Does aerogel "blow up" in a vacuum?
From NASA's article Aerogels: Thinner, Lighter, Stronger:
Since their invention, aerogels have primarily been made of silica. The silica is combined with a solvent to create a gel. This gel is then subjected to supercritical fluid extraction. This supercritical fluid extraction involves introducing liquid carbon dioxide into the gel. The liquid carbon dioxide surpasses its super critical point, where it can be either a gas or a liquid, and then is vented out. This exchange is performed multiple times to ensure that all liquids are removed from the gel. The resulting material is aerogel.
Removing all the liquid out of the gel implies that all the pockets made of silica that were filled with that liquid have to be interconnected, so the air in an aerogel can move from one pocket to another and eventually out of the aerogel !
So the trapped gas in your questions is not that "trapped" after all.
The polymer-based aerogel is 85-95% porous, meaning it offers the same advantages of traditional aerogels. It is equally light in weight, and has the same properties of thermal conductivity as silica-based aerogels. But these aerogels offer unprecedented flexibility, along with their durability and strength, and the ability to be made into a thin film.
Polymer aerogels are ideally suited for use in a vacuum, like in space, as well as in different gravity scenarios, such as the moon or other planets.
(Emphases by me)
Aerogel in a vacuum, from YouTube: nothing happens. My guess is that the structure is porous enough that the air is enclosed, but not really trapped. If I had a vacuum lab myself I would try to measure the outgassing time, but lately I just have YouTube.
Note from the other question that if the air entrained in the aerogel structure is at ambient pressure, the air is neutrally buoyant.
It would be very interesting to put some aerogel in a vacuum chamber, wrap the evacuated aerogel in something vapor-tight, like the Mylar used in helium balloons, and see if the assembly would float in air. The calculation is straightforward, but I haven't done it yet.