So far the altitude record for a balloon is BU-60-1's 173,900 ft (53 km). What would it take to reach the thermosphere, i.e. more than ~280,000 ft? How likely is it that eventually one day a (hydrogen or helium) balloon will reach the thermosphere? What effect would the different composition of the atmosphere there have on the balloon and its ascent? How big would a balloon need to be to reach the thermosphere and what material would be best?
Strangely I have some serious domain experience here, I have in the past been involved in commercial/research balloon operations to about 130,000’ at "industrial" scale, involving tens of thousands of commercial and military launches.
The answer to "how likely" is "almost certainly not."
Newtonian reaction, or mass ejection, (what we'd call a rocket) is really hard to do down low because at launch you are lofting the payload weight plus the much larger weight of all the fuel needed for the rest of the flight. But you get lighter as you go. The engineering problem gets easier as you climb.
Balloons instead produce "lift" by means of buoyancy. My vehicle will weigh just as much at the surface as it weighs at 150,000 feet. Neglecting envelope and gas weight, if my payload weighs 6 pounds, I have to produce >6 pounds of buoyant force at the surface, AND at 40,000 feet, AND at 150,000 feet, AND at 200,000 feet. Opposite the rocket, the engineering problem compounds geometrically with increasing altitude.
My balloon has to displace whatever volume of air is required to create a 6 pound delta. The size of 6 pounds of air at the surface is nothing at all like the size of 6 pounds of air at 100,000 feet, which is again nothing at all like the size of 6 pounds of air at 200,000 feet. So the balloon only climbs when it expands in rough proportion to the air density lapse rate. My 4-5 foot diameter balloon on the surface expands to about 40 feet at 100,000 feet. It will be profoundly larger at 200,000 feet. As air density approaches zero, the size of the balloon envelope approaches infinity.
A pound (or any mass) of air at sea level is 68 times larger in volume at 100,000' and... wait for it... 4,200 times larger at 200,000'. That's a lot of expansion.
And unlike a rocket, I have no orbital velocity to create a centripetal force that offsets gravity. My balloon still weighs a lot at 200,000 feet. I will eventually need the envelop to expand to the size of a domed stadium, and then a small city, and eventually, the planet, to keep climbing.
So there's the limiting factors:
I need to have meaningful air density to displace in order to create a buoyant force. By definition, the thermosphere is where I have essentially run out of air density. At the thermosphere, air becomes non-molecular and you have individual unbound atoms of oxygen, nitrogen, and helium, and you can't produce meaningful buoyancy.
I need a material that expands to potentially hundreds and then thousands of feet of diameter. And every pound of balloon material I have to add to make a more elastic balloon envelope means more weight I have to loft. The balloon will only climb so long as it can expand. I have three choices: (a) If the material structurally constrains expansion to prevent bursting, it will hover at its terminal expansion altitude, and then will plummet seconds after the balloon goes into the earth's shadow at night and starts cooling from the lack of solar radiation. (b) It can expand infinitely. Or (c) it eventually reaches its elasticity limit and bursts, which is what happens to all weather balloons. Those are the only 3 choices.
I need a material that can withstand profound, hard to image environmentals. It's going to be operating in a gas that has so few molecules that there is essentially no temperature (nearing absolute zero) while at the same time having to withstand easily 500°C of solar radiant heat, with spikes several times higher during periods of high solar activity. So I have a monumental materials science problem to overcome as well.
Well, there's more than you ever wanted to know about balloons, but if you look at an air density table and see how big 6 pounds of air is at 200,000 feet, the impossibility of it all becomes visible.