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The ionic selectivity of nanopores is crucial for the energy conversion based on nanoporous membranes. It can be significantly affected by various parameters of nanopores and the applied fields driving ions through porous membranes. Here, with finite element simulations, the selective transport of ions through nanopores is systematically investigated under three common fields, i.e. the electric field (V), hydrostatic pressure (p), and concentration gradient (C). For negatively charged nanopores, through the quantitative comparison of the cation selectivity (t+) under the three fields, the cation selectivity of nanopores follows the order of t+V > t+c > t+p. This is due to the transport characteristics of cations and anions through the nanopores. Because of the strong transport of counterions in electric double layers under electric fields and concentration gradients, the nanopore exhibits a relatively higher selectivity to counterions. We also explored the modulation of t+ on the properties of nanopores and solutions. Under all three fields, t+ is directly proportional to the pore length and surface charge density, and inversely correlated to the pore diameter and salt concentration. Under both the electric field and hydrostatic pressure, t+ has almost no dependence on the applied field strength or ion species, which can affect t+ in the case of the concentration gradient. Our results provide detailed insights into the comparison and regulation of ionic selectivity of nanopores under three fields which can be useful for the design of high-performance devices for energy conversion based on nanoporous membranes., Comment: 28 pages, 5 figures

During the dielectric breakdown process of thin solid-state nanopores, the application of high voltages may cause the formation of multi-nanopores on one chip, which number and sizes are important for their applications. Here, simulations were conducted to mimic the investigation of in situ nanopore detection with scanning ion conductance microscopy (SICM). Results show that SICM can provide accurate nanopore location and relative pore size. Detection resolution is influenced by the dimensions of the applied probe and separation between the probe and membranes, which can be enhanced under large voltages or a concentration gradient., Comment: 22 pages, 6 figuers

Bipolar nanopores, with asymmetric charge distributions, can induce significant ionic current rectification (ICR) at ultra-short lengths, finding potential applications in nanofluidic devices, energy conversion, and other related fields. Here, with simulations, we investigated the characteristics of ion transport and modulation of ICR inside bipolar nanopores. With bipolar nanopores of half-positive and half-negative surfaces, the most significant ICR phenomenon appears at various concentrations. In these cases, ICR ratios are independent of electrolyte types. In other cases where nanopores have oppositely charged surfaces in different lengths, ICR ratios are related to the mobility of anions and cations. The pore length and surface charge density can enhance ICR. As the pore length increases, ICR ratios first increase and then approach their saturation which is determined by the surface charge density. External surface charges of nanopores can promote the ICR phenomenon mainly due to the enhancement of ion enrichment inside nanopores by external surface conductance. The effective width of exterior charged surfaces under various conditions is also explored, which is inversely proportional to the pore length and salt concentration, and linearly related to the pore diameter, surface charge density, and applied voltage. Our results may provide guidance for the design of bipolar porous membranes., Comment: 31 pages, 7 figures

Ionic current rectification (ICR) of charged conical nanopores has various applications in fields including nanofluidics, bio-sensing, and energy conversion, whose function is closely related to the dynamic response of nanopores. The occurrence of ICR originates from the ion enrichment and depletion in conical pores, whose formation is found to be affected by the scanning rate of voltages. Here, through time-dependent simulations, we investigate the variation of ion current under electric fields and the dynamic formation of ion enrichment and depletion, which can reflect the response time of conical nanopores. The response time of nanopores when ion enrichment forms i.e. at the on state is significantly longer than that with the formation of ion depletion i.e. at the off state. Our simulation results reveal the regulation of response time by different nanopore parameters including the surface charge density, pore length, tip, and base radius, as well as the applied conditions such as the voltage and bulk concentration. The response time of nanopores is closely related to the surface charge density, pore length, voltage, and bulk concentration. Our uncovered dynamic response mechanism of the ionic current can guide the design of nanofluidic devices with conical nanopores, including memristors, ionic switches, and rectifiers., Comment: 30 pages, 5 figures

Solid-state micro/nanopores play an important role in the sensing field because of their high stability and controllable size. Aiming at problems of complex processes and high costs in pore manufacturing, we propose a convenient and low-cost micro/nanopore fabrication technique based on the needle punching method. The thin film is pierced by controlling the feed of a microscale tungsten needle, and the size variations of the micropore are monitored by the current feedback system. Based on the positive correlation between the micropore size and the current threshold, the size-controllable preparation of micropores is achieved. The preparation of nanopores is realized by the combination of needle punching and chemical etching. Firstly, a conical defect is prepared on the film with the tungsten needle. Then, nanopores are obtained by unilateral chemical etching of the film. Using the prepared conical micropores resistive-pulse detection of nanoparticles is performed. Significant ionic current rectification is also obtained with our conical nanopores. It is proved that the properties of micro/nanopores prepared by our method are comparable to those prepared by the track-etching method. The simple and controllable fabrication process proposed here will advance the development of low-cost micro/nanopore sensors., Comment: 27 pages, 6 figures

With the resistive-pulse technique (RPT), nanopores serve as the nanofluidic sensors of various analytes for their many physical and chemical properties. Here, we focus on the size measurement and its theoretical prediction for sub-200 nm nanoparticles with RPT. Through systematical investigation of the current blockade of nanoparticles across cylindrical nanopores with simulations, Maxwell method considering the shape coefficient and access resistances agrees well with simulation results. However, the widely used integration method of the resistance has distinct deviations in various cases. With the introduction of a correction factor \b{eta} to the integration method, our revised equations can provide good predictions for simulation results. \b{eta} shows a strong dependence on the diameter ratio (d over D) of the nanoparticle and nanopore. Following the same strategy, modified equations are provided for the accurate size prediction for nanoparticles across conical nanopores, where the integration method is the default convenient way. The correction factor \b{eta}' relates to \b{eta} in cylindrical nanopores. \b{eta}' exhibits independence on the pore geometry parameters and diameters of nanoparticles, but dependence on the surface charge density of conical nanopores. Our improved equations can provide theoretical predictions for the accurate size detection of 100-200 nm diameter nanoparticles across cylindrical and conical nanopores., Comment: 29 pages 7 figures

Short nanopores find extensive applications capitalizing on their high throughput and detection resolution. Ionic behaviors through long nanopores are mainly determined by charged inner-pore walls. When pore lengths decrease to sub-200 nm, charged exterior surfaces provide considerable modulation to ion current. We find that the charge status of inner-pore walls affects the modulation of ion current from charged exterior surfaces. For 50-nm-long nanopores with neutral inner-pore walls, charged exterior surfaces on the voltage (surfaceV) and ground (surfaceG) sides enhance and inhibit ion transport by forming ion enrichment and depletion zones inside nanopores, respectively. For nanopores with both charged inner-pore and exterior surfaces, continuous electric double layers enhance ion transport through nanopores significantly. The charged surfaceV results in higher ion current by simultaneously weakening ion depletion at pore entrances and enhancing the intra-pore ion enrichment. The charged surfaceG expedites the exit of ions from nanopores, resulting in a decrease in ion enrichment at pore exits. Through adjustment in the width of charged-ring regions near pore boundaries, the effective charged width of the charged exterior is explored at ~20nm. Our results may provide a theoretical guide for further optimizing the performance of nanopore-based applications, like seawater desalination, biosensing, and osmotic energy conversion., Comment: 18 pages, 5 figures

Short nanopores have various applications in biosensing, desalination, and energy conversion. Here, the modulation of charged exterior surfaces on ionic transport is investigated through simulations with sub-200 nm long nanopores under applied voltages. Detailed analysis of ionic current, electric field strength, and fluid flow inside and outside nanopores reveals that charged exterior surfaces can increase ionic conductance by increasing both the concentration and migration speed of charge carriers. The electric double layers near charged exterior surfaces provide an ion pool and an additional passageway for counterions, which lead to enhanced exterior surface conductance and ionic concentrations at pore entrances and inside the nanopore. We also report that charges on the membrane surfaces increase electric field strengths inside nanopores. The effective width of a ring with surface charges placed at pore entrances (Lcs) is considered as well by studying the dependence of the current on Lcs. We find a linear relationship between the effective Lcs and the surface charge density and voltage, and an inverse relationship between the geometrical pore length and salt concentration. Our results elucidate the modulation mechanism of charged exterior surfaces on ionic transport through short nanopores, which is important for the design and fabrication of porous membranes., Comment: 27 pages, 6 figures

Continuum simulations become an important tool to uncover the mysteries in nanofluidic experiments. However, fluid flow in simulation models is usually unconsidered. Here, systematical simulations are conducted to provide a quantitative understanding of influences from electroosmotic flow (EOF) on ionic transport through nanopores by both types of models with and without consideration of EOF. In nanopores of less than ~10 nm in diameter, counterions dominate ionic current which is always promoted obviously by the convective effect of EOF. In the diameter range from ~10 to ~30 nm, strong EOF induces ion concentration polarization or ion depletion inside nanopores which causes significant decreases in ionic current. For nanopores larger than ~30 nm, due to convective promotion and inhibition of EOF on the transport of counterions and anions, considerable nanopore selectivity to counterions maintains in cases with EOF. Though the difference in total current between both cases decreases with further pore size increasing, the difference in cation/anion current is still considerable. From our results under various pore parameters and applied conditions, the fluid flow should be considered in the simulation cases when EOF is strong. Our work may provide useful guidance for simulation conductance., Comment: 25 pages, 7 figures

Besides the dominant NaCl, natural seawater/river water contains trace multivalent ions, which can provide effective screening to surface charges. Here, in both negatively and positively charged nanopores, influences from divalent ions as counterions and coions have been investigated on the performance of osmotic energy conversion (OEC) under natural salt gradients. As counterions, trace Ca2+ ions can suppress the electric power and conversion efficiency significantly. The reduced OEC performance is due to the bivalence and low diffusion coefficient of Ca2 ions, instead of the uphill transport of divalent ions discovered in the previous work. Effectively screened charged surfaces by Ca2+ ions induce enhanced diffusion of Cl ions which simultaneously decreases the net ion penetration and ionic selectivity of the nanopore. While as coions, Ca2+ ions have weak effects on the OEC performance. The promotion from charged exterior surfaces on OEC processes for ultra-short nanopores is also studied, which effective region is ~200 nm in width beyond pore boundaries independent of the presence of Ca2+ ions. Our results shed light on the physical details of the nanofluidic OEC process under natural seawater/river water conditions, which can provide a useful guide for high-performance osmotic energy harvesting., Comment: 24 pages, 5 figures

As an important property of porous membranes, the surface charge property determines many ionic behaviors of nanopores, such as ionic conductance and selectivity. Based on the dependence of electric double layers on bulk concentrations, ionic conductance through nanopores at high and low concentrations is governed by the bulk conductance and surface charge density, respectively. Here, through the investigation of ionic conductance inside track-etched single polyethylene terephthalate (PET) nanopores under various concentrations, the surface charge density of PET membranes is extracted as around 0.021 C per m2 at pH 10 over measurements with 40 PET nanopores. Simulations show that surface roughness can cause underestimation in surface charge density due to the inhibited electroosmotic flow. Then, the averaged pore size and porosity of track-etched multipore PET membranes are characterized by the developed ionic conductance method. Through coupled theoretical predictions in ionic conductance under high and low concentrations, the averaged pore size and porosity of porous membranes can be obtained simultaneously. Our method provides a simple and precise way to characterize the pore size and porosity of multipore membranes, especially for those with sub-100 nm pores and low porosities., Comment: 25 pages, 4 figures

In charged nanopores, ionic diffusion current reflects the ionic selectivity and ionic permeability of nanopores which determines the performance of osmotic energy conversion, i.e. the output power and efficiency. Here, theoretical predictions of the diffusive currents through cation-selective nanopores have been developed based on the investigation of diffusive ionic transport under salt gradients with simulations. The ionic diffusion current I satisfies a reciprocal relationship with the pore length I correlates with a/L (a is a constant) in long nanopores. a is determined by the cross-sectional areas of diffusion paths for anions and cations inside nanopores which can be described with a quadratic power of the diameter, and the superposition of a quadratic power and a first power of the diameter, respectively. By using effective concentration gradients instead of nominal ones, the deviation caused by the concentration polarization can be effectively avoided in the prediction of ionic diffusion current. With developed equations of effective concentration difference and ionic diffusion current, the diffusion current across nanopores can be well predicted in cases of nanopores longer than 100 nm and without overlapping of electric double layers. Our results can provide a convenient way for the quantitative prediction of ionic diffusion currents under salt gradients.

High-performance osmotic energy conversion requires both large ionic throughput and high ionic selectivity, which can be significantly promoted by exterior surface charges simultaneously, especially for short nanopores. Here, we investigate the enhancement of ionic diffusion by charged exterior surfaces under various conditions and explore corresponding effective charged areas. From simulations, ionic diffusion is promoted more significantly by exterior surface charges through nanopores with a shorter length, wider diameter, and larger surface charge density, or under higher salt gradients. Effective widths of the charged ring regions near nanopores are reversely proportional to the pore length and linearly dependent on the pore diameter, salt gradient, and surface charge density. Due to the important role of effective charged areas in the propagation of ionic diffusion through single nanopores to cases with porous membranes, our results may provide useful guidance to the design and fabrication of porous membranes for practical high-performance osmotic energy harvesting., Comment: 24 Pages,5 figures

High-performance osmotic energy conversion (OEC) with perm-selective porous membrane requires both high ionic selectivity and permeability simultaneously. Here, hydrodynamic slip is considered on surfaces of nanopores to break the tradeoff between ionic selectivity and permeability, because it decreases the viscous friction at solid-liquid interfaces which can promote ionic diffusion during OEC. Taking advantage of simulations, influences from individual slipping surfaces on the OEC performance have been investigated, i.e. the slipping inner surface (surfaceinner) and exterior surfaces on the low- and high-concentration sides (surfaceL and surfaceH). Results show that the slipping surfaceL is crucial for high-performance OEC. For nanopores with various lengths, the slipping surfaceL simultaneously increases both ionic permeability and selectivity of nanopores, which results in both significantly enhanced electric power and energy conversion efficiency. While for nanopores longer than 30 nm, the slipping surfaceinner plays a dominant role in the increase of electric power, which induces a considerable decrease in energy conversion efficiency due to enhanced transport of both cations and anions. Considering the difficulty in hydrodynamic slip modification to the surfaceinner of nanopores, the surface modification to the surfaceL may be a better choice to achieve high-performance OEC. Our results provide feasible guidance to the design of porous membranes for high-performance osmotic energy harvesting., Comment: 25 pages, 7 figures

High-performance osmotic energy conversion (OEC) requires both high ionic selectivity and permeability in nanopores. Here, through systematical explorations of influences from individual charged nanopore surfaces on the performance of OEC, we find that the charged exterior surface on the low-concentration side (surfaceL) is essential to achieve high-performance osmotic power generation, which can significantly improve the ionic selectivity and permeability simultaneously. Detailed investigation of ionic transport indicates that electric double layers near charged surfaces provide high-speed passages for counterions. The charged surfaceL enhances cation diffusion through enlarging the effective diffusive area, and inhibits anion transport by electrostatic repulsion. Different areas of charged exterior surfaces have been considered to mimic membranes with different porosities in practical applications. Through adjusting the width of the charged ring region on the surfaceL, electric power in single nanopores increases from 0.3 to 3.4 pW with a plateau at the width of ~200 nm. The power density increases from 4200 to 4900 W/m2 and then decreases monotonously that reaches the commercial benchmark at the charged width of ~480 nm. While, energy conversion efficiency can be promoted from 4% to 26%. Our results provide useful guide in the design of nanoporous membranes for high-performance osmotic energy harvesting., Comment: 30 pages and 7 figures

Nanopores that exhibit ionic current rectification (ICR) behave like diodes, such that they transport ions more efficiently in one direction than the other. Conical nanopores have been shown to rectify ionic current, but only those with at least 500 nm in length exhibit significant ICR. Here, through the finite element method, we show how ICR of conical nanopores with length below 200 nm can be tuned by controlling individual charged surfaces i.e. inner pore surface (surface_inner), and exterior pore surfaces on the tip and base side (surface_tip and surface_base). The charged surface_inner and surface_tip can induce obvious ICR individually, while the effects of the charged surface_base on ICR can be ignored. The fully charged surface_inner alone could render the nanopore counterion-selective and induces significant ion concentration polarization in the tip region, which causes reverse ICR compared to nanopores with all surface charged. In addition, the direction and degree of rectification can be further tuned by the depth of the charged surface_inner. When considering the exterior membrane surface only, the charged surface_tip causes intra-pore ionic enrichment and depletion under opposite biases which results in significant ICR. Its effective region is within ~40 nm beyond the tip orifice. We also found that individual charged parts of the pore system contributed to ICR in an additive way due to the additive effect on the ion concentration regulation along the pore axis. With various combinations of fully/partially charged surface_inner and surface_tip, diverse ICR ratios from ~2 to ~170 can be achieved. Our findings shed light on the mechanism of ionic current rectification in ultra-short conical nanopores, and provide a useful guide to the design and modification of ultra-short conical nanopores in ionic circuits and nanofluidic sensors., Comment: 25 pages, 8 figures

Ion transport in highly-confined space is important to various applications, such as biosensing and seawater desalination with nanopores. All-atom molecular dynamics simulations are conducted to investigate the transport of Na$^+$ and Cl$^-$ ions through nanopores with the diameter below 6 nm. It is found that the formation of the contact ion pair plays a critical role in reducing the ion mobility inside a nanopore without surface charges. The mobility for both cations and anions decreases with the reduced pore size because it is easier to form the contact ion pairs inside the neutral nanopore with smaller diameter. Inside a charged nanopores, besides the contact ion pair formation, the surface charges also play a significant role in reducing the counterion mobility through surface trapping. It is uncovered that the mobility of Na$^+$ ions increases first and then decreases with the surface charge density, while Cl$^-$ ions have the opposite trend. A modified first-passage time model is proposed to take into account the ion pair formation and the trapped ions inside a nanopore, which provides a clear picture in describing ion transport through a nanopore.

Single nanopores have attracted much scientific interest due to their versatile applications. The majority of experiments have been performed with nanopores being in contact with the same electrolyte on both sides of the membrane, while solution gradients across semi-permeable membranes are omnipresent in natural systems. In this manuscript, we studied ionic and fluidic movement through thin nanopores under viscosity gradients both experimentally and using simulations. Ionic current rectification was observed under these conditions, due to solutions with different conductivities filled across the pore under different biases caused by electroosmotic flow. We found that a pore filled with high viscosity solutions exhibited current increase with applied voltage in a steeper slope beyond a threshold voltage, which abnormally reduced the current rectification ratio. Through simulations, we found reversed electroosmotic flow that filled the pore with aqueous solutions of lower viscosities was responsible for this behavior. The reversed electroosmotic flow could be explained by slower depletion of coions than counterions along the pore. By increasing the surface charge density of pore surfaces, current rectification ratio could reach the value of the viscosity gradient across thin nanopores. Our findings shed light on fundamental aspects to be considered when performing experiments with viscosity gradients across nanopores and nanofluidic channels., Comment: 7 figures https://pubs.acs.org/doi/10.1021/acs.analchem.8b04225, Analytical chemistry 2018

The resistive-pulse technique provides a fast and label-free method for nanoparticle detection. In order to achieve a higher sensitivity, thin nanopores, such as silicon nitride pores, are usually considered. In this paper, nanoparticle detection has been mimicked by simulations. We found the surface charges of the particle can affect the current blockade obviously in short pores, especially under high electric fields. For particles with a surface charge density higher than -0.02 C/m2, its current blockade ratio depends on the applied voltage closely. From our simulation results, an optimal voltage can be found for the particle detection, under which the current blockade ratio does not depend on the surface charge density of the particle. This optimal voltage was obtained by the balance of current increase and decrease caused by cations and anions, respectively, due to the negative surface charges of particles. From the systematical study, the optimal voltage was found to work like a property of the system which only depends on the electrolyte type. We think our finding can provide some help to the accurate particle detection in experiments.

Through molecular dynamics simulations considering thermal vibration of surface atoms, ionic behaviors in concentrated NaCl solutions confined between discretely charged silicon surfaces have been investigated. The electric double layer structure was found sensitive to the density and distribution of surface charges. Due to the surface charge discreteness, slight charge inversion appeared which depended on the surface charge density, bulk concentration and confinement. In the nanoconfined NaCl solutions differently concentrated from 0.2 M to 4.0 M, the locations of accumulation layers for Na+ and Cl- ions kept stable, but their peak values increased. The higher the concentration was, the more obvious charge inversion appeared. In 4.0 M NaCl solution, Na+ and Cl- ions show obvious alternating layered distributions which may be corresponding to the solidification found in experiments. By changing surface separation, the confinement had a large effect on ionic distributions. As both surfaces approached each other, many ions and water molecules were squeezed out of the confined space. Two adjacent layers in ion or water distribution profiles can be forced to closer to each other and merge together. From ionic hydration analysis, the coordination number of Na+ ions in highly-confined space was much lower than that in the bulk., Comment: 26 pages, 9 figures

Molecular dynamics simulations were used to explain the origin and properties of electrical double-layer capacitance in short graphene nanochannels with width below 2 nm. The results explain the previously reported experimental result on the non-monotonic dependence of the capacitance with the channel width. The mechanism for the anomalous increase of the capacitance in sub-1-nm in pore diameter is attributed here to the width-dependent radial location of counterions in the nanochannels, and the restricted number of co-ions. Decrease of the channel width lowers the number of co-ions and positions the counterions closer to the channel walls. For nanochannels with width ranging from 1 to 2 nm, co-ions are allowed to enter the nanochannel, and both types of ions assume alternating layered distributions leading to the decrease of the capacitance. Voltage is another control parameter which allows understanding capacitance in graphene nanochannels. As the voltage increases, due to limited space near the charged surface, more counterions need to be located in the center of the nanochannel resulting in further capacitance decrease., Comment: 23 papges,7 figures

In order to detect the effect of the surface charge discreteness on the properties at the solid-liquid interface, molecular dynamics simulation model taking consideration of the vibration of wall atoms was used to investigate the ion and water performance under different charge distributions. Through the comparison between simulation results and the theoretical prediction, it was found that, with the degree of discreteness increasing, much more counterions were attracted to the surface. These ions formed a denser accumulating layer which located much nearer to the surface and caused charge inversion. The ions in this layer were non-hydrated or partially hydrated. When a voltage was applied across the nanochannel, this dense accumulating layer did not move unlike the ions near uniformly charged surface. From the water density profiles obtained in nanochannels with different surface charge distributions, the influence of the surface charge discreteness on the water distributions could be neglected.

Porous graphene has high mechanical strength and atomic layer thickness, which make it a promising material for material separation and biomolecule sensing. Electrostatic interactions between charges in aqueous solution are a kind of strong long-range interaction which may have great influence on the fluid transport through nanopores. Here, molecular dynamics simulations were conducted to investigate ion and water transport through a 1.05-nm-in-diameter monolayer graphene nanopore with its edge charge-modified. From the results, it is found that the nanopores are selective to counterions when they are charged. As the charge amount increases, the total ionic currents show an increase-decrease profile while the co-ion currents monotonously decrease. The co-ions rejection can reach 75% and 90% when the nanopores are negatively and positively charged, respectively. Cl ions current increases and reaches a plateau, and Na+ current decreases with the charge amount in the systems where they act as counterions. Besides, the charge modification can enhance the water transport through nanopores obviously. This is mainly due to the ion selection of nanopores. Especially, positive charges on the pore edge facilitate the water transport much more than negative charges.