# 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?

• +1. Very nice first question! Right on time as we are seeking more questions! Jul 27, 2020 at 18:13
• Could you edit the title to reflect diffusion and remove the words barrier? The rate of an elementary step of a reaction involves an activation barrier but diffusion through a pore does not involve a single elementary step (usually) so that is confusing Jul 28, 2020 at 0:27
• @CodyAldaz I believe he means barrier in the more everyday sense of a physical blockage, rather than the more abstract, scientific usage of an energy barrier.
– Tyberius
Jul 28, 2020 at 1:34
• @tyberius that is precisely why I'm asking for an edit Jul 28, 2020 at 1:38
• For reference: the packaging community uses the terms transmission rate and barrier to indicate the rate at which a molecule diffuses through a physical material. sciencedirect.com/topics/engineering/oxygen-barrier. I realize that there may be confusion with quantum tunneling, so I'll edit the question accordingly. Jul 28, 2020 at 14:06

## 1 Answer

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:

1. 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

2. 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