) acting on the vacuum vessel is approximately equal to 10 000 kg per m2. It is this pressure that causes the vessel to implode.

No doubt the barrel had also become lighter, before the implosion anyway. How much lighter was the barrel then? Let’s assume that the barrel was perfectly empty (which in reality will not have been the case). Archimedes’ law says that the buoyancy force is equal to the volume of air the vessel displaces. I assume that the volume of the vessel is 160 liters. The density of air is 1.2 kg per m3, or also 1.2 grams per litre. With the foregoing we calculate that the barrel had become about 200 gr lighter. If the barrel weighed 20 kg, this would be about 1%. The lift forces involved are therefore not very large.

Scaling might help. With a design I would be inclined to go for a spherical structure. A sphere has a maximum volume in relation to its surface area. It is also the case that the surface area of ​​a sphere (= material cost and weight) increases with the 2nd power of the radius. However, the volume of a sphere (= potential lift force) increases with the 3rd power of the radius. So if we make the radius 10 times larger, the surface structure becomes 100 times larger, but the volume and therefore the lift force 1000 times larger. This is also why classic blimps are very large. They also make use of this scale phenomenon.

If we could make a structure, it should weigh something like a gram per liter of vacuum, and preferably much less. This is extremely little. I think soap suds can already be too heavy. We will see what the future brings, because in principle it is possible. Perhaps one will soon be able to make firm foam with vacuum cells…