Here I model the condensation of gas particles on a 2D solid interface.
The solid discs interact via a Lennard Jones force the potential of which has the form
Vsolid(r)=4*epsilon*((sigma/r)^12-(sigma/r)^6)
where r is the separation between disc centers, sigma has units of length, and epsilon is the depth of the potential well.
The first term provides a repelling force and the second term provides a weaker attractive force.
The potential for the gas discs is
Vgas(r)=4*epsilon*(sigma/r)^12.
since the gas has no attractive potential with itself. The potential for the interaction of the gas with the solid is
the same as that for the solid-solid interaction since the gas is attracted to the solid and vice versa.
The borders of the container also have an exponential potential to keep the discs from escaping.
The simulation takes about 1 minute to finish while storing some image video. I have therefore provided a movie so that the animation
can be run more rapidly.
I provide two plot windows: The number of condensed discs Vs time and a histogram of the distribution of discs as
a function of vertical height. It is seen that a single row of discs forms at the interface
between the gas and the solid. The depth can be only one row deep in this simulation because the gas
discs still in the gas phase are repelled by gas discs that are adsorbed at the gas-solid interface.