The composition remains approximately the same, as thermal diffusion is enough to ensure even mixing over the accessible atmosphere. There is some varying sedimentation that becomes a factor at vertical scales of many kilometers (although over that scale, one also needs to consider, e.g., gas reactions from cosmic rays). I go into the math here. The characteristic sedimentation height scales with kT/gM, with Boltzmann's constant k, temperature T, gravitational acceleration g, and molecular mass M.