You’ll never be able to get an evacuated balloon to float, for exactly the reason that Berkut implied: the materials just ain’t up to it.
Consider a spherical balloon, which is the strongest shape for its weight. The total weight of a hollow sphere is:
Weight = [symbol]r[/symbol][sub]mat’l[/sub]*(4[symbol]p[/symbol]R[sup]2[/sup]t)
where [symbol]r[/symbol][sub]mat’l[/sub] is the density of the material you’re making the balloon out of, R is the radius of the sphere, and t is its thickness. Likewise, the buoyancy of the evacuated sphere is
Buoyancy = [symbol]r[/symbol][sub]air[/sub]*(4/3[symbol]p[/symbol]R[sup]3[/sup])
To float, the sphere has to have more buoyancy than weight; i.e., buoyancy/weight > 1. An easy calculation:
Buoyancy/weight = ([symbol]r[/symbol][sub]air[/sub]/[symbol]r[/symbol][sub]mat’l[/sub])*(R/t)/3 > 1
So pick any material, and you can figure out how thin you have to make the spere walls (R/t, in other words) for it to float.
Now look at the other side of the coin: how thin can you make the walls of a sphere before it breaks? A sphere can break for two reasons: either the stress tears it apart, or it buckles. Consulting my reference book, I find two equations. To prevent overstressing,
(R/t) < 2[symbol]s[/symbol]/P
where [symbol]s[/symbol] is the material yield stress and P is the pressure (~14.5 lb/in in this case). To prevent buckling,
(R/t) < Sqrt(0.37E/P)
where E is the Young’s modulus of the material. In general, the second criterion is the hardest to satisfy. Substituting in values for, say, carbon fiber (E = 33,000,000 psi and [symbol]s[/symbol] = 500,000 psi) gives (R/t) < 69000 for the first criterion and (R/t) < 917 for the second.
Substituting the density of carbon fiber (108 lb/cubic ft) and air (0.075 lb/cubic ft) into the first equations above gives
Buoyancy/weight = 0.075/108/3*(R/t) = (1/4320)*(R/t)
To be buoyant, then, a carbon fiber sphere must have (R/t)> 4320. But, to avoid buckling, (R/t) < 917. Whoops. Big difference.
You can possibly do slightly better with another material (but I don’t know what). You also might be able to do better by adding in some struts to brace the sphere and keep it from buckling… but then of course you’re adding in more weight.