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In recent years, extensive research has used molecular dynamics simulations to investigate gas separation through nanoporous graphene (NPG) membranes. However, most studies have considered graphene membranes as rigid, overlooking the impact of their inherent flexibility. This study systematically quantifies the effect of graphene flexibility on gas permeation by comparing the diffusion of various gases through flexible and rigid single-layer NPG models. The results demonstrate that flexibility notably increases permeance, particularly for gases with larger molecular diameters/pore size ratios, by allowing gas molecules greater mobility within the pore. Interestingly, the effect of flexibility boils down to the expansion of the average pore size, and the detail of the membrane's vibrational dynamics is of little importance in quantifying permeance. Our work shows that accounting for flexibility in molecular models improves the alignment of simulation results with experimental data, emphasizing the importance of considering membrane flexibility in predictive models of NPG membrane performance.

In this paper, we study the permeation of polyatomic gas molecules through 2D graphene membranes. Using equilibrium molecular dynamics simulations, we investigate the permeation of pure gas compounds (CH4, CO2, O2, N2, and H2) through nanoporous graphene membranes with varying pore sizes and geometries. Our simulations consider the recrossing mechanism, often neglected in previous studies, which has a significant effect on permeation for intermediate pore size to molecular diameter ratios. We find that the permeation process can be decoupled into two steps: the crossing process of gas molecules through the pore plane and the escaping process from the pore region to a neighboring adsorption site, which prevents recrossing. To account for these mechanisms, we use a permeance model expressed as the product of the permeance for the crossing process and the probability of molecule escape. This phenomenological model is extended to account for small polyatomic gas molecules and to describe permeation regimes ranging from molecular sieving to effusion. The proposed model captures the temperature dependence and provides insights into the key parameters of the gas/membrane interaction controlling the permeance of the system. This work lays the foundation for predicting gas permeance and exploring membrane separation factors in 2D materials such as graphene., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Two-dimensional (2D) membranes based on perforated graphene have great potential in the field of separation of chemical species for a variety of applications, including gas treatment. In addition to recent experimental studies, several works simulate the mechanisms of gas permeation through this type of membrane using molecular dynamics, but few combine different techniques to ensure that their method of choice captures all relevant mechanisms. In particular, the re-crossing mechanism leading a gas molecule that has crossed the plane of the membrane to rapidly re-cross it in the opposite direction has never been documented. In this work, we study gas permeation through a simplified 2D membrane model. We combine equilibrium and non-equilibrium molecular dynamics simulations to quantify the impact of these re-crossing mechanisms on the values of the computed transport coefficients. Using non-equilibrium simulations as reference, we show that the equilibrium simulation techniques commonly used can lead to a significant overestimation of the transport properties of the membrane. We propose a simple method to probe the re-crossing dynamics during equilibrium simulations, making it possible to compute correct values of the transport coefficient without the need for non-equilibrium simulations. Furthermore, by analyzing the phenomenology observed in the simulations, we derive an analytical formula for the permeance that takes the form of an Arrhenius law with a non-trivial temperature dependent prefactor. In excellent agreement with our simulation results, this model provides a simple theoretical framework that captures the main mechanisms involved in gas permeation through 2D membranes, including the effect of re-crossing.

The predictive capabilities of some existing theoretical models to quantify thermodiffusion have been investigated in this work. To do so, the tests have been performed on two model fluids, the hard-sphere and the Lennard-Jones (including spheres and dimers) ones, exploring different mixtures and thermodynamic conditions thanks to extensive molecular simulations. It has been confirmed that the thermal diffusion factor should be expressed as the sum of one term related to the isotope effect and one term related to the "chemical" effects and that a kinetic term is required to quantify thermodiffusion from the gas state to the liquid state. In addition, regarding the isotope effects, it has been obtained that none of the available theoretical models are able to yield a reasonable prediction relatively to the molecular simulations results and that the moment of inertia contribution is one order of magnitude smaller than the mass contribution in the liquid state. Finally, concerning the chemical effects, it has been shown the Shukla and Firoozabadi model, complemented with a kinetic term, is probably the most reasonable option to estimate the chemical contribution to the thermal diffusion factor, even if it fails in capturing the effect of the asymmetry in size and in shape between the species. Overall, this works confirms that there is still a lack of a generic model able to predict accurately thermal diffusion factors, or equivalently Soret coefficient, in simple binary mixtures from the gas state to the liquid state., (© 2022. The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.)