Q:

Modelling Diffusion of Molecules Through a Physical Barrier

I would like to model the diffusion of various small molecules (e.g. $\ce{O2}$, $\ce{H2O}$, $\ce{MeOH}$, etc.)  through polymeric barrier material (e.g. polyethylene, ethylene vinyl alcohol, polyethylene terephthalate, etc.)  in order to predict their transmission rates.  I am initially looking for rough estimates to differentiate between classes of barrier materials, but would like to eventually be able to determine how small modifications of the polymers can affect their barrier properties. 
Is this possible?  If so, what codes and methods would be useful, and what should I read to get started? 

A:

The challenge of studying diffusion through physical barriers is that these processes can take on the order of microseconds or seconds.  Therefore studying the molecular dynamics of a long trajectory, for example to calculate the Free Energy or potential of mean force (PMF) is practically impossible. 
Nevertheless, a technique which is very promising for studying diffusion through membranes, and other porous materials is called Milestoning
In Milestoning the reaction coordinate e.g. the Z-direction is split into discrete sections aka "milestones", therefore smaller dynamics can be performed within the milestones in parallel and these can be stitched together to generate the complete free energy landscape
For example, see this image which is taken from the second reference

References:

Faradjianl, Anton K.; Elber, Ron;
Computing time scales from reaction coordinates by milestoning
J. Chem.  Phys.  120(23), 10880-10889 (2004) https://doi.org/10.1063/1.1738640

Mugnai, Mauro L.; Elber, Ron;
Extracting the diffusion tensor from molecular dynamics simulation with Milestoning
J. Chem.  Phys.  142, 014105 (2015) https://doi.org/10.1063/1.4904882

