even without convection (all those weather type things) the gases would not settle out. This is because the molecules of a gas have no real attraction to each other, and so no fixed relationship to each other. thus the motion induced by rising temperature translates into a free , random motion rather than a vibration about a fixed mean point. this means that the only damper on free motion is the gravitational force on each individual atom. this is so tiny in comparison to the kinetic energy of the atom that it has almost no effect. There is a slight effect over very large distances: the air at the top of a mountain has a very slight difference in the balance between the gases compared to the air at ground level, but to really separate layers out like this you need to observe tens of kilometres of gas at the least.