Trajectory-Extending Kinetic Monte Carlo Simulations to Evaluate Pure and Gas Mixture Diffusivities through a Dense Polymeric Membrane

With renewed interest in CO₂ separations, carbon molecular sieving (CMS) membrane performance evaluation requires diffusion coefficients as inputs to have a reliable estimate of the permeability. An optimal material is desired to have both high selectivity and permeability. Gases diffusing through dense CMS and polymeric membranes experience extended subdiffusive regimes, which hinders reliable extraction of diffusion coefficients from mean squared displacement data. We improve the sampling of the diffusive landscape by implementing the trajectory-extending kinetic Monte Carlo (TEKMC) technique to efficiently extend molecular dynamics (MD) trajectories from ns to μs time scales. The obtained self-diffusion coefficient of pure CO₂ in CMS membranes derived from a 6FDA/BPDA-DAM precursor polymer melt is found to linearly increase from 0.8-1.3 × 10^-6 cm² s^-1 in the pressure range of 1-20 bar, which supports previous experimental findings. We also extended the TEKMC algorithm to evaluate the mixture diffusivities in binary mixtures to determine the permselectivity of CO₂ in CH₄ and N₂ mixtures. The mixture diffusion coefficient of CO₂ ranges from 1.3-7 × 10^-6 cm² s^-1 in the binary mixture CO₂/CH₄, which is significantly higher than the pure gas diffusion coefficient. Robeson plot comparisons show that the permselectivity obtained from pure gas diffusion data is significantly lower than that predicted using mixture diffusivity data. Specifically, in the case of the CO₂/N₂ mixture, we find that using mixture diffusivities led to permselectivities lying above the Robeson limit highlighting the importance of using mixture diffusivity data for an accurate evaluation of the membrane performance. Combined with gas solubilities obtained from grand canonical Monte Carlo (GCMC) simulations, our work shows that simulations with the TEKMC method can be used to reliably evaluate the performance of materials for gas separations.