Ion transport through a graphene nanopore

Controlling Electroosmosis in Nanopores Without Altering the Nanopore Sensing Region

Nanopores are powerful tools for single-molecule sensing of biomolecules and nanoparticles. The signal coming from the molecule to be analyzed strongly depends on its interaction with the narrower section of the nanopore (constriction) that may be tailored to increase sensing accuracy. Modifications of nanopore constriction have also been commonly used to induce electroosmosis, that favors the capture of molecules in the nanopore under a voltage bias and independently of their charge. However, engineering nanopores for increasing both electroosmosis and sensing accuracy is challenging. Here it is shown that large electroosmotic flows can be achieved without altering the nanopore constriction. Using continuum electrohydrodynamic simulations, it is found that an external charged ring generates strong electroosmosis in cylindrical nanopores. Similarly, for conical nanopores it is shown that moving charges away from the cone tip still results in an electroosmotic flow (EOF), whose intensity reduces increasing the diameter of the nanopore section where charges are placed. This paradigm is applied to engineered biological nanopores showing, via atomistic simulations and experiments, that mutations outside the constriction induce a relatively intense electroosmosis. This strategy provides much more flexibility in nanopore design since electroosmosis can be controlled independently from the constriction, which can be optimized to improve sensing accuracy.

Selective Capture and Manipulation of DNA through Double Charged Nanopores

In the past few decades, nanometer-scale pores have been employed as powerful tools for sensing biological molecules. Owing to its unique structure and properties, solid-state nanopores provide interesting opportunities for the development of DNA sequencing technology. Controlling DNA translocation in nanopores is an important means of improving the accuracy of sequencing. Here we present a proof of principle study of accelerating DNA captured across targeted graphene nanopores using surface charge density and find the intrinsic mechanism of the combination of electroosmotic flow induced by charges of nanopore and electrostatic attraction/repulsion between the nanopore and ssDNA. The theoretical study performed here provides a new means for controlling DNA transport dynamics and makes better and cheaper application of graphene in molecular sequencing.

Construction of angstrom-scale ion channels with versatile pore configurations and sizes by metal-organic frameworks

Controllable fabrication of angstrom-size channels has been long desired to mimic biological ion channels for the fundamental study of ion transport. Here we report a strategy for fabricating angstrom-scale ion channels with one-dimensional (1D) to three-dimensional (3D) pore structures by the growth of metal-organic frameworks (MOFs) into nanochannels. The 1D MIL-53 channels of flexible pore sizes around 5.2 × 8.9 Å can transport cations rapidly, with one to two orders of magnitude higher conductivities and mobilities than MOF channels of hybrid pore configurations and sizes, including Al-TCPP with 1D ~8 Å channels connected by 2D ~6 Å interlayers, and 3D UiO-66 channels of ~6 Å windows and 9 - 12 Å cavities. Furthermore, the 3D MOF channels exhibit better ion sieving properties than those of 1D and 2D MOF channels. Theoretical simulations reveal that ion transport through 2D and 3D MOF channels should undergo multiple dehydration-rehydration processes, resulting in higher energy barriers than pure 1D channels. These findings offer a platform for studying ion transport properties at angstrom-scale confinement and provide guidelines for improving the efficiency of ionic separations and nanofluidics.

Molecular modeling of thin-film nanocomposite membranes for reverse osmosis water desalination

The scarcity of freshwater resources is a major global challenge causedby population and economic growth. Water desalination using a reverse osmosis (RO) membrane is a promising technology to supply potable water from seawater and brackish water. The advancement of RO desalination highly depends on new membrane materials. Currently, the RO technology mainly relies on polyamide thin-film composite (TFC) membranes, which suffer from several drawbacks (e.g., low water permeability, permeability-selectivity tradeoff, and low fouling resistance) that hamper their real-world applications. Nanoscale fillers with specific characteristics can be used to improve the properties of TFC membranes. Embedding nanofillers into TFC membranes using interfacial polymerization allows the creation of thin-film nanocomposite (TFNC) membranes, and has become an emerging strategy in the fabrication of high-performance membranes for advanced RO water desalination. To achieve optimal design, it is indispensable to search for reliable methods that can provide fast and accurate predictions of the structural and transport properties of the TFNC membranes. However, molecular understanding of permeability-selectivity characteristics of nanofillers remains limited, partially due to the challenges in experimentally exploring microscopic behaviors of water and salt ions in confinement. Molecular modeling and simulations can fill this gap by generating molecular-level insights into the effects of nanofillers' characteristics (e.g., shape, size, surface chemistry, and density) on water permeability and ion selectivity. In this review, we summarize molecular simulations of a diverse range of nanofillers including nanotubes (carbon nanotubes, boron nitride nanotubes, and aquaporin-mimicking nanochannels) and nanosheets (graphene, graphene oxide, boron nitride sheets, molybdenum disulfide, metal and covalent organic frameworks) for water desalination applications. These simulations reveal that water permeability and salt rejection, as the major factors determining the desalination performance of TFNC membranes, significantly depend on the size, topology, density, and chemical modifications of the nanofillers. Identifying their influences and the physicochemical processes behind, via molecular modeling, is expected to yield important insights for the fabrication and optimization of the next generation high-performance TFNC membranes for RO water desalination.

Effective Modulation of Ion Mobility through Solid-State Single-Digit Nanopores

Many experimental studies have proved that ion dynamics in a single-digit nanopore with dimensions comparable to the Debye length deviate from the bulk values, but we still have critical knowledge gaps in our understanding of ion transport in nanoconfinement. For many energy devices and sensor designs of nanoporous materials, ion mobility is a key parameter for the performance of nanofluidic equipment. However, investigating ion mobility remains an experimental challenge. This study experimentally investigated the monovalent ion dynamics of single-digit nanopores from the perspective of ionic conductance. In this article, we present a theory that is sufficient for a basic understanding of ion transport through a single-digit nanopore, and we subdivided and separately analyzed the contribution of each conductance component. These conclusions will be useful not only in understanding the behavior of ion migration but also in the design of high-performance nanofluidic devices.

Separation of C1/C3 binary organic gas mixtures via flexible nanoporous carbon molecular sieves: DFT calculations and MD simulations

The C₁/C₃ hydrocarbon gas separation characteristics of nanoporous carbon molecular sieves (CMS) are studied using DFT calculations and MD simulations. To efficiently separate the equimolar CH₄/C₃H₈ and CH₄/C₃H₆ gas mixtures, CNT gas transport channels are embed between the polyphenylene membranes which created structural deformation for both CNT and membrane. The adsorption and permeation of gas molecules via CMS and the effect of nanochannel density and electric field on gas selectivity are analyzed. In addition to the direct permeation, gas molecules that adsorbed on the NPG surface also making a significant contribution to the gas permeability comes from a surface mechanism. Results also uncovered that the gas selectivity is enhanced by the electric field along the + x and +y axes, whereas reduced by the electric field along the + z and -z axes. Plainly, this CMS provides a feasible way for the efficient separation of the C₁/C₃ organic gas mixtures.

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.

Controlling ion transport in a C2N-based nanochannel with tunable interlayer spacing

Selective ion transport through a nanochannel formed by stacked two-dimensional materials plays a key role in water desalination, nanofiltration, and ion separation. Although there have been many functional nanomaterials used in these applications, how to well control ion transport in a laminar structure so as to obtain the desired selectivity still remains a challenging problem. In the present work, the transport of ions through a C₂N-based nanochannel is investigated by using all-atom molecular dynamics simulation. It is found that C₂N-based nanochannels with different interlayer spacing posses diverse ion selectivity, which is mainly attributed to the distinct loading capability among ions and the different velocity of ions inside the nanochannel. Moreover, we also find that the ion selectivity is dependent on the electric field, but nearly independent of the salt concentration. The present study may provide some physical insights into the experimental design of C₂N-based nanodevices in nanofiltration.

Transport of hydrated nitrate and nitrite ions through graphene nanopores in aqueous medium

Nitrate ( NO 3 - ) and nitrite ( NO 2 - ) ions are naturally occurring inorganic ions that are part of the nitrogen cycle. High doses of these ions in drinking water impose a potential risk to public health. In this work, molecular dynamics simulations are carried out to study the passage of nitrate and nitrite ions from water through graphene nanosheets (GNS) with hydrogen-functionalized narrow pores in presence of an external electric field. The passage of ions through the pores is investigated through calculations of ion flux, and the results are analyzed through calculations of various structural and thermodynamic properties such as the density of ions and water, ion-water radial distribution functions, two-dimensional density distribution functions, and the potentials of mean force of the ions. Current simulations show that the nitrite ions can pass more in numbers than the nitrate ions in a given time through GNS hydrogen-functionalized pore of different geometry. It is found that the nitrite ions can permeate faster than the nitrate ions despite the former having higher hydration energy in the bulk. This can be explained in terms of the competition between the number density of the ions along the pore axis and the free energy barrier calculated from the potential of mean force. Also, an externally applied electric field is found to be important for faster permeation of the nitrite over the nitrate ions. The current study suggests that graphene nanosheets with carefully created pores can be effective in achieving selective passage of ions from aqueous solutions.

Computational investigation of geometrical effects in 2D boron nitride nanopores for DNA detection

Nanopore-based DNA detection and analysis have been intensively pursued theoretically and experimentally over the past decade. Owing to their nanometer thickness, 2D nanopores, such as boron nitride nanopores, show great potential for achieving DNA detection at base resolution. Although 2D nanopore devices hold great promise for next-generation DNA detection, efficiently and reliably detecting different DNA sequences is still a challenging problem. To date, most of the investigated nanopores adopt circular shapes. Because of the successful fabrication of triangular nanopores, investigating the shape effect of nanopores for DNA detection has become more and more important. In this study, boron nitride nanopores with circular, hexagonal, quadrangular and triangular shapes were modeled at various sizes. The translocation of homogeneous dsDNA through these nanopores was investigated by all-atom molecular dynamic simulations. The ionic conductivity of these nanopores was characterized and formulas for the total resistance based on the pore and access resistance were derived. The ionic current, dwell time and conductance blockade of homogeneous dsDNA were compared for nanopores with different shapes. We demonstrate that the charge distribution at the pore mouth plays an important role in the transportation of ions and DNA molecules. Our findings may shed light on the design of 2D nanopores and can facilitate the development of fast, low-cost and reliable nanopore-based DNA detection.

Exploring the pore charge dependence of K+ and Cl- permeation across a graphene monolayer: a molecular dynamics study

Selective permeation through graphene nanopores is attracting increasing interest as an efficient and cost-effective technique for water desalination and purification. In this work, using umbrella sampling and molecular dynamics simulations with constant electric field, we analyze the influence of pore charge on potassium and chloride ion permeation. As pore charge is increased, the barrier of the potential of mean force (PMF) gradually decreases until it turns into a well split in two subminima. While in the case of K+ this pattern can be explained as an increasing electrostatic compensation of the desolvation cost, in the case of Cl- the pattern can be attributed to the accumulation of a concentration polarization layer of potassium ions screening pore charge. The analysis of potassium PMFs in terms of forces revealed a conflicting influence on permeation of van der Waals and electrostatic forces that both undergo an inversion of their direction as pore charge is increased. Even if the most important transition involves the interplay between the electrostatic forces exerted by graphene and water, the simulations also revealed an important role of the changing distribution of potassium and chloride ions. The influence of pore charge on the orientation of water molecules was also found to affect the van der Waals forces they exert on potassium.

Fast and selective fluoride ion conduction in sub-1-nanometer metal-organic framework channels

Biological fluoride ion channels are sub-1-nanometer protein pores with ultrahigh F⁻ conductivity and selectivity over other halogen ions. Developing synthetic F⁻ channels with biological-level selectivity is highly desirable for ion separations such as water defluoridation, but it remains a great challenge. Here we report synthetic F⁻ channels fabricated from zirconium-based metal-organic frameworks (MOFs), UiO-66-X (X = H, NH₂, and N⁺(CH₃)₃). These MOFs are comprised of nanometer-sized cavities connected by sub-1-nanometer-sized windows and have specific F⁻ binding sites along the channels, sharing some features of biological F⁻ channels. UiO-66-X channels consistently show ultrahigh F⁻ conductivity up to ~10 S m⁻¹, and ultrahigh F⁻/Cl⁻ selectivity, from ~13 to ~240. Molecular dynamics simulations reveal that the ultrahigh F⁻ conductivity and selectivity can be ascribed mainly to the high F⁻ concentration in the UiO-66 channels, arising from specific interactions between F⁻ ions and F⁻ binding sites in the MOF channels.

While biological fluoride ion channels display excellent F⁻ conductivity and selectivity, designing synthetic analogues remains highly challenging. Here the authors show that zirconium-based metal–organic frameworks with F⁻ binding sites and sub-1-nanometer channels exhibit ultrahigh F⁻ conductivity and selectivity.

Colloquium: Ionic phenomena in nanoscale pores through 2D materials

Ion transport through nanopores permeates through many areas of science and technology, from cell behavior to sensing and separation to catalysis and batteries. Two-dimensional materials, such as graphene, molybdenum disulfide (MoS2), and hexagonal boron nitride (hBN), are recent additions to these fields. Low-dimensional materials present new opportunities to develop filtration, sensing, and power technologies, encompassing ion exclusion membranes, DNA sequencing, single molecule detection, osmotic power generation, and beyond. Moreover, the physics of ionic transport through pores and constrictions within these materials is a distinct realm of competing many-particle interactions (e.g., solvation/dehydration, electrostatic blockade, hydrogen bond dynamics) and confinement. This opens up alternative routes to creating biomimetic pores and may even give analogues of quantum phenomena, such as quantized conductance, in the classical domain. These prospects make membranes of 2D materials - i.e., 2D membranes - fascinating. We will discuss the physics and applications of ionic transport through nanopores in 2D membranes.

Driven water/ion transport through narrow nanopores: a molecular dynamics perspective

Atomistic Molecular Dynamics (MD) simulations provide numerous insights into the process whereby water is driven through a narrow nanopore (diameter on the order of a few water molecules) by application of hydrostatic pressure. If there are ions in the water, e.g., from dissolved salt, these may be swept along with the flowing water. If the surface of the nanopore is charged, electrostatic interaction between the surface charges and the ions as well as with partial charges on the water molecules will influence the details of the water/ion flow through the channel. Water and ion permeability depend on the geometry of the channel and the degree to which it is charged. Interesting collective features of the water molecules such as water wires that form along the pore axis and rings of water molecules that can insert into the pore perpendicular to the channel axis strongly influence the permeation process, thus emphasizing the importance of molecular level interactions in the mechanism of water and ion flow through conduits with dimensions on the molecular scale.

Effect of pore density on gas permeation through nanoporous graphene membranes

Pore density is an important factor dictating gas separations through one-atom-thin nanoporous membranes, but how it influences the gas permeation is not fully understood. Here we use molecular dynamics (MD) simulations to investigate gas permeation through nanoporous graphene membranes with the same pore size (3.0 Å × 3.8 Å in dimensions) but varying pore densities (from 0.01 to 1.28 nm-2). We find that higher pore density leads to higher permeation per unit area of membrane for both CO2 and He, but the rate of the increase decreases greatly for CO2 at high pore densities. As a result, the per-pore permeance decreases for CO2 but remains relatively constant for He with the pore density, leading to a dramatic change in CO2/He selectivity. By separating the total flux into direct flux and surface flux, we find that He permeation is dominated by direct flux and hence the per-pore permeation rate is roughly constant with the pore density. In contrast, CO2 permeation is dominated by surface flux and the overall decreasing trend of the per-pore permeation rate of CO2 with the pore density can be explained by the decreasing per-pore coverage of CO2 on the feed side with the pore density. Our work now provides a complete picture of the pore-density dependence of gas permeation through one-atom-thin nanoporous membranes.

Incremental update of electrostatic interactions in adaptively restrained particle simulations

The computation of long-range potentials is one of the demanding tasks in Molecular Dynamics. During the last decades, an inventive panoply of methods was developed to reduce the CPU time of this task. In this work, we propose a fast method dedicated to the computation of the electrostatic potential in adaptively restrained systems. We exploit the fact that, in such systems, only some particles are allowed to move at each timestep. We developed an incremental algorithm derived from a multigrid-based alternative to traditional Fourier-based methods. Our algorithm was implemented inside LAMMPS, a popular molecular dynamics simulation package. We evaluated the method on different systems. We showed that the new algorithm's computational complexity scales with the number of active particles in the simulated system, and is able to outperform the well-established Particle Particle Particle Mesh (P3M) for adaptively restrained simulations. © 2018 Wiley Periodicals, Inc.

Maxwell-Hall access resistance in graphene nanopores

The resistance due to the convergence from bulk to a constriction, for example, a nanopore, is a mainstay of transport phenomena. In classical electrical conduction, Maxwell, and later Hall for ionic conduction, predicted this access or convergence resistance to be independent of the bulk dimensions and inversely dependent on the pore radius, a, for a perfectly circular pore. More generally, though, this resistance is contextual, it depends on the presence of functional groups/charges and fluctuations, as well as the (effective) constriction geometry/dimensions. Addressing the context generically requires all-atom simulations, but this demands enormous resources due to the algebraically decaying nature of convergence. We develop a finite-size scaling analysis, reminiscent of the treatment of critical phenomena, that makes the convergence resistance accessible in such simulations. This analysis suggests that there is a "golden aspect ratio" for the simulation cell that yields the infinite system result with a finite system. We employ this approach to resolve the experimental and theoretical discrepancies in the radius-dependence of graphene nanopore resistance.

Ion transport through a nanoporous C2N membrane: the effect of electric field and layer number

Using all-atom molecular dynamic simulations, we show that a monolayer C₂N membrane possesses higher permeability and excellent ion selectivity, and that multilayer C₂N membranes have promising potential for water desalination.

Water desalination using graphene nanopores: influence of the water models used in simulations

Water desalination using graphene nanopores was studied using different water models. The water permeation was found to be influenced by the bulk transport properties and the hydrogen-bond dynamics of the simulated water.

The collision of a hypervelocity massive projectile with free-standing graphene: Investigation of secondary ion emission and projectile fragmentation

We present here the study of the individual hypervelocity massive projectiles (440-540 keV, 33-36 km/s Au₄₀₀⁴⁺ cluster) impact on 1-layer free-standing graphene. The secondary ions were detected and recorded separately from each individual impact in the transmission direction using a time-of-flight mass spectrometer. We observed C_1-10^± ions emitted from graphene, the projectiles which penetrated the graphene, and the Au_1-3^± fragment ions in mass spectra. During the projectile-graphene interaction, the projectile loses ∼15% of its initial kinetic energy (∼0.18 keV/atom, 72 keV/projectile). The Au projectiles are neutralized when approaching the graphene and then partially ionized again via electron tunneling from the hot rims of the holes on graphene, obtaining positive and negative charges. The projectile reaches an internal energy of ∼450-500 eV (∼4400-4900 K) after the impact and then undergoes a ∼90-100 step fragmentation with the ejection of Au₁ atoms in the experimental time range of ∼0.1 μs.

Highly Sensitive and Patchable Pressure Sensors Mimicking Ion-Channel-Engaged Sensory Organs

Biological ion channels have led to much inspiration because of their unique and exquisite operational functions in living cells. Specifically, their extreme and dynamic sensing abilities can be realized by the combination of receptors and nanopores coupled together to construct an ion channel system. In the current study, we demonstrated that artificial ion channel pressure sensors inspired by nature for detecting pressure are highly sensitive and patchable. Our ion channel pressure sensors basically consisted of receptors and nanopore membranes, enabling dynamic current responses to external forces for multiple applications. The ion channel pressure sensors had a sensitivity of ∼5.6 kPa(-1) and a response time of ∼12 ms at a frequency of 1 Hz. The power consumption was recorded as less than a few μW. Moreover, a reliability test showed stability over 10 000 loading-unloading cycles. Additionally, linear regression was performed in terms of temperature, which showed no significant variations, and there were no significant current variations with humidity. The patchable ion channel pressure sensors were then used to detect blood pressure/pulse in humans, and different signals were clearly observed for each person. Additionally, modified ion channel pressure sensors detected complex motions including pressing and folding in a high-pressure range (10-20 kPa).

Water and ion permeability of a claudin model: A computational study

At present, the three-dimensional structure of the multimeric paracellular claudin pore is unknown. Using extant biophysical data concerning the size of the pore and permeation of water and cations through it, two three-dimensional models of the pore are constructed in silico. Molecular Dynamics (MD) calculations are then performed to compute water and sodium ion permeation fluxes under the influence of applied hydrostatic pressure. Comparison to experiment is made, under the assumption that the hydrostatic pressure applied in the simulations is equivalent to osmotic pressure induced in experimental measurements of water/ion permeability. One model, in which pore-lining charged is distributed evenly over a selectivity filter section 10-16 Å in length, is found to be generally consistent with experimental data concerning the dependence of water and ion permeation on channel pore diameter, pore length, and the sign and magnitude of pore lining charge. The molecular coupling mechanism between water and ion flow under conditions where hydrostatic pressure is applied is computationally elucidated.

Analysis of Time-Varying, Stochastic Gas Transport through Graphene Membranes

Molecular transport measurements through isolated nanopores can greatly inform our understanding of how such systems can select for molecular size and shape. In this work, we present a detailed analysis of experimental gas permeation data through single layer graphene membranes under batch depletion conditions parametric in starting pressure for He, H2, Ne, and CO2 between 100 and 670 kPa. We show mathematically that the observed intersections of the membrane deflection curves parametric in starting pressure are indicative of a time dependent membrane permeance (pressure normalized molecular flow). Analyzing these time dependent permeance data for He, Ne, H2, and CO2 shows remarkably that the latter three gases exhibit discretized permeance values that are temporally repeated. Such quantized fluctuations (called "gating" for liquid phase nanopore and ion channel systems) are a hallmark of isolated nanopores, since small, but rapid changes in the transport pathway necessarily influence a single detectable flux. We analyze the fluctuations using a Hidden Markov model to fit to discrete states and estimate the activation barrier for switching at 1.0 eV. This barrier is and the relative fluxes are consistent with a chemical bond rearrangement of an 8-10 atom vacancy pore. Furthermore, we use the relations between the states given by the Markov network for few pores to determine that three pores, each exhibiting two state switching, are responsible for the observed fluctuations; and we compare simulated control data sets with and without the Markov network for comparison and to establish confidence in our evaluation of the limited experimental data set.

Manipulation of a neutral and nonpolar nanoparticle in water using a nonuniform electric field

The manipulation of nanoparticles in water is of essential importance in chemical physics, nanotechnology, medical technology, and biotechnology applications. Generally, a particle with net charges or charge polarity can be driven by an electric field. However, many practical particles only have weak and even negligible charge and polarity, which hinders the electric field to exert a force large enough to drive these nanoparticles directly. Here, we use molecular dynamics simulations to show that a neutral and nonpolar nanoparticle in liquid water can be driven directionally by an external electric field. The directed motion benefits from a nonuniform water environment produced by a nonuniform external electric field, since lower water energies exist under a higher intensity electric field. The nanoparticle spontaneously moves toward locations with a weaker electric field intensity to minimize the energy of the whole system. Considering that the distance between adjacent regions of nonuniform field intensity can reach the micrometer scale, this finding provides a new mechanism of manipulating nanoparticles from the nanoscale to the microscale.

Ion transport in sub-5-nm graphene nanopores

Graphene nanopore is a promising device for single molecule sensing, including DNA bases, as its single atom thickness provides high spatial resolution. To attain high sensitivity, the size of the molecule should be comparable to the pore diameter. However, when the pore diameter approaches the size of the molecule, ion properties and dynamics may deviate from the bulk values and continuum analysis may not be accurate. In this paper, we investigate the static and dynamic properties of ions with and without an external voltage drop in sub-5-nm graphene nanopores using molecular dynamics simulations. Ion concentration in graphene nanopores sharply drops from the bulk concentration when the pore radius is smaller than 0.9 nm. Ion mobility in the pore is also smaller than bulk ion mobility due to the layered liquid structure in the pore-axial direction. Our results show that a continuum analysis can be appropriate when the pore radius is larger than 0.9 nm if pore conductivity is properly defined. Since many applications of graphene nanopores, such as DNA and protein sensing, involve ion transport, the results presented here will be useful not only in understanding the behavior of ion transport but also in designing bio-molecular sensors.

Nanomembrane Containing a Nanopore in an Electrolyte Solution: A Molecular Dynamics Approach

Molecular dynamics simulation is used to acquire information about the characteristics of a nanographene membrane immersed in an electrolyte solution of KCl and subjected to an electric field. The membrane possesses one nanopore. It is shown that the solution contains in addition to hydrated ions, hydrated ion pairs, and hydrated clusters with more than two ions. The fractions of hydrated ions, hydrated ion pairs and hydrated clusters as well as their hydration numbers were also calculated. It was found that the hydration numbers remain constant at low electric fields but decrease at high electric fields. Under the action of an electric field, the K(+) and Cl(-) ions separate on the two sides of graphene, thus generating hydrated ion polarization layers, which result in negative charge density layers and positive ones on the left and right interfaces of the water/graphene. Thus, the neutral graphene becomes asymmetrically charged.

Surface modification of graphene nanopores for protein translocation

Studies of DNA translocation through graphene nanopores have revealed their potential for DNA sequencing. Here we report a study of protein translocation through chemically modified graphene nanopores. A transmission electron microscope (TEM) was used to cut nanopores with diameters between 5 and 20 nm in multilayer graphene prepared by chemical vapor deposition (CVD). After oxygen plasma treatment, the dependence of the measured ionic current on salt concentration and pH was consistent with a small surface charge induced by the formation of carboxyl groups. While translocation of gold nanoparticles (10 nm) was readily detected through such treated pores of a larger diameter, translocation of the protein ferritin was not observed either for oxygen plasma treated pores, or for pores modified with mercaptohexadecanoic acid. Ferritin translocation events were reliably observed after the pores were modified with the phospholipid-PEG (DPPE-PEG750) amphiphile. The ion current signature of translocation events was complex, suggesting that a series of interactions between the protein and pores occurs during the process.

Hydrodynamic flow in the vicinity of a nanopore induced by an applied voltage

Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. The results show the existence of concentration polarization layers on the surfaces of the membrane. The nonuniformity of the ionic distribution gives rise to an electric pressure that drives vortical motion in the fluid. There is also a net hydrodynamic flow through the nanopore due to an asymmetry induced by the membrane surface charge. The qualitative behavior is similar to that observed in a previous study using molecular dynamic simulations. The current-voltage characteristics show some nonlinear features but are not greatly affected by the hydrodynamic flow in the parameter regime studied. In the limit of thin Debye layers, the electric resistance of the system can be characterized using an equivalent circuit with lumped parameters. Generation of vorticity can be understood qualitatively from elementary considerations of the Maxwell stresses. However, the flow strength is a strongly nonlinear function of the applied field. Combination of electrophoretic and hydrodynamic effects can lead to ion selectivity in terms of valences and this could have some practical applications in separations.

Mechanisms of gas permeation through single layer graphene membranes

Graphene has enormous potential as a unique molecular barrier material with atomic layer thickness, enabling new types of membranes for separation and manipulation. However, the conventional analysis of diffusive transport through a membrane fails in the case of single layer graphene (SLG) and other 2D atomically thin membranes. In this work, analytical expressions are derived for gas permeation through such atomically thin membranes in various limits of gas diffusion, surface adsorption, or pore translocation as the rate-limiting step. Gas permeation can proceed via direct gas-phase interaction with the pore, or interaction via the adsorbed phase on the membrane exterior surface. A series of van der Waals force fields allows for the estimation of the energy barriers present for various types of graphene nanopores. These analytical models will assist in the understanding of molecular dynamics and experimental studies of such membranes.