Nanochannel‐Based Ion Transport and Its Application in Osmotic Energy Conversion: A Critical Review

Nanochannel‐based ion transport is an important field of study in various disciplines, including physics, chemistry, energy, materials science, biology, and earth science. The unique features of natural nanochannels have inspired numerous innovative designs that seek to achieve high ion permeability, selectivity, and rectification. A notable example is osmotic energy conversion, which harvests sustainable salinity‐gradient energy to generate electricity without moving parts, noise, or carbon emissions and thus serves as a promising alternative to traditional fossil fuel utilization. This review focuses on the fundamental principles, regulatory methods, and practical applications of nanochannel‐based ion transport for osmotic energy conversion. The physical mechanisms of ion transport and the intriguing phenomena of ion behaviors in nanoconfined spaces are discussed first, followed by a thorough examination of the overall process of osmotic power generation from mathematical, numerical, parametric, first‐principles, molecular simulation, and modeling perspectives. Strategies for enhancing the osmotic performance are then discussed to overcome the trade‐off between ion selectivity and ion flux, including the theoretical design of nanochannel geometry and electrification, experimental optimization of nanoporous membranes, and electrolyte thermal enhancement. The existing challenges and opportunities for the future development of nanochannel‐based ion transport and osmotic power generation are addressed at the end.


Introduction
Ions are essential charge carriers that possess unique sizes, masses, and mobilities that are distinct from those of electrons in electron conductors.The transportation of ions in nature often occurs through nanochannels such as cell membranes, [1] DOI: 10.1002/apxr.202300016tree fibers, [2] and porous rock silts. [3]n particular, biological membrane channels have exceptional permeability, selectivity, and rectification properties, which arise from the regulation of the channel size, [4] heterogeneous pore structure, [5] and surface chemical modifications. [6]These properties have garnered widespread attention across interdisciplinary fields including physics, chemistry, energy, materials, biology, and earth science.This has inspired the development of various nanochannel-based biomimetic applications, such as the use of porous electrodes in electrocatalysis, [7] ion batteries, [8] supercapacitors, [9] and nanoporous membranes for osmotic power generation, [10] water purification, [11] desalination, [12] and ion separation. [13]owever, the mechanisms underlying ion transport in nanochannels remain unclear to date.Ions in aqueous solutions exist as hydrated ions, surrounded by polar water molecules, and their transport performance is a combination of their intrinsic properties and environmental characteristics.The diffusion of hydrated ions is influenced by the rotation or local translational movement of the surrounding water molecules, resulting in different diffusion paths and speeds on solid surfaces depending on the hydration number. [14]In nanochannels with geometric and chemical confinement, the solid-liquid contact forms an electrified surface and electric double layer (EDL). [15]In this case, ion transport laws in the bulk solution are no longer applicable, because of interfacial phenomena such as solvation structure rearrangement, interfacial H-bonds, and chemical reactions. [16]hen the channel size exceeds that of typical inorganic ions, exitentry effects and steric exclusion occur.As the channel size decreases to the sub-nanometer range and approaches the size of the ions and water molecules, the ion size effect is amplified, leading to energy-consuming hydration shell deformation. [17]he repeated dehydration-hydration process of divalent ions creates a higher migration energy barrier than that of monovalent ions. [18]When the wall has hydrophilic functional groups, such as the interlayer spacing of graphene oxide, the additional cation- and cation-functional group interactions cause electron redistribution and cation enrichment, [19] thus affecting ion migration kinetics.
These phenomena have been extensively explored and experimentally applied using nanofabrication techniques.One notable application of nanochannel-based ion transport is osmotic energy conversion, in which salinity-gradient energy at the sea-river interface is harvested to generate electricity without moving parts, noise, or carbon emissions. [20]The enormous reserves of salinitygradient energy (≈0.8 kWh m −3 , ≈30 TW in total) make this technology very appealing as a potential alternative to fossil fuels. [21]n principle, selective nanochannels for osmotic energy conversion are related to multiple ion transport modes, including salinity gradient-driven diffusion, pressure gradient-driven convection, and potential difference-driven electrochemical migration.The resulting net ion flux is then converted into external circuit current by the electrodes, enabling power generation. [22]Therefore, the entire process of osmotic power generation involves coupled multi-physical fields that require interdisciplinary efforts among materials science, engineering thermophysics, physical chemistry, electrochemistry, and nanotechnology.For instance, from a materials science perspective, artificial nanochannels with varying structural dimensions have been widely studied to achieve high permeability, selectivity, and rectification effects, including 1D single nanochannels, [23] 2D layered nanochannels, [24] and 3D interconnected nanochannels. [25]Following the idea of engineering thermophysics, system assistance methods have been extensively explored to increase osmotic power density.Specifically, electrolyte thermal regulation provides an additional driving force for ion transport and can be achieved by introducing external energy sources, such as solar energy, [26] low-grade waste heat, [27] and geothermal energy. [28]is review provides a comprehensive overview of the current state-of-the-art advancements in nanochannel-based ion transport and its application in osmotic energy conversion (Figure 1).The discussion begins by clarifying the underlying physical mechanisms of ion transport.Next, microscopic physical images of the ion behavior in nanoconfined spaces are presented, with a focus on the interfacial phenomena.Based on the existing theoretical studies, the osmotic power generation process is further revisited.Various strategies are also provided to overcome the trade-off between ion selectivity and ion flux for enhanced osmotic energy conversion.A perspective for further research on nanochannel-based ion transport and osmotic energy conversion is also presented.

Basic Principle of Ion Transport and Osmotic Energy Conversion
Macroscopic ion flux and osmotic power generation capabilities are rooted in directional ion transport in the nanochannels.To gain a deeper understanding, it is important to first delve into the fundamental principles of the interfacial EDL structure, Gibbs-Donnan effect, and ion selectivity.

Interfacial Electric Double Layer
In general, after an electrified surface immerses into an electrolyte solution to form a solid-liquid interface, spatially nonuniform ion distributions emerge owing to the interactions between ions and the surface electrostatic potential.This interface region in solution is called the EDL, in which enrichment of counter-ions (with opposite polarity to the surface) and depletion of co-ions (with the same polarity as the surface) are generated, thereby breaking the local charge electroneutrality.The conventional Gouy-Champan-Stern (G-C-S) model provides a sound explanation of the EDL structure in aqueous solutions. [29]With the advancements in experimental characterization and computational technology, more sophisticated models have been proposed.
As shown in Figure 2a, a compact layer of water adheres to the surface, which is related to ion-specific adsorption by removing a part of the hydrated shell.This results in the formation of the inner-Helmholtz plane (IHP).Counter-ions are then strongly drawn to the surface owing to electrostatically-induced non-specific adsorption, and their ion centers form an outer-Helmholtz plane (OHP). [30]The region extending from the solid surface to the OHP is commonly referred to as Stern layer.Subsequently, a diffuse layer acts as a transition zone between the Stern layer and the neutral solution, resulting from the balance between the electrostatic force and ion thermal motion.This nonuniform arrangement of ions in the solution results in a gradual distribution of the electrical potential.Specifically, the surface electrical potential ( surf ) decreases at a steep rate in the Stern layer, transitioning to the zeta potential ( zeta ) at the shear layer.In the diffuse layer, the relationship between ion concentration and an electrical potential  is described by the Poisson equation: [31]  0  r ∇ 2  = − e (1)   where  0 and  r are the vacuum and relative permittivity, respectively.The space charge density  e is related to ion concentration distribution described by Boltzmann statistics: where z i is the ion valence of i (e.g., +1, −1, +2, −2), and F is the Faraday constant (96 485 C mol −1 ).C i is ion concentration in the EDL region, C i,∞ is bulk concentration, R is the gas constant, and T is the absolute temperature.Therefore, the Poisson-Boltzmann equation and its dimensionless form are derived as follows: where *, C * i, ∞ , and L* represent the normalized electrical potential, ion concentration, and length, respectively, as defined by where the ion strength I c and Debye length  D are defined as [32] I c = 1 2 The Debye length is usually referred to as the characteristic EDL thickness, and its magnitude depends solely on the solution properties (temperature, ion valence, and bulk ion concentration) and not on any surface properties such as charge or potential.For a monovalent electrolyte (|z i | = 1, e.g., NaCl solution) at 298K,  D is 0.3 nm at 1 m, 9.6 nm at 1 mm, and 30.4 nm at 0.1 mm.It is further extended to 960 nm in pure water at pH 7.
As shown in Figure 2b, the interfacial EDLs overlap when the nanochannel height is less than twice the EDL thickness.The overlap degree and intensity of the EDL are the physical basis of selective ion transport in nanochannels, and they are influenced by the nanochannel characteristics (such as size and surface charge density), ion properties (such as concentration and species), and electrolyte environment (such as pH and temperature).For the nanochannel characteristics, the reduced channel size implies a decreased distance between the upper and lower surfaces, which enhances the EDL overlap and ion selectivity.The increased surface charge density of the nanoporous membrane enhances the absorption of counter-ions and the repelling of co-ions, further strengthening the ion selectivity.However, recent research has revealed that as the surface charge density of covalent-organic framework (COF) membranes increases, the ion selectivity declines. [33]This is attributed to the influence of the increased number of charged points on the nanoporous structure, thereby hindering selective ion transport.For the ion properties, according to the definition of Debye length, a higher concentration means a higher space charge density, thus causing the attenuation of the EDL thickness, EDL overlap, and ion selectivity.The high-concentration side has a worse EDL overlap than the low-concentration side.When multivalent and monovalent ions are mixed, the EDL achieves electrical balance at a shorter solid-liquid distance owing to the greater charge of multivalent ions, which has the same effect on the EDL with increasing ion concentration.
The effect of the electrolyte pH on ion selectivity is determined by the type of surface functional groups, as shown in Fig- ure 2c.The presence of acidic functional groups (such as ─OH and ─COOH) on the nanochannel wall enhances cation selectivity when the pH is alkaline, owing to the generation of negative surface charges and hydrogen ions. [34]However, an extremely alkaline pH reduces cation selectivity by causing ion concentration polarization.Conversely, basic functional groups (such as ─NH 2 ) lead to higher anion selectivity in acidic environments.Thermal regulation of the electrolyte also has a significant impact on selective ion transport, as shown in Figure 2d.An elevated temperature not only reduces the solution viscosity for accelerating ion diffusion, but also increases the Debye length for more effective EDL overlap and ion selectivity.
Figure 2e shows a schematic of the complete osmotic energy conversion device from an integral perspective.It comprises a nanochannel-based membrane, high-and low-concentration reservoirs, electrodes, and an external circuit.Owing to the transmembrane concentration gradient, selective nanochannels are preferred for the directional transport of cations over anions, and the difference between the cationic and anionic fluxes generates a net ion flux.The electrodes convert the ion flux into an external circuit current through an electrochemical reaction on the electrode surface, resulting in power generation.Ion selectivity inside the nanochannels is the basis for osmotic power generation, and the power generation performance can be further consolidated by the ionic rectification effect originating from the asymmetric structure or surface charge of the nanochannels.Based on this concept, the overall device performance is influenced by various factors such as the geometric shape, area, porosity, and thickness of the nanoporous membranes, ion concentration gradient, electrode type, and other supplementary units.
The above elucidation provides a foundation for understanding the basic properties of interfacial EDLs in nanochannels.However, more complex EDL structures can arise when considering additional factors, including surface properties (such as the electron-donating/capturing ability, [35] wettability, type of functional groups, [36] and microscopic roughness and curvature), environmental conditions (such as the temperature, [37] magnetic, [38] and electric fields, which can vary dynamically and non-uniformly), and electrolyte characteristics (such as the type of solvent, presence of ionic liquids, [39] heavy metal ions, [40] and active substances in wastewater).For example, the orientation variations of the interfacial water molecules under the action of an electric field significantly affect the EDL capacitance. [41]Water flow at the solid-liquid interface causes quantum friction and produces a dielectric response, [42] thus changing the local electric field.
To address these challenges, advanced experimental spectroscopic techniques with high surface sensitivity and high temporal resolution are necessary for the direct observation and characterization of the atomic-level features of solid-liquid interfaces.The development of quantum mechanical methods such as density functional theory (DFT) and ab initio molecular dynamics (AIMD) [43] are required to simulate these complex interface systems.Therefore, a more detailed understanding of the interfacial EDLs in nanochannels is important in fields beyond osmotic energy conversion, including supercapacitors, electrocatalysis, colloidal science, water treatment, and cell biology.

Gibbs−Donnan Effect
When a charged ion-selective nanochannel is in contact with an adjacent electrolyte solution, the electrochemical potentials of the two systems reach equilibrium with identical Gibbs free energies.This electrochemical equilibrium is referred to as the Gibbs-Donnan effect (also known as the Donnan equilibrium or Donnan exclusion effect), which is realized as long as the electric potential difference is compensated by an ion concentration difference. [44]As shown in Figure 3a, when an ion-selective nanochannel separates two compartments containing aqueous solutions at different bulk concentrations (C  i and C  i ), the chemical potential (represented by ion concentration) and electric potential vary across the nanochannel, whereas the electrochemical potentials of cation or anion are constant across the entire system.Taking the solution  as an example, the electrochemical potential μ i for ion i is expressed by where z i F  refers to the electrostatic energy per mole of i relative to a reference state.  i is the chemical potential of i relative to a reference state, and it is defined as the partial molar Gibbs Initially, the left chamber is filled with anionic dye aqueous solution (40 mg L −1 ), and the right chamber is filled with deionized water (0 mg L −1 ).b) Reproduced with permission. [52]Copyright 2022, Elsevier.c) Reproduced with permission. [53]Copyright 2023, American Chemical Society.free energy ignoring electrostatic contributions.In principle, the chemical potential in a mixture is determined by the activity a  i : where  o i is the chemical potential at the standard state, relative to a reference state (e.g.,  o H + = 0 at 298.15 K in water).  i is the activity coefficient.C o, i is a reference concentration (1 m for soluble species).Hence, the chemical potential of i increases with the concentration.Similarly, the electrochemical potential in the nanochannel ( μc i ) and solution  ( μ i ) can be written as where a c i and a  i are the ion activities in the nanochannel and solution .The electrochemical equilibrium is expressed as Therefore, as shown in Figure 3a, the Donnan potential  D at both sides of the nanochannel-solution interfaces (I and II) is calculated from ion activities in the solution and nanochannel: [45] Because a  i ≠ a c,I i ≠ a c,II i ≠ a  i , the counter-ions flow from one compartment to the other to reach equilibrium.Therefore, a charge imbalance and non-zero Donnan potential exist at both sides of the nanochannel-solution interfaces.To simplify the description, a negatively charged nanochannel and an ideal monovalent solution (the activity of a component is identical to its concentration, a  i = C  i ) are then considered.At the interface I, the Donnan ratio r D of counter-ions (cations, i = ca, z i = 1) and co-ions (anions, i = an, z i = −1) can thus be defined as Consequently, the relationship between the ion concentration inside the nanochannel and in the solution  is as follows: Inside the nanochannel, electroneutrality is established between the cation concentration, anion concentration, and negative surface charge: where C c s denotes the surface charge concentration averaged over the channel volume.The bulk concentrations C  ca and C  an are usually known beforehand in nanofluidic applications, and C c s are obtained from the measurements of zeta potential and surface charge density.Hence, the cation and anion concentrations inside the nanochannel can be calculated: [46] C c,I ca = 1 2 Therefore, at interface I, these concentration values have the following order: According to the above results, a charge imbalance exists at the nanochannel-solution interface, as represented by the enrichment of counter-ions (cations) and exclusion of co-ions (anions) from the nanochannel entrance, which is caused by electrostatic interactions between the tethered surface charges and mobile ions.Hence, the co-ions are inhibited across the nanochannel due to the sum of two driving forces acting in opposite directions: the ion concentration gradient and the Gibbs−Donnan effect itself.In contrast, counterions prefer to be transported to the low-concentration side, resulting in cation selectivity.Hence, the Gibbs−Donnan effect is at the root of nanofluidic diodes and surface-charge-governed ion transport, and it accounts for most of the transport selectivity observed in experiments. [47]It should be noted that protons have different transport mechanisms and small hydrated ionic sizes compared with common ions in seawater, so their transport through nanochannels is not significantly affected by the electrostatic field. [48]In addition, the nanochannel-solution interface also forms a diffusion boundary layer because of the different ion transport numbers in the solution compared with those in the nanochannel.This phenomenon is known as ion concentration polarization (ICP), which indicates a partially reduced concentration on the high-concentration side and an increased concentration on the low-concentration side, thereby decreasing the effective concentration gradient across the nanochannel.Hence, the distributions of the concentration and electric potential near the nanochannel opening are more complex when the Gibbs-Donnan effect and ICP phenomenon are considered simultaneously.When attention is drawn from interface I to the entire process of ion transport across the nanochannel, the Gibbs-Donnan effect emerges again at interface II.In this case, several discrepancies and new terms appear.In detail, an ion flux across the nanochannel creates a membrane potential  m , which has three components: The terms   and   are the electric potential on each edge of the nanochannel.The term E diff is the diffusion potential along the nanochannel caused by the discrepant mobilities between cations and anions, as described by the gradually increasing electric potential inside the nanochannel.In principle, compared with the low-concentration side, the surface negative charges of the nanochannel near the high-concentration side are more effectively screened.Consequently, the magnitude of the Donnan potential at the high-concentration side ( D 1 ) is relatively smaller than that at the low-concentration side ( D 2 ).When the surface charge is uniformly distributed and at a low to medium salinity gradient, the difference between the  D 1 and  D 2 values could be neglected. [49]Under this circumstance, the membrane potential  m has the same value as the diffusion potential E diff , and this approximation is widely adopted in the simulation and experimental research of osmotic energy conversion. [50]Hence, for a monovalent salt, the membrane potential can be directly measured and is related to the experimental variables: [51] where S is the ion selectivity, and a H and a L are the salt activities on the high-concentration and low-concentration sides, respectively.
The Gibbs−Donnan effect and its induced ion selectivity have been examined by simulations and experiments.As shown in Figure 3b, when the concentration gradient drives ion transport across a negatively charged nanochannel, the ion concentrations exhibit sharp variations, generating a charge imbalance on both sides of the nanochannel. [52]Particularly, significant cation accumulation and anion depletion occur at the entrance, and then the concentration profiles slowly decrease inside the nanochannel and reproduce drastic changes at the exit.Hence, the co-ion exclusion and counter-ion enrichment imply preferable cation selectivity.As shown in Figure 3c, the cation selectivity is visualized by monitoring the ion concentration evolution. [53]Because a vacancy-introduced NbP (V-NbP) membrane separates the left chamber at a high concentration and the right chamber containing only deionized water, both the left and right chambers maintain constant anion concentrations at their initial values.In contrast, the cation concentration in the left chamber decreases over time, and it increases in the right chamber at a gradually decreasing rate.These phenomena indicate that cations prefer to transport through the nanochannels in the V-NbP membrane, whereas anions are prohibited completely, confirming the cation selectivity due to the Gibbs−Donnan effect.
In principle, the Gibbs−Donnan effect originates from the electrostatic interactions at the nanochannel-solution interfaces, it could be consolidated by altering both the properties of electrolyte solution and nanochannels.For example, ion species with high valence can be used to increase the charge of ions.The introduction of locally concentrated surface charges at the channel openings is another effective approach, which can be realized by designing the physical geometry and chemically modifying the nanochannel surface.

Ion Selectivity
Ion selectivity is a crucial aspect of nanochannel-based mass transfer.In principle, the relationship between the channel height h and the Debye length  D is the widely used theoretical framework to evaluate ion selectivity in nanochannels.When h < 2 D , the Debye layers overlap to induce counter-ion enrichment and co-ion exclusion from the channel opening, due to the electrostatic interactions with the surface charge.Permselectivity is  [49] Copyright 2021, American Chemical Society.b) Reproduced with permission. [16]Copyright 2022, American Chemical Society.c) Reproduced with permission. [56]Copyright 2015, National Academy of Sciences.
then achieved to allow only the counter-ions to migrate across the nanochannels, and a narrower channel size and lower ion concentration are beneficial to counter-ion selectivity.Because the solution property is the only consideration of the Debye length, a more complete criterion of ion selectivity involving both solutionand surface-side characteristics is pursued, which is achieved using the Dukhin length (l Du ). [54]The Dukhin length is expressed in terms of the surface charge density  s as where C ∞ is the bulk ion concentration.Consequently, the Dukhin length is the channel scale characterizing the competition between the surface and bulk conductance (representing the number of free charge carriers, here ions), below which the surface conductance is dominant over the bulk conductance.The nanochannels then exhibit ion selectivity when h < l Du (or the Dukhin number Du = l Du /h > 1), and a highly charged nanochannel surface has a greater tendency to induce ion selectivity.For the typical surface charge density of 50 mC cm −2 , l Du varies from 0.5 nm at 1 m to 500 nm at 0.1 mm.Hence, the l Du value is 1 to 2 orders of magnitude larger than the corresponding  D values under the same concentration conditions.Thus, this ion selectivity criterion using the Dukhin length is looser than that using the Debye length.Significant selectivity may be realized in large nanochannels (10-100 nm) with adequate surface charges, which has meaningful implications for osmotic energy generation and other nanochannel-based nanofluidic applications.
In experiments, the ion selectivity S of a charged nanochannel can be related to experimental variables: where J + and J − are the cationic and anionic fluxes, respectively.t + and t − are the cationic and anionic transference numbers, respectively.E oc is the open-circuit potential obtained from the current-voltage (I-V) test.R, T, z, F, and  are the gas constant, temperature, ion valence, Faraday constant, and ion activity coefficient, respectively.C H and C L are the high and low ion concentrations in the reservoir, respectively.Higher selectivity is indicated by a larger S value.The selectivity is unity for a perfectly selective nanochannel that completely prevents the co-ion transport.In contrast, because an uncharged nanochannel cannot distinguish between the transport of counter-ions and co-ions, selectivity becomes zero.This evaluation criterion is widely used in simulation and experimental studies, and is determined through frequent testing. [49]Figure 4a shows the ion selectivity contours for the different combinations of salt concentrations.The ion selectivity reaches a maximum value of close to 1 when the salt concentration on both sides of the negatively charged nanopores are less than 100 mm.However, it exhibits a significant decline once the solution concentrations increase, which is attributed to the less EDL overlap at high ion concentrations.This contour has crucial guiding significance for practical applications, such as osmotic power generation, in which a salinity gradient between 500 and 10 mm electrolytes is involved.
Along with the idea of considering the solution-and surfaceside characteristics concurrently, our group has made significant advancements in exploring and pushing forward this physical theoretical framework for selectivity evaluation.The cation selectivity is evaluated using the Se parameter: [55] Se = In this expression, Se is a dimensionless parameter derived from the non-dimensionalized Poisson-Nernst-Planck (P-N-P) equation coupled with the Navier-Stokes equations. s (T, C) is the surface charge density influenced by the absolute temperature T and local cation concentration in nanochannels C. Therefore, C has a complex impact on selectivity as it appears both explicitly in the denominator and implicitly in the numerator.Overall, a more positive Se value indicates better selectivity in nanochannels.Figure 4b shows a comparison of the cation selectivities of graphene oxide sheets under different temperature and concentration conditions.An increase in temperature improves the cation selectivity, whereas an excessive ion concentration has the opposite effect, which can be attributed to environmentdependent hydroxyl deprotonation reactions.
In addition to the aforementioned conceptual, experimental, and physical perspectives, ion selectivity can be understood from an energy perspective.The divergence of thermodynamic properties of hydrated ions plays a crucial role in the selective ion transport in nanochannels.The formation energy ΔE of a hydrated ion is regarded as the energy difference of the hydrated ion in the nanochannel compared to that in bulk water.For example, the formation energy of hydrated K + and Na + ions in carbon nanotube (CNT) can be defined as The formation energy can be calculated using DFT methods.Moreover, the relative stability of hydrated K + and Na + ions in CNTs can be determined by the difference between their formation energies (ΔΔE): Then, the K + /Na + selectivity S (K + /Na + ) can be defined by substituting the ΔΔE(K + -Na + ) into the Arrhenius equation: where k B is Boltzmann constant.Hence, a negative ΔΔE(K + /Na + ) value indicates that it requires more energy to move an Na + ion from the bulk solution into the CNT than a K + ion.This results in an S (K + /Na + ) value greater than 1, indicating a higher selectivity for K + ions than for Na + ions.A similar derivation process can be implemented for synthetic organic nanopores (SONP) and other nanochannels.Figure 4c shows the S (K + /Na + ) value as a function of the channel size in CNTs and SONP at a temperature of 290 K. [56] The highest S (K + /Na + ) value of ≈15 000 is observed in (8, 8) CNT with a radius of ≈3.7 Å, indicating exceptional selectivity for K + ions over Na + ions.This derivation can be popularized to obtain selectivity between two random ions, providing important information for determining ion transport priorities for applications such as osmotic power generation and ion sieving.

Ion Behavior in Nanoconfined Space
The overall osmotic performance of nanochannels is a result of the microscopic ion behavior, which involves ion-wall, ion-ion, and ion-solvent interactions at solid-liquid interfaces under the integrated impacts of diverse factors.These fascinating phenomena, owing to geometric and chemical factors, deserve an underlying understanding based on fundamental insights.

Electron Transfer at Solid-Liquid Interface
The relationship between the ion transport and electron transfer is complex and intertwined.Insufficient outermost electrons lead to the formation of charged ions, resulting in electrostatic interactions between other ions and the polar solvents.Moreover, interfacial electron transfer rearranges the ion distributions upon ion adsorption, which is an electronic-level description of the interfacial interactions, thereby regulating the EDL overlapping, ion selectivity, and ion diffusivity.These processes are influenced by various elements including ion contents, concentration, and temperature.To fully understand ion behaviors in nanochannels, it is essential to first clarify the physical mechanisms of electron transfer at solid-liquid interfaces, including the origin, characteristics, impact factors, and consequences of ion transport.Interfacial electron transfer stems from the angstrom-scale solid-liquid contact distance.This phenomenon can be observed in a variety of materials including graphite, [57] MoS 2 , [58] and hexagonal boron nitride. [59]As shown in Figure 5a, when these solid materials are isolated from aqueous solutions, electron transfer is prevented because of the high energy barrier between the solid and liquid atoms.However, when these materials come into contact with electrolytes, the distance between the solid surface atoms and aqueous ions and water molecules becomes shorter than the equilibrium distance owing to thermal motion and liquid pressure.Consequently, the valence electron clouds of the interfacial atoms can overlap, reducing the energy barriers and allowing electron transfer between the solid surface atoms and aqueous atoms. [60]This results in surface electrification as the electrolyte solution flows on the solid surface.It is important to note that electron transfer is sensitive to temperature and ion concentration.As confirmed by experiments, [61] the surface electrons obtained by interfacial electron transfer get more energy during the heating process, thereby being thermally excited and emitted from the surface.Hence, a temperature increase would lead to a surface electron discharge.Surface electron discharge can also be facilitated by increasing the salt ion concentration through an increase in the dielectric constant of the solution.
In addition to external factors, the intrinsic element that plays a dominant role in the electron transfer effects is the hydrophilicity of the solid walls.From a microscopic chemical perspective, surface hydrophilicity is determined by the coverage of hydrophilic  [60] Copyright 2019, Elsevier.d) Reproduced with permission. [62]Copyright 2018, Royal Society of Chemistry.e,f) Reproduced with permission. [16]Copyright 2022, American Chemical Society.functional groups.As depicted in Figure 5b, when the solid surface lacks hydrophilic groups and is flat, dehydration occurs because of the size effect of the hydrated ions in a confined space. [17]his leads to a solid-liquid contact distance that is typically on the angstrom scale, which is favorable for interfacial electron transfer.On the other hand, the functional groups like amino (─NH 2 ), hydroxyl (─COH), epoxide ( ⏜ ⏜ C-O-C ), carboxyl (─COOH), and aldehyde (─CHO) groups are hydrophilic, and they are widely present in a variety of nanochannel materials.As shown in Fig- ure 5c, when hydrophilic nanochannels are used for aqueous ion transport, the channel walls become rough and extended into the solution.Strong interactions thus exist between the hydrated cations and functional groups.Hence, the solid-liquid interface becomes indented, further reducing the contact distance compared with flat channels, causing more obvious electron transfer effects.
The extent of the interfacial electron transfer can be assessed using first-principles calculations that measure the electron density difference.As demonstrated by Figure 5d, the flat interface between a platinum surface and water has a close contact distance of ≈3 Å, making it possible for electron transfer to occur by overcoming the energy barrier. [62]The same phenomenon can be observed on other smooth surfaces, such as carbon nanotubes, [17] graphene, [63] and boron nitride.In contrast, rough interfaces, such as those between graphene oxide and an aqueous solution (Figure 5e), exhibit clear contours of the electron density difference. [16]This electron transfer can be observed on the aqueous surfaces of functionalized MXene, metal-organic framework (MOF), and COF.
The electron transfer that occurs at the solid-liquid interface has both direct and indirect effects on ion transport in nanochannels.A direct impact is observed on surface electrification, which is quantified by the Bader charge population in Figure 5f.For example, when graphene oxide is in contact with an NaCl solution, the oxygen atoms in the surface functional groups have the most negative charges, leading to an overall negatively charged surface (−0.08|e|).This negative surface charge creates electrostatic interactions between the charged walls and counter-ions.Particularly, the surface charge causes ion adsorption and produces a concentrated hydrated ion layer near the solid wall.Subsequently, the concentration of residual ions decreases with increasing distance from the wall.These processes explain the origin of the interfacial EDLs, as described by the G-C-S model.After combining multiple solid-liquid interfaces to form nanochannels, the EDL overlap leads to the selective passage of counterions and inhibition of co-ions, known as ion selectivity, which is critical for osmotic energy conversion.On the other hand, the indirect impact of electron transfer on ion transport is observed in the formation of chemically active interfacial regions, especially in wall materials with hydrophilic groups, as shown in Figure 5c.Specifically, the accumulation and depletion of electrons around the extended surface groups cause charge redistributions near hydrated ions and water molecules, serving as the basis for the unique ion behaviors in nanochannels.

Interfacial Effects
Hydrated ions are formed when the central bare ions in an aqueous solution attract a certain number of polar water molecules.The size of these hydrated ions varies and depends on the ion type and surrounding environment.In bulk seawater, the cationic hydrated shells are complete and follow a specific order of size: Mg 2+ > Ca 2+ > Na + > K + .However, when these ions migrate in confined spaces such as nanochannels, interfacial effects such as solvation structure rearrangement (also known as dehydration), [64] H-bond generation, and chemical reactions occur.These interfacial effects result in fascinating ion migration kinetics that differs from those of bulk solutions.Therefore, it is meaningful to delve into these effects, gain a deeper insight into microscopic ion behavior, and explain the macroscopic performance of ion transport in nanochannels.
As shown in Figure 6a, when ions migrate into nanochannels, the ion hydration shells are disrupted as the channel size becomes equivalent to the original hydrated ion size.This process is accompanied by energy consumption, which results in discrepant ion diffusivities in the lateral and vertical directions as the ion solvation environment is altered at the solid-liquid interface.Meanwhile, the close distance between the hydrophilic surface and hydrated ions generates H-bonds, linking the surface groups and solvated water molecules.The H-bond type depends on the donor and acceptor atoms, as determined by the functional group characteristics.For example, if hydrophilic groups only have electronegative oxygen atoms, such as epoxide groups, hydrogen atoms in the interfacial water molecules serve as donors forming a single H-bond (Figure 6a).However, if the hydrophilic groups have both oxygen and hydrogen atoms, such as hydroxyl and carboxyl groups, the water molecules can act as both H-bond donors and acceptors (Figure 6b).Additionally, functional groups provide natural sites for chemical reactions because of their intrinsic activity and the participation of aqueous species.These interfacial reactions create rapid lateral pathways for hydrated ions, leading to anisotropic ion diffusion in nanochannels.Furthermore, upon spontaneous bond formation and breaking, the epoxide-opening reaction produces a negative alcoholate group CO − and a positive carbon atom C + on the surface (Figure 6a), which do not contribute to the surface charge.Conversely, owing to the involvement of interfacial water molecules, hydroxyl deprotonation generates a negative surface charge through the formation of a surface CO − and a positive hydronium ion H 3 O + in aqueous solutions (Figure 6b).Consequently, an EDL is formed and attracts counter-ions at the solid-liquid interface.
In addition to the intrinsic properties, interfacial effects are also influenced by external factors such as temperature and local ion concentration in confined spaces.As shown in Figure 6c, the Na + ions maintain their first hydration shells with stable and incomplete structures, indicating environment-insensitive interactions between the central Na + ion and solvated water molecules.In contrast, the Na + -Na + structure represents interactions between hydrated ions.An elevated temperature causes the ordered Na + -Na + structure to become disordered, thereby promoting ion diffusion.A higher concentration leads to a more crowded ion distribution in the confined space, which causes the two hydrated ions to overlap, thereby restricting ion diffusion.The local environment exerts a more complex effect on the interfacial H-bonds by altering their numbers.As shown in Figure 6d, a 50 K increase in temperature has a limited impact on the average number of H-bonds under the same coverage of hydrophilic groups.However, a higher concentration means more solvated water and more H-bonding sites at the interface, causing an increase in the number of H-bonds, particularly when graphene oxide is used as an acceptor.Consequently, a slower diffusion of hydrated ions can be expected in nanochannels at excessive concentrations.
The dynamic impacts of external factors on interfacial reactions can be visualized through time-evolving reaction events, which demonstrate reaction continuity and strength.As illustrated in Figure 6e, an increase in temperature leads to a transformation from mild, sporadic reactions to frequent, consistent reactions, and an increase in concentration has a detrimental effect on the reactions as a whole.Because continuous chemical reactions provide fast lateral ion pathways, the temperature rise and concentration enlargement play positive and negative roles in the anisotropy of interfacial ion transport, respectively.Moreover, the impacts of hydroxyl deprotonation reaction on surface electrification can be assessed by the surface charge density  s as a function of temperature T and local ion concentration C: where N 2,avg is the time-averaged number of hydroxyl deprotonation, e is the elementary charge (16 022 × 10 −20 mC), and A is the graphene oxide area.This surface electrification is a defining characteristic of hydrophilic surfaces that can undergo deprotonation reactions, distinguishing it from the surface electrification arising from intrinsic interfacial electron transfer.As shown in Figure 6f, both an increase in temperature and ion concentration contribute to an increase in the negative surface charge density, which is a result of the enhanced interfacial hydroxyl deprotonation.Average number of H-bonds depending on temperature and ion concentration.e) Time-evolved chemical reaction numbers.f) Surface charge density stemming from the hydroxyl deprotonation process.a-f) Reproduced with permission. [16]Copyright 2022, American Chemical Society.

Surface Conductance
The processes of hydrated ions entering and transporting through electrified nanochannels require energy consumption owing to the nanoconfined space.This energy consumption can be regarded as an energy barrier E a , which is reflected in dehydration and steric hindrance under the integrated impacts of surface charge and nanochannel geometry.For instance, as shown in Figure 7a, a more negative surface charge density  s can attract more cations, thus providing an additional driving force for cation transport.Hence, any method of inducing more surface charges can reduce the energy barrier, [65] and the same consequence can also stem from nanochannel geometry regulation.This energy barrier E a has a direct correlation with the ionic conductance G, which characterizes the ion transport performance of nanochannels, as described by the empirical Arrhenius equation: where A is a constant.This equation treats the energy barrier as a temperature-independent constant, agreeing with experimental results within a certain temperature range.
In these experiments, the ionic conductance of nanochannels is measured in the presence of symmetric salt concentrations. [66]nder these conditions, a nanoporous membrane with nanochannels is used to separate two reservoirs filled with two identical electrolyte solutions.Subsequently, by implementing a cyclic linear sweep voltage program, the anions and  [65] Copyright 2020, Wiley-VCH.Reproduced with permission. [69]Copyright 2022, Royal Society of Chemistry.c) Reproduced with permission. [46]Copyright 2008, American Physical Society.d) Reproduced with permission. [74]Copyright 2022, Springer Nature.e) Reproduced with permission. [75]Copyright 2004, American Physical Society.f) Reproduced with permission. [53]Copyright 2023, American Chemical Society.
cations in the solution are driven to migrate directionally by the electric field, resulting in an ion current.The ion current passing through the nanochannel is measured using non-polarized electrodes (e.g., Ag/AgCl electrodes), thus obtaining serial I-V curves, as shown in the inset of Figure 7b.Finally, the linear relationship between the transmembrane current and voltage (slope of the I-V curve) is regarded as the ionic conductance.As shown in Figure 7b, the ionic conductance G of the MOF membrane is recorded in 0.001 m KCl reservoirs at different temperatures ranging from 298 to 318 K before light illumination, and it is experimentally tested by applying a voltage to provide the driving force for ion migration. [65]The G value varies exponentially with the inverse of the temperature, showing Arrhenius behavior.This Arrhenius behavior is typical of ion transport in extremely narrow nanochannels, such as the sub-nanometer layer spacing of graphene oxide membranes. [67]The corresponding E a value is calculated to be 0.229 eV according to the Arrhenius equation.Using the same test procedure, the ionic conductance is monitored during light illumination on the membrane.The E a value reduces proportionately with an enhanced light power density, and a light power density of up to 48.1 mW cm −2 can cause a decline in E a value by ≈0.025 eV.These results are based on the fact that light can generate additional surface charges on the dielectric surface. [68]Accordingly, more cations are attracted into the nanochannels, enhancing ion driving force and reducing the energy barrier.Because ion transport regulation in conventional solid-state nanochannels is challenging due to the limited Debye length at high concentrations, the above energy-barrier-based approach enables robust ion transport modulation over a wide concentration range.Along the same idea, ionic conductance is also measured in 0.01 m NaCl electrolyte at different temperatures from 298 to 333 K, to investigate ion transport behavior in the graphene oxide/aramid nanofiber (GO/ANF/GO) composite membrane. [69]A similar Arrhenius behavior is observed, and the energy barrier E a for ion transport becomes 0.159 eV, which is even lower than that of other 2D layered membranes. [70]This excellent ion transport performance is attributed to the higher surface charge density of nanochannels, due to the presence of more oxygen-containing functional groups after the introduction of ANF.
The aforementioned energy barrier and ionic conductance are empirical summaries based on the experimental data obtained at a single concentration ignoring the temperature-dependent energy barrier.The expression for ionic conductance needs to be further derived to decouple the effects of various parameters.In principle, as the reciprocal of electrical resistance R e , the conductance G of a conductor is defined from the electric current I versus electric potential drop Δ relationship: where  is the conductivity.s and d are the cross-sectional area and length of the conductor, respectively.G is proportional to  for a certain conductor with the known s and d values.In a nanofluidic system, conductance probes the number of free charge carriers (ions).For the monovalent electrolyte, the conductivity of a bulk solution  bulk is expressed by: where μ i , μ + , and μ − are the mobilities of ions i, cation, and anion, respectively.N A is Avogadro constant (6.022 × 10 23 ).The bulk ionic conductance G bulk can be then calculated as Hence, given a certain nanochannel size, both  and G are expected to be proportional to the bulk concentration C i,∞ (or ionic strength) in the bulk solution.
Similarly, when an aqueous solution is transported through a nanochannel with negative surface charges and complete cation selectivity, its contribution to the conductivity becomes: where C e is the excess mobile counter-ion concentration inside the nanochannel, and it is obtained by considering an overall electroneutrality in the nanochannel where the negative surface charge density  s is balanced by counter-ions (cations): where h is the nanochannel height.Therefore, the ionic conductance contributed by the excess ion concentration is usually termed the surface conductance G surface , and it is expressed as Consequently, the surface conductance is governed by the surface charge density and is affected by the channel geometry and counter-ion mobility.Specifically, the counter-ion mobility in nanochannels can be altered by several factors such as surface hydrophilicity, binding between ions and channel walls, and hydration force.
When the system consists of a nanochannel and an aqueous solution of monovalent ion, the total nanochannel ionic conductance G is the superimposition of the bulk conductance G bulk and the surface conductance G surface , as expressed by When the nanochannel has a width w, height h, and length d, this expression is rewritten as: [53] Therefore, in the presence of electrified nanochannel surfaces, the surface charges can provide a supplementary contribution to conductance.High ionic conductance is essential for energy conversion applications.
Figure 7c shows the ionic conductance against the monovalent electrolyte concentration under the effects of channel width w, height h, and length d. [46] The trend of the nanochannel conductance G can be divided into two regions according to the relationship between the magnitude of the bulk concentration and transition concentration C t .At a concentration much higher than C t , the nanochannel conductance demonstrates a linear increase, which is therefore a bulk behavior depending on the channel geometry.When the bulk concentration is equal to C t , the surface and total conductance are identical.In this case, the C t value can be calculated to be 0.5 times the excess mobile counter-ion concentration in the nanochannel C e .At a concentration much lower than C t , the nanochannel conductance remains almost constant and is independent of the channel height, representing a typical surface-charge-governed ion transport phenomenon.In this plateau region, the bulk conductance is expected to disappear, whereas the surface contribution to the total conductance exhibits saturation.This saturation stems from the charge carriers brought by surface charge, which promotes counter-ion enrichment inside the nanochannels.Surface-charge-governed ion transport has been widely reported in nanofluidic membranes, such as carbonaceous mesoporous nanowires (CMWs), [71] mesoporous titania nanopillararrays/anodic aluminum oxide (MTI/AAO) membrane, [72] and MOF membrane. [73]ased on the above basic expression, the channel geometry has discrepant impacts on the surface and bulk conductance, as shown by the log-log scale ionic conductance in Figure 7c.An increment in the channel width w can concurrently improve surface and bulk conductance, whereas an increased channel length d has the opposite effect, and both modulations do not change the location of the transition concentration C t .Reducing the surface charge density  s only diminishes the surface conductance, but not the bulk conductance, and it also shifts the C t toward lower concentrations.By contrast, decreasing the channel height can only reduce the bulk conductance, and it pushes the C t toward higher concentrations.
Figure 7d shows an experimental example of concentrationdependent nanochannel conductance obtained by altering the surface charge density. [74]COF-EB x BD y /PAN membranes are used, where x/y refers to the molar ratio of ethidium bromide (EB) and monomer benzidine (BD) used during membrane synthesis.An increased proportion of EB boosts the surface charge density and provides additional surface conductance.Hence, at the KCl concentration of 10 −5 m, the G value is enlarged from 2.23 × 10 −4 μS to 4.40 × 10 −3 μS and 9.34 × 10 −2 μS for COF-BD/PAN, COF-EB 1 BD 5 /PAN, and COF-EB/PAN membranes, respectively, implying ultrafast ion migration through membranes.In contrast, because the boosted surface charge does not affect the bulk conductance, the G values at ultrahigh concentrations remain unchanged.Figure 7e shows the nanochannel conductance as a function of the height of the silica channel with an approximately constant surface charge density. [75]Larger channel heights mean larger bulk conductance values, whereas the surface conductance is almost unaffected.Figure 7f shows the synergistic optimization of the surface charge density and channel width for promoting nanochannel conductance. [53]In principle, both the  [78] Copyright 2014, American Chemical Society.d) Reproduced with permission. [4]Copyright 2019, Wiley-VCH.e) Reproduced with permission. [86]Copyright 2022, American Association for the Advancement of Science (AAAS).f) Reproduced with permission. [89]Copyright 2020, American Chemical Society.
original NbP and the V-NbP membranes have the same interlayer spacing (channel height) of about 8 Å, whereas the latter has the augmented negative surface density due to the introduction of phosphorus vacancy.This modification enhances membrane hydrophilicity and boosts interfacial contact with water molecules, thereby facilitating ion transport in the membrane and improving surface conductance.In contrast, V-NbP has an increased porosity (channel width), which can accelerate ion migration dynamics and promote bulk conductance.Compared with NbP, V-NbP demonstrates a higher surface and bulk conductance over the entire concentration region.The corresponding transition NaCl concentration C t is also increased from ≈0.1 mm for NbP to ≈1 mm for V-NbP.These results confirm the availability of surface charge and channel geometry regulations for boosting the nanochannel ionic conductance in energy conversion applications.

Ionic Rectification
The aforementioned ion-selective nanochannels have symmetric geometries and surface charge distributions, so the measured currents have identical absolute values under voltages with the same amplitude but opposing polarities.However, as shown in Figure 8a, when the nanochannel possesses an asymmetric size and/or surface electrification, an asymmetric potential-dependent ion flux across the nanochannel emerges.These asymmetries give rise to nonlinear and diode-like I-V curves under symmetric electrolyte conditions (Figure 8b).This unique electrodynamic phenomenon is termed the ionic rectification effect, which is induced by the asymmetric EDL structures and thus the asymmetric ion transport of anions and cations inside nanochannels.Therefore, the rectification feature means a unidirectional ion transport, which is described by an enhanced current response at a given voltage polarity, similar to the semiconductor diode.Ion transport in nanochannels can thus switch between the "on" and "off" states, depending on the polarity of the applied voltage. [76]he rectification efficiency is quantified using the rectification ratio f, which is defined as the absolute ratio of the currents measured under voltages of identical amplitude but opposite polarities: Therefore, a rectification ratio close to one means a linear I-V relationship without the rectification effect.According to literature, either geometric or surface charge asymmetries can induce rectifying ion transport, and their combination can achieve the highest rectification ratio.From a more underlying perspective, the occurrence and intensity of ionic rectification are determined by the EDL structure in the nanochannel.Consequently, depending on how the EDL structure is regulated, the factors affecting the rectification ratio can be classified into thermodynamic and kinetic factors.The thermodynamic factors primarily include the electrolyte concentration, channel geometry, and surface charge; the kinetic factors include the convective flow disturbing ion distribution in the nanochannel and the scan rate during the I-V tests.The relationship between the rectification ratio f and all these factors can be qualitatively summarized as follows: [77] f In this expression, A represents the asymmetry of channel geometry h, ion concentration C i , and surface charge density  s .f sur indicates factors related to the amount of surface charge.f e illustrates the factors related to ion concentration C i .K represents the kinetics factors including the scan rate and convective flow velocity.The underlying mechanisms of these factors in the ionic rectification effect deserve a detailed discussion.
The electrolyte concentration determines the EDL thickness, thereby directly influencing ionic rectification.This influence can be discussed from the absolute concentration in the solution reservoirs and the asymmetric concentration distribution (concentration gradient).As shown in Figure 8c, the diode-like behavior almost disappears (f = 8) in the saturated KCl solution owing to the decrease in the EDL. [78]However, the ionic rectification becomes more pronounced with the dilution process, and the highest rectification ratio reaches 449 in 0.1 m KCl.The same trend is observed in a euryhaline-fish-inspired nanofluidic diode system. [79]Meanwhile, excessive dilution of the solution concentration (e.g., less than 1 mm) is detrimental to ion rectification due to the decreased number of ions in confined nanochannels.On the other hand, a concentration gradient can also contribute to ionic rectification in symmetric nanochannels owing to the asymmetric concentration distribution at opposite voltages. [80]s a widely used method to regulate the ion transport properties, the nanochannel geometry can be designed to be conical, [81] cigar-like, [82] or bullet-like. [83]In asymmetric channel geometries, the tip shape particularly affects the electric field distribution, thus enhancing ion mobility inside nanochannels, and a reduced tip size promotes the rectification phenomenon.In addition, the dynamic change in the nanochannel curvature can adjust ionic rectification in real-time.As shown in Figure 8d, the unbent carbon nanochannel exhibits a linear I-V curve, whereas the asymmetric bending of nanochannels can induce a rectification effect. [4]Despite these progresses, the precise determination of the correlation between the degree of geometric symmetry breaking and asymmetric ion transport characteristics remains challenging.A combination of more refined experimental tools and simulation methods may lead to achieving the goal.
Surface charge is another decisive factor that modulates the ion transport behavior in nanochannels.Several geometrically asymmetric nanochannels present a zero rectification ratio when the surface charge is neutralized, [84] implying the importance of the surface charge in the occurrence of ionic rectification phenomenon.The amount and distribution of the surface charge further alters the rectification intensity by regulating the ion dis-tribution inside the EDL. [85]A higher surface charge usually leads to a higher rectification ratio, which can be realized experimentally using diverse chemical modification methods.Besides, the rectification direction could be directly turned by the inverse surface charge, which implies the exchanged "on" and "off" states in a nanofluidic diode.
In addition to the thermodynamic factors involved in the above qualitative expression, the ion size, electrolyte pH, and temperature also serve as potential factors modulating the direction and intensity of ionic rectification.As shown in Figure 8e, alkaline metal ions and protons exhibit counter-directional rectifying transport in the MOF nanochannels, which is attributed to their distinct transport mechanisms in such confined spaces. [86]The highly ordered arrangement of water molecule clusters under the confinement effect provides a more effective medium for proton conduction via the Grotthuss mechanism.Electrolyte pH can alter the dissociation of functional groups, thus adjusting the sign and density of the surface charge.An elevated temperature can accelerate ion movement and promote the above dissociation reactions, thus influencing the ion transport behavior. [87]onic rectification can be further adjusted by kinetic factors, including convective flow and scan rate.As a well-known concept, fluid convective flow induced by a pressure gradient generally causes a decrease in the rectification ratio, which is attributed to the changed ion distribution inside nanochannels, as observed in conical nanochannels. [88]This phenomenon becomes negligible in small nanochannels owing to the limited influence of pressure.As a counter-example, Figure 8f shows that the rectification ratio can exhibit an anomalous increment with applied pressure up to 0.5 bar despite the lack of the usually required geometrical asymmetry, [89] which is rationalized in terms of the entrance effects disturbing ion distributions around nanochannels.The ion distribution in nanochannels can also be controlled by the scan rate.The rectification ratio at a low scan rate is maintained at its maximum due to the relatively stationary ion transport.Under a high scan rate, the ion redistribution process appears sluggish with respect to the fast variation in applied potentials, so the I-V curves tend to be linear and the rectification phenomenon is depressed. [90]ltogether, these asymmetric diode-like ion transport behaviors have inspired innovative materials and devices for applications in numerous fields, such as ion sieving, [91] desalination, [92] ionic circuits, [93] nanofluidic biosensors, [94] and energy conversion. [95]

Ion Diffusion and Fluid Diffusio-Osmosis
In a confined space, the interfacial EDL has a significant impact on the motion of ions and water molecules. [96]Various transport modes exist for ions and fluids in nanochannels, including ionic self-diffusion due to random thermal motion and macroscopic transport driven by thermodynamic forces, such as a concentration, pressure, potential (electric field), and temperature gradients.In particular, the concentration gradient can drive the ionic Fick diffusion, and the pressure gradient caused by the concentration gradient can generate a diffusio-osmosis of the overall fluid.These transport modes play crucial roles in nanochannel-based applications, such as  [16] Copyright 2022, American Chemical Society.b) Reproduced with permission. [56]Copyright 2015, National Academy of Sciences.d) Reproduced with permission. [108]Copyright 2021, Wiley-VCH.
Ionic self-diffusion refers to ion thermal motion without a concentration gradient, and the corresponding self-diffusion coefficient represents the activity of Brownian motion in a local aqueous environment.Because it is difficult to focus on the local nanochannel environment using common experimental methods, the ion self-diffusion coefficient D is typically calculated through molecular simulation using the Einstein relation and mean-square displacement (MSD).This criterion for evaluating ion diffusivity has been extensively used in various studies, such as proton transport in the interlayer spacing of MXene, [100] proton transfer in confined water environments, [101] and hydroxide ion diffusion on the surface of 2D material. [63]According to the aforementioned nanochannel classification, the studies of tubelike and plate-like channels are focuses on to discuss the research progress in simulating the ion self-diffusion coefficient, given the challenge of modeling complex porous channels.As a quantitative presentation, Figure 9a shows the Na + ion self-diffusion coefficient (diffusivity) on the graphene oxide surface under the temperature and concentration regulations. [16]The interface features a rough plate-like configuration, where the molecular-scale roughness is a result of the extended surface functional groups.All diffusivities are lower than those in bulk dilute solutions, indicating the restriction imposed by the solid-liquid interface.In this case, although Na + ion exhibits 3D movement, its lateral diffusion is faster than the vertical diffusion due to the hindrance caused by the graphene oxide sheet.An increase in temperature further leads to an improvement in ion diffusivity and anisotropy, whereas an excessive concentration has the opposite effect.To maximize the ion flux, a combination of elevated temperature and low concentration is recommended for osmotic energy conversion because the lateral diffusion (parallel to the EDL) is favorable in this case.In Figure 9b, the axial diffusivities of cations in CNTs and SONP are compared using water diffusivity as a reference. [56]The anisotropy is present again in these tubelike structures, with a focus on the axial-direction ion diffusion.Specifically, the smooth and hydrophobic walls of CNT result in accelerated ion movement, whereas the rough inner surface of SONP due to dangling C─H groups impedes ion translational movement.As the CNT radius increases, both Na + and K + ion diffusivities show non-monotonic variations with different turning points.In particular, Na + and K + ions exhibit high axial diffusivities in the (8, 8) and (10, 10) CNTs, respectively.This discrepancy is caused by the difference in the hydration shells of hydrated Na + and K + ions in the confined channels.Therefore, sub-nanometer CNTs have been found to enhance ion diffusivity, whereas the confined SONP slow ion transport.
In contrast, ionic Fick diffusion, driven by a concentration gradient, can generate a net ion flux.The chemical diffusion coefficient (CDC) is commonly used to quantify this behavior.This parameter reflects the ion diffusion-mass-transfer rate and has been measured experimentally using various electrochemical methods, such as cyclic voltammetry (CV), [102] electrochemical impedance spectroscopy (EIS), [103] and the galvanostatic intermittent titration technique (GITT). [104]The chemical diffusion coefficient is an important metric for studying ion dynamics in nanoporous materials and is widely used in nanochannel-based electrochemical systems, such as nanogenerator devices, supercapacitors, and ion batteries.
Moreover, the diffusio-osmotic flow of fluid is a unique phenomenon occurring in nanochannels, and its origin and mechanism deserve a detailed explanation.In principle, the EDL at an electrified interface of the nanochannel represents the attraction to counter-ions and the repulsion of co-ions, which implies that discrepant forces act separately on the solvent and solute.These specific forces can induce interfacially driven osmotic flow.As shown in Figure 9c, the ion-surface electrical interaction causes an attractive electrostatic force on the fluid, as described by a perpendicular interaction potential.This interaction is stronger at higher salt concentrations.Accordingly, when a salt concentration gradient exists parallel to the charged interface, the normal body force is converted into a parallel osmotic pressure gradient in the diffuse layer close to the electrified surface.Eventually, net fluid motion from high to low concentrations is produced to form a flux with a plug-like profile, which is termed diffusioosmotic flow.This diffusio-osmotic transport can drag ions inside the EDL, thereby resulting in charge separation and osmotic current generation.
Based on the above fundamental concept, the diffusio-osmotic velocity far from the surface (in the bulk fluid) can be derived according to the Stokes equation and the spatial distribution of counter-ions and co-ions in the EDL, which follows the Poisson-Boltzmann distribution.The detailed derivation can be reproduced according to the pioneering study by Derjaguin, [105] the milestone summary by Bocquet, [106] and other relevant studies. [43]The exact and approximate results are discussed as follows.In a system consisting of an electrified surface and an electrolyte, the diffusio-osmotic velocity V DO is exactly expressed as where D DO is the diffusio-osmotic mobility,  is the fluid viscosity, l B is the Bjerrum length (≈0.7 nm in monovalent electrolyte solution at ambient temperature),  * 0 is dimensionless electrical potential on the surface, C ∞ is bulk concentration inside the nanochannel far away from the surface.When the difference in diffusivity between cation and anion is negligible, no electric field arises from the difference in ion mobility.In this case, the diffuse layer thickness is described by the concentration-dependent Debye length, and the V DO expression can be simplified as: [107] V where x denotes the direction parallel to the surface.Therefore, the amplitude of diffusio-osmotic velocity is proportional to the gradient of the logarithm of salt concentration, which has been confirmed by numerous experimental investigations.For instance, Figure 9d compares the diffusio-osmotic velocity V DO depending on the KCl concentration gradient in different nanopores. [108]All the V DO values exhibit linear variations with differences in the logarithmic electrolyte concentration.In summary, interfacial electron transfer and ion-wall electrostatic interactions provide the basis for diversified interfacial effects and surface-charge-governed ion transport inside nanocon-fined spaces.The manipulability of channel geometries and electrified conditions also offers opportunities for novel ion transport behaviors, including ionic rectification, anomalous ion diffusivity different from that of bulk solutions, and fluid diffusio-osmotic flow stemming from interfacial interactions.Given the coupled effects of channel-side and electrolyte-side properties and complex nanoconfined spaces composed of various particles (including electrons, ions, surface atoms, and water molecules), the study of ion behavior and its underlying physical mechanisms inside nanochannels continues to be a dynamic area of research.

Theoretical Study on Osmotic Energy Conversion
The electronic and atomic insights described above have primarily focused on ion behavior in the local environment.To further investigate the nanochannel-based ion transport, we can scale it up to a continuum viewpoint and apply nanoscale fluid mechanics concepts to establish universal mathematical descriptions.Various theoretical and numerical methods can be used for parameter analysis and performance prediction, allowing us to directly relate the microscopic ion behavior to the macroscopic osmotic power generation performance.In this section, a comprehensive mathematical expression for ion transport and osmotic energy conversion is first discussed, and the research progress in finite element simulations is introduced.An original similarityprinciple perspective developed by our group for the parameter analysis of osmotic energy conversion is described.Atomic-level simulation is then discussed to probe the fundamental physical phenomena.Finally, an advanced equivalent circuit model for predicting the transient osmotic performance is presented.

Mathematical Description and Finite Element Simulation
In essence, a nanoporous membrane are tortuous porous media with various nanochannel configurations.The behavior of ions in nanochannels for osmotic power generation is highly intricate because it involves the interplay of multiple physical fields, including potential, concentration, velocity, and temperature.This complexity is reflected in the different ion transport modes, including Fick diffusion owing to concentration gradients, Soret thermal diffusion owing to temperature gradients, convection migration driven by pressure differences, and electrochemical migration driven by potential differences. [109]A precise mathematical description is crucial for elucidating the intricate relationships among the various physical fields involved in ion transport in nanochannels.
To describe the ion transport occurring in nanochannels for osmotic energy conversion, researchers commonly assume that the temperature distribution is uniform.In this case, the coupled multi-physical fields of potential, concentration, velocity, and temperature can be described by the Poisson-Nernst-Planck (P-N-P), Navier-Stokes (N-S), and continuity equations, [110] as summarized in Table 1.The Poisson and flux continuity equations describe charge and ion flux conservation, respectively.The N-S equation reflects momentum conservation under pressure, viscosity, and electrostatic forces.The N-P equation describes the Table 1.Governing equations of uniform-temperature and thermal-regulated osmotic energy conversion., , T, u, p, μ, R, and F are the permittivity, potential, temperature, velocity, pressure, dynamic viscosity, universal gas constant, and Faraday constant, respectively.z i , C i , D i ,  i , and J i are the valence, concentration, diffusivity, reduced Soret coefficient, and flux of the ith ionic species (i = 1 for cation, i = 2 for anion), respectively., c p ,  f , and k f are the density, specific capacity, electrical conductivity, and thermal conductivity of electrolyte solutions, respectively.k s is the thermal conductivity of the solid-part nanoporous membrane.

Equation name
Uniform-temperature osmotic energy conversion Thermal-regulated osmotic energy conversion Energy equation for solid -k s ∇ 2 T = 0 ion flux driven by ion convection, diffusion, and electromigration.Therefore, this is a critical area of focus for researchers.
To enhance osmotic performance, a temperature gradient is commonly applied between high-and low-concentration reservoirs, creating a temperature gradient in nanochannels, which requires a comprehensive mathematical description.Thermalregulated osmotic energy conversion can be explained by coupling P-N-P, N-S, continuity, and energy equations, considering the ion Soret effect, thermoelectrical flow, and heat transfer. [111]he non-uniform temperature distribution in nanochannels is reflected in the additional ionic driving forces and altered physical properties of the solution.Table 1 illustrates the effects of the non-uniform temperature distribution on the various equations.The − 2D i  i c i T ∇T term in the N-P equation indicates the contribution of the Soret effect-induced ion thermal diffusion to ion flux.The − 1 2 |∇| 2 ∇ term in the N-S equation is the electrothermal force caused by the altered permittivity.The energy equation for fluid describes the thermal convection, thermal conduction, and Joule heat from left to right.The ion velocity, primarily determined by electrostatic and electrothermal forces, is negligible at the device scale.Hence, the inertia force (defined by u∇u) in the N-S equation and the energy dissipation (approximately defined by μ(∇u) 2 ) in the energy equation for fluid are not involved.Additionally, the physical properties of the fluid, such as permittivity , dynamic viscosity μ, fluid conductivity  f , and diffusivity D i , are significantly affected by the fluid temperature.
In the field of osmotic energy conversion, the most important output performance indicators include current-voltage (I-V) curves, diffusion potential E diff , maximum output power P max , and energy conversion efficiency .To obtain I-V curves, potential gradients are scanned across the reservoir ends, and the resulting current I and cationic transference number t + are calculated as follows: where I, I + , and I − are current, cationic current, and anionic current, respectively.A is the cross-sectional area of the nanochan-nel.The short-circuit current, also known as the osmotic current (I osm ), is determined by the current intercept of the I-V curve, while the open-circuit voltage, which is defined as E diff , is determined by the voltage intercept, as written approximately: [112] where  H and  L are the high and low ion activity.Because the above I-V characteristics are approximately linear, P max is calculated as The relationship between electrical energy and Gibbs free energy can be used to obtain : where Δμ o is the standard chemical potential.Detailed derivation has been reported. [37]he above theoretical understanding of nanochannel-based osmotic power generation has led to a focus on numerical calculations.The finite element method (FEM) has proven to be highly accurate in solving the boundary value problems of nonlinear partial differential equations such as the P-N-P and N-S equations, and it also has high shape adaptability. [113]Consequently, numerous advances in the field of osmotic energy conversion have been achieved using FEM calculations.
Previous studies have primarily focused on uniform nanochannel configurations with a constant surface charge.For example, as depicted in Figure 10a, a short nanochannel (100 nm) exhibits excellent cation selectivity, resulting in a higher power outputs. [114]More recently, researchers explored the use of Janus membranes with asymmetric radius and surface charge to achieve unidirectional ion flow.As illustrated in Figure 10b, the ion concentration contour exhibits a distinct ion accumulation in nanochannels, creating an ionic rectification effect. [115]The nanochannel surface charge can also be controlled by asymmetric illumination, as demonstrated in Figure 10c for carbon  [114] Copyright 2019, Royal Society of Chemistry.b) Reproduced with permission. [115]Copyright 2017, American Chemical Society.c) Reproduced with permission. [116]opyright 2019, Springer Nature.d) Reproduced with permission. [117]Copyright 2020, Elsevier.
nitride nanotube membranes, which produce a light-driven ion pump for power generation. [116]Specifically, illumination results in an anomalously high concentration of K + ions in the nanochannel near the low-concentration side, indicating cation transport against the concentration gradient.The intrinsic heat transfer and thermal conductivity of nanoporous membranes also affect the thermal-regulated osmotic energy conversion.Figure 10d shows that under negative temperature differences, adjusting the membrane thermal conductivity to nearly thermal insulation can increase the electric power by up to 120%. [117]ltogether, FEM simulations provide insights into complex phenomena that are difficult to measure experimentally, enabling parametric analyses to optimize osmotic energy conversion.Despite these advantages, FEM simulations have highly variable accuracies depending on the level of modeling and boundary conditions.The size effect and hydration structure of ions are particularly neglected, which may lead to an overestimation of the local ion concentration inside nanochannels.Hence, a unified framework, atomic-level insight, and accurate prediction models are required for a comprehensive understanding of nanoconfined ion transport and osmotic energy conversion.

Similarity Principle-Based Parameter Analysis
The salinity-gradient osmotic energy conversion process is influenced by multiple physical parameters, making parameter analysis a complex task.Researchers have used the control variable method to investigate power generation performance dependent on a single variable, such as temperature, nanochannel radius, and surface charge density.However, a comprehensive study covering all parameters is lacking, which hinders a complete understanding of the relationships between various parameters and performance.
Similarity principle analysis can help identify dimensionless variables from the governing equations and provide a theoretical framework for the experimental design.Our group has utilized this approach to conduct parameter analyses and gain a unified understanding of the complex phenomena in nanochannelbased ion transport and osmotic energy conversion. [55]For instance, we non-dimensionalized the governing equations in Table 1 for a Janus nanochannel and summarized them in Table 2.
Then, the dimensional power P max and dimensionless power P max * are expressed by fifteen dimensional parameters and nine dimensionless parameters, respectively: Nernst-Planck equation for anions Hence, the number of parameters that determine performance is significantly reduced.In detail, originate from the coefficient of dimensionless equations, and are derived from boundary conditions.According to the physical essences, these dimensionless parameters could further be categorized into ion-driving source ( ), ion transport characteristics (

RT𝜀 ), and nanoporous membrane configuration (
). Particularly, the ion selectivity is proportional to surface charge density but inversely proportional to ion concentration and channel radius.
These dimensionless parameters can be used to obtain the unified phenomena.In detail, multiple situations can be set by altering the combinations of the dimensional parameters while maintaining a fixed value of the dimensionless parameters.Figure 11 presents the detailed parameter analysis results based on this approach.The dimensional maximum power P max significantly varies among all the cases, and its maximum relative difference is ≈300% (Figure 11a).In contrast, the dimensionless power remains almost constant with a maximum relative error of just −0.065% (Figure 11b).Therefore, the osmotic power generation phenomena with multiple parameters can be unified into a single phenomenon described by the above dimensionless parameters.Based on this understanding, the dominant parameters during the osmotic energy conversion process can be determined by sensitivity analysis.Figure 11c,d demonstrates that the high-concentration reservoir concentration and channel radius play dominant roles in both the maximum power and energy conversion efficiency, so they deserve more attention in practical osmotic energy conversion experiments.
In summary, the similarity principle-based dimensionless and sensitivity analyses of multi-physical parameters are superior in offering intrinsic insight into ion transport in nanochannels, guiding the practical applications of salinity-gradient osmotic energy conversion.Because an additional non-uniform temperature distribution is generally involved in nanochannels, similarity principle-based parameter analysis can be upgraded and extended to describe the thermal-regulated ion transport process in  B, C, D, and E, respectively.a-d) Reproduced with permission. [55]Copyright 2022, Elsevier.
porous media, such as ionic thermoelectric energy conversion, [37] ion sieving, and desalination. [118]This approach offers a superior idea for understanding these complex phenomena and has significant potential for developing practical applications in various fields.

First-Principles Calculation and Molecular Dynamics Simulation
Atomic-scale simulation is another powerful theoretical tool for probing fundamental physical phenomena that occur at nanoconfined solid-liquid interfaces.Based on the welldescribed atom-atom, atom-electron, and even electron-electron interactions, the electronic, physicochemical, thermodynamic, and kinetic properties of both solid and liquid species can be investigated, thus guiding the reformation and innovation of nanostructured materials and nanofluidic devices.The widely used atomic-scale computational methods include firstprinciples calculations and molecular dynamics (MD) simulations, where the latter can be further classified into ab initio molecular dynamics (AIMD) and classical molecular dynamics (CMD) according to how interatomic forces are obtained.This part first introduces the basic principles of the first-principles, AIMD, and CMD simulations.We also discuss their widespread applications in delving into interfacial phenomena in nanoconfined spaces and ion transport behaviors for nanofluidic osmotic energy conversion.
First-principles calculations focus on electronic ground states and probe electron movement using elementary equations in many-body quantum mechanics discarding any empirical parameters.Under the framework of the DFT, the approximate solutions of the Schrödinger equation can be obtained with sufficient accuracy.The subtle electronic and energetic properties in a specific configuration can be then calculated from electroniclevel insights, such as the surface electrification of nanoporous membranes, interfacial electron transfer, electrostatic potential distribution, and ion migration energy barrier inside nanochannels.Figure 12a shows a contour map of the differential charge density of water molecules inside the MOF sub-nanochannels. [86]s the distance to the polarity sites on MOF walls decreases, more obvious electron accumulation and depletion are observed, implying consolidated interfacial charge transfer.Hence, water molecules adjacent to the MOF walls appear in the activation state for a higher proton conduction capacity during the proton conduction process.Figure 12b shows the molecular electrostatic potential distribution on the pristine NbP and V-NbP nanosheets. [53]Electrons are localized around the oxygen atoms in the NbP nanosheet, indicating inhomogeneously distributed negative surface charges.In contrast, the P vacancies in the V-NbP nanosheet result in more uniform and negative electrostatic charge distribution, implying more negative surface charges.Correspondingly, Figure 12c compares the energy barriers of Na + ion diffusion in the horizontal pathways.The energy barrier for the V-NbP nanosheet (0.186 eV) is much lower than that for the NbP nanosheet (0.263 eV).This result implies a decreased ion transport resistance and accelerated ion dynamics due to the presence of P vacancies, thus significantly promoting the energy conversion efficiency of osmotic power generation.
MD simulations can be used to monitor atomic trajectories and collect thermodynamic and kinetic information to discuss physical, chemical, and energetic characteristics.An important factor that determines the computational accuracy of any MD scheme is the description of the interatomic interactions.Generally, complete interactions include two-body and many-body contributions, long-range and short-range terms, and electrostatic and non-electrostatic interactions, which must be represented by suitable functional forms.The independent first-principles calculations can directly determine the interatomic forces, which correspond to the branch of AIMD simulation.AIMD simulations update interatomic interactions at each MD steps using accurate ab initio methods, and the obtained potentials serve as input parameters for subsequent evolution of atomic positions.Accordingly, it unifies MD and electronic structure theory to observe subtle physical and chemical processes.In the aspects of nanochannel-based ion transport and nanofluidic application, AIMD involves accurate investigations of structural, kinetic, and thermodynamics characteristics, such as the stability of hydrated ions, dynamic solvation structures, stability of hydrated ions, Hbond evolution, interfacial chemical reactions, and ion diffusivity.
As a typical AIMD application, Figure 12d shows the ionic hydration structures and radial distributions of ions and water molecules inside the sub-nanometer graphene channels. [119]wo water layers are presented adjacent to the graphene surface.K + ion prefers a distribution between the two water layers, whereas Cl -ion prefers an intra-layer accommodation close to the wall.Moreover, the water molecules around the K + ion have a broader H distribution toward the graphene walls than the concentrated O distribution.This implies that the OH bonds of these water molecules are directed outward, which is a typical feature of orientation polarization around cations.In contrast, water molecules around the Cl − ion have approximately overlapping H and O distribution regions along the radial direction.These subtle differences in the hydration structures of K + and Cl − ions originate from the balance of the structural competition between the hydration shell and bilayer water, which plays a crucial role in the charge asymmetric effect on ion mobility.It is noted that only one peak of Cl − ion distribution emerges, which contradicts the intuition of two symmetrical peaks.This phenomenon is attributed to the short AIMD duration of picoseconds, which is insufficient for Cl − ion shuttling between the two water layers.Figure 12e displays the time evolutions of orientation and displacement of an OH − ion on graphene. [63]The OH − ion mainly points toward or away from the surface, and it locates at the z position about 3 Å away from the sheet with some residence time at 4 Å.In contrast, it becomes highly active in the xy plane and diffuses through proton transfer, implying significant anisotropic diffusion.
In contrast, the interatomic forces can be obtained based on empirical data, corresponding to the branch of the CMD simulation.In the past few decades, diverse interaction models have been devised and parameterized to serve as predefined force fields applied in CMD simulations.In principle, the CMD calculates the accelerations of classical particles (such as atoms, ions, and molecules) based on Newton's equation of motion and a predefined empirical potential.Hence, all atoms update their positions and velocities from the initial velocities.During the simulations, periodic boundary conditions and a temperature control method are applied.Therefore, the evolutions of trajectories Red and blue colors denote the regions with positive and negative charges, respectively.c) Energy barriers of Na + ion migration.d) Ionic hydration structures and radial distributions of ions and water molecules in graphene channels.e) Timeevolved orientation and vertical and lateral displacements of an OH − ion on graphene.a) Reproduced with permission. [86]Copyright 2022, American Association for the Advancement of Science (AAAS).b,c) Reproduced with permission. [53]Copyright 2023, American Chemical Society.d) Reproduced with permission. [119]Copyright 2019, American Chemical Society.e) Reproduced with permission. [63]Copyright 2019, Springer Nature.and energies over time are recorded as raw data, and the statistical average over time provides details regarding various properties.However, a fixed predefined potential may be unsuitable for myriad systems consisting of different atomic and molecular types, which poses a significant challenge to the parameterization of intricate interatomic interactions.Even though a satisfactory interaction potential is devised to describe a certain system, the introduction of new substances will require new parameterization operations.Moreover, chemical bonding patterns cannot be captured without the assistance of more sophisticated reactive force fields, which limits the extension of CMD to multifarious condensed matter systems.Despite the above inherent shortcomings, CMD simulation can easily introduce and modulate of external fields (such as concentration, potential, and pressure gra-dients) in a macroscopic system within nanosecond duration, in comparison to AIMD, which can only probe a local nanometerscale interface within a period of picoseconds.In the field of nanofluidic ion transport, CMD is used to calculate the amount of ion transport through common nanochannels, I-V curves under a bias voltage, and distributions of solvent molecules and charged ions.
Figure 13a shows the ionic transfer quantity and ionic current through the sub-nanometer NbP and V-NbP nanosheets, which are under the cooperative driving forces of the NaCl salinity gradient and horizontal electric fields in the CMD simulations. [53]a + ion current in the V-NbP nanosheet is higher than that of the NbP nanosheet, whereas Cl − ion current has the opposite order.Therefore, the simulated cation transference number of  [53] Copyright 2023, American Chemical Society.b) Reproduced with permission. [120]Copyright 2023, Wiley-VCH.c) Reproduced with permission. [121]Copyright 2022, American Association for the Advancement of Science (AAAS).the V-NbP nanosheet is higher than that of the NbP nanosheet, thus benefiting the osmotic energy conversion performance.Figure 13b demonstrates a nanofluidic system in which a 1 m KCl aqueous solution is separated by different types of COF membranes with sub-nanometer pore sizes. [120]The ionic currents at different electric field intensities across the system (I-V curves) are recorded.A linear I-V relationship emerges in the singlelayer COF, indicating the behavior of electronic resistors without an ionic rectification effect.In contrast, unidirectional diode behavior is observed in the hybrid-bilayer COF, which is represented by the "on" and "off" states under the positive and negative electric fields, respectively.Figure 13c displays the net charge distribution and local current density vectors around the graphene nanopore under the synergistic electric field and pressure gradient. [121]The net charge distribution represents the population of cations and anions.Obvious net ionic charge layers are observed near the graphene surface due to electrostatic capacitive adsorption.The cation-enriched layer is further dragged and transported to the cathode side because of water streaming under the mechanical driving forces from the pressure difference.
In summary, atomic-scale simulations have proven successful in clarifying physical and chemical mechanisms and describing several different observables, holding promise for further extension to diversified nanofluidic systems.Despite these advancements, the practical processes of ion transport and nanofluidic device operation cover a wide range of spatial and temporal scales.This situation requires more accurate multiscale computational approaches from first-principles calculations, AIMD, and CMD to FEM, thus guiding the experimental design and optimization for nanofluidic energy conversion.

Equivalent Circuit Model for Osmotic Performance Prediction
Performance evaluation and prediction are important subjects for osmotic energy conversion.In principle, as the transmembrane ion transport proceeds, the reduced salinity gradient leads to a decline in the chemical potential difference, which weakens the dominant driving force for ion migration.This results in a gradual decay of the output voltage and current during the osmotic power generation process, requiring the use of transient differential equations for precise descriptions.However, current research mainly focuses on time-averaged indices of nanoporous membranes, while performance degradation over time is not given enough attention.Traditional equivalent circuit models assume a constant transmembrane concentration difference, which can only provide steady-state voltammetry characteristics, neglecting transient variations and potentially leading to misguided experimental system optimization.Our group has developed a transient capacitor-capacitor/resistor (C-CR) model to accurately describe the circuit characteristics and transport of energy and mass during the osmotic power generation process. [122]his innovative model offers a superior performance prediction compared to the traditional constant voltage source (V-source) model. [114]In this part, by comparing the V-source model, the key idea and prediction accuracy of the C-CR model for osmotic energy conversion would be discussed.
The traditional V-source model is based on two assumptions: first, the solution volume is much larger than the nanochannels, which means that the impact of ion adsorption in nanochannels on the ion concentration is negligible, and second, the salt  [122] Copyright 2021, Elsevier.
concentration of the two solution reservoirs is constant.Consequently, ions diffuse steadily across nanochannels to maintain a constant voltage output, leading to the osmotic system being regarded as a constant voltage source.Figure 14a illustrates that the V-source model is composed of three parts: the membrane, electrode, and external circuit.Specifically, the membrane part involves ion diffusion potential E d and internal resistance R i , which are determined by the nanochannel geometry and electrified properties.The electrode part generates redox potential E r at the Ag/AgCl electrode-solution interface.The external circuit comprises the external load R L and source meter R A , thus forming an open circuit voltage V oc .Hence, diffusion current I can be calculated using Ohm's law: where R A value is generally neglected.Then, the power density under an external load R L is determined using Joule's law with a nanoporous membrane osmotic area of A: According to the above deductions, E d and E r are concentrationdependent, whereas ion concentration variation in reservoirs and fluid resistance at the nanochannel entrance are not considered, which results in an inaccurate reflection of the ion diffusion process.
In contrast, the proposed C-CR model is based on two assumptions: the solution volume in two reservoirs remains constant; the total amounts of salt ions in the solution are conserved.Therefore, the gradually reduced salinity gradient over time leads to a continuously decreased current, which is similar to a discharged capacitor based on ion transport and storage.The C-CR model thus incorporates salt concentration variation and fluid resistance under actual operational conditions, resulting in a more accurate representation of the ion transport process in the nanoporous membrane.As shown in Figure 14b, the fluid resistance is added as a terminal resistance R T ; the unsteady ion transport in the nanoporous membrane is regraded to a capacitive discharge process (C eq ); the concentration effect on electrode reaction is replaced by a CR circuit (C E and R E ).Consequently, besides ion amount conservation, the C-CR model allows for the calculation of the time-dependent diffusion potential E d (t) and diffusion current I(t) of the membrane part.Specifically, I(t) can also be obtained by focusing on the electrode part and the whole closed circuit through Kirchhoff's current law, which are equal in this series circuit.A linear homogeneous second-order differential equation of E d (t) and its general solution are thus exhibited.Accordingly, to represent the osmotic power generation performance, taking C E , R T , R A , R L , and R E as inputs, the timedependent transient diffusion current I(t) is obtained: The short-circuit current I sc (t) corresponding to R A = R L = 0 is calculated by: The time-integrated average power density ( P * ) are then obtained: The C-CR model has been proven to be superior to the V-source model in predicting short-circuit current and power density using a multi-chip GOM-based osmotic experimental system (0.01 m/0.5 m NaCl).As shown in Figure 14c, I sc (t) measured in experiments decreases rapidly at first and then gradually, whereas the diffusion current predicted by the V-source model remains constant, leading to a significant deviation from the actual osmotic power generation.In contrast, the I sc (t) predicted by the C-CR model matches well with the experimental data, with a maximum deviation of only 7.06% and 4.87% for the 2-GOMs and 5-GOMs systems, respectively.Additionally, the time-dependent power density of the 2-GOMs system serves as the second validated indicator, as shown in Figure 14d.Compared to experimental data, the relative deviation of power density in the C-CR model is only 0.19-14.22%,which is significantly smaller than the deviation in the V-source model (28.63-38.14%).Therefore, the proposed C-CR model is more practical and accurate in predicting the transient performance and effective lifetime of an osmotic power generator.Altogether, the extensive research described above, which includes mathematical, parametric, numerical, atomic-level, and model-based studies, has greatly enhanced our understanding of the underlying processes in salinity-gradient osmotic power generation.These academic insights can be applied to the development of more integrated systems that meet practical demands.For example, the output performance can be improved by using advanced materials, physical methods, and thermophysics methods, such as optimizing the membrane, applying external magnetic fields, and regulating the electrolyte temperature.These effects can be readily incorporated into the governing equations and numerical solution processes based on making appropriate modifications.They can also be reflected by adjusting expressions in the membrane and fluid components of the C-CR model to enhance the accuracy of performance prediction.Overall, these findings are expected to pave the way for the development of more efficient and effective osmotic power generation technologies.

Enhancement of Osmotic Power Generation Performance
Current nanoporous membranes for osmotic energy conversion face the trade-off between ion selectivity and permeability, which significantly constrains the output power density (P) and energy conversion efficiency (), as illustrated in Figure 15a.To address this issue, three effective paths denoted as A, B, and C, have been developed.
Path A is intended to increase the ion permeability at a slight cost to ion selectivity, thus improving the ion flux and enhancing the power density.Typical applications of path A in experiments include thermal regulation, [123] and porosity manipulation. [124]ecause ion selectivity determines the energy conversion efficiency, path A has a limitation in situations where scarce salinityenergy sources need to be efficiently utilized and the efficiency index receives more attention.Path B aims at consolidating ion selectivity with a tiny sacrifice in ion permeability, thereby promoting osmotic energy conversion.Its practical applications involve surface geometry design, [52] the addition of nanoparticle (NP), [125] and the addition of nanofiber. [126]Path C is intended to increase ion selectivity and permeability simultaneously, and the corresponding operations include material development, [73] and surface engineering strategy. [53]The eventual effectiveness of these paths depends on the specific strategy in experiments.For instance, thermal regulation in path A can steadily enhance the osmotic power by 250%, [123] which is superior to most of the material developments in path C. Furthermore, two or three paths are jointly adopted in practical experiments to combine the advantages of each path and achieve optimal performance.Moreover, the testing area of the membrane is an important factor in experiments.Although the osmotic power density can easily achieve 5 W m −2 when the testing area is 0.03 mm 2 , [127] it suffers severe deterioration due to the ICP as the testing area is further enlarged. [128]The dramatically decreased output power density with the working area has also been observed in a covalent organic polymers membrane. [129]As an alternative, the ionselective MOF membrane can achieve a stable power density of 1.7 W m −2 at the working area of 7 mm 2 under a 5 m/0.5 m concentration gradient, [130] Hence, it is an effective strategy to suppress ICP and to improve the osmotic energy conversion performance of nanochannel under high working area, showing the potential for a scalable application.
Based on the above statements, the ideal target of strategy development is to realize ultra-high ion selectivity and permeability and to achieve perfect power density and energy conversion efficiency in a large-scale working area, as marked by the fivepointed star in Figure 15a.Around this target, this section first discusses the basic nanochannel geometry and explore strategies for optimizing the geometry and space charge, guided by FEM simulations.Next, various methods for preparing nanoporous ) Tube-like nanochannels, such as 1) carbon nitride nanotube and 2) polyimide.c) Plate-like nanochannels, such as 3) graphene oxide and 4) MXene.c) Complex porous nanochannels, such as 5) PES-Py/PAEK-HS and 6) zwitterionic hydrogel.1) Reproduced with permission. [133]Copyright 2020, Elsevier.
membranes and integrating them into experimental systems are discussed to provide comprehensive knowledge of the practical applications of osmotic devices.Finally, the impact of electrolyte photothermal regulation is emphasized through a comparative analysis.

Basic Nanochannel Geometry
The above discussions treat the local nanochannels as 2D flat pathways for ion migration.However, nanochannel geometry plays an essential role in ion behaviors and osmotic energy conversion, and it can be manipulated to tackle the obstacle of the selectivity/permeability trade-off.Nanochannels can be classified into three basic categories: tube-like, plate-like, and complex porous structures.
The general structures of tube-like nanochannels include nanotubes, conical solid-state nanochannels, and other 1D arrays, the shapes of which are shown in Figure 15b.Their interfacial EDLs exist between the circular surfaces and central solutions, so the degree of EDL overlap is large and beneficial to ion selectivity.For instance, the boron nitride nanotube with channel sizes of 15-40 nm and length of ≈1 μm generates a high ion conductivity and giant osmotic power density of 4 kW m −2 . [131]However, the ion selectivity of tube-like nanochannels is sensitive to the channel diameter, and the ion permeability decreases as the channel size decreases.In this case, a higher channel density is necessary to generate more osmotic current and osmotic power. [132]The ultrathin silica membrane has been prepared to obtain multiple cylindric nanochannels, and it can generate osmotic power larger than 0.4 nW. [114]This higher power than that of boron nitride single nanotubes is attributed to the low membrane resistance due to the higher porosity and shorter length of ≈90 nm.Carbon nitride nanotube (1) exhibits regulated selective ion transport behavior under light. [133]However, tube-like nanochannels easily confront strong ICP, and the power density decays.To suppress the ICP, nanochannel heterostructures have been developed to introduce ion rectification and promote directional ion transport.One such example is a polyimide conical nanochannel (2), which exhibits ion rectification under an electrical potential bias, resulting in exceptional osmotic performance. [134]Another example is a heterogeneous membrane consisting of a conical PET membrane and a silica membrane, which demonstrates high permselectivity. [135]late-like nanochannels with rectangular cross-sections generate EDLs between the upper and lower surfaces, as illustrated in Figure 15c.The channel size must be extremely small to achieve a high degree of EDL overlap and ion selectivity.Conventional plate-like nanochannels fabricated by silica can produce an osmotic power density of 7.7 W m −2 under a 1000-fold concentration gradient. [136]2D materials have an interlayer spacing of approximately 1 nm, which is narrower than the EDL thickness, thereby exhibiting excellent ion selectivity. [137]Hence, 2D membranes, such as graphene oxide (3), MXene (4), and black phosphorus have been considered as potential candidates for osmotic power generation.Nevertheless, the irregular nanosheet shapes of 2D materials create tortuous ion transport pathways, and a channel size comparable to the hydrated ion size leads to high ion resistance.The addition of charged nanofibers into the interlayer spacing is beneficial for reducing the ion resistance by enlarging the channel size, [126] and it can also enhance the ion selectivity by introducing an abundance of functional groups and improving the space charge.Recently, the arrangement of drill holes on  [52] Copyright 2022, Elsevier.
nanosheets has been developed to increase the porosity and ion permeability, which is another effective method for reducing the ion resistance of 2D membrane. [138]omplex porous membranes are commonly fabricated from 3D materials such as polymers (5), nanofibers, and hydrogel (6), as depicted in Figure 15d.These membranes contain numerous irregular and disordered nanochannels, allowing the entire membrane area to be utilized for efficient ion transport and enhanced ion permeability. [15]The high surface charge density caused by the abundant functional groups in 3D porous materials enables selective ion transport and osmotic energy conversion.

Theoretical Design of Nanochannel Geometry and Charge Distribution
Researchers have conducted extensive studies on the design of nanochannel structures to address the trade-off between ion selectivity and ion flux.Solid materials can be processed into nanochannels with various structures using different preparation methods, thereby enabling the design of asymmetric or heterogeneous geometries.For instance, silica nanochannels can be shaped into nanotubes, [134] planes, [136] or connected configurations. [142]Layered graphene oxide can be fabricated as a single 2D membrane, [139] or assembled with a cylindrical membrane. [143]Based on these experimental technologies, considerable progress has been made in optimizing nanochannel geometry for optimal osmotic energy harvesting.Outstanding performance in harvesting osmotic energy has been demonstrated by conical, [135] bullet-shaped, [144] and funnel-shaped nanochannels. [145]Moreover, bio-inspired trifurcated nanochannels have yielded a 3.5-fold improvement in osmotic power compared with straight nanochannels, highlighting the potential of the overall nanochannel design to boost osmotic power generation. [146]n addition to the overall geometry, the surface geometry also plays a vital role in nanochannel-based ion transport by influencing the EDL properties.If an electrified nanochannel wall is rough, the ridges and grooves would expand the surface area and increase the amount of surface charge, whereas they can reduce the channel size and weaken ion permeability.Roughness can even alter ion transport by affecting surface hydrophilicity and slippage.Hence, the influence of surface roughness on ion transport and osmotic energy conversion is complex and requires an in-depth analysis.We have investigated the ion transport characteristics in nanochannels with artificial nanoroughness (ANR) using FEM simulations. [52]By optimizing the ANR positions and sizes, we developed a unique structural design strategy that breaks the balance between ion selectivity and permeability, leading to enhanced osmotic power generation.
As shown in Figure 16a, the rectangular convex regions on the channel walls represent the ANR in the osmotic energy conversion device.This nanochannel is simplified to a 2D axisymmetric model to enable faster simulations, as shown in Figure 16b.The ANR consists of hundreds of rectangular units with a height of H, width of W, and pitch of P, and it can be arranged in frontal regions with different lengths (L A ).Alternatively, it can be optimized for distribution in the rear regions (L A * , Figure 16c).The positive effects of ANR on the osmotic power generation can be explained by comparing it with a simple reduction in the radius Figure 17.ANR-enhanced osmotic power generation performance.a,b) Osmotic power and energy conversion efficiency when the ANR is arranged in frontal regions, respectively.c,d) Osmotic power and energy conversion efficiency when the ANR is arranged in rear regions, respectively.e,f) Osmotic power and energy conversion efficiency when the ANR sizes are optimized, respectively.a-f) Reproduced with permission. [52]Copyright 2022, Elsevier.
of the smooth nanochannels (Figure 16d).Figure 16e shows the impact of the ANR length in the frontal regions on the axial ion concentration distributions in nanochannels.The designed ANR significantly increases the cation concentration and reduce the anion concentration, resulting in an enhanced EDL intensity and ion selectivity.As a visual representation, Figure 16f compares the space charge density at the solid-liquid interface, which represents the net content difference between cations and anions in nanochannels.The maximum space charge density increases from 8.0 × 10 6 to 2.5 × 10 7 C m −3 after arranging ANR, indicating an obvious improvement in cation selectivity due to the presence of ANR.
To emphasize the ANR-enhanced osmotic performance, the concentration gradient is partitioned according to the competition between ion selectivity and permeability, as depicted in Figure 17.In the ion selectivity-sufficient zone (3 < C H /C L ≤ 10), the low concentration ensures adequate selectivity due to the full EDL overlap, whereas it causes a limited ion driving force and flux.In the driving force-sufficient zone (300 < C H /C L ≤ 600), the high concentration gradient provides a strong driving force, but the ion selectivity is extremely poor caused by the weak EDL overlap.In the balanced zone (10 < C H /C L ≤ 300), both the ion selectivity and driving force are moderate.The ANR design has discrepant outcomes in all three zones.As shown in Figure 17a, based on the introduction of ANR in the frontal regions, the osmotic power is evidently enhanced, and it increases by 69.8% in the balanced zone when the LA-800 ANR is used.This improvement arises from the enhanced cation selectivity of the nanochan-nels.Consequently, the energy conversion efficiency is consolidated particularly in the balanced zone, as shown in Figure 17b.These findings demonstrate the feasibility and effectiveness of improving ion selectivity through interfacial geometry designs, thus overcoming the trade-off between ion permeability and selectivity and enhancing osmotic power generation.
The position and geometric parameters of the ANR also have significant influences.As shown in Figure 17c, despite the same length of the region decorated with the ANR, the ANR arranged in the rear region can generate a higher maximum power (LA * -400, 0.102 pW) than that arranged in the frontal region (LA-400, 0.065 pW).The same comparative relationship is also observed when examining the energy conversion efficiency, as shown in Figure 17d.The higher overlap degree of the EDL adjacent to the low-concentration side explains these results.Hence, when reforming nanoporous membranes for osmotic power generation, nanochannels with higher ion selectivity, as achieved through the above geometry design, should be placed on the lowconcentration side rather than on the high-concentration side.In addition to optimizing the ANR positions, adjusting the ANR size can also enhance osmotic power generation.According to the FEM results, reducing the width W and pitch P of the ANR can improve the osmotic power and energy conversion efficiency monotonically, whereas an increase in the height H has a nonmonotonic effect on the osmotic power.Hence, the LA * -400 ANR with H = 1.5 nm, W = 0.5 nm, and P = 0.5 nm serves as the optimized ANR (O-ANR) size for the best osmotic performance.As shown in Figure 17e, under a 100-fold concentration gradient,  [125] Copyright 2022, Elsevier.
applying O-ANR resulted in a 124.2% higher osmotic power compared with simply reducing the nanochannel radius to 8.5 nm.A similar improvement is observed in the energy conversion efficiency (Figure 17f).These results confirm the superiority of optimizing the nanochannel structure by incorporating ANR over conventional methods.
In addition to optimizing the interfacial roughness, ion selectivity can be improved by regulating the space charge density in nanochannels.This approach been implemented the MXene/nanofiber composite membrane, which introduces additional space charges through the nanofibers, leading to a significant improvement in the energy conversion performance. [126]imilar to nanofibers, electrified NPs can also regulate the space charge density. [125]When NPs are dispersed to an aqueous solution inside nanochannels, their surfaces are charged, attracting ions with opposite charges to cluster around.An EDL between the NP and aqueous solution is then formed, thereby enhancing the space charge density and promoting ion selectivity.Under these circumstances, the NP content is essential for determining the ion behavior in nanochannels.
An NP-enhanced osmotic energy conversion device is shown in Figure 18a.The addition of NPs to the nanochannel leads to the formation of a negatively charged surface, which increases the EDL coverage and consolidates the space charge distribution.This method prevents anions from entering the nanochannels and promotes directional cationic transport, leading to the generation of an osmotic current.The positive effects of NPs on the osmotic energy conversion are clarified using FEM simulations.As shown in Figure 18b, when a 50-fold salinity gradient and 10% volume fraction of NPs are used, the maximum space charge density increases from 1.3 × 10 7 to 1.8 × 10 7 C m −3 , indicating NP-enhanced cation selectivity.In addition, an increase in NP content leads to a higher maximum osmotic power.As shown in Figure 18c, a 43.1% increase is observed when a 10% volume fraction of NPs is used under a 50-fold salinity gradient.
However, these small nanometer-sized channels magnify the ion size effect, and disordered channel structures present challenges in the numerical modeling of ion transport.To gain a deeper understanding of ion dynamics in charged porous nanochannels for osmotic energy harvesting, both molecular simulations and experimental methods are required.

Experimental Optimization of Membrane
Building on these design strategies, several techniques for nanoporous membrane fabrication have been developed to increase the ion permeability, selectivity, stability, and durability, all of which are essential for practical osmotic energy conversion. [147]In this part, a range of experimental approaches for the production of membranes with high selectivity/permeability is introduced, including vacuum filtration, spin coating, and chemical etching.
As shown in Figure 19a, hybrid silk nanofibril (SNF)/anodic aluminum oxide (AAO) membranes are fabricated via the vacuum filtration of SNF onto AAO. [148]The hybrid membranes demonstrate excellent stability, which stems from the strong H-bonding mediated by the hydrophilic groups on the SNF and AAO surfaces.AAO nanochannels have large diameters for ion storage and conductivity, while small SNF nanochannels provide ion selectivity.Thus, the hybrid membranes achieve a balance between ion selectivity and permeability and exhibit  [148] Copyright 2019, Springer Nature.b) Reproduced with permission. [149]Copyright 2021, American Chemical Society.c) Reproduced with permission. [124]Copyright 2021, Royal Society of Chemistry.d) Reproduced with permission. [53]Copyright 2023, American Chemical Society.e) Reproduced with permission. [153]Copyright 2022, American Chemical Society.f-h) Reproduced with permission. [123]Copyright 2022, Elsevier.
excellent performance in osmotic energy conversion.Besides, the mesoporous silica/macroporous alumina (MS/AAO) frameworkbased heterostructure membranes are prepared by employing the spin coating method, as shown in Figure 19b. [149]The thin and ordered MS layer offers a high specific surface area, which confers on the membrane low resistance and high ion selectivity.
Asymmetric membranes with different channel sizes and charge polarities can suppress concentration polarization and facilitate excellent osmotic power generation.Similarly, mesoporous carbon-silica/anodized aluminum (MCS/AAO) membranes are constructed through interfacial super-assembly interaction. [150]he two-component MCS layer possesses an ordered structure and a higher surface charge density owing to the carboxyl functional groups brought by the polymer, endowing the membranes to promote ion permeability and osmotic power output under a salinity-gradient.
The 2D membranes have high ion selectivity due to the subnanometer-scale interlayer space and high surface charges provided by sufficient functional groups, which shows great potential in harnessing osmotic energy.Graphene oxide membrane (GOM) is the representative one.The freestanding GOM, [151] and the oppositely charged GOM pairs, [152] exhibit outstanding power density and energy conversion efficiency.Moreover, mechanically stable GOM/polydimethylsiloxane (PDMS) films have been developed to exploit vertical nanochannels for ultrafast ion permeation. [122]However, the 2D nanochannel along the horizontal direction is tortuous and long, creating a high ion transport barrier and obstructing the practical application of horizontal 2D membranes.Increasing the porosity of 2D membranes is an effective way to reduce the path length for ion transport and enhance the osmotic energy conversion.For example, chemical etching has been adopted to create nano-hole on 2D nanosheets, which are assembled to the porous vermiculite membranes with a higher porosity than that of the pristine membrane (Figure 19c). [124]The obtained porous vermiculite membranes improve the ion permeability while maintaining excellent ion selectivity, and exhibit an elevated ion flux and a 16-fold increase in power density.Additionally, the H 2 SO 4 oxidation of Ti 3 C 2 T x nanosheets is conducted to produce nanopores with more connections between the interlayers. [138]orous Ti 3 C 2 T x MXene membranes simultaneously consolidate ion permeability and selectivity because the larger number and shorter pathways provided by the interplanar nanopores decrease the ion transport energy barrier and increase charge-selective transport.
In contrast to the aforementioned strategies, vacancy engineering has recently been employed to remove phosphorus from NbOPO 4 (NbP) membranes, thereby enhancing their negative surface charge (Figure 19d). [53]The vacancy-introduced NbP (V-NbP) membranes exhibit fast ion migration and selectivity in osmotic energy conversion, generating a power density of 10.7 W m −2 that is threefold higher than that of the pristine NbP membrane and 100% larger than that of the commercial benchmark.The 2D COF membranes possess well-ordered and oriented nanochannels (Figure 19e), [153] molecular-scale thickness, [154] and modifiable functional groups, [33] rendering them promising candidates for overcoming the ion selectivity/permeability tradeoff and achieving an ultrahigh power density and energy conversion efficiency.
The unique properties of nanoporous membranes prepared using the aforementioned methods can be characterized using various strategies.The chemical compositions of the membranes can be determined using X-ray diffraction (XRD), Xray photoelectron spectroscopy (XPS), and Fourier transform infrared spectroscopy (FT-IR), while their surface microstructures can be observed using scanning electron microscopy (SEM) and transmission electron microscopy (TEM).Moreover, the surface charge density and hydrophilicity of the membrane can be measured using the zeta potential and contact angle, respectively.Limited by space, we will not discuss the characterization technologies in more depth, but focus on the application of nanoporous membranes in osmotic energy conversion experimental systems.
Figure 19f shows a basic experimental system comprising several components, including an osmotic power generator, external resistance boxes, electrochemical workstations, data acquisition instruments, and data processing instruments.The osmotic power generator comprises assembled nanoporous membranes and redox electrodes, where various physicochemical processes and phenomena occur.To enhance the output, the electrolyte temperature increase and temperature gradient arrangement serve as candidate factors.Hence, the basic system must be further reformed by introducing other supplementary units, such as heating components, solar simulators, and thermal insulation structures.The integral system can achieve superior performance in osmotic energy conversion.
Following the above arrangements, an experimental system for osmotic power generation is typically evaluated through I-V scanning at a specific concentration.As shown in Figure 19g, the short-circuit current (I SC ) is reflected by the vertical intercept of the blue curve, and the open-circuit potential (V OC ) is denoted by the horizontal intercept of the blue curve.The orange curve is obtained by translating the blue curve to the right by a value of redox potential (E redox ).The vertical and horizontal intercepts of the orange curve represent osmotic current (I osm ) and diffusion potential (E diff ), respectively, which characterize the electrical properties of the membrane.The power density represents the comprehensive output performance of the system.As shown in Figure 19h, the power density is calculated based on the current values measured at different external resistance, and then a maximum power density (P max ) can be determined.

Electrolyte Photothermal Regulation
Apart from advancements in nanoporous membranes, an increase in electrolyte temperature can also act as an auxiliary factor to boost ion transport in nanochannels and enhance the osmotic power density.Solar energy, a widely available renewable energy source, can serve as a free heat source when combined with photothermal materials, realizing electrolyte thermal enhancement from a thermophysical standpoint, without any additional electricity consumption for heating. [155]Photothermal heating methods can be divided into two categories, bulk and interfacial, depending on the selection and arrangement of the photothermal materials.
NPs are commonly used as a medium for bulk photothermal conversion because of their high light absorption and thermal conductivity and can be incorporated into photothermalenhanced osmotic power generators.As shown in Figure 20a, the AgNPs are dispersed in both artificial seawater and river water, and a solar light source simulator is arranged above the osmotic device with thermal insulation.The NP photothermal effect is then verified by tracking the transient temperature of electrolytes.Figure 20b shows that after adding NPs with a 1% mass fraction, the solution temperature increases faster, reaching 340.9 K in 285 min under one sun solar irradiation.Therefore, accelerated ion diffusion in nanochannels can be deduced from an increase in temperature, which promotes ion flux.This leads to a significant improvement in osmotic power density from 2.41 to 8.43 W m −2  c) equilibrium temperature and power density.d-i) Interfacial photothermal heating based on the photothermal material and the heat transfer porous media, wherein, d) diagram of osmotic power generation device, e) heat transfer analysis, f) solution temperature variation, g) I-V curve, h,i) power density.a-c) Reproduced with permission. [125]Copyright 2022, Elsevier.d-i) Reproduced with permission. [123]Copyright 2022, Elsevier.
using the GOM under a 50-fold salinity gradient (Figure 20c).This performance is superior to that obtained by directly heating the electrolyte to 323 K in a graphene oxide/cellulose nanofiber assembled membrane. [156]These results demonstrate the potential of NP-based bulk photothermal enhancement for osmotic energy conversion.
Interfacial heating can also positively affect osmotic power generation.As shown in Figure 20d, the CuO film can serve as a photothermal material owing to its excellent spectral absorption ability, and the SiC foam can be used as a heat transfer porous medium owing to its high thermal conductivity and superior chemical stability. [123]Solar radiation is absorbed by the CuO surface film and converted into heat, which is then transferred to an aqueous solution through the SiC foam.The thermal insulation structure reduces energy dissipation in the environment.The heated solution then promotes ion transport and improves osmotic performance.Figure 20e illustrates the heat transfer pro-cess of the entire experimental system, which follows an energy balance: where the first term represents the heating power of the electrolyte.The second term represents the heat flux absorbed by the CuO film and entering the solution, and the third term represents the heat flux exiting the solution owing to thermal conduction and convection.Specifically, the absorptivity  s of the aqueous solution is only 20-30%, whereas it reaches 89.3% in the photothermal conversion structure (PCS). [123]Accordingly, the osmotic system can absorb more solar energy due to the assistance of the PCS, leading to a higher solution temperature.As shown in Figure 20f, the entire heating process can be divided into rapid and slow temperature response zones, depending on the heating rate.After introducing the PCS, the solution temperature is always higher and eventually reaches 68 °C, compared to the situation without the PCS.The promoting effect of interfacial photothermal heating on ion transport in nanochannels is characterized by experimental I-V tests, as shown in Figure 20g.As a temperature rise, the I-V curves exhibit an increased slope, horizontal intercept, and vertical intercept, indicating consolidated membrane conductance, open-circuit voltage, and short-circuit current, respectively.These results benefit from accelerated ion diffusion and reduced fluid viscosity.The enhancement effect of electrolyte heating on the osmotic power generation is reflected in the power densities under different concentration gradients and pH conditions.Figure 20h shows that the power density linearly increases with the solution temperature, and a higher concentration gradient always leads to a higher power density.In comparison, Figure 20i shows that the power density increases at an accelerated rate with increasing solution temperature.At a fixed temperature, the power density is the highest in alkaline solutions, followed by neutral and acidic solutions.This can be explained by the pH-dependent EDL structure shown in Figure 2c.Specifically, GOM carrying acidic functional groups has an isoelectric point (IEP) of 1-2, [157] which is lower than all the pH values used in the above experiments.Therefore, the deprotonation reactions of functional groups dominate the generation of negative surface charges.According to chemical equilibrium, these reactions are promoted in an alkaline environment, thus improving the surface charge density and consolidating ion selectivity for osmotic energy conversion.
In summary, the nanochannel design and experimental membrane preparation approaches offer feasible solutions for enhancing the performance of osmotic power generation.Moreover, the thermophysical perspective presented above provides insights into the development of an integrated energy system that incorporates various renewable energy sources, including ocean salinity-gradient energy, solar energy, and low-grade heat.This could pave the way for a compact multifunctional device capable of osmotic energy generation, photovoltaic power generation, and desalination with potential applications in diverse locations such as estuaries, islands, and salt lakes.

Summary and Outlook
In this review, the physical mechanisms behind nanochannelbased ion transport and its application in osmotic energy conversion are presented.By integrating recent findings from both theoretical and experimental perspectives, the microscopic images of ion behavior with macroscopic performance are preliminarily connected, and diverse experimental strategies are also discussed to enhance the device output.Despite the significant achievements, there are many challenges due to the complex multiphysical coupling issues among various phenomena, which still require further investigation.
The solid-liquid interface is a complex system composed of various particles interacting with each other, including electrons, ions, surface atoms, and solvent molecules.As a multidisciplinary subject, the dynamic EDL structures are dominated by surface features, electrolyte properties, and environmental conditions simultaneously, making it difficult to fully understand and predict ion behaviors in nanoconfined spaces.Hence, the combination of multiscale simulation methods, such as DFT, AIMD, CMD, and FEM, as well as advanced characterization techniques, such as infrared, Raman, and sum-frequency generation spectroscopy, is needed to gain a deeper understanding of the hydrated ion transport and EDL structures at interfaces.This understanding is essential for fields beyond osmotic energy conversion, such as supercapacitors, ion batteries, electrocatalysis, and water treatment.
The structure-property relationship between nanochannel geometry and osmotic power generation performance has been widely investigated.However, traditional FEM simulations usually simplify the nanochannels into 2D cavities, ignoring the electrified and geometric properties of solid walls.The continuum assumption also ignores the size effect of hydrated ions, which can cause deviation when simulating extremely narrow channels.To overcome these limitations, molecular simulation can be utilized to provide atomic insights to accurately represent physicochemical phenomena occurring at interfaces.Additionally, numerical reconstruction of porous media can create sophisticated models that capture the intrinsic roughness and curvature of 3D nanoporous membranes, bridging the gap between microscopic ion behaviors and macroscopic transport capabilities for various applications.
In the field of osmotic energy conversion, various nanoporous membranes have been developed, each with its own advantages, such as high ion permeability, selectivity, rectification, stability, and durability.The future development of nanoporous membranes should follow a path of theoretical and simulation optimization, followed by precise and targeted preparation in experiments and eventually leading to large-scale practical applications.As another important subject, the design of these devices and their performance prediction still lack clear guidance.Theoretical methods, such as the similarity principle, can help reduce the number of experimental samples needed.Universal equivalent circuit models have the potential to monitor the dynamic performance of the osmotic energy conversion system under varying conditions.Finally, given the shared principles of nanochannel-based ion transport and the availability of renewable energy sources such as salinity gradients, solar energy, and low-grade heat, it is possible to develop an integrated device that can perform multiple functions beyond osmotic power generation, including photovoltaic power generation and desalination.

Figure 1 .
Figure 1.Review topics of ion transport in nanochannels and its application in osmotic energy conversion.

Figure 2 .
Figure 2. EDL structure and its environmental dependence.a) EDL structure at the solid-liquid interface.b) EDL overlap in nanochannels under the impacts of channel size, surface charge density, ion concentration, and ion species.c) Impact of electrolyte pH.d) Impact of electrolyte thermal regulation.e) Diagram of osmotic energy conversion device and its influencing factors.

Figure 3 .
Figure 3. Gibbs−Donnan effect and the induced cation selectivity of nanochannels.a) Schematic of the nanochannel-solution interface, where the Gibbs−Donnan effect is reflected by the profiles of ion concentration and electric potential along the nanochannel.b) Ion concentration distribution along the axial line under the NaCl concentration gradient of 10, which is obtained by numerical simulations.The yellow-filled region represents the nanochannel.c) Ion concentration evolution in each chamber to exhibit cation selectivity of the V-NbP membrane.Initially, the left chamber is filled with anionic dye aqueous solution (40 mg L −1 ), and the right chamber is filled with deionized water (0 mg L −1 ).b) Reproduced with permission.[52]Copyright 2022, Elsevier.c) Reproduced with permission.[53]Copyright 2023, American Chemical Society.

Figure 4 .
Figure 4. Ion selectivity in nanochannels.a) Contour of the concentration-dependent ion selectivity in a negatively charged nanopore, calculated from the cationic and anionic fluxes.b) Normalized cation selectivity on the graphene oxide surface under different temperature and concentration conditions, calculated from the dimensionless parameter.c) Channel size-dependent K + /Na + selectivity in CNTs and SONP, calculated from the formation energy difference.a) Reproduced with permission.[49]Copyright 2021, American Chemical Society.b) Reproduced with permission.[16]Copyright 2022, American Chemical Society.c) Reproduced with permission.[56]Copyright 2015, National Academy of Sciences.

Figure 5 .
Figure 5. Electron transfer at solid-liquid interface.a) Principle of contact-induced electron transfer and surface electrification.b) Diagram of hydrated ions in flat nanochannels.c) Diagram of hydrated ions in rough nanochannels.d) Electron density difference at flat Pt-water interface.e) Electron density difference at rough graphene oxide-NaCl solution interface.The green circle indicates the interfacial region with chemical activeness.f) Bader charge population to quantify the electron transfer and surface electrification at the graphene oxide-NaCl solution interface.a) Reproduced with permission.[60]Copyright 2019, Elsevier.d) Reproduced with permission.[62]Copyright 2018, Royal Society of Chemistry.e,f) Reproduced with permission.[16]Copyright 2022, American Chemical Society.

Figure 6 .
Figure 6.Interfacial effects.a,b) Diagram of interfacial effects involved by epoxide and hydroxyl groups, respectively.c) Na + -Na + structure evolution.d)Average number of H-bonds depending on temperature and ion concentration.e) Time-evolved chemical reaction numbers.f) Surface charge density stemming from the hydroxyl deprotonation process.a-f) Reproduced with permission.[16]Copyright 2022, American Chemical Society.

Figure 7 .
Figure 7. Surface and bulk conductance behavior.a) Regulation mechanism of nanochannel conductance based on energy barrier, considering surface charge density, and geometry of nanochannels.b) Arrhenius-like behavior of nanochannel conductance.c) Nanochannel conductance as a function of monovalent electrolyte concentration for different nanochannel sizes.d-f) Experimental example of concentration-dependent nanochannel conductance by altering surface charge density, channel height, and both surface charge density and membrane porosity, respectively.b) Reproduced with permission.[65]Copyright 2020, Wiley-VCH.Reproduced with permission.[69]Copyright 2022, Royal Society of Chemistry.c) Reproduced with permission.[46]Copyright 2008, American Physical Society.d) Reproduced with permission.[74]Copyright 2022, Springer Nature.e) Reproduced with permission.[75]Copyright 2004, American Physical Society.f) Reproduced with permission.[53]Copyright 2023, American Chemical Society.

Figure 8 .
Figure 8. Ionic rectification.a) Ionic rectification caused by the asymmetric size and surface electrification.b) Typical I−V curves.c) Concentrationdependent rectification ratio of ionic diode membrane composed of negatively charged mesoporous carbon and positively charged macroporous alumina.d) I−V curves for unbent and curved carbon nanochannels.e) Counter-directional rectifying transport of alkaline metal ions and protons in MOF nanochannels.The rectification ratio larger than 1.0 indicates the preferential tip-to-base cation transport, whereas the rectification ratio below 1.0 indicates the preferential base-to-tip cation transport.f) Rectification ratio as a function of pressure under different driving voltages.c) Reproduced with permission.[78]Copyright 2014, American Chemical Society.d) Reproduced with permission.[4]Copyright 2019, Wiley-VCH.e) Reproduced with permission.[86]Copyright 2022, American Association for the Advancement of Science (AAAS).f) Reproduced with permission.[89]Copyright 2020, American Chemical Society.

Figure 9 .
Figure 9. Ion diffusion and fluid diffusion-osmosis in nanochannels.a) Na + ion self-diffusion coefficient on the graphene oxide surface with a rough plate-like configuration.b) Axial self-diffusion coefficients of cations and water in bulk water as well as tube-like carbon nanotube and synthetic organic nanopore.c) Principle of diffusio-osmotic flow in nanochannels.d) Diffusio-osmotic velocity as a function of KCl concentration gradient in different nanopores.a) Reproduced with permission.[16]Copyright 2022, American Chemical Society.b) Reproduced with permission.[56]Copyright 2015, National Academy of Sciences.d) Reproduced with permission.[108]Copyright 2021, Wiley-VCH.

Figure 10 .
Figure 10.Finite element simulation for nanochannel-based osmotic energy conversion.a) Effect of nanochannel length on output power based on the silica isoporous membrane with a uniform diameter of 2.3 nm.b) Ionic rectification effect in Janus membrane.c) Light-driven ion pump.d) Effect of heat transfer and membrane thermal conductivity on the thermal-regulated osmotic energy conversion.a) Reproduced with permission.[114]Copyright 2019, Royal Society of Chemistry.b) Reproduced with permission.[115]Copyright 2017, American Chemical Society.c) Reproduced with permission.[116]Copyright 2019, Springer Nature.d) Reproduced with permission.[117]Copyright 2020, Elsevier.

Figure 11 .
Figure 11.Parameter analysis results upon similarity principle for osmotic energy conversion.a,b) Dimensional and dimensionless osmotic power, respectively.c,d) Contribution rate of impact factors on osmotic power and energy conversion efficiency, respectively.Surface charge density, highconcentration-reservoir concentration, cation diffusivity, channel length, and channel radius are coded as A, B, C, D, and E, respectively.a-d) Reproduced with permission.[55]Copyright 2022, Elsevier.

Figure 12 .
Figure12.First-principles and AIMD simulations applied in nanoconfined ion transport.a) First-principles-derived differential charge density of water molecules in MOF channels.Red and blue colors represent electron accumulation and depletion, respectively.b) Molecular electrostatic potential distribution on the pristine NbP and V-NbP nanosheets.Red and blue colors denote the regions with positive and negative charges, respectively.c) Energy barriers of Na + ion migration.d) Ionic hydration structures and radial distributions of ions and water molecules in graphene channels.e) Timeevolved orientation and vertical and lateral displacements of an OH − ion on graphene.a) Reproduced with permission.[86]Copyright 2022, American Association for the Advancement of Science (AAAS).b,c) Reproduced with permission.[53]Copyright 2023, American Chemical Society.d) Reproduced with permission.[119]Copyright 2019, American Chemical Society.e) Reproduced with permission.[63]Copyright 2019, Springer Nature.

Figure 13 .
Figure 13.CMD simulation applied in the artificial nanofluidic systems.a) Ionic transfer quantity through the sub-nanometer NbP and V-NbP nanosheets.The slopes represent ionic currents.b) COF-based nanofluidic system and the simulated I-V curves.c) Visualized net charge distribution and current density vectors around the graphene nanopore under the synergistic electric field and pressure gradient.a) Reproduced with permission.[53]Copyright 2023, American Chemical Society.b) Reproduced with permission.[120]Copyright 2023, Wiley-VCH.c) Reproduced with permission.[121]Copyright 2022, American Association for the Advancement of Science (AAAS).

Figure 14 .
Figure 14.Equivalent circuit model for osmotic energy conversion.a) Traditional V-source model.b) C-CR model.c,d) Experimental verification of models by time-dependent short-circuit current and power density, respectively.a-d) Reproduced with permission.[122]Copyright 2021, Elsevier.

Figure 16 .
Figure 16.Nanochannel geometry design for enhanced osmotic energy conversion.a) Diagram of osmotic energy conversion device with the designed ANR.b-d) Geometrical model of nanochannel with and without ANR.e) Local ion concentration distribution along the axial line.f) Space charge density distribution.a-f) Reproduced with permission.[52]Copyright 2022, Elsevier.

Figure 18 .
Figure 18.NP-enhanced space charge density and osmotic power generation performance.a) Schematic of NP-enhanced osmotic power generation.b) Space charge density distribution in nanochannels.c) Maximum osmotic power as a function of NP volume fraction.a-c) Reproduced with permission.[125]Copyright 2022, Elsevier.

Figure 19 .
Figure 19.Ion-selective membranes with different structures.a) Fabrication process of the SNF/AAO membrane using a vacuum filtration method.b) Fabrication process of MS/AAO membranes by a spin coating method.c) Porous vermiculite nanosheets prepared by chemical etching.d) Fabrication process of V-NbP membranes.e) Illustration of COF membranes.f) Osmotic energy conversion experimental system.g) I-V scanning.h) Current and power density varied with external resistance.a) Reproduced with permission.[148]Copyright 2019, Springer Nature.b) Reproduced with permission.[149]Copyright 2021, American Chemical Society.c) Reproduced with permission.[124]Copyright 2021, Royal Society of Chemistry.d) Reproduced with permission.[53]Copyright 2023, American Chemical Society.e) Reproduced with permission.[153]Copyright 2022, American Chemical Society.f-h) Reproduced with permission.[123]Copyright 2022, Elsevier.

Figure 20 .
Figure 20.Ion transport and osmotic energy conversion under electrolyte photothermal heating.a-c) Bulk photothermal heating based on metal NPs, wherein, a) osmotic power generator device, b) transient temperature variation, c) equilibrium temperature and power density.d-i) Interfacial photothermal heating based on the photothermal material and the heat transfer porous media, wherein, d) diagram of osmotic power generation device, e) heat transfer analysis, f) solution temperature variation, g) I-V curve, h,i) power density.a-c) Reproduced with permission.[125]Copyright 2022, Elsevier.d-i) Reproduced with permission.[123]Copyright 2022, Elsevier.

Table 2 .
Dimensionless governing equations of Janus nanochannel-based osmotic energy conversion. 1 and  2 , R p1 and R p2 , and L 1 and L 2 are the surface charge density, radius, and length of two nanochannels, respectively.Superscript * represents the dimensionless parameters.