note: I expect that a microscopic treatment of the rate of heat transfer between gases and solid surfaces will likely need to address this as well and so I'm looking in to that today, but if someone beats me to it that would be great!

For example Singh et al. (2009) J. App. Phys. 106, 024314 Modeling of subcontinuum thermal transport across semiconductor-gasinterfaces seems to address this using a Boltzman distribution for the gas atoms in the vauum and for phonons rather than individual atoms of the solid. However I can’t see how to apply that microscopically on a per-collision basis without estimating how many phonons are involved; is it one phonon on average? More? Less?

Figures at the end of The Interaction of Molecular Beams with Solid Surfaces show that the spread in angles of atoms incident at 45 degrees does get wider with increased surface temperature, but there is no information on changes in kinetic energy, but Wikipedia's Helium atom scattering; Inelastic measurements suggests that interactions with phonons can lead to a much more complicated picture.

I'm writing a simple Monte-Carlo simulation for an ultra-high vacuum chamber. I'll initially distribute atoms randomly in position and direction and with speeds derived from a Maxwell-Boltzmann distribution. At one end there is a tube of variable length; once a particle passes the far end of it it will be considered "pumped" and no longer tracked.

The idea is to address the effect of a long narrow tube between the chamber and the pump on the effective pumping speed.

I'll assume a monatomic gas with no internal degrees of freedom.

I can introduce the effect of wall roughness by randomly varying the microscopic surface normal from the macroscopic normal at each collision, but I can't think of a way to handle the random momentum transfer effects due to thermal vibrations of the atoms in the wall. These can both change the kinetic energy and the direction of scattering.

What would be a simple, first principles way to introduce it?

I can imagine treating the atom in the wall as a free particle with a similar thermal distribution of speed and direction, but the atoms of the wall are not free, they're constrained by bonds to adjacent atoms.


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    $\begingroup$ There's a silent drive-by close vote for "needs more focus" but I think the problem is very clear and focused; an atom collides with a wall, what would be a simple first principles way to address the momentum transfer due to thermal motion of bound atoms in the wall? $\endgroup$
    – uhoh
    Mar 28 '20 at 16:17
  • $\begingroup$ Depends on the wall, right? If it's an ideally insulating wall, then microscopically that corresponds to the atom just bouncing off without any further effect. If it's an ideally conducting wall, you should just draw the atom's final speed from the Maxwell-Boltzmann distribution of temperature $T$, where $T$ is the wall temperature. $\endgroup$
    – knzhou
    Mar 28 '20 at 16:54
  • $\begingroup$ @knzhou only the top layer of atoms of the wall interact with the atoms of gas, so for individual collisions with real walls and UHV gas densities I don't think it matters if the walls are made of ceramic or metal. What you've described doesn't take into account the incoming energy of the gas atom and instead simply resets it based on the wall temperature. I suppose after several collisions that's fine, but I don't see how to include the effect of the thermal motion of wall atoms on the direction of scatter. Are you proposing to completely randomize scatter direction isotropically each time? $\endgroup$
    – uhoh
    Mar 28 '20 at 18:37
  • $\begingroup$ Right, that's what I meant by "ideally conducting", i.e. the effect of one collision is like what happens after many collisions with a nonideal wall. This should completely randomize direction as well. $\endgroup$
    – knzhou
    Mar 28 '20 at 18:41
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    $\begingroup$ Perhaps look to what MolFlow does. $\endgroup$
    – Jon Custer
    Jul 13 at 12:39