Asymmetry-induced electric current rectification in permselective systems

Advances in Two-Dimensional Ion-Selective Membranes: Bridging Nanoscale Insights to Industrial-Scale Salinity Gradient Energy Harvesting

Salinity gradient energy, often referred to as the Gibbs free energy difference between saltwater and freshwater, is recognized as "blue energy" due to its inherent cleanliness, renewability, and continuous availability. Reverse electrodialysis (RED), relying on ion-selective membranes, stands as one of the most prevalent and promising methods for harnessing salinity gradient energy to generate electricity. Nevertheless, conventional RED membranes face challenges such as insufficient ion selectivity and transport rates and the difficulty of achieving the minimum commercial energy density threshold of 5 W/m2. In contrast, two-dimensional nanostructured materials, featuring nanoscale channels and abundant functional groups, offer a breakthrough by facilitating rapid ion transport and heightened selectivity. This comprehensive review delves into the mechanisms of osmotic power generation within a single nanopore and nanochannel, exploring optimal nanopore dimensions and nanochannel lengths. We subsequently examine the current landscape of power generation using two-dimensional nanostructured materials in laboratory-scale settings across various test areas. Furthermore, we address the notable decline in power density observed as test areas expand and propose essential criteria for the industrialization of two-dimensional ion-selective membranes. The review concludes with a forward-looking perspective, outlining future research directions, including scalable membrane fabrication, enhanced environmental adaptability, and integration into multiple industries. This review aims to bridge the gap between previous laboratory-scale investigations of two-dimensional ion-selective membranes in salinity gradient energy conversion and their potential large-scale industrial applications.

Influence of the Dielectric Constant on the Ionic Current Rectification of Bipolar Nanopores

In this paper, we investigate how the dielectric constant, ϵ, of an electrolyte solvent influences the current rectification characteristics of bipolar nanopores. It is well recognized that bipolar nanopores with two oppositely charged regions rectify current when exposed to an alternating electric potential difference. Here, we consider dilute electrolytes with NaCl only and with a mixture of NaCl and charged nanoparticles. These systems are studied using two levels of description, all-atom explicit water molecular dynamics (MD) simulations and coarse-grained implicit solvent MD simulations. The charge density and electric potential profiles and current-voltage relationship predicted by the implicit solvent simulations with ϵ = 11.3 show good agreement with the predictions from the explicit water simulations. Under nonequilibrium conditions, the predictions of the implicit solvent simulations with a dielectric constant closer to the one of bulk water are significantly different from the predictions obtained with the explicit water model. These findings are closely aligned with experimental data on the dielectric constant of water when confined to nanometric spaces, which suggests that ϵ decreases significantly compared to its value in the bulk. Moreover, the largest electric current rectification is observed in systems containing nanoparticles when ϵ = 78.8. Using enhanced sampling, we have shown that this larger rectification arises from the presence of a significantly deeper minimum in the free energy of the system with a larger ϵ, and when a negative voltage bias is applied. Since implicit solvent models and mean-field continuum theories are often used to design Janus membranes based on bipolar nanopores, this work highlights the importance of properly accounting for the effects of confinement on the dielectric constant of the electrolyte solvent. The results presented here indicate that the dielectric constant in implicit solvent simulations may be used as an adjustable parameter to approximately account for the effects of nanometric confinement on aqueous electrolyte solvents.

Ion Transport in Multi-Nanochannels Regulated by pH and Ion Concentration

Nanochannels are a powerful technique for detecting a wide range of biomolecules without labeling. The ion transport phenomena in nanochannel arrays differ from those in single nanochannels and are caused by interchannel communication. This study uses a fully coupled Poisson-Nernst-Planck (PNP) and Navier-Stokes model to investigate ion transport in nanochannel arrays. Instead of being set at a constant value, the surface charge density used in this study is established by the protonation and deprotonation of the silanol groups that are present on the walls of the silicon-based nanochannels. The surface charge density of the nanochannel walls varies with the number of nanochannels, the channel lateral distance, and the background solution properties, which consequently influence the ionic concentration distribution, flow velocity, and electric field strength. For example, in different numbers of nanochannel systems, the ion concentration in nanochannels is not much different, but it is different in reservoirs, especially near the openings of nanochannels. The number of nanochannels and the distance between nanochannels can also affect the formation of electro-convective vortex zones under certain conditions. These findings can aid in optimizing the nanochannel array design by regulating the number and distance of nanochannels and facilitating the construction of solid-state nanochannel arrays with any desired nanochannel dimensions.

Electrical Conductance of Charged Nanopores

A nanopore's response to an electrical potential drop is characterized by its electrical conductance, . For the last two decades, it has been thought that at low electrolyte concentrations, , the conductance is concentration-independent such that . It has been recently demonstrated that surface charge regulation changes the dependency to , whereby the slope typically takes the values α = 1/3 or 1/2. However, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. Here, we elucidate the interplay between three mechanisms: surface charge regulation, convection, and slip lengths. We show that the inclusion of convection does not change the slope, and when the effects of hydrodynamic slip are included, the slope is doubled. We show that when all effects are accounted for, α can take any value between 0 and 1 where the exact value of the slope depends on the material properties. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.

Bipolar Nanochannels: A Systematic Approach to Asymmetric Problems

Nanofluidic diodes are capable of rectifying the electrical current by several orders of magnitude. In the current state of affairs, determining the rectification factor is not possible as it depends on many system parameters. In this work, we systematically scan the effects of geometry and excess counterion concentrations (i.e., surface charge effects). We show that the current-voltage response varies between the two extreme behaviors of unipolar and bipolar responses. The exact behavior depends on the geometry and surface charge properties of the system. Here, we have gone beyond the typical setup that only considers the dynamics within the nanochannel itself and we have included the effects of the adjoining microchannels. Systems that include both nanochannels and microchannels exhibit the classical signatures of concentration polarization, such as ionic depletion and enrichment. Here, where we have scanned a wide range of parameters, we show that bipolar and semi-bipolar systems exhibit a wider range of phenomena that are intrinsically more complicated. Our system characterization is for both, the much more investigated case of steady state and the less investigated, but equally interesting, time-transient case. For example, it is common to characterize the system by its steady-state result (current-voltage response, rectification factor, and transport number). Here, we demonstrate that the time-transient behavior of the fluxes can also be used to characterize the system, and that the time-dependent rectification factors and transport numbers are meaningful. The systematic approach taken in this work, and the results presented herein, can be used to further elucidate the complicated behavior of the current-voltage response of nanofluidic diodes and to rationalize experimental results. The insights of this work can be used to enhance and improve the design of all nanofluidic diodes.

Ion transport in nanopores with highly overlapping electric double layers

Investigation of ion transport through nanopores with highly overlapping electric double layers is extremely challenging. This can be attributed to the non-linear Poisson-Boltzmann equation that governs the behavior of the electrical potential distribution as well as other characteristics of ion transport. In this work, we leverage the approach of Schnitzer and Yariv [Phys. Rev. E 87, 054301 (2013)] to reduce the complexity of the governing equation. An asymptotic solution is derived, which shows remarkable correspondence to simulations of the non-approximated equations. This new solution is leveraged to address a number of highly debated issues. We derive the equivalent of the Gouy-Chapman equation for systems with highly overlapping electric double layers. This new relationship between the surface charge density and the surface potential is then utilized to determine the power-law scaling of nanopore conductances as a function of the bulk concentrations. We derive the coefficients of transport for the case of overlapping electric double layers and compare it to the renowned uniform potential model. We show that the uniform potential model is only an approximation for the exact solution for small surface charges. The findings of this work can be leveraged to uncover additional hidden attributes of ion transport through nanopores.

A Simulation Analysis of Nanofluidic Ion Current Rectification Using a Metal-Dielectric Janus Nanopore Driven by Induced-Charge Electrokinetic Phenomena

We propose herein a unique mechanism of generating tunable surface charges in a metal-dielectric Janus nanopore for the development of nanofluidic ion diode, wherein an uncharged metallic nanochannel is in serial connection with a dielectric nanopore of fixed surface charge. In response to an external electric field supplied by two probes located on both sides of the asymmetric Janus nanopore, the metallic portion of the nanochannel is electrochemically polarized, so that a critical junction is formed between regions with an enriched concentration of positive and negative ions in the bulk electrolyte adjacent to the conducting wall. The combined action of the field-induced bipolar induced double layer and the native unipolar double layer full of cations within the negatively-charged dielectric nanopore leads to a voltage-controllable heterogenous volumetric charge distribution. The electrochemical transport of field-induced counterions along the nanopore length direction creates an internal zone of ion enrichment/depletion, and thereby enhancement/suppression of the resulting electric current inside the Janus nanopore for reverse working status of the nanofluidic ion diode. A mathematical model based upon continuum mechanics is established to study the feasibility of the Janus nanochannel in causing sufficient ion current rectification, and we find that only a good matching between pore diameter and Debye length is able to result in a reliable rectifying functionality for practical applications. This rectification effect is reminiscent of the typical bipolar membrane, but much more flexible on account of the nature of a voltage-based control due to induced-charge electrokinetic polarization of the conducting end, which may hold promise for osmotic energy conversion wherein an electric current appears due to a difference in salt concentration. Our theoretical demonstration of a composite metal-dielectric ion-selective medium provides useful guidelines for construction of flexible on-chip platforms utilizing induced-charge electrokinetic phenomena for a high degree of freedom ion current control.

Thermal Dependence of the Mesoscale Ionic Diode: Modeling and Experimental Verification

Mesoscale ionic diodes, which can rectify ionic current at conditions at which their pore size is larger than 100 nm and thus over 100 times larger than the Debye length, have been recently discovered with potential applications in ionic circuits as well as osmotic power generation. Compared with the conventional nanoscale ionic diodes, the mesoscale ionic diodes can offer much higher conductance, ionic current resolution, and power generated. However, the thermal response, which has been proven playing a crucial role in nanofluidic devices, of the mesoscale ionic diode remains significantly unexplored. Here, we report the thermal dependence of the mesoscale ionic diode comprising a conical pore with a tip opening diameter of ∼400 nm. To capture its underlying physics more accurately, our model takes into account the practical equilibrium chemistry reaction of functional carboxyl groups on the pore surface. Modeling results predict that in the mesoscale ionic diode prepared currents increase but the performance decreases with the increase of temperature, which is consistent with our experimental data and indicates that the ion transport properties apparently depend on the presence of highly mobile hydroxide ions. The results gathered can provide important guidance for the design of new mesoscale ionic diodes, enriching their applications in thermoelectric power and thermoresponsive chemical sensors.

Approximate time-dependent current-voltage relations for currents exceeding the diffusion limit

The time-dependent behavior of one-dimensional ion transport into a permselective medium is theoretically modeled in this work for currents exceeding the diffusion limit. Leveraging the findings of Yariv [E. Yariv, Phys. Rev. E 80, 051201 (2009)10.1103/PhysRevE.80.051201], we derive three separate expressions for the potential drop for short, intermediate, and long times. We show that the potential drop correlates to the time evolution of the space-charge layer adjacent to the permselective interface. Our approximate models show remarkable correspondence to numerical simulations.

Cationic Rectifier Based on a Graphene Oxide-Covered Microhole: Theory and Experiment

Cation transport through nanochannels in graphene oxide can be rectified to give ionic diode devices for future applications, for example, in desalination. A film of graphene oxide is applied to a 6 μm thick poly(ethylene terephthalate) substrate with a 20 μm diameter microhole and immersed in aqueous HCl solution. Strong diode effects are observed even at high ionic strength (0.5 M). Switching between open and closed states, microhole size effects, and time-dependent phenomena are explained on the basis of a simplified theoretical model focusing on the field-driven transport within the microhole region. In aqueous NaCl, competition between Na⁺ transport and field-driven heterolytic water splitting is observed but shown to be significant only at low ionic strength. Therefore, nanostructured graphene oxide is demonstrated to exhibit close to ideal behavior for future application in ionic diode desalination of seawater.

Photo-switchable two-dimensional nanofluidic ionic diodes

The bottom-up assembly of ion-channel-mimetic nanofluidic devices and materials with two-dimensional (2D) nano-building blocks paves a straightforward way towards the real-world applications of the novel transport phenomena on a nano- or sub-nanoscale. One immediate challenge is to provide the 2D nanofluidic systems with adaptive responsibilities and asymmetric ion transport characteristics. Herein, we introduce a facile and general strategy to provide a graphene-oxide-based 2D nanofluidic system with photo-switchable ionic current rectification (ICR). The degree of ICR can be prominently enhanced upon UV irradiation and it can be perfectly retrieved under irradiation with visible light. A maximum ICR ratio of about 48 was achieved. The smart and functional nanofluidic devices have applications in energy conversion, chemical sensing, water treatment, etc.

Geometrical control of ionic current rectification in a configurable nanofluidic diode

Control of ionic current in a nanofluidic system and development of the elements analogous to electrical circuits have been the subject of theoretical and experimental investigations over the past decade. Here, we theoretically and experimentally explore a new technique for rectification of ionic current using asymmetric 2D nanochannels. These nanochannels have a rectangular cross section and a stepped structure consisting of a shallow and a deep side. Control of height and length of each side enables us to obtain optimum rectification at each ionic strength. A 1D model based on the Poisson-Nernst-Planck equation is derived and validated against the full 2D numerical solution, and a nondimensional concentration is presented as a function of nanochannel dimensions, surface charge, and the electrolyte concentration that summarizes the rectification behavior of such geometries. The rectification factor reaches a maximum at certain electrolyte concentration predicted by this nondimensional number and decays away from it. This method of fabrication and control of a nanofluidic diode does not require modification of the surface charge and facilitates the integration with lab-on-a-chip fluidic circuits. Experimental results obtained from the stepped nanochannels are in good agreement with the 1D theoretical model.

Interplay between Nanochannel and Microchannel Resistances

Current nanochannel system paradigm commonly neglects the role of the interfacing microchannels and assumes that the ohmic electrical response of a microchannel-nanochannel system is solely determined by the geometric properties of the nanochannel. In this work, we demonstrate that the overall response is determined by the interplay between the nanochannel resistance and various microchannel attributed resistances. Our experiments confirm a recent theoretical prediction that in contrast to what was previously assumed at very low concentrations the role of the interfacing microchannels on the overall resistance becomes increasingly important. We argue that the current nanochannel-dominated conductance paradigm can be replaced with a more correct and intuitive microchannel-nanochannel-resistance-model-based paradigm.