Escape, temperature and atmosphere relationship

What is the critical escape speed needed to hold atmosphere, and how
will it depend on the temperature?

Let us take the major Solar System examples, from outside in:

Pluto: 1,18 km per second, approaches to 30 a. u.. Appreciable nitrogen
atmosphere restricted by freezing.
Triton: 1,45 km per second, orbits at 30 a. u.. Appreciable nitrogen
atmosphere restricted by freezing.
Titan: 2,64 km per second, orbits at 10 a. u.. A nonfreezing nitrogen
atmosphere, the inventory being 160 000 Pa.
Io: 2,57 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Europa: 2,03 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Ganymede: 2,73 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Callisto: 2,44 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Mars: 5,03 km per second, orbits at 1.52 a. u.. A freezing carbon
dioxide atmosphere, contains nonfreezing nitrogen inventory of 20 Pa.
Moon: 2,38 km per second, orbits at 1 a. u.. Not much atmosphere.
Earth: 11,2 km per second, orbits at 1 a. u.. Nitrogen atmosphere of
approximately 80 000 Pa.
Venus: 10,4 km per second, orbits at 0,72 a. u.. Carbon dioxide
atmosphere with nitrogen inventory of about 300 000 Pa.
Mercury: 4,44 km per second, orbits at 0,39 a. u.. Not much atmosphere.

I wonder if there is any rule between the nitrogen contents of the
three dense nitrogen atmospheres?