Simple lattice model explains equilibrium separation phenomena in glassy polymers

Abstract

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 CO2/N2 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.

How 2D Nanoflakes Improve Transport in Mixed Matrix Membranes: Insights from a Simple Lattice Model and Dynamic Mean Field Theory

“…The convention of the calculation closely follows our previous study. ,, The flux from site i to its neighbors j of species a (where a can be either A or B in this work), J i , j a , is defined in eq . We note here that the net flux in both y and z directions is zero due to the absence of the chemical potential gradient along these axes.…”

“…To make the process of setting the model tractable and systematic, we set the A – A interactions as our unit of energy, ϵ AA = 1 and all other parameters of interactions are expressed in these units. In particular, starting from this point, the B – B interactions are scaled with respect to A – A to reflect the relative values of the bulk critical temperatures of CO 2 and N 2 , ϵ BB = 0.415, following our previous study . Now, let us consider the interaction between filler species f and fluid species A and B .…”

“…60 In a follow-up study, we investigated two-component systems to explain separation phenomena in sorption-driven membrane processes. 102 ■ METHODS Mean Field Theory. The theoretical framework applied in the work closely follows the work by Edison and Monson, 88,95 and we refer the readers to the original articles for additional details.…”

“…This method has been applied extensively to study the adsorption/desorption hysteresis, capillary condensation, and diffusion in porous materials. − Previously, we have demonstrated the utility of the DMFT in studies of single component fluid transport in simple slit pores, and complex, heterogeneous media . In a follow-up study, we investigated two-component systems to explain separation phenomena in sorption-driven membrane processes …”

“…Specifically, we configured the membrane inlet conditions to replicate the composition of exhaust from a coal power plant, featuring 15% carbon dioxide (component A) and 85% nitrogen (B) at 1 bar and 308.15 K. Considering the mean-field prediction for the critical temperature of a simple cubic lattice, denoted as Tcrit* = 1.5, we scale the system's temperature relative to the critical temperature to match the temperature ratio of flue gas to the critical temperature of carbon dioxide, resulting in The convention of the calculation closely follows our previous study. 60,101,102 The flux from site i to its neighbors j of species a (where a can be either A or B in this work), J i,j a , is defined in eq 7. We note here that the net flux in both y and z directions is zero due to the absence of the chemical potential gradient along these axes.…”