¹²⁹ Xe Nuclear Magnetic Resonance in Polymeric Membranes: A Computational Study of the Effect of Pore Size and Void Distribution on the Xenon Chemical Shift

We present the results of a computational investigation of the structure and distribution of pore size in a polymer of intrinsic microporosity (PIM), a class of compounds with applications as sensors and membranes for gas separation. The high performance of PIMs, in our case PIM-EA-TB, meaning a PIM based on ethanoanthracene (EA) units linked by a Tröger's base (TB, i.e., methanodiazocene), is largely due to the presence of interconnected micropores within the rigid polymer matrix. We have applied a computational NMR protocol based on a combination of MD simulations to generate several trajectories of xenon within the polymeric matrix and DFT calculations of the ¹²⁹Xe chemical shift using clusters extracted from the MD trajectories. The comparison of experimental NMR data previously obtained and the results of the calculations allows to validate the bulk structure resulting from the MD simulations and to obtain a quantitative dependence of the ¹²⁹Xe chemical shift on the distance of xenon from the pores' internal walls. Such dependence is in very good agreement with the results reported in the literature concerning small model systems of Xe-alkane pairs and hints at a more general law that can be expected to hold for many different systems.