Simple lattice model explains equilibrium separation phenomena in glassy polymers

The Robeson bound is a theoretical limit that applies to kinetics-driven membrane separations of gas mixtures. However, this bound does not apply to sorption-driven membrane processes such as CO$_\text{2}$/N$_\text{2}$ separation, which lacks a theoretical explanation. As a result, we are uncertain about the factors that control the limiting behavior of sorption-driven separations. To address this issue, we employed a simple lattice model and dynamic mean field theory to examine the transport properties of disordered model structures, isolating sorption effects from purely kinetic effects. Our findings indicate that transport effects play a crucial role in sorption-driven processes, and perm-selectivity is consistently lower than sorption selectivity, which is an unattainable limit. We used basic geometric fragments of the structure to explain how transport effects emerge and manifest themselves in sorption-driven processes.