Investigation of entrance and exit effects on liquid transport through a cylindrical nanopore

The entrance and exit effects on liquid transport through a nano-sized cylindrical pore under different solid wall-liquid interactions were studied by comparing molecular dynamics (MD) results of a finite length nanopore in a membrane with those of an infinite length one. The liquid transport through a finite length nanopore in a membrane was carried out by using a pressure-driven non-equilibrium molecular dynamics (NEMD) method proposed by Huang et al. [C. Huang, K. Nandakumar, P. Choi and L. W. Kostiuk, J. Chem. Phys., 2006, 124, 234701]. The fluid motion through an infinite length nanopore, which had the same cross-stream dimension as the finite length channel in the membrane, but with periodic boundary conditions in the stream-wise direction, was carried out by using the external-field driven NEMD approach [J. Koplik, J. R. Bavanar and J. F. Willemsen, Phys. Rev. Lett., 1988, 60, 1282]. The NEMD results show that the pressure and density distributions averaged over the channel in the radial direction in both finite and infinite length channels are similar, but the radial distributions of the stream-wise velocity were significantly different when the solid wall was repulsive. The entrance and exit effects lead to a decrease in flow rate at about 39% for the repulsive wall and 6% for the neutral-like wall.     

Molecular simulation of pressure-driven fluid flow in nanoporous membranes

An extended nonequilibrium molecular dynamics technique has been developed to investigate the transport properties of pressure-driven fluid flow in thin nanoporous membranes. Our simulation technique allows the simulation of the pressure-driven permeation of liquids through membranes while keeping a constant driving pressure using fluctuating walls. The flow of argon in the liquid state was simulated on applying an external pressure difference of 2.4x10(6) Pa through the slitlike and cylindrical pores. The volume flux and velocity distribution in the membrane pores were examined as a function of pore size, along with the interaction with the pore walls, and these were compared with values estimated using the Hagen-Poiseuille flow. The calculated velocity strongly depends on the strength of the interaction between the fluid and the atoms in the wall when the pore size is approximately<20sigma. The calculated volume flux also shows a dependence on the interaction between the fluid and the atoms in the wall. The Hagen-Poiseuille law overestimates or underestimates the flux depending on the interaction. From the analysis of calculated results, a good linear correlation between the density of the fluid in the membrane pores and the deviation of the flux estimated from the Hagen-Poiseuille flow was found. This suggests that the flux deviation in nanopore from the Hagen-Poiseuille flow can be predicted based on the fluid density in the pores.     

On the Origin of Water Flow through Carbon Nanotubes

The transport of water molecules through carbon nanotubes (CNTs) is of primary importance for understanding water‐mediated biological activities as well as for the design of novel nanoporous materials. Herein, we analyze the water flow through CNTs by using molecular dynamics simulations with the hope of finding basic parameters determining the flow value. Of particular interest is that a simple equation as a function of water diffusion, occupancy and CNT size, can well describe the water flow through CNTs with different sizes. Specifically, both the simulation and equation flow exhibit power law relations with the CNT diameter and length, where the two exponents are close to each other. The water occupancy and translocation time also demonstrate interesting relations with the CNT size. The water dipole orientations and density profiles are also sensitive to the change of CNT size. These results greatly enhance our knowledge on the nature of water flow through CNTs and are helpful in predicting the water flow of CNTs up to the experimental length scale.     

Fluid structure and transport properties of water inside carbon nanotubes

The fluid structure and transport properties of water confined in single-walled carbon nanotubes (CNTs) with different diameters have been investigated by molecular-dynamics simulation. The effects of CNT diameter, density of water, and temperature on the molecular distributions and transport behaviors of water were analyzed. It is interesting that the water molecules ordered in helix inside the (10, 10) CNT, and the layered distribution was clearly observed. It was found that the axial and radial diffusivities in CNTs were much lower than that of the bulk, and it ever decreased as the diameter of CNT decreases. The axial thermal conductivity and shear viscosity in CNTs are obviously larger than that of the bulk and those in the radial direction, they increase sharply as the diameter of CNT decreases, which is clearly in contrast to the diffusivity. The inner space of CNT and the interactions between water molecules and the confining walls play a key role in the structure and transport properties of water confined in the CNTs.     

Factors influencing the transport of short-chain alcohols through mesoporous gamma-alumina membranes

The pressure-driven transport of water, ethanol, and 1-propanol through supported gamma-alumina membranes with different pore diameters is reported. Water and alcohols had similar permeabilities when they were transported through gamma-alumina membranes with average pore diameters of 4.4 and 6.0 nm, and the permeability coefficient was found to be proportional to the square of pore size, in accordance with a viscous flow mechanism. For transport through membranes with an average diameter of 3.2 nm, the behavior of water was in accordance with the viscous flow mechanism, but the permeability of the membrane for ethanol and 1-propanol was much smaller than expected and could not be explained in terms of viscous flow. Although the low permeability of the membrane with 3.2 nm pores for ethanol and 1-propanol was partly due to the presence of small amounts of water in the alcohols, the permeability coefficients were still substantially smaller when water was absent. This intrinsic difference between water and alcohol may be due to differences in molecular size, chemisorption of alcohols on the oxide pore wall, which would lead to a reduction of the effective pore size, and/or a certain degree of translational ordering of the alcohol molecules inside the membrane pores, which leads to an effectively higher viscosity and, therefore, to a higher transport resistance.     

Effect of Size and Temperature on Water Dynamics inside Carbon Nano-Tubes Studied by Molecular Dynamics Simulation

Water transport inside carbon nano-tubes (CNTs) has attracted considerable attention due to its nano-fluidic properties, its importance in nonporous systems, and the wide range of applications in membrane desalination and biological medicine. Recent studies show an enhancement of water diffusion inside nano-channels depending on the size of the nano-confinement. However, the underlying mechanism of this enhancement is not well understood yet. In this study, we performed Molecular Dynamics (MD) simulations to study water flow inside CNT systems. The length of CNTs considered in this study is 20 nm, but their diameters vary from 1 to 10 nm. The simulations are conducted at temperatures ranging from 260 K to 320 K. We observe that water molecules are arranged into coaxial water tubular sheets. The number of these tubular sheets depends on the CNT size. Further analysis reveals that the diffusion of water molecules along the CNT axis deviates from the Arrhenius temperature dependence. The non-Arrhenius relationship results from a fragile liquid-like water component persisting at low temperatures with fragility higher than that of the bulk water.     

Effect of nanotube-length on the transport properties of single-file water molecules: transition from bidirectional to unidirectional

We use molecular dynamics (MD) simulations to study the transport of single-file water molecules through carbon nanotubes (CNTs) with various lengths in an electric field. Most importantly, we find that even the water dipoles inside the CNT are maintained along the field direction, a large amount of water molecules can still transport against the field direction for short CNTs, leading to a low unidirectional transport efficiency (η). As the CNT length increases, the efficiency η will increase remarkably, and achieves the maximum value of 1.0 at or exceeding a critical CNT length. Consequently, the transition from bidirectional to unidirectional transport is observed and is found to be relevant to thermal fluctuations of the two reservoirs, which is explored by the interaction between water molecules inside and outside the CNT. We also find that the water flow vs CNT length follows an exponential decay of f ～ exp?(- L/L(0)), and the average translocation time of individual water molecules yields to a power law of τ(trans) ～ L(υ), where L(0) and ν are constant and slightly depend on the field strength. We further compare our results with the continuous-time random-walk (CTRW) model and find that the water flow can also be described by a power law of f ～ L(-μ) modified from CTRW. Our results provide some new physical insights into the biased transport of single-file water molecules, which show the feasibility of using CNTs with any length to pump water in an electric field. The mechanism is important for designing efficient nanofluidic apparatuses.     

正渗透过程中纳米碳管膜的盐水通道行为

以纳米碳管(CNT)仿生构筑正渗透(FO)膜, 采用分子动力学模拟的方法考察水和盐在由CNT(6,6)、CNT(7,7)、CNT(8,8)、CNT(9,9)、CNT(10,10)、CNT(11,11)等不同尺寸纳米碳管构筑膜中, 于2.5、3.75、5.0mol·L^-1等不同汲取液浓度下的传递行为. 纳秒级的模拟得到水分子在不同尺寸纳米碳管膜内的分布, 水通量的变化以及盐截留等情况. 模拟结果表明, 由CNT(8,8)构筑的正渗透膜表现出优异的通水阻盐性能.     

Molecular dynamics simulation of a pressure-driven liquid transport process in a cylindrical nanopore using two self-adjusting plates

Fluid transport through a nanopore in a membrane was investigated by using a novel molecular dynamics approach proposed in this study. The advantages of this method, relative to dual-control-volume grand-canonical molecular dynamics method, are that it eliminates disruptions to the system dynamics that are normally created by inserting or deleting particles from control volumes, and that it functions well for dense systems due to the number of particles being fixed in the system. Using the proposed method, we examined liquid argon transport through a nanopore by performing nonequilibrium molecular dynamics (NEMD) simulations under different back pressures. Validation of the code was performed by comparing simulation results to published experimental data obtained under equilibrium conditions. NEMD results show that constant pressure difference across the membrane was readily achieved.     

Slip length of water on graphene: limitations of non-equilibrium molecular dynamics simulations

Data for the flow rate of water in carbon nanopores is widely scattered, both in experiments and simulations. In this work, we aim at precisely quantifying the characteristic large slip length and flow rate of water flowing in a planar graphene nanochannel. First, we quantify the slip length using the intrinsic interfacial friction coefficient between water and graphene, which is found from equilibrium molecular dynamics (EMD) simulations. We then calculate the flow rate and the slip length from the streaming velocity profiles obtained using non-equilibrium molecular dynamics (NEMD) simulations and compare with the predictions from the EMD simulations. The slip length calculated from NEMD simulations is found to be extremely sensitive to the curvature of the velocity profile and it possesses large statistical errors. We therefore pose the question: Can a micrometer range slip length be reliably determined using velocity profiles obtained from NEMD simulations? Our answer is "not practical, if not impossible" based on the analysis given as the results. In the case of high slip systems such as water in carbon nanochannels, the EMD method results are more reliable, accurate, and computationally more efficient compared to the direct NEMD method for predicting the nanofluidic flow rate and hydrodynamic boundary condition.     

Characterization of the flow of the CO/CO2 gases through carbon nanotube junctions using molecular dynamic simulations

A detailed study of the gas flow in carbon nanotubes (CNT) and carbon nanotube junctions (CNTJ) can open the way towards the study of the reaction mixture flow in prospective nano-reactors. In this work, flow of the pure and mixed CO/CO₂ gases through some selected CNTs and three types of CNT1-J-CNT2 CNTJs, (12,12)-J-(3,8), (12,8)-J-(8,12) and (8,8)-J-(13,0), are studied using molecular dynamic simulations. Results of this study show that regardless of the diameter and helicity type of the CNT1 and CNT2, when the flow starts with the molecules in the CNT1, the number density of molecules in the CNT2 is higher than that in the CNT1. Projected radial distribution of the molecules are calculated and analyzed in terms of the molecule–molecule and molecule-wall interactions. The well-structured projected radial distribution results show that the CNT radius and helicity as well as the type of molecules determine the lateral distribution of the gas molecules along the flow.     

Water transport coefficient distribution through the membrane in a polymer electrolyte fuel cell

The net water transport coefficient through the membrane, defined as the ratio of the net water flux from the anode to cathode to the protonic flux, is used as a quantitative measure of water management in a polymer electrolyte fuel cell (PEFC). In this paper we report on experimental measurements of the net water transport coefficient distribution for the first time. This is accomplished by making simultaneous current and species distribution measurements along the flow channel of an instrumented PEFC via a multi-channel potentiostat and two micro gas chromatographs. The net water transport coefficient profile along the flow channels is then determined by a control-volume analysis under various anode and cathode inlet relative humidity (RH) at 80 °C and 2 atm. It is found that the local current density is dominated by the membrane hydration and that the gas RH has a large effect on water transport through the membrane. Very small or negative water transport coefficients are obtained, indicating strong water back diffusion through the 30 μm Gore-Select^® membrane used in this study.     

Voltage gated carbon nanotube membranes

Membranes composed of an array of aligned carbon nanotubes, functionalized with charged molecular tethers, show voltage gated control of ionic transport through the cores of carbon nanotubes. The functional density of tethered charge molecules is substantially increased by the use of electrochemical grafting of diazonium salts. Functionality can be forced to occur at the CNT tip entrances by fast fluid flow of an inert solvent through the core during electrochemical functionalization. The selectivity between Ru(bi-pyridine)(3)2+ and methyl viologen2+ flux is found to be as high as 23 with -130 mV bias applied to the membrane as the working electrode. Changes in the flux and selectivity support a model where charged tethered molecules at the tips are drawn into the CNT core at positive bias. For molecules grafted along the CNT core, negative bias extends the tethered molecules into the core. Electrostatically actuated tethers induce steric hindrance in the CNT core to mimic voltage gated ion channels in a robust large area platform.     

Mathematical modelling of adsorption and transport processes in capillary electrochromatography: open-tubular geometry

A mathematical modelling approach for open-tubular capillary electrochromatography is presented. The spatially one-dimensional model takes into account (i) a coupling of (non)linear adsorption of positively or negatively charged analyte molecules (at a negatively charged capillary inner surface) with the equilibrium electrokinetics at this solid-liquid interface, (ii) mobile phase transport by electroosmosis and pressure-driven flow, as well as (iii) transport of species by electrophoresis and molecular diffusion. Under these conditions the local zeta-potential and electroosmotic mobility become a function of the concentration of the charged analyte. The resulting inhomogeneity of electroosmotic flow through the capillary produces a compensating pore pressure as requirement for incompressible mobile phase flow (i.e., for constant volumetric flow along the capillary). The results of the simulations are discussed in view of the surface-to-volume ratio of the capillary lumen, the analyte concentration (in combination with a Langmuir isotherm for the adsorption process), and buffer effects.     

Shear viscosity of molten alkali halides from equilibrium and nonequilibrium molecular-dynamics simulations

The shear viscosity of molten NaCl and KCl was calculated through equilibrium (EMD) and nonequilibrium molecular-dynamics (NEMD) simulations in the canonical (N,V,T) ensemble. Two rigid-ion potentials were investigated, namely, the Born-Mayer-Huggins-Tosi-Fumi potential and the Michielsen-Woerlee-Graaf-Ketelaar potential with the parameters proposed by Ladd. The NEMD simulations were performed using the SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] with a Gaussian isokinetic thermostat and the results are compared with those obtained from Green-Kubo EMD (N,V,T) simulations and experimental shear viscosity data. The NEMD zero strain rate shear viscosity, eta(0), was obtained by fitting a simplified Carreau-type equation and by application of mode-coupling theory, i.e., a eta-gamma(1/2) linear relationship. The values obtained from the first method are found to be significantly lower than those predicted by the second. The agreement between the EMD and NEMD results with experimental data is satisfactory for the two potentials investigated. The ion-ion radial distribution functions obtained with the two rigid-ion potentials for both molten salts are discussed in terms of the differences between the two models.     

Fluorine-functionalized nanoporous graphene as an effective membrane for water desalination

Most water in the world is as saline water in seas and oceans. Desalination technology is a promising method to solve the global water crisis. Recently, many attentions have been paid to the graphene-based membranes in water desalination due to their low production cost and high efficiency. In this paper, molecular dynamics simulations are employed to investigate the effect of functionalized graphene nanosheet (GNS) membranes on the performance of salt separation from seawater in terms of water permeability and salt rejection. For this purpose, the hydrogenated (–H) and fluorinated (–F) pores were created on the GNS membrane. Then, the functionalized graphene membrane was placed in the middle of the simulation box in an aqueous ionic solution containing Na⁺ and Cl^? ions. The applied pressure (in the range of 10–100 MPa) was used as the driving force for transport of water molecules across the reverse osmosis (RO) graphene-based membrane in order to obtain the water permeability and salt rejection. Also, radial distribution functions (RDFs) of ion–water and water–water as well as the water density map around the membrane were obtained. The results indicated that the hydrophilic chemical functions such as fluorine (–F) can improve the water permeability at low pressures.

     

Biomimetic Approach for Highly Selective Artificial Water Channels Based on Tubular Pillar[5]arene Dimers

Artificial water channels mimicking natural aquaporins (AQPs) can be used for selective and fast transport of water. Here, we quantify the transport performances of peralkyl-carboxylate-pillar[5]arenes dimers in bilayer membranes. They can transport ≈10⁷ water molecules/channel/second, within one order of magnitude of the transport rates of AQPs, rejecting Na⁺ and K⁺ cations. The dimers have a tubular structure, superposing pillar[5]arene pores of 5 Å diameter with twisted carboxy-phenyl pores of 2.8 Å diameter. This biomimetic platform, with variable pore dimensions within the same structure, offers size restriction reminiscent of natural proteins. It allows water molecules to selectively transit and prevents bigger hydrated cations from passing through the 2.8 Å pore. Molecular simulations prove that dimeric or multimeric honeycomb aggregates are stable in the membrane and form water pathways through the bilayer. Over time, a significant shift of the upper vs. lower layer occurs initiating new unexpected water permeation events through toroidal pores.     

Flow structure of water in carbon nanotubes: poiseuille type or plug-like?

We have conducted molecular dynamics simulations of water flow in carbon nanotubes (CNTs) for (6,6) to (20,20) CNTs at a streaming velocity of 100 ms. The fluidized piston model (FPM) and the ice piston model (IPM) are employed to drive flow through the CNTs. The results show that the single-file water flow inside (6,6) CNT has a convex upward streaming velocity profile, whereas the velocity profiles in (10,10) to (20,20) CNTs are flat except near the tube wall. The flow structure of cylindrical water in the (8,8) CNT is intermediate between that for the (6,6) CNT and the larger CNTs. The flow parameters are found not to exhibit any dependence on streaming velocity at up to 300 ms in the (12,12) CNT. The hydrogen bond lifetimes of water flowing in CNTs tend to be longer than for the corresponding equilibrium states, and nonzero flow does not reduce the microscopic structure or structural robustness (hydrogen bond lifetime). Although the atomic density profile varies with tube diameter, reflecting the change in static microscopic structure of flow from single file to cylindrical, tube diameter does not induce a clear transition in streaming velocity, temperature, or hydrogen bond lifetime over this diameter range. The results suggest that water flow in CNTs of this size is more pluglike than Poiseuille type, although the flow structure does not strictly accord with either definition.     

Computer modelling of adsorbate transport in nanospaces

The passage of adsorbed molecules, through pores of nanometre dimensions, under a concentration gradient, is important in several processes. The basic equations for single-component flow in pores identify a diffusive and cooperative (viscous) component to the flux. Three simulation techniques, including non-equilibrium molecular dynamics (NEMD), have been used to investigate (spherical) methane and ethane adsorbates in model graphite pores at ambient temperatures. The NEMD method measures flux directly and shows an interesting behaviour in the total diffusion coefficients, including transitions and values substantially in excess of the Darken diffusion coefficient, calculated from self-diffusion. A simple Stokes–Einstein type of model can account for some results. The instances where this model fails can be rationalised in terms of confinement effects, and the relative contribution of kinetic energy to the Hamiltonian.