While I heard that we cannot make aerogel float in the air because air would fill the space inside
Then I just think that, why we don't seal it with something and then we would have lighter than air brick that might be used to build floating structure
Is it possible in theory?
As explained in other answers, you need to remove air from aerogel, and the compressive strength must be higher than atmospheric pressure. I don't think this is possible. Furthermore, elastic modulus of aerogels is proportional, say, to density squared, so I suspect aerogel without air, even if its compressive strength is higher than the atmospheric pressure, will be significantly compressed, and its density can exceed the density of air.
There is, however, another theoretical approach to manufacturing of lighter-than-air solid structures that can provide the required structural strength to withstand atmospheric pressure. Our finite element analysis showed that spherical sandwich structures with honeycomb core can be made of commercially available materials and satisfy the above requirements (Akhmeteli, Gavrilin, US patent application 20070001053 (https://www.google.com/patents/US20070001053). However, manufacturing such structures is technologically challenging.
Theoretically, yes.
Aerogels are fabricated of various materials; silica, i.e. quartz, is one suitable material. To make a flotation solid with vacuum fill, one has to have a compressive strength that exceeds atmospheric pressure (15 psi), and an atmosphere-impermeable outer layer.
For a sufficiently large object, volume (goes as dimension cubed) will always dominate area (goes as dimension squared), so the weight of the impermeable outer layer may be regarded as insignificant. We need only consider the density of the aerogel structure as it relates to the compressive strength.
Silica aerogels have been made 0.04 g/cc Aerogel Technologies, and air density is about 0.0012 g/cc, so our technology isn't up to this challenge yet. Still, if we COULD make a lower density, say 0.001 g/cc, would silica hold the strain? Instead of 15 psi, the silica (density 2.65 g/cc) will form columns in all three directions, and have to hold off about 120 kpsi in compression.
Fused quartz can handle 160 kpsi in compression. So, if one can make lower density silica aerogel, and with good microstructure, it MIGHT someday be made to float in air.
Firstly, my apologies for my earlier comment, I did not read the title of your question correctly. Please let me know if if I have misunderstood you again.
To lift something in the Earth's atmosphere, we need to remove the air from the aerogel, (as small as a volume of air as it is), to create a vacuum, otherwise we still have a heavier than air structure. Then we need to seal the sides of the aerogel with graphene, to maintain the vacuum. At least, I hope I understand your idea properly here.
This source : Graphene Properties
Graphene aerogel is also very light at 0.77 milligrams per square metre (for comparison purposes, 1 square metre of paper is roughly 1000 times heavier). It is often said that a single sheet of graphene (being only 1 atom thick), sufficient in size enough to cover a whole football field, would weigh under 1 single gram.
This is incredibly light, and the slightest breeze would mean trouble in working with it, but would it be buoyant in air?
The problem seems to me to be mainly structural integrity. Graphene may be strong in certain directions, but I am sure you have seen what happens to a steel can, when you create a vacuum inside off of it. You can take the aerogel and remove as much air as possible, and seal the sides with graphene, but this only increases the chances of crushing by normal air pressure as you create a "harder" vacuum. The displacement by volume, creating a bouyant force, will also unfortunately collapse.