Optimizing Water Transport through Graphene-Based Membranes: Insights from Nonequilibrium Molecular Dynamics

Solar-driven abnormal evaporation of nanoconfined water

Intrinsic water evaporation demands a high energy input, which limits the efficacy of conventional interfacial solar evaporators. Here, we propose a nanoconfinement strategy altering inherent properties of water for solar-driven water evaporation using a highly uniform composite of vertically aligned Janus carbon nanotubes (CNTs). The water evaporation from the CNT shows the unexpected diameter-dependent evaporation rate, increasing abnormally with decreasing nanochannel diameter. The evaporation rate of CNT10@AAO evaporator thermodynamically exceeds the theoretical limit (1.47 kg m-2 hour-1 under one sun). A hybrid experimental, theoretical, and molecular simulation approach provided fundamental evidence of different nanoconfined water properties. The decreased number of H-bonds and lower interaction energy barrier of water molecules within CNT and formed water clusters may be one of the reasons for the less evaporative energy activating rapid nanoconfined water vaporization.

Multiscale modelling of transport in polymer-based reverse-osmosis/nanofiltration membranes: present and future

Nanofiltration (NF) and reverse osmosis (RO) processes are physical separation technologies used to remove contaminants from liquid streams by employing dense polymer-based membranes with nanometric voids that confine fluids at the nanoscale. At this level, physical properties such as solvent and solute permeabilities are intricately linked to molecular interactions. Initially, numerous studies focused on developing macroscopic transport models to gain insights into separation properties at the nanometer scale. However, continuum-based models have limitations in nanoconfined situations that can be overcome by force field molecular simulations. Continuum-based models heavily rely on bulk properties, often neglecting critical factors like liquid structuring, pore geometry, and molecular/chemical specifics. Molecular/mesoscale simulations, while encompassing these details, often face limitations in time and spatial scales. Therefore, achieving a comprehensive understanding of transport requires a synergistic integration of both approaches through a multiscale approach that effectively combines and merges both scales. This review aims to provide a comprehensive overview of the state-of-the-art in multiscale modeling of transport through NF/RO membranes, spanning from the nanoscale to continuum media.

Molecular Simulation for Guiding the Design and Optimization of Mixed Matrix Membranes (MMMs) in the Pervaporation Process

Molecular simulation has been used extensively in the study of pervaporation membranes as a new economical and environmentally friendly research method. In this paper, A-SiO₂/PDMS-PTFE mixed matrix membranes (MMMs) were prepared by molecular-simulation-guided experiments to achieve the separation of dimethyl carbonate/methanol (DMC/MeOH)) azeotropes. The interaction energy, X-ray diffraction pattern mean square displacement, and density field between PDMS and inorganic particles were analyzed by molecular dynamics simulations. The dissolution and diffusion processes of the DMC/MeOH azeotropes system in the MMM were simulated, and the surface-silylated silica (A-SiO₂) with relatively better performance was screened. Based on the simulation results, A-SiO₂/PDMS-PTFE MMMs were prepared by the coblending method, and the pervaporation separation performance of MMM membranes for DMC/MeOH azeotropes with different A-SiO₂ loadings was investigated. When the A-SiO₂ loading was 15 wt %, the separation factor of DMC/MeOH azeotropes at 50 °C was 4.74 and the flux was 1178 g m^-2 h^-1, which was consistent with the expected results of the simulation. The MMMs showed good stability in pervaporation over a period of up to 120 h. This study demonstrates that molecular simulations can provide a viable means for pretest screening and validation of experimental mechanisms, and to a certain extent, guide the design and optimization of pervaporation membranes.

Membranes Coated with Graphene-Based Materials: A Review

Graphene is a popular material with outstanding properties due to its single layer. Graphene and its oxide have been put to the test as nano-sized building components for separation membranes with distinctive structures and adjustable physicochemical attributes. Graphene-based membranes have exhibited excellent water and gas purification abilities, which have garnered the spotlight over the past decade. This work aims to examine the most recent science and engineering cutting-edge advances of graphene-based membranes in regard to design, production and use. Additional effort will be directed towards the breakthroughs in synthesizing graphene and its composites to create various forms of membranes, such as nanoporous layers, laminates and graphene-based compounds. Their efficiency in separating and decontaminating water via different techniques such as cross-linking, layer by layer and coating will also be explored. This review intends to offer comprehensive, up-to-date information that will be useful to scientists of multiple disciplines interested in graphene-based membranes.

Molecular simulation of enhanced separation of humid air components using GO-PVA nanocomposite membranes under differential pressures

Hydrophilic nanocomposite membranes have significant advantages in the separation of water vapor which is the core process in air dehumidification. This paper focuses on exploring the micro-mechanism of enhanced separation using graphene oxide-polyvinyl alcohol (GO-PVA) nanocomposite membranes. The sorption and diffusion behaviors of water vapor and nitrogen in GO-PVA membranes were investigated using molecular dynamics (MD) and Monte Carlo (MC) methods. The study showed that embedding GO into a PVA matrix results in a higher glass transition temperature and fractional free volume. The latter is believed to enhance the diffusivity of gas molecules in polymeric membranes. The interaction between the polymer chains and GO nanoparticles notably promotes the adsorption capacity of water vapor and inhibits nitrogen adsorption in the membrane. A water vapor permeance of 8844.07 Barrer and a separation factor of 3.53 could be achieved with the GO-PVA-0.5 membrane. The analysis confirmed that GO has the same effect on single gas and binary gas mixtures, i.e., increasing the water vapor permeability and selectivity. The calculated water vapor permeance of binary gas is 83% lower than that of single gas permeation. It is expected that this research could provide fundamentals for the optimization and synthesis of gas separation membranes.

A molecular simulation study into the stability of hydrated graphene nanochannels used in nanofluidics devices

Graphene-based nanochannels are a popular choice in emerging nanofluidics applications because of their tunable and nanometer-scale channels. In this work, molecular dynamics (MD) simulations were employed both to (i) assess the stability of dry and hydrated graphene nanochannels and (ii) elucidate the properties of water confined in these channels, using replica-scale models with 0.66-2.38 nm channel heights. The use of flexible nanochannel walls allows the nanochannel height to relax in response to the solvation forces arising from the confined fluid and the forces between the confining surfaces, without the need for application of arbitrarily high external pressures. Dry nanochannels were found to completely collapse if the initial nanochannel height was less than 2 nm, due to attractive van der Waals interactions between the confining graphene surfaces. However, the presence of water was found to prevent total nanochannel collapse, due to repulsive hydration forces opposing the attractive van der Waals force. For nanochannel heights less than ∼1.7 nm, the confining surfaces must be relaxed to obtain accurate hydration pressures and water diffusion coefficients, by ensuring commensurability between the number of confined water layers and the channel height. For very small (∼0.7 nm), hydrated channels a pressure of 231 MPa due to the van der Waals forces was obtained. In the same system, the confined water forms a mobile, liquid monolayer with a diffusion coefficient of 4.0 × 10^-5 cm² s^-1, much higher than bulk liquid water. Although this finding conflicts with most classical MD simulations, which predict in-plane order and arrested dynamics, it is supported by experiments and recently published first-principles MD simulations. Classical simulations can therefore be used to predict the properties of water confined in sub-nanometre graphene channels, providing sufficiently realistic molecular models and accurate intermolecular potentials are employed.

Use of Boundary-Driven Nonequilibrium Molecular Dynamics for Determining Transport Diffusivities of Multicomponent Mixtures in Nanoporous Materials

The boundary-driven molecular modeling strategy to evaluate mass transport coefficients of fluids in nanoconfined media is revisited and expanded to multicomponent mixtures. The method requires setting up a simulation with bulk fluid reservoirs upstream and downstream of a porous media. A fluid flow is induced by applying an external force at the periodic boundary between the upstream and downstream reservoirs. The relationship between the resulting flow and the density gradient of the adsorbed fluid at the entrance/exit of the porous media provides for a direct path for the calculation of the transport diffusivities. It is shown how the transport diffusivities found this way relate to the collective, Onsager, and self-diffusion coefficients, typically used in other contexts to describe fluid transport in porous media. Examples are provided by calculating the diffusion coefficients of a Lennard-Jones (LJ) fluid and mixtures of differently sized LJ particles in slit pores, a realistic model of methane in carbon-based slit pores, and binary mixtures of methane with hypothetical counterparts having different attractions to the solid. The method is seen to be robust and particularly suited for the study of study of transport of dense fluids and liquids in nanoconfined media.

Enhancing H2O2 Tolerance and Separation Performance through the Modification of the Polyamide Layer of a Thin-Film Composite Nanofiltration Membrane by Using Graphene Oxide

Through interfacial polymerization (IP), a polyamide (PA) layer was synthesized on the top of a commercialized polysulfone substrate to form a thin-film composite (TFC) nanofiltration membrane. Graphene oxide (GO) was dosed during the IP process to modify the NF membrane, termed TFC-GO, to enhance oxidant resistance and membrane performance. TFC-GO exhibited increased surface hydrophilicity, water permeability, salt rejection, removal efficiency of pharmaceutical and personal care products (PPCPs), and H₂O₂ resistance compared with TFC. When H₂O₂ exposure was 0–96,000 ppm-h, the surfaces of the TFC and TFC-GO membranes were damaged, and swelling was observed using scanning electron microscopy. However, the permeate flux of TFC-GO remained stable, with significantly higher NaCl, MgSO₄, and PPCP rejection with increasing H₂O₂ exposure intensity than TFC, which exhibited a 3.5-fold flux increase with an approximate 50% decrease in salt and PPCP rejection. GO incorporated into a PA layer could react with oxidants to mitigate membrane surface damage and increase the negative charge on the membrane surface, resulting in the enhancement of the electrostatic repulsion of negatively charged PPCPs. This hypothesis was confirmed by the significant decrease in PPCP adsorption onto the surface of TFC-GO compared with TFC. Therefore, TFC-GO membranes exhibited superior water permeability, salt rejection, and PPCP rejection and satisfactory resistance to H₂O₂, indicating its great potential for practical applications.

Scale Effect on Simple Liquid Transport through a Nanoporous Graphene Membrane

The transport mechanism of a simple liquid through nanoporous graphene membranes (NPGMs) with pores of various diameters has been explored by utilizing nonequilibrium molecular dynamics (NEMD) simulation. The flow is initiated using a pressure-driven flow mechanism that moves the specular reflection wall at a constant velocity. Both the local density peak near the membrane and the pressure drop are dependent on the pore diameter. For accurate calculation of the velocity profile inside the nanopore, we implemented three boundary approaches and local nanoscale variants to see the effect of these factors on the nature of the nanoscale flow. We found an optimized definition of the pore boundary, which minimizes the deviation between MD results and slip-viscosity-modified Sampson's prediction for nanopores of various diameters. Additionally, we observed that with decreasing pore size, the pore center velocity increases, as does the slip velocity, which we attributed to van der Waals interaction between the liquid and wall atoms inside the nanopore. However, the effects of slip velocity, interfacial viscosity, and pore boundary decay exponentially with increasing pore diameter because of the dominance of van der Waals repulsive forces at the molecular level.

Aqueous films on pore surfaces mediate adsorption and transport of gases through crowded nanopores

Interactions of trapped reservoir gases within organic-rich and brine-bearing sedimentary rocks have direct relevance to many geoenergy applications. Extracting generalizable information from experimental campaigns is hindered by the fact that geological systems are extremely complex. However, modern computational tools offer the opportunity of studying systems with controlled complexity, in an effort to better understand the mechanisms at play. Employing molecular dynamics, we examine here adsorption and transport of gases containing CH₄ and either CO₂ or H₂S within amorphous silica nanopores filled with benzene. We explicitly quantify the effect of small amounts of water/brines at geological temperature and pressure conditions. Because of wetting, the presence of brines lessens the adsorption capacity of the aromatic-filled pore. The simulation results show salt-specific effects on the transport properties of the gases when either KCl or CaCl₂ brines are considered, although adsorption was not affected. The acid gases considered either facilitate or hinder CH₄ transport depending on whether they are more or less preferentially adsorbed within the pore as compared to benzene, and this effect is mediated by the presence of water/brines. Our simulation results could be used to extract thermodynamic quantities that in the future will help to optimize transport of various gases through organic-rich and brine-bearing sedimentary rocks, which is likely to have a positive impact on both hydrocarbon production and carbon sequestration applications. As a first step, a phenomenological model is presented here, which allows one to predict permeability based on interatomic energies.

Aquaporin-like water transport in nanoporous crystalline layered carbon nitride

Designing next-generation fuel cell and filtration devices requires the development of nanoporous materials that allow rapid and reversible uptake and directed transport of water molecules. Here, we combine neutron spectroscopy and first-principles calculations to demonstrate rapid transport of molecular H2O through nanometer-sized voids ordered within the layers of crystalline carbon nitride with a polytriazine imide structure. The transport mechanism involves a sequence of molecular orientation reversals directed by hydrogen-bonding interactions as the neutral molecules traverse the interlayer gap and pass through the intralayer voids that show similarities with the transport of water through transmembrane aquaporin channels in biological systems. The results suggest that nanoporous layered carbon nitrides can be useful for developing high-performance membranes.

Nanofluidic Behaviors of Water and Ions in Covalent Triazine Framework (CTF) Multilayers

Covalent triazine frameworks (CTFs) hosting arrays of highly ordered sub-2-nm pores are expected to exhibit unusual nanofluidic behaviors, which may enable important applications such as desalination. Herein, nonequilibrium molecular dynamics simulations are applied to investigate transport of water and ions inside two typical CTFs-CTF-1, and CTF-2-having intrinsic pores of 1.2 and 1.5 nm, respectively. Their monolayers exhibit extremely high water permeance but weak ion rejection. CTF multilayers are then investigated. Transport resistances composed of interior and interfacial contribution are correlated with stacking numbers of CTF monolayers to develop equations of predicting water permeance. It is revealed that both the stacking fashion and the number of CTF monolayers forming multilayers significantly influence permeation and ion rejection. Staggered multilayers exhibit much higher ion rejection than eclipsed ones. Staggered CTF-2 multilayers completely reject ions because the interlayer paths between two adjacent staggered monolayers allow only water molecules to pass through. Importantly, it is predicted from the equations that few-layered staggered CTF-2 multilayers, which can be relatively easily produced by experimental methods, exhibit 100% NaCl rejection and up to 100 times higher permeance than commercial reverse osmosis membranes, implying their great potential as building blocks to prepare next-generation desalination membranes.

Insights into water permeability and Hg2+ removal using two-dimensional nanoporous boron nitride

Industrial wastewater containing Hg²⁺, when discharged into nature, will pose a serious threat to ecological security.

Atomistic insights into the separation mechanism of multilayer graphene membranes for water desalination

Graphene-based membranes have been extensively explored owing to their excellent separation properties. In this paper, multiple factors regarding desalination performance were investigated by molecular dynamics (MD) simulations. These factors include the interlayer spacing distance (H), the gap width (dG), offset (O), and the number of gaps and layers in a multilayer graphene membrane (MGM). It is found that salt rejection is influenced significantly by the interlayer spacing distance owing to the largest free energy between ions and graphene sheets as well as the relatively larger size of the hydration layer around the ions. The optimal desalting parameter (dG = 1 nm, H = 0.8 nm) was selected; MGM systems based on the optimized parameter exhibited excellent salt rejection for NaCl, MgCl2 and CaCl2 solutions. These results can provide some ideas for the future design of graphene-based membranes.

Theory and simulation developments of confined mass transport through graphene-based separation membranes

The perspectives of graphene-based membranes based on confined mass transport from simulations and experiments for water desalination.

Nano-/Micro-confined Water in Graphene Hydrogel as Superadsorbents for Water Purification

Confined water has been proven to be of great importance due to its pervasiveness and contribution to life and many fields of scientific research. However, the control and characterization of confined water are a challenge. Herein, a confined space is constructed by flexibly changing the pH of a graphene oxide dispersion under the self-assembly process of a graphene hydrogel (GH), and the confined space is adjusted with variation from 10.04 to 3.52 nm. Confined water content in GH increases when the pore diameter of the confined space decreases; the corresponding adsorption capacity increases from 243.04 to 442.91 mg g^-1. Moreover, attenuated total reflectance Fourier transform infrared spectroscopy and Raman spectroscopy are utilized to analyze the hydrogen bonding structure qualitatively and quantitatively, and correlation analysis reveals that the improvement in the adsorption capacity is caused by incomplete hydrogen bonding in the confined water. Further, confined water is assembled into four typical porous commercial adsorbents, and a remarkable enhancement of the adsorption capacity is achieved. This research demonstrates the application potential for the extraordinary properties of confined water and has implications for the development of highly effective confined water-modified adsorbents.

Ion Rejection in Covalent Organic Frameworks: Revealing the Overlooked Effect of In-Pore Transport

Covalent organic frameworks (COFs), possessing highly ordered and intrinsic nanopores with high density and tunable sizes, are expected to find important applications in ion separation and desalination. The design of COF membranes with outstanding permselectivity requires understanding the ion rejection behaviors of COF multilayers. However, the ion rejection mechanism of COF multilayers remains to be elucidated because it may significantly differ from that of conventional polyamide membranes. Herein, we use nonequilibrium molecular dynamics simulations to investigate the ion transport through multilayers of TpHZ, which is a stable, imine-linked COF. Surprisingly, we find that the rejection to NaCl is determined by its rejection to Na⁺ rather than to Cl^-, although hydrated Cl^- is bigger than hydrated Na⁺. Inside the channels of the TpHZ multilayers, Na⁺ ions transport evidently slower than water molecules, implying that the in-pore transport effect instead of the commonly thought pore-entrance sieving effect governs ion rejection. The in-pore transport effect of Na⁺ is mainly due to the hydration of Na⁺ with pore wall and stronger capability of the hydrated Na⁺ ions to form hydrogen bonds with pore wall, both of which are primarily originated from the polarity of the COF. This work reveals the significant role of in-pore transport in ion rejection, which is overlooked in commonly used polyamide desalination membranes, and develops a universal equation capable of describing ion rejections of all membranes, especially those that contain structures of nanopores or nanochannels by considering both the effects of pore-entrance sieving and in-pore transport.

Dynamic Properties of Water Confined in Graphene-Based Membrane: A Classical Molecular Dynamics Simulation Study

We performed molecular dynamics simulations of water molecules inside a hydrophobic membrane composed of stacked graphene sheets. By decreasing the density of water molecules inside the membrane, we observed that water molecules form a droplet through a hydrogen bond with each other in the hydrophobic environment that stacked graphene sheets create. We found that the water droplet translates as a whole body rather than a dissipate. The translational diffusion coefficient along the graphene surface increases as the number of water molecules in the droplet decreases, because the bigger water droplet has a stronger van der Waals interaction with the graphene surface that hampers the translational motion. We also observed a longer hydrogen bond lifetime as the density of water decreased, because the hydrophobic environment limits the libration motion of the water molecules. We also calculated the reorientational correlation time of the water molecules, and we found that the rotational motion of confined water inside the membrane is anisotropic and the reorientational correlation time of confined water is slower than that of bulk water. In addition, we employed steered molecular dynamics simulations for guiding the target molecule, and measured the free energy profile of water and ion penetration through the interstice between graphene sheets. The free energy profile of penetration revealed that the optimum interlayer distance for desalination is ~10 Å, where the minimum distance for water penetration is 7 Å. With a 7 Å interlayer distance between the graphene sheets, water molecules are stabilized inside the interlayer space because of the van der Waals interaction with the graphene sheets where sodium and chloride ions suffer from a 3–8 kcal/mol energy barrier for penetration. We believe that our simulation results would be a significant contribution for designing a new graphene-based membrane for desalination.

Fast Desalination by Multilayered Covalent Organic Framework (COF) Nanosheets

Covalent organic frameworks (COFs) are penetrated with uniform and ordered nanopores, implying their great potential in molecular/ion separations. As an imine-linked, stable COF, TpPa-1 is receiving tremendous interest for molecular sieving membranes. Theoretically, atomically thin TpPa-1 monolayers exhibit extremely high water permeance but unfortunately no rejection to ions because of its large pore size (∼1.58 nm). The COF monolayers tend to stack to form laminated multilayers, but how this stacking influences water transport and ion rejections remains unknown. Herein, we investigate the transport behavior of water and salt ions through multilayered TpPa-1 COFs by nonequilibrium molecular dynamics simulations. By analyzing both the interfacial and interior resistance for water transport, we reveal that with rising stacking number of COF multilayers exhibit increasing ion rejections at the expense of water permeance. More importantly, stacking in the offset eclipsed fashion significantly reduces the equivalent pore size of COF multilayers to 0.89 nm, and ion rejection is correspondingly increased. Remarkably, 25 COF monolayers stacked in this fashion give 100% MgCl₂ rejection, whereas water permeance remains 1 to 2 orders of magnitude higher than that of commercial nanofiltration membranes. This work demonstrates the rational design of fast membranes for desalination by tailoring stacking number and fashion of the COF monolayers.

In Silico Design and Characterization of Graphene Oxide Membranes with Variable Water Content and Flake Oxygen Content

Graphene oxide (GO) membranes offer exceptional promise for certain aqueous separation challenges, such as desalination. Central to unlocking this promise and optimizing performance for a given separation is the establishment of a detailed molecular-level understanding of how the membrane's composition affects its structural and transport properties. This understanding is currently lacking, in part due to the fact that, until recently, molecular models with a realistic distribution of oxygen functionalities and interlayer flake structure were unavailable. To understand the effect of composition on the properties of GO membranes, models with water contents and oxygen contents, varying between 0% and 40% by weight, were prepared in this work using classical molecular dynamics simulations. The change in membrane interlayer distance distribution, water connectivity, and water diffusivity with water and oxygen content was quantified. Interlayer distance distribution analysis showed that the swelling of GO membranes could be controlled by separately tuning both the flake oxygen content and the membrane water content. Water-molecule cluster analysis showed that a continuous and fully connected network of water nanopores is not formed until the water content reaches ∼20%. The diffusivity of water in the membrane was also found to strongly depend on both the water and the oxygen content. These insights help understand the structure and transport properties of GO membranes with sub-nanometer interlayer distances and could be exploited to enhance the performance of GO membranes for aqueous separation applications. More broadly, the high-throughput in silico approach adopted could be applied to other nanomaterials with intrinsic non-stoichiometry and structural heterogeneity.

How Pore Hydrophilicity Influences Water Permeability?

Membrane separation is playing increasingly important role in providing clean water. Simulations predict that membrane pores with strong hydrophobicity produce ultrahigh water permeability as a result of low friction. However, experiments demonstrate that hydrophilic pores favor higher permeability. Herein we simulate water molecules transporting through interlayers of two-dimensional nanosheets with various hydrophilicities using nonequilibrium molecular dynamics. We reveal that there is a threshold pressure drop (ΔP _T), exceeding which stable water permeability appears. Strongly hydrophobic pores exhibit extremely high ΔP _T, prohibiting the achievement of ultrahigh water permeability under the experimentally accessible pressures. Under pressures < ΔP _T, water flows in hydrophobic pores in a running-stop mode because of alternative wetting and nonwetting, thus leading to significantly reduced permeability. We discover that hydrophilic modification to one surface of the nanosheet can remarkably reduce ΔP _T by > 99%, indicating a promising strategy to experimentally realize ultrafast membranes.

Breakdown of continuum model for water transport and desalination through ultrathin graphene nanopores: insights from molecular dynamics simulations

In the quest for identifying a graphene membrane for efficient water desalination, molecular dynamics simulations were performed for the pressure-driven flow of salty water across a multilayer graphene membrane.

Resistance of water transport in carbon nanotube membranes

Carbon nanotube (CNT) membranes have long been considered as next-generation membranes due to superfast water transport inside tubes. However, a large pressure loss occurs at the pore mouth, and consequently water transport through the whole tubes is significantly retarded. To find out the reason behind this, we conduct systematic non-equilibrium molecular dynamics (NEMD) simulations on water transport through CNT membranes with various tube diameters and lengths. The whole transport resistance is contributed by the interfacial and interior parts, and the interfacial contribution plays a dominating role in short tubes and only can be ignored when the tube length reaches a scale of several micrometers. With regard to the origin of the interfacial resistance, the hydrogen bonding rearrangement (HBR) effect accounts for at least 45%, and the rest is attributed to the geometrical or steric crowding of water molecules near the pore mouth. To reduce the dominant interfacial resistance, we change the shape of the pore mouth from plate to hourglass by mimicking the aquaporin water channels. The interfacial resistance is thus decreased by >27%. It is also found that the reduction is originated from the optimized HBR rather than the subdued steric crowding of water molecules near the pore mouth.

Effects of gas reservoir configuration and pore radius on shale gas nanoflow: A molecular dynamics study

We calculated methane transport through cylindrical graphite nanopores in cyclical steady-state flows using non-equilibrium molecular dynamics simulations. First, two typical gas reservoir configurations were evaluated: open (OS) and closed (CS) systems in which pores connect to the gas reservoir without/with a graphite wall parallel to the gas flow. We found that the OS configuration, which is commonly used to study nanoflows, exhibited obvious size effects. Smaller gas reservoir cross-sectional areas were associated with faster gas flows. Because Knudsen diffusion and slip flow in pores are interrupted in a gas reservoir that does not have walls as constraints, OSs cannot be relied upon in cyclical nanoflow simulations. Although CSs eliminated size effects, they introduced surface roughness effects that stem from the junction surface between the gas reservoir and the pore. To obtain a convergent nanoflow, the length of a side of the gas reservoir cross-section should be at least 2 nm larger than the pore diameter. Second, we obtained methane flux data for various pore radii (0.5-2.5 nm) in CSs and found that they could be described accurately using the Javadpour formula. This is the first direct molecular simulation evidence to validate this formula. Finally, the radial density and flow-velocity distributions of methane in CS pores were analyzed in detail. We tested pores with a radius between 0.5 nm and 2.5 nm and determined that the maximum ratio (∼34%) of slip flow to overall flow occurred in the pore with a radius of 1.25 nm. This study will aid in the design of gas reservoir configurations for nanoflow simulations and is helpful in understanding shale gas nanoflows.

Understanding the role of pore size homogeneity in the water transport through graphene layers

Graphene is a versatile 2D material and attracts an increasing amount of attention from a broad scientific community, including novel nanofluidic devices. In this work, we use molecular dynamics simulations to study the pressure driven water transport through graphene layers, focusing on the pore size homogeneity, realized by the arrangement of two pore sizes. For a given layer number, we find that water flux exhibits an excellent linear behavior with pressure, in agreement with the prediction of the Hagen-Poiseuille equation. Interestingly, the flux for concentrated pore size distribution is around two times larger than that of a uniform distribution. More surprisingly, under a given pressure, the water flux changes in an opposite way for these two distributions, where the flux ratio almost increases linearly with the layer number. For the largest layer number, more distributions suggest the same conclusion that higher water flux can be attained for more concentrated pore size distributions. Similar differences for the water translocation time and occupancy are also identified. The major reason for these results should clearly be due to the hydrogen bond and density profile distributions. Our results are helpful to delineate the exquisite role of pore size homogeneity, and should have great implications for the design of high flux nanofluidic devices and inversely the detection of pore structures.

Fast water transport in graphene nanofluidic channels

Superfast water transport discovered in graphitic nanoconduits, including carbon nanotubes and graphene nanochannels, implicates crucial applications in separation processes and energy conversion. Yet lack of complete understanding at the single-conduit level limits development of new carbon nanofluidic structures and devices with desired transport properties for practical applications. Here, we show that the hydraulic resistance and slippage of single graphene nanochannels can be accurately determined using capillary flow and a novel hybrid nanochannel design without estimating the capillary pressure. Our results reveal that the slip length of graphene in the graphene nanochannels is around 16 nm, albeit with a large variation from 0 to 200 nm regardless of the channel height. We corroborate this finding with molecular dynamics simulation results, which indicate that this wide distribution of the slip length is due to the surface charge of graphene as well as the interaction between graphene and its silica substrate.

Computational characterisation of dried and hydrated graphene oxide membranes

A multi-step molecular dynamics procedure was developed to construct fully flexible atomistic models of graphene oxide (GO) membranes. The method of preparation replicates the experimental synthesis of the material; i.e. the flow-directed self-assembly of individual flakes onto a substrate or filter. A total of 180 GO membrane models were prepared with water contents varying between 0 and 20%, providing an insight into changes in the membrane's interlayer distance with swelling. Membranes with 15% water content have an average interlayer distance (0.80 nm), bulk density (1.77 g cm^-3) and tensile modulus (18.1 GPa) in excellent agreement with the experimental literature, demonstrating that air-dried membranes have 15% water content. The models reveal the intrinsic structural heterogeneity and complex morphology of GO membranes. This feature has previously been unaccounted for in both experimental interpretations and GO nanopore models, which often use pre-defined and idealised 2D geometries. Completely dried membranes have considerable free pore volume. This observation explains the modest change in interlayer distance (0.02 nm) as the membrane's water content is increased from 0% to 10% compared to a much more significant change (0.12 nm) as the water content is increased from 10% to 20%. Combined with this new understanding of membrane swelling, the availability of such representative models opens the possibility of the molecular-level design of GO membranes for a variety of applications, such as gaseous and aqueous separations.

Effects of slit width on water permeation through graphene membrane by molecular dynamics simulations

Graphene membranes can be used for nanoscale filtration to remove atoms and are expected to be used for separation. To realize high-permeability and high-filtration performance, we must understand the flow configuration in the nanochannels. In this study, we investigated the applicability of continuum-dynamics laws to water flow through a graphene slit. We calculated the permeability of the flow through a slit using classical molecular dynamics (MD) and compared the MD simulation results for different Knudsen numbers (Kn) to predictions based on the no-slip model and slip model. Consequently, the flow through the graphene nanoslit was treated as slip flow only in the range of Kn < 0.375. This study provides guidelines for the development of graphene filtration membranes.

Water transport and desalination through double-layer graphyne membranes

Double-layer graphyne sheets with carefully chosen layer spacing are promising candidates as membranes in reverse osmosis desalination.

Non-Continuum Intercalated Water Diffusion Explains Fast Permeation through Graphene Oxide Membranes

Recent experimental studies have revealed unconventional phase and transport behaviors of water confined within lamellar graphene oxide membranes, which hold great promise not only in improving our current understanding of nanoconfined water but also in developing high-performance filtration and separation applications. In this work, we explore molecular structures and diffusive dynamics of water intercalated between graphene or graphene oxide sheets. We identify the monolayer structured water between graphene sheets at temperature T below T_c = ∼315 K and an interlayer distance d = 0.65 nm, which is absent as the sheets are oxidized. The non-continuum collective diffusion of water intercalation between graphene layers facilitates fast molecular transport due to reduced wall friction. This solid-like structural order of intercalated water is disturbed as T or d increases to a critical value, with abnormal declines in the coefficients of collective diffusion. Based on a patched model of graphene oxide sheets consisting of spatially distributed pristine and oxidized regions, we conclude that the non-continuum collective diffusion of intercalated water can explain fast water permeation through graphene oxide membranes as reported in recent experimental studies, in stark contrast to the conventional picture of pressure-driven continuum flow with boundary slip, which has been widely adopted in literature but may apply only at high humidity or in the fully hydrated conditions.