Mechanism and Prediction of Gas Permeation through Sub-Nanometer Graphene Pores: Comparison of Theory and Simulation

Abstract

Due to its atomic thickness, porous graphene with sub-nanometer pore sizes constitutes a promising candidate for gas separation membranes that exhibit ultrahigh permeances. While graphene pores can greatly facilitate gas mixture separation, there is currently no validated analytical framework with which one can predict gas permeation through a given graphene pore. In this work, we simulate the permeation of adsorptive gases, such as CO and CH, through sub-nanometer graphene pores using molecular dynamics simulations. We show that gas permeation can typically be decoupled into two steps: (1) adsorption of gas molecules to the pore mouth and (2) translocation of gas molecules from the pore mouth on one side of the graphene membrane to the pore mouth on the other side. We find that the translocation rate coefficient can be expressed using an Arrhenius-type equation, where the energy barrier and the pre-exponential factor can be theoretically predicted using the transition state theory for classical barrier crossing events. We propose a relation between the pre-exponential factor and the entropy penalty of a gas molecule crossing the pore. Furthermore, on the basis of the theory, we propose an efficient algorithm to calculate CO and CH permeances per pore for sub-nanometer graphene pores of any shape. For the CO/CH mixture, the graphene nanopores exhibit a trade-off between the CO permeance and the CO/CH separation factor. This upper bound on a Robeson plot of selectivity versus permeance for a given pore density is predicted and described by the theory. Pores with CO/CH separation factors higher than 10 have CO permeances per pore lower than 10 mol s Pa, and pores with separation factors of ∼10 have CO permeances per pore between 10 and 10 mol s Pa. Finally, we show that a pore density of 10 m is required for a porous graphene membrane to exceed the permeance-selectivity upper bound of polymeric materials. Moreover, we show that a higher pore density can potentially further boost the permeation performance of a porous graphene membrane above all existing membranes. Our findings provide insights into the potential and the limitations of porous graphene membranes for gas separation and provide an efficient methodology for screening nanopore configurations and sizes for the efficient separation of desired gas mixtures.

Single-layer graphene membranes by crack-free transfer for gas mixture separation

“…3e , Supplementary Table 2 ). A slightly smaller E act for CH 4 in comparison to CO 2 can be explained by the fact that diffusion of CH 4 takes place from a smaller number of pores (average C o A act A sur for He, H 2 , CO 2 , and CH 4 were 1.5 × 10 −5 , 2.6 × 10 −5 , 3.8 × 10 −6 , and 1.3 × 10 −6 , respectively, Supplementary Table 3 ), assuming A act A sur do not change significantly for CO 2 and CH 4 37 . The activation energy for H 2 was similar to that from hydrogen-functionalized pore-10 reported by Jiang et al (0.22 eV) 3 , providing an indication that the average pore in this study is close to that made from missing 10 carbon atoms, which is supported by the HRTEM images (Fig.…”

State‐of‐the‐Art and Future Prospects for Atomically Thin Membranes from 2D Materials

“…Several theoretical and computational studies have focused on elucidating transport of gases, ions, and molecules across nanoscale pores in 2D materials for membrane applications, and experimental studies are rapidly emerging . Here, we focus on i) the mechanisms of transport in 2D material membranes, ii) summarize experimental advances in realizing atomically thin membranes, and iii) discuss technological opportunities and challenges to enable applications.…”

Efficient Kr/Xe separation from triangular g-C3N4 nanopores, a simulation study

“…In the present case, based on the relative size of Kr (kinetic diameter of 3.6Å) and Xe (kinetic diameter of 3.96Å) with respect to PTI nanopore (3.4 nm), it is expected that size-sieving is the predominant separation mechanism. 69 However, while the vdW-DFT calculations reveal that PTI nanopores are promising for sieving Kr from Xe by the sizesieving mechanism, the selectivity calculations do not take entropic effects into account (loss of entropy of the gas in the adsorbed phase and in the transition state with respect to that in the gas phase). The calculations of entropic loss, for example using an enhanced method like umbrella sampling in the framework of classical MD simulations, allow one to accurately Fig.…”

“…predict the gas permeance using a gas transport model across 2d nanopores, as e.g., recently proposed by Strano and coworkers, 53,68 and more recently by Blankschtein and co-workers. 69 A unique advantage of this route is that one can avoid unaffordable long MD simulations to track the passage of gases. This is especially relevant when the activation barriers are high, making translocation of gases a rare event.…”