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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The computation of diffusion coefficients in molecular systems ranks among the most useful applications of equilibrium molecular dynamics simulations. However, when dealing with the problem of fluid diffusion through vanishingly thin interfaces, classical techniques are not applicable. This is because the volume of space in which molecules diffuse is ill-defined. In such conditions, non-equilibrium techniques allow for the computation of transport coefficients per unit interface width, but their weak point lies in their inability to isolate the contribution of the different physical mechanisms prone to impact the flux of permeating molecules. In this work, we propose a simple and accurate method to compute the diffusional transport coefficient of a pure fluid through a planar interface from equilibrium molecular dynamics simulations, in the form of a diffusion coefficient per unit interface width. In order to demonstrate its validity and accuracy, we apply our method to the case study of a dilute gas diffusing through a smoothly repulsive single-layer porous solid. We believe this complementary technique can benefit to the interpretation of the results obtained on single-layer membranes by means of complex non-equilibrium methods. [ABSTRACT FROM AUTHOR]

With the advent of graphene material, membranes based on single-layer nanoporous solids appear as promising devices for fluid separation, be it liquid or gaseous mixtures. The design of such architectured porous materials would greatly benefit from accurate models that can predict their transport and separation properties. More specifically, there is no universal understanding of how parameters such as temperature, fluid loading conditions, or the ratio of the pore size to the fluid molecular diameter influence the permeation process. In this study, we address the problem of pure supercritical fluids diffusing through simplified models of single-layer porous materials. Basically, we investigate a toy model that consists of a single-layer lattice of Lennard-Jones interaction sites with a slit gap of controllable width. We performed extensive equilibrium and biased molecular dynamics simulations to document the physical mechanisms involved at the molecular scale. We propose a general constitutive equation for the diffusional transport coefficient derived from classical statistical mechanics and kinetic theory, which can be further simplified in the ideal gas limit. This transport coefficient relates the molecular flux to the fluid density jump across the single-layer membrane. It is found to be proportional to the accessible surface porosity of the single-layer porous solid and to a thermodynamic factor accounting for the inhomogeneity of the fluid close to the pore entrance. Both quantities directly depend on the potential of mean force that results from molecular interactions between solid and fluid atoms. Comparisons with the simulations data show that the kinetic model captures how narrowing the pore size below the fluid molecular diameter lowers dramatically the value of the transport coefficient. Furthermore, we demonstrate that our general constitutive equation allows for a consistent interpretation of the intricate effects of temperature and fluid loading conditions on the permeation process. [ABSTRACT FROM AUTHOR]

Fluidtransport through microporous carbon-based materials is inherentin numerous applications, ranging from gas separation by carbon molecularsieves to natural gas production from coal seams and gas shales. Thepresent study investigates the steady-state permeation of supercriticalmethane in response to a constant cross-membrane pressure drop. Weperformed dual control volume grand canonical molecular dynamics (DCV-GCMD)simulations to mimic the conditions of actual permeation experiments.To overcome arbitrary assumptions regarding the investigated porousstructures, the membranes were modeled after the CS1000a and CS1000molecular models, which are representative of real microporous carbonmaterials. When adsorption-induced molecular trapping (AIMT) mechanismsare negligible, we show that the permeability of the microporous material,although not significantly sensitive to the pressure gradient, monotonicallydecreases with temperature and reservoir pressures, consistent withdiffusion theory. However, when AIMT occurs, the permeability increaseswith temperature in agreement with experimental data found in theliterature. [ABSTRACT FROM AUTHOR]

In this study, the adsorption and competitive diffusion of methane (CH 4) and carbon dioxide (CO 2) mixtures through a molecular model of mature type-2 kerogen was investigated using molecular dynamics simulations. The Dual Control Volume-Grand Canonical Molecular Dynamics method was used to analyze the system and the results were focused on the selectivity of kerogen towards mixtures under a wide range of thermodynamic conditions. The results showed that the adsorption selectivity of CO 2 /CH 4 was around 2–4 and decreased with temperature in the range 350–450 K. The Extended Langmuir (EL) model was found to underestimate the selectivity, and a correction was proposed in the form of the Corrected Extended Langmuir (CEL) model, which improved the estimations of the adsorption of CH 4 / CO 2 mixtures in kerogen with only one adjustable parameter independent of thermodynamic conditions. Interestingly, we noticed that, out of equilibrium, the adsorption selectivity was not affected by the flow conditions when a pressure gradient was imposed, and the CEL model can thus be used to describe the contribution of adsorption to the selectivity under flow conditions. The results showed that the ratio of the collective diffusion coefficients of CH 4 and CO 2 was around 0. 3 − 0. 4 , which was about two times lower than other simulations found in the literature. To describe the global selectivity, a simple approach combining the CEL model and the average ratio of diffusion coefficients was proposed, resulting in a selectivity of around 1. [Display omitted] • Extensive simulations data of adsorption and diffusion of CO 2 /CH 4 in kerogen. • Corrected Extended Langmuir model to improve estimation of adsorption isotherms. • Adsorption selectivity of CO 2 /CH 4 is in the range of 2–4 in and out of equilibrium. • Ratio of CO 2 /CH 4 collective diffusion coefficients is in the range of 0.3–0.4. • A formal framework for CO 2 /CH 4 separation transferable to larger scale models. [ABSTRACT FROM AUTHOR]