Flow enhancement in nanotubes of different materials and lengths

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.

Predicting Quantum-Mechanical Partial Charges in Arbitrarily Long Boron Nitride Nanotubes to Accurately Simulate Nanoscale Water Transport

Single-walled boron nitride nanotubes (BNNTs) have been explored for various applications, ranging from water desalination to osmotic power harvesting. However, no simulation work so far has modeled the changes in the partial charge distribution when a flat sheet is rolled into a tube, hindering the ability to perform accurate molecular dynamics (MD) simulations of water flow through BNNTs. To address this knowledge gap, we employ electronic density functional theory (DFT) calculations to precisely estimate quantum-mechanically derived partial charges on boron (B) and nitrogen (N) atoms in BNNTs of varying lengths and diameters. We observe a spatially varying charge distribution inside both armchair and zigzag nanotubes of finite lengths. Performing DFT calculations for longer BNNTs is computationally intractable, even with state-of-the-art computing resources. To solve this issue, we devise a charge assignment scheme to predict partial charges for longer BNNTs using DFT data for shorter nanotubes, thus overcoming the need to perform more expensive DFT calculations. We show that these charges reproduce the electrostatic potential predicted from first-principles simulations. Subsequently, we carried out MD simulations to predict the effect of the charge distribution inside BNNTs on water flow enhancement via them. We find that using uniform charges leads to an underprediction in flow enhancement, as compared to using quantum-mechanical charges for both armchair and zigzag BNNTs. We also incorporate atomic vibrations into our simulations and show that these vibrations lead to a reduction in the water flow through aperiodic BNNTs. Our work demonstrates the requirement of a quantum-mechanical charge assignment scheme for BNNTs and evolves a framework to assign charges to nanotubes of arbitrary length, thus allowing realistic MD simulations of long BNNTs using accurate partial charges.

Pressure-dependent flow enhancement in carbon nanotubes

It is a known and experimentally verified fact that the flow of pressure-driven nanoconfined fluids cannot be accurately described by the Navier-Stokes (NS) equations with non-slip boundary conditions, and the measured volumetric flow rates are much higher than those predicted by macroscopical continuum models. In particular, the flow enhancement factors (the ratio between the flow rates directly measured by experiments or simulations and those predicted by the non-slip NS equation) reported by previous studies have more than five orders of magnitude differences. We showcased an anomalous phenomenon in which the flow enhancement exhibits a non-monotonic correlation with fluid pressure within the carbon nanotube with a diameter of 2 nm. Molecular dynamics simulations indicate that the inconsistency of flow behaviors is attributed to the phase transition of nanoconfined fluid induced by fluid pressures. The nanomechanical mechanisms are contributed by complex hydrogen-bonding interactions and regulated water orientations. This study suggests a method for explaining the inconsistency of flow enhancements by considering the pressure-dependent molecular structures.

Uniqueness of Nanoscale Confinement for Fast Water Transport: Effect of Nanotube Diameter and Hydrophobicity

Inspired by the enhanced water permeability of carbon nanotubes (CNTs), molecular dynamics simulations were performed to investigate the transport behavior through nanotubes made of boron nitride (BNNT), silicon carbide (SiC), and silicon nitride (SiN) alongside carbon nanotubes (which have different hydrophobic attributes) considering their implication for reverse osmosis (RO) membranes under different practical environments. According to our findings, not only do CNTs but also other kinds of nanotubes exhibit transition anomalies with increasing diameter. Utilizing the robust two-phase thermodynamic (2PT) methods, the current examinations shed light on thermodynamic origin of favorable water filling of these nanotubes. The results show that regardless of the nanotube material, the filling of water inside small nanopores (d < 10 Å) as well as within pores of diameter larger than 15 Å will always be favored by the entropy of filling. However, the entropic preference for filling nanotubes with a diameter of 10-15 Å depends on the constituent material. In particular, the enhancement in total entropy of confined water was mainly due to the increased rotational freedom of confined water molecules. The thermodynamic origin of water transport was correlated with the structural and fluidic behavior of water inside these nanotubes. The observed data for density, flow, structure correlation functions, water-water coordination, tetrahedral order parameter, hydrogen bonds, and density of states functions quantitatively support the observed entropy behavior. Of critical importance is that the present study demonstrates the effectiveness of RO filtration using nanotubes of boron nitride rather than carbon. Furthermore, it was found that one should avoid the use of silicon nanotubes unless filtration needs to be performed under harsh environments where nanotube of other materials cannot survive. Specifically, the results show that both the structural and dynamic properties of water confined in BNNTs are similar to those of CNT's, and for SiNT it is similar as SiC. Our results show that besides the nanotube material, the chirality index of the nanotube also plays a significant role in determining the structure, dynamics and thermodynamics of confined water molecules.

Effects of channel size, wall wettability, and electric field strength on ion removal from water in nanochannels

Molecular dynamics simulations are employed to estimate the effect of nanopore size, wall wettability, and the external field strength on successful ion removal from water solutions. It is demonstrated that the presence of ions, along with the additive effect of an external electric field, constitute a multivariate environment that affect fluidic interactions and facilitate, or block, ion drift to the walls. The potential energy is calculated across every channel case investigated, indicating possible ion localization, while electric field lines are presented, to reveal ion routing throughout the channel. The electric field strength is the dominant ion separation factor, while wall wettability strength, which characterizes if the walls are hydrophobic or hydrophilic has not been found to affect ion movement significantly at the scale studied here. Moreover, the diffusion coefficient values along the three dimensions are reported. Diffusion coefficients have shown a decreasing tendency as the external electric field increases, and do not seem to be affected by the degree of wall wettability at the scale investigated here.

Untangling the physics of water transport in boron nitride nanotubes

Carbon nanotubes (CNTs) have long been heralded as the material of choice for next-generation membranes. Some studies have suggested that boron nitride nanotubes (BNNTs) may offer higher transport of pure water than CNTs, while others conclude otherwise. In this work, we use a combination of simulations and experimental data to uncover the causes of this discrepancy and investigate the flow resistance through BNNT membranes in detail. By dividing the resistance of the nanotube membranes into their contributing components, we study the effects of pore end configuration, membrane length, and BNNT atom partial charges. Most molecular simulation studies of BNNT membranes use short membranes connected to high and low pressure reservoirs. Here we find that flow resistances in these short membranes are dominated by the resistance at the pore ends, which can obscure the understanding of water transport performance through the nanotubes and comparison between different nanotube materials. In contrast, it is the flow resistance inside the nanotubes that dominates microscale-thick laboratory membranes, and end resistances tend to be negligible. Judged by the nanotube flow resistance alone, we therefore find that CNTs are likely to consistently outperform BNNTs. Furthermore, we find a large role played by the choice of partial charges on the BN atoms in the flow resistance measurements in our molecular simulations. This paper highlights a way forward for comparing molecular simulations and experimental results.

Hydration of a small protein under carbon nanotube confinement: Adsorbed substates induce selective separation of the dynamical response

The co-involvement of biological molecules and nanomaterials has increasingly come to the fore in modern-day applications. While the "bio-nano" (BN) interface presents physico-chemical characteristics that are manifestly different from those observed in isotropic bulk conditions, the underlying molecular reasons remain little understood; this is especially true of anomalies in interfacial hydration. In this paper, we leverage atomistic simulations to study differential adsorption characteristics of a small protein on the inner (concave) surface of a single-walled carbon nanotube whose diameter exceeds dimensions conducive to single-file water movement. Our findings indicate that the extent of adsorption is decided by the degree of foldedness of the protein conformational substate. Importantly, we find that partially folded substates, but not the natively folded one, induce reorganization of the protein hydration layer into an inner layer water closer to the nanotube axis and an outer layer water in the interstitial space near the nanotube walls. Further analyses reveal sharp dynamical differences between water molecules in the two layers as observed in the onset of increased heterogeneity in rotational relaxation and the enhanced deviation from Fickian behavior. The vibrational density of states reveals that the dynamical distinctions are correlated with differences in crucial bands in the power spectra. The current results set the stage for further systematic studies of various BN interfaces vis-à-vis control of hydration properties.

Nanoscale slip length prediction with machine learning tools

This work incorporates machine learning (ML) techniques, such as multivariate regression, the multi-layer perceptron, and random forest to predict the slip length at the nanoscale. Data points are collected both from our simulation data and data from the literature, and comprise Molecular Dynamics simulations of simple monoatomic, polar, and molecular liquids. Training and test points cover a wide range of input parameters which have been found to affect the slip length value, concerning dynamical and geometrical characteristics of the model, along with simulation parameters that constitute the simulation conditions. The aim of this work is to suggest an accurate and efficient procedure capable of reproducing physical properties, such as the slip length, acting parallel to simulation methods. Non-linear models, based on neural networks and decision trees, have been found to achieve better performance compared to linear regression methods. After the model is trained on representative simulation data, it is capable of accurately predicting the slip length values in regions between or in close proximity to the input data range, at the nanoscale. Results also reveal that, as channel dimensions increase, the slip length turns into a size-independent material property, affected mainly by wall roughness and wettability.

Enhanced nanoparticle rejection in aligned boron nitride nanotube membranes

The rejection of particles with different charges and sizes, ranging from a few Ångstroms to tens of nanometers, is key to a wide range of industrial applications, from wastewater treatment to product purification in biotech processes. Carbon nanotubes (CNTs) have long held the promise to revolutionize filtration, with orders of magnitude higher fluxes compared to commercial membranes. CNTs, however, can only reject particles and ions wider than their internal diameter. In this work, the fabrication of aligned boron nitride nanotube (BNNT) membranes capable of rejecting nanoparticles smaller than their internal diameter is reported for the first time. This is due to a mechanism of charge-based rejection in addition to the size-based one, enabled by the BNNTs surface structure and chemistry and elucidated here using high fidelity molecular dynamics and Brownian dynamics simulations. This results in ∼40% higher rejection of the same particles by BNNT membranes than CNT ones with comparable nanotube diameter. Furthermore, since permeance is proportional to the square of the nanotubes' diameter, using BNNT membranes with ∼30% larger nanotube diameter than a CNT membrane with comparable rejection would result in up to 70% higher permeance. These results open the way to the design of more effective nanotube membranes, capable of high particle rejection and, at the same time, high water permeance.

Mesoscopic method to study water flow in nanochannels with different wettability

Molecular dynamics (MD) simulations is currently the most popular and credible tool to model water flow in nanoscale where the conventional continuum equations break down due to the dominance of fluid-surface interactions. However, current MD simulations are computationally challenging for the water flow in complex tube geometries or a network of nanopores, e.g., membrane, shale matrix, and aquaporins. We present a novel mesoscopic lattice Boltzmann method (LBM) for capturing fluctuated density distribution and a nonparabolic velocity profile of water flow through nanochannels. We incorporated molecular interactions between water and the solid inner wall into LBM formulations. Details of the molecular interactions were translated into true and apparent slippage, which were both correlated to the surface wettability, e.g., contact angle. Our proposed LBM was tested against 47 published cases of water flow through infinite-length nanochannels made of different materials and dimensions-flow rates as high as seven orders of magnitude when compared with predictions of the classical no-slip Hagen-Poiseuille (HP) flow. Using the developed LBM model, we also studied water flow through finite-length nanochannels with tube entrance and exit effects. Results were found to be in good agreement with 44 published finite-length cases in the literature. The proposed LBM model is nearly as accurate as MD simulations for a nanochannel, while being computationally efficient enough to allow implications for much larger and more complex geometrical nanostructures.

Equilibrium structures of water molecules confined within a multiply connected carbon nanotube: a molecular dynamics study

Water confinement inside a carbon nanotube (CNT) has been one of the most exciting subjects of both experimental and theoretical interest. Most of the previous studies, however, considered CNT structures with simple cylindrical shapes. In this paper, we report a classical molecular dynamics study of the equilibrium structural arrangement of water molecules confined in a multiply connected carbon nanotube (MCCNT) containing two Y-junctions. We investigate the structural arrangement of the water molecules in the MCCNT in terms of the density of water molecules and the average number of hydrogen bonds per water molecule. Our results show that the structural rearrangement of the H2O molecules takes place several angstroms ahead of the Y-junction, rather than only at the CNT junction itself. This phenomenon arises because it is difficult to match the boundary condition for hydrogen bonding in the region where two different hydrogen-bonded structures are interconnected with each other.

High Polymer Mass Densities at the Mouths of Carbon Nanotubes (CNTs) Control the Diffusion of Small Molecules through CNT-Based Polymer Nanocomposite Membranes

Detailed molecular dynamics (MD) simulations of model single-walled carbon nanotube (CNT) membranes based on atactic poly(methyl methacrylate) (aPMMA) indicate that PMMA chains significantly penetrate nanotubes through their faces. They predict very high-density values of the polymer in the interfacial area around the CNT mouths that can exceed by 50% the density of the bulk polymer at the same thermodynamic conditions. This dramatically decreases the diffusivity of relatively small penetrants (in our study, water molecules) in the nanocomposite membrane, because of the exceedingly long times needed by these small molecules to diffuse through such a dense interfacial layer before accessing the interior of the nanotubes where they can travel really fast. According to our simulations, the escape time of a confined water molecule from the blocked mouths of a CNT can exceed by several orders of magnitude the time needed by the same molecule to move through the CNT pore. Our work indicates the importance of completely avoiding (or at least minimizing) penetration of polymer chains into the CNT pores through the mouths of the tubes in enabling the efficient transport of small- to moderate-size molecules in model CNT-based polymer membranes, since this provides the highest resistance to their mobility through the membrane.

Surface-Controlled Water Flow in Nanotube Membranes

The independent effect of nanotube surface chemistry and structure on the flow of water under nanoscale confinement is demonstrated in this paper for the first time via the synthesis of novel carbon nitride nanotube (CNNT) membranes. Using a combination of experiments and high-fidelity molecular dynamics (MD) simulations, it is shown here that the hydrophilization of the sp² carbon structure, induced by the presence of the C-N bonds, decreases the pure water permeance in CNNTs when compared with pristine and turbostratic carbon nanotubes (CNTs). The MD simulations are based on a model true to the chemical structure of the synthesized nanotubes, built from spectroscopy measurements and calibrated potentials using droplet experiments. The effect on permeance is explained in terms of solid-liquid interactions at the nanotube wall with increased water viscosity and decreased surface diffusion near the CNNT wall, when compared to CNTs. A model directly linking the solid-liquid interactions to the water permeance is presented, showing good agreement with both experiments and MD simulations. This work opens the way to tailoring surface chemistry and structure inside nanotube membranes for a wide range of transport and separation processes.

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.

VP, Sathian SP. Water flow in carbon nanotubes: the role of tube chirality

Flow rate of water in CNTs of different types.

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.

Slip divergence of water flow in graphene nanochannels: the role of chirality

Graphene has attracted considerable attention due to its characteristics as a 2D material and its fascinating properties, providing a potential building block for fabrication of nanofluidic conduits.

Confined Water Determines Transport Properties of Guest Molecules in Narrow Pores

We computed the transport of methane through 1 nm wide slit-shaped pores carved out of solid substrates. Models for silica, magnesium oxide, and alumina were used as solid substrates. The pores were filled with water. The results show that the methane permeability through the hydrated pores is strongly dependent on the solid substrate. Detailed analysis of the simulated systems reveals that local properties of confined water, including its structure, and more importantly, evolution of solvation free energy and hydrogen bond structure are responsible for the pronounced differences observed. The simulations are extended to multicomponent systems representative of natural gas, containing methane, ethane, and H2S. The results show that all pores considered have high affinity for H2S, moderate affinity for methane, and low affinity for ethane. The H2S/methane transport selectivity through the hydrated alumina pore is comparable, or superior, to that reported for existing commercial membranes. A multiscale approach was then implemented to demonstrate that a Smoluchowski one-dimensional model is able to reproduce the molecular-level results for short pores when appropriate values for the local self-diffusion coefficients are used as input parameters. We propose that the model can be extended to predict methane transport through uniform hydrated pores of macroscopic length. When verified by experiments, our simulation results could have important implications in applications such as natural gas sweetening and predictions of methane migration through hydraulically fractured shale formations.

Observation and analysis of the Coulter effect through carbon nanotube and graphene nanopores

Carbon nanotubes (CNTs) and graphene are the rolled and flat analogues of graphitic carbon, respectively, with hexagonal crystalline lattices, and show exceptional molecular transport properties. The empirical study of a single isolated nanopore requires, as evidence, the observation of stochastic, telegraphic noise from a blocking molecule commensurate in size with the pore. This standard is used ubiquitously in patch clamp studies of single, isolated biological ion channels and a wide range of inorganic, synthetic nanopores. In this work, we show that observation and study of stochastic fluctuations for carbon nanopores, both CNTs and graphene-based, enable precision characterization of pore properties that is otherwise unattainable. In the case of voltage clamp measurements of long (0.5-1 mm) CNTs between 0.9 and 2.2 nm in diameter, Coulter blocking of cationic species reveals the complex structuring of the fluid phase for confined water in this diameter range. In the case of graphene, we have pioneered the study and the analysis of stochastic fluctuations in gas transport from a pressurized, graphene-covered micro-well compartment that reveal switching between different values of the membrane permeance attributed to chemical rearrangements of individual graphene pores. This analysis remains the only way to study such single isolated graphene nanopores under these realistic transport conditions of pore rearrangements, in keeping with the thesis of this work. In summary, observation and analysis of Coulter blocking or stochastic fluctuations of permeating flux is an invaluable tool to understand graphene and graphitic nanopores including CNTs.

A computational assessment of the permeability and salt rejection of carbon nanotube membranes and their application to water desalination

Membranes made from nanomaterials such as nanotubes and graphene have been suggested to have a range of applications in water filtration and desalination, but determining their suitability for these purposes requires an accurate assessment of the properties of these novel materials. In this study, we use molecular dynamics simulations to determine the permeability and salt rejection capabilities for membranes incorporating carbon nanotubes (CNTs) at a range of pore sizes, pressures and concentrations. We include the influence of osmotic gradients and concentration build up and simulate at realistic pressures to improve the reliability of estimated membrane transport properties. We find that salt rejection is highly dependent on the applied hydrostatic pressure, meaning high rejection can be achieved with wider tubes than previously thought; while membrane permeability depends on salt concentration. The ideal size of the CNTs for desalination applications yielding high permeability and high salt rejection is found to be around 1.1 nm diameter. While there are limited energy gains to be achieved in using ultra-permeable CNT membranes in desalination by reverse osmosis, such membranes may allow for smaller plants to be built as is required when size or weight must be minimized. There are diminishing returns in further increasing membrane permeability, so efforts should focus on the fabrication of membranes containing narrow or functionalized CNTs that yield the desired rejection or selection properties rather than trying to optimize pore densities.

Electric fields can control the transport of water in carbon nanotubes

The properties of water confined inside nanotubes are of considerable scientific and technological interest. We use molecular dynamics to investigate the structure and average orientation of water flowing within a carbon nanotube. We find that water exhibits biaxial paranematic liquid crystal ordering both within the nanotube and close to its ends. This preferred molecular ordering is enhanced when an axial electric field is applied, affecting the water flow rate through the nanotube. A spatially patterned electric field can minimize nanotube entrance effects and significantly increase the flow rate.

The good, the bad and the user in soft matter simulations

Molecular dynamics (MD) simulations have become popular in materials science, biochemistry, biophysics and several other fields. Improvements in computational resources, in quality of force field parameters and algorithms have yielded significant improvements in performance and reliability. On the other hand, no method of research is error free. In this review, we discuss a few examples of errors and artifacts due to various sources and discuss how to avoid them. Besides bringing attention to artifacts and proper practices in simulations, we also aim to provide the reader with a starting point to explore these issues further. In particular, we hope that the discussion encourages researchers to check software, parameters, protocols and, most importantly, their own practices in order to minimize the possibility of errors. The focus here is on practical issues. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Determination of the effective diffusivity of water in a poly (methyl methacrylate) membrane containing carbon nanotubes using kinetic Monte Carlo simulations

A kinetic Monte Carlo (kMC) simulation algorithm is developed for computing the effective diffusivity of water molecules in a poly(methyl methacrylate) (PMMA) matrix containing carbon nanotubes (CNTs) at several loadings. The simulations are conducted on a cubic lattice to the bonds of which rate constants are assigned governing the elementary jump events of water molecules from one lattice site to another. Lattice sites belonging to PMMA domains of the membrane are assigned different rates than lattice sites belonging to CNT domains. Values of these two rate constants are extracted from available numerical data for water diffusivity within a PMMA matrix and a CNT pre-computed on the basis of independent atomistic molecular dynamics simulations, which show that water diffusivity in CNTs is 3 orders of magnitude faster than in PMMA. Our discrete-space, continuum-time kMC simulation results for several PMMA-CNT nanocomposite membranes (characterized by different values of CNT length L and diameter D and by different loadings of the matrix in CNTs) demonstrate that the overall or effective diffusivity, D(eff), of water in the entire polymeric membrane is of the same order of magnitude as its diffusivity in PMMA domains and increases only linearly with the concentration C (vol. %) in nanotubes. For a constant value of the concentration C, D(eff) is found to vary practically linearly also with the CNT aspect ratio L/D. The kMC data allow us to propose a simple bilinear expression for D(eff) as a function of C and L/D that can describe the numerical data for water mobility in the membrane extremely accurately. Additional simulations with two different CNT configurations (completely random versus aligned) show that CNT orientation in the polymeric matrix has only a minor effect on D(eff) (as long as CNTs do not fully penetrate the membrane). We have also extensively analyzed and quantified sublinear (anomalous) diffusive phenomena over small to moderate times and correlated them with the time needed for penetrant water molecules to explore the available large, fast-diffusing CNT pores before Fickian diffusion is reached.