  With renewed interest in CO2 separations, carbon molecular sieving (CMS)
membrane performance evaluation requires diffusion coefficients as inputs to
have 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 sub-diffusive 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 MD trajectories from ns to {\mu}s timescales. The obtained
self-diffusion coefficient of pure CO2 in CMS membranes derived from
6FDA/BPDA-DAM precursor polymer melt is found in agreement with previous
experimental findings. We also extend 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 x 10^{-6} cm6{2}s^{-1} in 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
are 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 permeslectivites 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 simulations, our work shows that simulations
with the TEKMC method can be used to reliably evaluate the performance of
materials for gas separations.
