Molecular dynamics simulations of ion transport through carbon nanotubes. I. Influence of geometry, ion specificity, and many-body interactions

Impact of Confinement and Zwitterionic Ligand Chemistry on Ion-Ion Selectivity of Functionalized Nanopores

Membranes incorporating zwitterionic chemistries have recently emerged as promising candidates for facilitating challenging ion-ion separations. Transport of ions in such membranes predominantly occurs in hydrated nanopores lined with zwitterionic monomers. To shed light on the physics of ion-ion selectivity underlying such materials, we conducted molecular dynamics simulations of sodium halide transport in model nanopores grafted with sulfobetaine methacrylate molecules. Our results reveal that in both functionalized and unfunctionalized nanopores smaller ions prefer to reside near the pore center, while the larger ions tend to reside near the pore walls. An enhancement in the selective transport of larger anions is observed within the unfunctionalized nanopores relative to that in salt-in-water solutions. Upon functionalization of the nanopores with zwitterions (ZIs), the disparities in the anionic distribution profiles within the pores coupled with differences in the anion-ZI interactions result in a slowdown of larger anions relative to smaller anions. Increasing the ZI grafting density exacerbates these effects, further promoting the selective transport of smaller anions. Our results suggest that selectivity toward large anions can be realized by using nanoporous membranes with ZI content that is high enough to facilitate ion/water partitioning into the pores while preserving the characteristic tendency of the unfunctionalized pores to facilitate faster transport of the larger anions. On the other hand, selectivity toward smaller anions can be achieved by targeting ZI content within the pores that is high enough to significantly slow down the transport of large anions but not high enough to hinder the partitioning of ions/water molecules into the pore due to steric effects.

Correlations in Charged Multipore Systems: Implications for Enhancing Selectivity and Permeability in Nanoporous Membranes

Nanoporous membranes have emerged as powerful tools for diverse applications, including gas separation and water desalination. Achieving high permeability for desired molecules alongside exceptional rejection of other species presents a significant design challenge. One potential strategy involves optimizing the chemistry and geometry of isolated nanopores to enhance permeability and selectivity while maximizing their density within a membrane. However, the impact of the pore proximity on membrane performance remains an open question. Through path sampling simulations of model graphitic membranes with multiple subnanometer pores, we reveal that nanoscale proximity between pores detrimentally affects water permeability and salt rejection. Specifically, counterion transport is decelerated, while co-ion transport is accelerated, due to direct interactions among water molecules, salt ions, and the dipoles within neighboring pores. Notably, the observed ionic transport time scales significantly deviate from established theories such as the access resistance model but are well explained using the simple phenomenological model that we develop in this work. We use this model to prescreen and optimize pore arrangements that elicit minimal correlations at a target pore density. These findings deepen our understanding of multipore systems, informing the rational design of nanoporous membranes for enhanced separation processes such as water desalination. They also shed light on the physiology of biological cells that employ ion channel proteins to modulate ion transport and reversal potentials.

Ideal conductor/dielectric model (ICDM): A generalized technique to correct for finite-size effects in molecular simulations of hindered ion transport

Molecular simulations serve as indispensable tools for investigating the kinetics and elucidating the mechanism of hindered ion transport across nanoporous membranes. In particular, recent advancements in advanced sampling techniques have made it possible to access translocation timescales spanning several orders of magnitude. In our prior study [Shoemaker et al., J. Chem. Theory Comput. 18, 7142 (2022)], we identified significant finite size artifacts in simulations of pressure-driven hindered ion transport through nanoporous graphitic membranes. We introduced the ideal conductor model, which effectively corrects for such artifacts by assuming the feed to be an ideal conductor. In the present work, we introduce the ideal conductor dielectric model (Icdm), a generalization of our earlier model, which accounts for the dielectric properties of both the membrane and the filtrate. Using the Icdm model substantially enhances the agreement among corrected free energy profiles obtained from systems of varying sizes, with notable improvements observed in regions proximate to the pore exit. Moreover, the model has the capability to consider secondary ion passage events, including the transport of a co-ion subsequent to the traversal of a counter-ion, a feature that is absent in our original model. We also investigate the sensitivity of the new model to various implementation details. The Icdm model offers a universally applicable framework for addressing finite size artifacts in molecular simulations of ion transport. It stands as a significant advancement in our quest to use molecular simulations to comprehensively understand and manipulate ion transport processes through nanoporous membranes.

Free energy change in the complete transport of all water molecules through a carbon nanotube

In this work, we investigated the free energy barrier for transporting water molecules from one place to another. To properly address this issue, we considered a simple model system in which two separate compartments were connected via a subnanometer channel; all water molecules were initially in one compartment, and the other compartment was empty. Using umbrella sampling in molecular dynamics simulations, we calculated the free energy change for transporting all water molecules to the initially empty compartment. The free energy profile clearly indicated the presence of a free energy barrier, and the magnitude and shape of the barrier were dependent on the number of water molecules to be transported. To better understand the nature of the profile, we performed additional analyses on the potential energy of the system and hydrogen bonding between water molecules. Our study sheds light on a method for calculating the free energy of a transport system as well as the fundamental aspects of water transport.

Ideal Conductor Model: An Analytical Finite-Size Correction for Nonequilibrium Molecular Dynamics Simulations of Ion Transport through Nanoporous Membranes

Modulating ion transport through nanoporous membranes is critical to many important chemical and biological separation processes. The corresponding transport timescales, however, are often too long to capture accurately using conventional molecular dynamics (MD). Recently, path sampling techniques, such as forward-flux sampling (FFS), have emerged as attractive alternatives for efficiently and accurately estimating arbitrarily long ionic passage times. Here, we use non-equilibrium MD and FFS to explore how the kinetics and mechanisms of pressure-driven chloride transport through a nanoporous graphitic membrane are affected by its lateral dimensions. We not only find ionic passage times and free energy barriers to decrease dramatically upon increasing the membrane surface area but also observe an abrupt and discontinuous change in the locus of the transition state. These strong finite size effects arise due to the cumulative effect of the periodic images of the leading ion entering the pore on the distribution of the induced excess charge at the membrane surface in the feed. By assuming that the feed is an ideal conductor, we analytically derive a finite size correction term that can be computed from the information obtained from a single simulation and successfully use it to obtain corrected free energy profiles with no dependence on the system size. We then estimate ionic passage times in the thermodynamic limit by assuming an Eyring-type dependence of rates on barriers with a size-independent prefactor. This approach constitutes a universal framework for removing finite size artifacts in molecular simulations of ion transport through nanoporous membranes and biological channel proteins.

Molecular Dynamics Simulation of Transport Mechanism of Graphene Quantum Dots Through Different Cell Membranes

Exploring the mechanisms underlying the permeation of graphene quantum dots (GQDs) through different cell membranes is key for the practical application of GQDs in medicine. Here, the permeation process of GQDs through different lipid membranes was evaluated using molecular dynamics (MD) simulations. Our results showed that GQDs can easily permeate into 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) lipid membranes with low phospholipid molecule densities but cannot permeate into 1-palmitoyl-2-oleoyl phosphatidylethanolamine (POPE) lipid membranes with high phospholipid densities. Free energy calculation showed that a high-energy barrier exists on the surface of the POPE lipid membrane, which prevents GQDs from entering the cell membrane interior. Further analysis of the POPE membrane structure showed that sparsely arranged phospholipid molecules of the low-density lipid membrane facilitated the entry of GQDs into the interior of the membrane, compared to compactly arranged molecules in the high-density lipid membrane. Our simulation study provides new insights into the transmembrane transport of GQDs.

Putting together the puzzle of ion transfer in single-digit carbon nanotubes: mean-field meets ab initio

Nature employs channel proteins to selectively pass water across cell membranes, which inspires the search for bio-mimetic analogues. Carbon nanotube porins (CNTPs) are intriguing mimics of water channels, yet ion transport in CNTPs still poses questions. As an alternative to continuum models, here we present a molecular mean-field model that transparently describes ion coupling, yet unlike continuum models, computes ab initio all required thermodynamic quantities for the KCl salt and H⁺ and OH^- ions present in water. Starting from water transfer, the model considers the transfer of free ions, along with ion-pair formation as a proxy of non-mean-field ion-ion interactions. High affinity to hydroxide, suggested by experiments, making it a dominant charge carrier in CNTPs, is revealed as an exceptionally favorable transfer of KOH pairs. Nevertheless, free ions, coexisting with less mobile ion-pairs, apparently control ion transport. The model well explains the observed effects of salt concentration and pH on conductivity, transport numbers, anion permeation and its activation energies, and current rectification. The proposed approach is extendable to other sub-nanochannels and helps design novel osmotic materials and devices.

Highly efficient desalination performance of carbon honeycomb based reverse osmosis membranes unveiled by molecular dynamics simulations

Seawater desalination is vital to our modern civilization. Here, we report that the carbon honeycomb (CHC) has an outstanding water permeability and salt rejection in the seawater desalination, as revealed by molecular dynamics simulations. More than 92% of ions are rejected by CHC at applied pressures ranging from 50 to 250 MPa. CHC has a perfect salt rejection at pressures below 150 Mpa. On increasing the applied pressure up to 150 MPa, the salt rejection reduces only to 92%. Pressure, temperature and temperature gradient are noted to play a significant role in modulating the water flux. The water flux increases with pressure and temperature. With the introduction of a temperature gradient of 3.5 K nm^-1, the seawater permeability increases by 33% as compared to room temperature. The water permeability of the CHC is greater than other carbon materials and osmosis membranes including graphene (8.7 times) and graphyne (2.1 times). It indicates the significant potential of the CHC for commercial application in water purification.

Associated molecular liquids at the graphene monolayer interface

We report molecular simulations of the interaction between a graphene sheet and different liquids such as water, ethanol, and ethylene glycol. We describe the structural arrangements at the graphene interface in terms of density profiles, number of hydrogen bonds (HBs), and local structuration in neighboring layers close to the surface. We establish the formation of a two-dimensional HB network in the layer closest to the graphene. We also calculate the interfacial tension of liquids with a graphene monolayer and its profile along the direction normal to the graphene to rationalize and quantify the strengthening of the intermolecular interactions in the liquid due to the presence of the surface.

The effect of an electric field on ion separation and water desalination using molecular dynamics simulations

Using molecular dynamics simulations, we analyze ion separation and water purification through a piston-driven graphene/carbon-nanotube filter in the presence of an external electric field. Three different magnitudes of electric field are applied along the nanotube's axial direction with the goal of separating sodium and chloride ions in a NaCl aqueous solution. For comparison purposes, we also study the same system in zero fields. Our results show that sufficiently large values of the electric field strength greatly improve the ion separation process. At the highest field strength, the theoretical efficiency of the filter in removing salt from water exceeds 95% indicating its applicability in commercial filtration processes to produce fresh water. These results suggest that the proposed set-up can be used to design highly efficient nanostructured membranes for water desalination.

Electric control of ionic transport in sub-nm nanopores

The ion transport behavior through sub-nm nanopores (length (L) ≈ radius (R)) on a film is different from that in nanochannels (L ≫ R), and even more different from the bulk behavior. The many intriguing phenomena in ionic transport are the key to the design and fabrication of solid-state nanofluidic devices. However, ion transport through sub-nm nanopores is not yet clearly understood. We investigate the ionic transport behavior of sub-nm nanopores from the perspective of conductance via molecular dynamics (MD) and experimental methods. Under the action of surface charge, the average ion concentration inside the nanopore is much higher than the bulk value. It is found that 100 mM is the transition point between the surface-charge-governed and the bulk behavior regimes, which is different from the transition point for nanochannels (10 mM). Moreover, by investigating the access, pores, surface charge, electroosmosis and potential leakage conductance, it is found that the conductive properties of the nanopore at low bulk concentration are determined by the surface charge potential leaks into the reservoir. Specifically, there is a huge increase in cation mobility through a cylindrical nanopore, which implies potential applications for the fast charging of supercapacitors and batteries. Sub-nm nanopores also show a strong selectivity toward Na⁺, and a strong repellence toward Cl⁻. These conclusions presented here will be useful not only in understanding the behavior of ion transport, but also in the design of nanofluidic devices.

The ion transport behavior through sub-nm nanopores (length (L) ≈ radius (R)) on a film is different from that in nanochannels (L ≫ R), and even more different from the bulk behavior.

The effect of temperature on water desalination through two-dimensional nanopores

Two-dimensional (2D) materials such as graphene, molybdenum sulfide, and hexagonal boron nitride are widely studied for separation applications such as water desalination. Desalination across such 2D nanoporous membranes is largely influenced by the bulk transport properties of water, which are, in turn, sensitive to the operating temperature. However, there have been no studies on the effect of temperature on desalination through 2D nanopores. We investigated water desalination through hydrogen functionalized graphene nanopores of varying pore areas at temperatures 275.0 K, 300.0 K, 325.0 K, and 350.0 K. The water flux showed a direct relation with the diffusion coefficient and an inverse relation with the hydrogen-bond lifetime. As a direct consequence, the water flux was found to be related to the temperature as per the Arrhenius equation, similar to an activated process. The results from the present study improve the understanding on water and ion permeation across nanoporous 2D materials at different temperatures. Furthermore, the present investigation suggests a kinetic model, which can predict the water and ion permeation based on the characteristics of the nanopore.

Ultrahigh Permeable C2N-Inspired Graphene Nanomesh Membranes versus Highly Strained C2N for Reverse Osmosis Desalination

The reverse osmosis (RO) desalination capability of hydrogenated and hydroxylated graphene nanomesh membranes (GNMs) inspired by the morphology of carbon nitride (C₂N) has been studied by using molecular dynamics simulation. As an advantage, water permeance of the GNMs is found to be several orders of magnitude higher than that of the available RO filters and comparable with highly strained C₂N (S-C₂N) as follows: 6,6-H,OH > 12-H > S-C₂N > 5,5-H,OH > 10-H. The reverse order is found for salt rejection, regardless of S-C₂N. The hydrophilic character of the incorporated -OH functional group is believed to be responsible for linking the water molecules in feed and permeate sides via the formation of strong hydrogen bonds. This leads to a remarkable reduction in resistance of water molecules during penetration across GNMs. In fact, water permeance and salt rejection of the GNMs are controllable by adjusting the effective size and chemistry of their nanopores, while these kinds of adjustments are principally impossible for C₂N, resulting in limiting the water permeance. More importantly, the C₂N nanofilter works efficiently only under high tensile strain, which is not so straightforward in practice. These observations are also verified by computing electrostatic potential map interaction and barrier energies for transportation of water molecules/ions through GNMs based on quantum chemistry aspects.

Equilibration of molecules between two compartments through a nanochannel in the presence of osmolytes: a molecular dynamics simulation study

Osmolytes can drain an initially filled compartment and induce the complete transfer of molecules to another unfilled compartment.

Carboxylated carbon nanotubes corked with tetraalkylammonium cations: A concept of nanocarriers in aqueous solutions

An explicit water molecular dynamics simulations were used to probe (6,6) and (9,9) single-walled carbon nanotubes, functionalized with three carboxylate ion groups at each of the two openings, as potential nanocarriers in aqueous solutions. Three tetraalkylammonium cations (i.e., tetraethyl-, tetrapropyl-, and tetrabuthylammonium) were tested as corks to cap the nanotube openings. The variation of the sizes of the nanotubes (diameter) and of the cork cations (bulkiness) allowed us to select the proper corks that fit the nanotube openings best. Smaller tetraalkylammonium ions could easily fit the openings, but since they are less hydrophobic compared to their larger analogues they showed less affinity for the interior of the nanotubes. On the other hand, the hydrophobicity (and thus the affinity for the nanotubes) can be adjusted through the increase of tetraalkylammonium cation size, providing that the cork still fits the opening. Additionally, an external electric field was tested as a means of nanotube uncorking. The field is capable of disjoining corked ions from the functionalized nanotube openings, triggering in this way a potential cargo release stored inside the nanotubes.

Multilevel Molecular Modeling Approach for a Rational Design of Ionic Current Sensors for Nanofluidics

The complexity displayed by nanofluidic-based systems involves electronic and dynamic aspects occurring across different size and time scales. To properly model such kind of system, we introduced a top-down multilevel approach, combining molecular dynamics simulations (MD) with first-principles electronic transport calculations. The potential of this technique was demonstrated by investigating how the water and ionic flow through a (6,6) carbon nanotube (CNT) influences its electronic transport properties. We showed that the confinement on the CNT favors the partially hydrated Na, Cl, and Li ions to exchange charge with the nanotube. This leads to a change in the electronic transmittance, allowing for the distinguishing of cations from anions. Such an ionic trace may handle an indirect measurement of the ionic current that is recorded as a sensing output. With this case study, we are able to show the potential of this top-down multilevel approach, to be applied on the design of novel nanofluidic devices.

Ultra-fast vapor generation by a graphene nano-ratchet: a theoretical and simulation study

Vapor generation is of prime importance for a broad range of applications: domestic water heating, desalination and wastewater treatment, etc. However, slow and inefficient evaporation limits its development. In this study, a nano-ratchet, a multilayer graphene with cone-shaped nanopores (MGCN), to accelerate vapor generation has been proposed. By performing molecular dynamics simulation, we found that air molecules were spontaneously transported across MGCN and resulted in a remarkable pressure difference, 21 kPa, between the two sides of MGCN. We studied the dependence of the pressure difference on the ambient temperature and geometry of MGCN in detail. Through further analysis of the diffusive transport, we found that pressure difference depended on the competition between ratchet transport and Knudsen diffusion and it was further found that ratchet transport is dominant. The significant pressure difference could lead to a 15-fold or greater enhancement of vapor generation, which shows the wide applications of this nano-ratchet.

Voltage-activated transport of ions through single-walled carbon nanotubes

Ionic transport through single-walled carbon nanotubes (SWCNTs) is promising for many applications but remains both experimentally challenging and highly debated. Here we report ionic current measurements through microfluidic devices containing one or several SWCNTs of diameter of 1.2 to 2 nm unexpectedly showing a linear or a voltage-activated I-V dependence. Transition from an activated to a linear behavior, and stochastic fluctuations between different current levels were notably observed. For linear devices, the high conductance confirmed with different chloride salts indicates that the nanotube/water interface exhibits both a high surface charge density and flow slippage, in agreement with previous reports. In addition, the sublinear dependence of the conductance on the salt concentration points toward a charge-regulation mechanism. Theoretical modelling and computer simulations show that the voltage-activated behavior can be accounted for by the presence of local energy barriers along or at the ends of the nanotube. Raman spectroscopy reveals strain fluctuations along the tubes induced by the polymer matrix but displays insufficient doping or variations of doping to account for the apparent surface charge density and energy barriers revealed by ion transport measurements. Finally, experimental evidence points toward environment-sensitive chemical moieties at the nanotube mouths as being responsible for the energy barriers causing the activated transport of ions through SWCNTs within this diameter range.

Tunable phenol remediation from wastewater using SWCNT-based, sub-nanometer porous membranes: reactive molecular dynamics simulations and DFT calculations

Reactive molecular dynamic (MD) simulations and first-principle density functional theory (DFT) calculations were used to investigate the performance of SWCNT-based, sub-nanometer porous membranes for phenol remediation from wastewater.

Investigating the Potential of Single-Walled Aluminosilicate Nanotubes in Water Desalination

Water shortage has become a critical issue. To facilitate the large-scale deployment of reverse-osmosis water desalination to produce fresh water, discovering novel membranes is essential. Here, we computationally demonstrate the great potential of single-walled aluminosilicate nanotubes (AlSiNTs), materials that can be synthesized through scalable methods, in desalination. State-of-the-art molecular dynamics simulations were employed to investigate the desalination performance and structure-performance relationship of AlSiNTs. Free energy profiles, passage time distribution, and water density map were also analyzed to further understand the dependence of transport properties on diameter and water dynamics in the nanotubes. AlSiNTs with an inner diameter of 0.86 nm were found to fully reject NaCl ions while allowing orders of magnitude higher water fluxes compared to currently available reverse osmosis membranes, providing opportunities in water desalination.

Significant curvature effects of partially charged carbon nanotubes on electrolyte behavior investigated using Monte Carlo simulations

Carbon nanotubes and graphene are among the major nanomaterials in nanoscience and technology. Despite having π electrons, these nanocarbon allotropes have been simply considered as neutral in classical calculations. In this study, the effects of partial charges on graphene and curved interfaces on molecular adsorption were investigated using Monte Carlo simulations of N2 and NaCl aqueous solutions on graphene and carbon nanotubes. The simulated N2 adsorption behavior and adsorption potential on partially charged and non-charged graphene coincided with each other. The adsorption potentials suggested that partially charged graphene attracted Na ions and repelled Cl ions. However, those tendencies were not present in NaCl aqueous solutions on graphene. Conversely, in partially charged carbon nanotube models, a preference for Na ions and repulsion of Cl ions in the internal nanospaces were observed in the adsorption potentials using Monte Carlo simulations. Curved interfaces in the internal nanospaces of carbon nanotubes enhanced these properties, suggesting significant electrostatic interactions in a curved π-conjugated system.

Multilayer Nanoporous Graphene Membranes for Water Desalination

While single-layer nanoporous graphene (NPG) has shown promise as a reverse osmosis (RO) desalination membrane, multilayer graphene membranes can be synthesized more economically than the single-layer material. In this work, we build upon the knowledge gained to date toward single-layer graphene to explore how multilayer NPG might serve as a RO membrane in water desalination using classical molecular dynamic simulations. We show that, while multilayer NPG exhibits similarly promising desalination properties to single-layer membranes, their separation performance can be designed by manipulating various configurational variables in the multilayer case. This work establishes an atomic-level understanding of the effects of additional NPG layers, layer separation, and pore alignment on desalination performance, providing useful guidelines for the design of multilayer NPG membranes.

Sensitive Detection of a Modified Base in Single-Stranded DNA by a Single-Walled Carbon Nanotube

In this work, we use molecular dynamics simulations to study the responses of the configuration of single-strand DNA (ssDNA) within a carbon nanotube (CNT) and the concomitant ion flow to a single modified base, i.e., benzoimidazole (Bzim)-modified 5-hydroxymethyl cytosine (5hmC). Our simulation results show the Bzim-modified 5hmC can considerably increase the ion flow through a single-walled carbon nanotube (SWCNT), despite its larger size, which is consistent with prior experimental results. This phenomenon is attributed to enhanced adsorption of DNA to the interior wall of the CNT driven by the Bzim-modified 5hmC, leading to a reduced steric effect on ion transport through the CNT. As revealed in this work, the distribution of ssDNA can be affected by limited change in the interactions with the CNT surface. Such behavior of ssDNA within small-sized CNTs can be exploited to further improve the sensitivity of nanopore detection.

Porous carbon nanotubes: molecular absorption, transport, and separation

We use classical molecular dynamics simulations to study nanofluidic properties of porous carbon nanotubes. We show that saturated water vapor condenses on the porous nanotubes, can be absorbed by them and transported in their interior. When these nanotubes are charged and placed in ionic solutions, they can selectively absorb ions in their interior and transport them. Porous carbon nanotubes can also be used as selective molecular sieves, as illustrated on a room temperature separation of benzene and ethanol.

A mechanical nanogate based on a carbon nanotube for reversible control of ion conduction

Control of mass transport through nanochannels is of critical importance in many nanoscale devices and nanofiltration membranes. The gates in biological channels, which control the transport of substances across cell membranes, can provide inspiration for this purpose. Gates in many biological channels are formed by a constriction ringed with hydrophobic residues which can prevent ion conduction even when they are not completely physically occluded. In this work, we use molecular dynamics simulations to design a nanogate inspired by this hydrophobic gating mechanism. Deforming a carbon nanotube (12,12) with an external force can form a hydrophobic constriction in the centre of the tube that controls ion conduction. The simulation results show that increasing the magnitude of the applied force narrows the constriction and lowers the fluxes of K(+) and Cl(-) found under an electric field. With the exerted force larger than 5 nN, the constriction blocks the conduction of K(+) and Cl(-) due to partial dehydration while allowing for a noticeable water flux. Ion conduction can revert back to the unperturbed level upon force retraction, suggesting the reversibility of the nanogate. The force can be exerted by available experimental facilities, such as atomic force microscope (AFM) tips. It is found that partial dehydration in a continuous water-filled hydrophobic constriction is enough to close the channel, while full dewetting is not necessarily required. This mechanically deformed nanogate has many potential applications, such as a valve in nanofluidic systems to reversibly control ion conduction and a high-performance nanomachine for desalination and water treatment.