From molecular sieving to gas effusion through nanoporous 2D graphenes: Comparison between analytical predictions and molecular simulations.

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.

Modeling gas permeation mechanisms through 2D membranes: Comparison between a phenomenological model and extensive molecular simulations.

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.

Diffusion of Supercritical Fluids through Single-Layer Nanoporous Solids: Theory and Molecular Simulations.

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.

Thermodiffusion in multicomponent n-alkane mixtures.

Compositional grading within a mixture has a strong impact on the evaluation of the pre-exploitation distribution of hydrocarbons in underground layers and sediments. Thermodiffusion, which leads to a partial diffusive separation of species in a mixture due to the geothermal gradient, is thought to play an important role in determining the distribution of species in a reservoir. However, despite recent progress, thermodiffusion is still difficult to measure and model in multicomponent mixtures. In this work, we report on experimental investigations of the thermodiffusion of multicomponent n-alkane mixtures at pressure above 30 MPa. The experiments have been conducted in space onboard the Shi Jian 10 spacecraft so as to isolate the studied phenomena from convection. For the two exploitable cells, containing a ternary liquid mixture and a condensate gas, measurements have shown that the lightest and heaviest species had a tendency to migrate, relatively to the rest of the species, to the hot and cold region, respectively. These trends have been confirmed by molecular dynamics simulations. The measured condensate gas data have been used to quantify the influence of thermodiffusion on the initial fluid distribution of an idealised one dimension reservoir. The results obtained indicate that thermodiffusion tends to noticeably counteract the influence of gravitational segregation on the vertical distribution of species, which could result in an unstable fluid column. This confirms that, in oil and gas reservoirs, the availability of thermodiffusion data for multicomponent mixtures is crucial for a correct evaluation of the initial state fluid distribution.

Communication: A method to compute the transport coefficient of pure fluids diffusing through planar interfaces from equilibrium molecular dynamics simulations.

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.

Molecular simulations of supercritical fluid permeation through disordered microporous carbons.

Fluid transport through microporous carbon-based materials is inherent in numerous applications, ranging from gas separation by carbon molecular sieves to natural gas production from coal seams and gas shales. The present study investigates the steady-state permeation of supercritical methane in response to a constant cross-membrane pressure drop. We performed 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 porous structures, the membranes were modeled after the CS1000a and CS1000 molecular models, which are representative of real microporous carbon materials. When adsorption-induced molecular trapping (AIMT) mechanisms are negligible, we show that the permeability of the microporous material, although not significantly sensitive to the pressure gradient, monotonically decreases with temperature and reservoir pressures, consistent with diffusion theory. However, when AIMT occurs, the permeability increases with temperature in agreement with experimental data found in the literature.

Star-shaped crack pattern of broken windows.

Broken thin brittle plates like windows and windshields are ubiquitous in our environment. When impacted locally, they typically present a pattern of cracks extending radially outward from the impact point. We study the variation of the pattern of cracks by performing controlled transverse impacts on brittle plates over a broad range of impact speed, plate thickness, and material properties, and we establish from experiments a global scaling law for the number of radial cracks incorporating all these parameters. A model based on Griffith's theory of fracture combining bending elastic energy and fracture energy accounts for our observations. These findings indicate how the postmortem shape of broken samples are related to material properties and impact parameters, a procedure relevant to forensic science, archaeology, or astrophysics.

Radial cracks in perforated thin sheets.

When a rigid cone is slowly pushed through a thin elastic sheet, the material breaks, exhibiting a network of cracks expanding in the radial direction. Experiments conducted with aluminum sheets show that the number of cracks is selected at the beginning of the perforation process and then remains stable. A simple model predicts the number of cracks as the result of a competition between the elastic energy stored in the sheet, and the energy dissipated during crack extension. We also evidence the subtle rearrangements of randomly distributed cracks into uniform radial patterns with fewer cracks. In that respect, this study exemplifies how relaxation mechanisms in fragmenting solids can attenuate the influence of defects in the material.