Nanofluidic systems for ion transport with tunable surface charges: fabrications, characterizations, and applications

Nanofluidics deals with the statics and dynamics of simple and complex fluids in systems with at least one dimension below 100 nm. Under strong nanoconfinements, flows may show diverse phenomena, which find rich applications in a variety of areas. In the past decades, nanofluidics has attracted great interest. Particularly, surface charge-governed ion transport in nanofluidic systems shows new flow fashions that cannot be observed in bulk systems and have been applied in different fields in science and engineering. These applications have motivated many efforts in developing surface charge-governed nanofluidic systems, including device fabrications and characterizations. Recent advances in nanotechnology have led to significant progress in surface modifications, which offer new opportunities for surface charge-governed nanofluidics systems. In this review, we discuss recent development of nanofluidic systems with tunable surface charges. Specifically, relevant theories, experimental approaches, and performance comparisons regarding the state-of-the-art fabrication techniques, characterization methods, and applications are presented. Finally, we provide a perspective about the possible future topics and applications for advancing nanofluidic systems with tunable surface charge properties.

1 Introduction

Nanofluidics is a subject dealing with fluid statics and dynamics in systems with a least one dimension below 100 nm. Due to strong confinement effects at the nanoscale, flows in nanofluidic systems may exhibit unique phenomena, which are different from what can be observed in micro- and macro-systems (Rauscher and Dietrich, 2008; Schoch et al., 2008; Bocquet and Charlaix, 2010; Li, 2018; Timperman, 2019; Qian and Xuan, 2020; Li, 2022). Therefore, nanofluidics has attracted great attention in the past decades. Among various flows, ion transport at the nanoscale is a popular topic in nanofluidics (Daiguji, 2010; Han and Chen, 2020; Tao et al., 2021). Because the characteristic dimensions of nanofluidic systems is comparable to or even smaller than the Debye length, the surface charge of a nanofluidic system is of essential importance in ion transport (Stein et al., 2004; Vlassiouk et al., 2008; Ma et al., 2017). In addition to be a scientific focus, nanoscale surface charge-governed ion transport plays a critical role in industrial applications as it can be used in a variety of areas, including lab on a chip technologies (Fu et al., 2007; Zhou et al., 2008; Napoli et al., 2010; Utko et al., 2011; Rems et al., 2016), various sensing (Vlassiouk et al., 2009; Zhou et al., 2011; Kang et al., 2012; Sang et al., 2013; Zhao et al., 2016; Li et al., 2021; Jia et al., 2022), ionic flow regulation (Daiguji et al., 2005; Fan et al., 2005; Karnik et al., 2007; Miedema et al., 2007; Vlassiouk and Siwy, 2007; Yeh et al., 2013; Fuest et al., 2017; Li et al., 2019; Wang and Chen, 2022), energy harvesting (van der Heyden et al., 2006; Bakli and Chakraborty, 2015; Xiao et al., 2018; Gao et al., 2019; Zhou et al., 2019; Zhang et al., 2022) and storage (Daiguji et al., 2006; Pan et al., 2017; Yan et al., 2017; Jin et al., 2020; Liu et al., 2022; Si et al., 2023), to name a few. In the literature, many efforts have been made to design and fabricate nanofluidic systems with tunable surface charges. Surface charge properties of different materials have been studied and characterized. However, a review of nanofluidic systems with tunable surface charges for ion transport is lacking.

It is known that the surface charge density of a material may vary if it undergoes different fabrication processes (Stein et al., 2004). The surface charge density can also be altered through surface modifications using functional groups (Vlassiouk and Siwy, 2007) or external factors such as electric fields (Guan, 2013). These methods provide diverse options for tuning the surface charge density to regulate ion transport. A review that summarizes different methods for surface charge tunning and characterization is necessary. Furthermore, analyses and comparisons of the mechanisms for surface charge modification and the predictions of surface charges are needed.

In this work, we provide a mini review of nanofluidic systems with tunable surface charges for ion transport. Three aspects of the fluidic systems: fabrications, characterizations, and applications, are discussed, as shown in Figure 1. In Section 2, three methods for tuning surface charges, which use pristine materials, achieve charge variation through surface modifications, and utilize external fields, are introduced. In Section 3, four primary approaches for characterizing the surface charge density using ionic conductance, electroosmotic flow velocity (V_EOF), streaming current (I_str), and density of functional groups, are discussed. Enabled by various fabrication and characterization technologies, a variety of applications are summarized in Section 4. The applications include ionic diodes, osmotic power generators, and ion transport enhancement. Finally, a perspective about the future development of nanofluidic systems with tunable surface charge properties for ion transport is provided in Section 5.

FIGURE 1

FIGURE 1. Three aspects of nanofluidic systems with tunable surface charges for ion transport. (A) Fabrication techniques. (B) Characterization methods. (C) Applications.

2 Fabrications of nanofluidic systems with tunable surface charges

2.1 Surface charge tuning using pristine materials

Many pristine surfaces can carry charges during a fabrication process and the charge polarity and density depend on the specific method for creating the surface of flow channels and the properties of the surface material, as will be discussed later. As the surface charge of pristine surfaces does not require chemical modifications, nanofluidic systems with pristine surfaces have been widely used to study surface charge-governed ionic flows. Table 1 lists various materials and the surface charge densities generated by different fabrication methods.

TABLE 1

TABLE 1. Surface charge densities of different materials under various fabrication processes.

Silicon-dioxide (SiO₂)-based materials have been used in early studies that revealed the effects of surface charges on the ion transport in nanochannels. In most of those work, nanochannels were fabricated on a fused silica substrate by reactive CHF₃/O₂ plasma etching. The silica substrate was then bonded with a fused silica cover. Eventually, the nanofluidic system was accomplished by connecting the nanochannels with two micro reservoirs. The surface charge density of nanoslits fabricated through this method was reported to be −60 mC m^-2 (Stein et al., 2004). A similar configuration consisting a substrate with etched structures and a cover plate was achieved by using two pieces of Pyrex^® glass. Schoch et al. fabricated a nanoslit array on a Pyrex^® glass substrate, which was enclosed by another piece of Pyrex^® glass through a field-assisted bonding process. The fluidic system showed a surface charge density of −25 mC m^-2 (Schoch and Renaud, 2005). Besides commercially available SiO₂-based materials, laboratory-made SiO₂ layers can also be used for nanofluidic system fabrications. Cheng et al. developed a nanoslit system by utilizing a glass substrate as the bottom surface and growing a SiO₂ layer on the substrate through a plasma-enhanced chemical vapor deposition (PECVD) method. The as-prepared nanoslits showed a surface charge density of −4.24 mC m^-2 (Cheng and Guo, 2009).

SiO₂ layers can also be grown on substrates through thermal oxidation. Lebedev et al. first grew a SiO₂ layer on a Si substrate through thermal oxidation, which was followed by engraving nanometer-deep trenches in the SiO₂ layer by focusing ion beam (FIB) milling. Then, the substrate was encapsulated by a glass cover and a nanoslit array was achieved. The nanoslits made using this method displayed a surface charge density of −1.5 mC m^-2 (Lebedev et al., 2021). Special nanochannels formed by assembling silica nanoparticles in micropores has been demonstrated and the resulting nanochannels were showed to have a surface charge density of −18 mC m^-2. Pristine carbon-based materials also display a negatively charged surface. Xie et al. proposed a two-dimensional (2D) nanofluidic system consisting of a graphene layer on the bottom surface of nanochannels and a glass cover. The system showed surface charge densities ranging from −5.5 to −4.7 mC m^-2 (Xie et al., 2016). A similar nanofluidic system with nanoslits partially covered by graphene was also fabricated, and the surface charge density was determined as −8 mC m^-2 (Xie et al., 2018). However, graphite, consisting of several graphene layers, demonstrates a relatively weak surface charge density. Esfandiar et al. fabricated graphite nanoconduits by the van der Waals (vdW) assembly, which demonstrated a surface charge density of −0.02 mC m^-2. The low surface charge density was attributed to the spotless fabrication environment and the defect-free graphite (Esfandiar et al., 2017). Using single-walled and double-walled carbon nanotubes grown by chemical vapor deposition (CVD), one-dimensional (1D) nanofluidic systems were fabricated. The performance of these systems indicated that the surface charge densities for single-walled and double-walled carbon nanotubes were −16 to −13 and −203.8 to −1.2 mC m^-2 respectively (Pang et al., 2011; Cui et al., 2023). Nanofluidic systems made of other 2D or 1D materials, such as hexagonal boron nitride (hBN), MoS₂, black phosphorus (BP), and boron nitride nanotubes (BNNTs), have also been developed. These systems exhibited a surface charge density of −0.12, −0.3, −4, and −1000 to −100 mC m^-2, respectively (Siria et al., 2013; Esfandiar et al., 2017; Cui et al., 2023).

Polyethylene terephthalate (PET) is another popular material for fabricating nanofluidic systems. The track-etch method, which uses accelerated heavy ions to hit and etch a substrate, has been widely used to create PET nanochannels or nanopores (Siwy et al., 2003). The PET surfaces under this fabrication method are usually negatively charged due to intrinsic carboxylate groups on the surfaces. The surface charge density covers a wide range, from −240 mC m^-2 (Siwy et al., 2005) to −10 mC m^-2 (Xue et al., 2009). Such a large range is caused by various fabrication parameters, such as post-bombard etchant concentration and etching time.

Membrane-based nanofluidic systems using the phenomenon of nanoscale capillary effects have also been used to study the surface charge effects. Graphene oxide (GO) nanosheet membranes show relatively weak surface charge densities (−20.1 to −0.12 mC m^-2) (Hong et al., 2017). However, high surface charge densities can be reached in boron nitride (BN) membrane (−840 mC m^-2) (Qin et al., 2017). MXene Ti₃C₂T_x membranes and metal-organic framework (MOF) UiO-66-COOH membranes can be fabricated with surface charge densities ranging from −800 to −100 mC m^-2 (Hong et al., 2019; Lu et al., 2021).

In addition to negatively charged surfaces, some materials can carry positive charges, such as Al₂O₃, MgO, and NiO. Al₂O₃ layers can be grown by electron-beam (e-beam) evaporation or thermal atomic layer deposition (ALD). E-beam evaporation is usually performed in a high vacuum chamber, which usually results in a lower surface charge density. Thermal ALD is performed in a relatively high-pressure chamber, where there is certain oxygen and the surface may contain a high charge density. MgO layers can only be grown by e-beam evaporation and NiO layers can be created using e-beam evaporation of Ni and a subsequent oxidation process. The positive charge sites on these oxide surfaces originate from the protonate process of the surface chemical equilibrium, i.e., -MO + H⁺ ⇋ -MOH⁺, where -MO represents the surface oxide group. The surface charge densities of these materials may vary from ∼2.0 to ∼4.0 mC m^-2 (Cheng, 2008; Cheng and Guo, 2009).

2.2 Surface charge tuning by surface modifications

Surface charge polarity and density can also be regulated through surface chemical modifications. Table 2 summarizes some surface chemical modification methods. For SiO₂-base materials, such as fused silica and lead-rich glass, several modification methods have been developed for tuning the surface charge density. One strategy is to block the surface charges on pristine surfaces by attaching the surface with neutral chemical groups. Octodecyltrichlorosilane (OTS) modification for fused silica surface is an example. OTS treatment allows OTS molecules to form a self-assembled monolayer, which can hinder the surface charges. Since the CH₃ head groups of the OTS monolayer do not carry any surface charges, the modified fused silica surface shows a weak surface charge density. The coverage of OTS molecules can be tuned by adjusting the duration of modification or the modification solution concentration. Different OTS molecule coverages make the modified surface exhibit various surface charge densities. Stein et al. reported that the surface charge density of fused silica could be changed from −60 to −10.8 mC m^-2 through OTS treatments (Stein et al., 2004).

TABLE 2

TABLE 2. Surface charge polarity and density achieved by surface modifications.

The second strategy is by introducing charged functional groups. 3-aminopropyldimethyl-ethoxy silane acetonitrile solution treatment can attach -NH₂ groups to lead-rich glass capillaries. In electrolyte solutions with a low pH value, the -NH₂ groups attached on the surface experience a protonation process, becoming positively charged -NH₃⁺ groups. Thus, the modified surface carries positive charges (Wang et al., 2006; Liu et al., 2012). Polymer poly-L-lysine (PLL) treatment can also achieve the same goal as well. PLL treatment adds -NH₂ groups to the fused silica surface and the -NH₂ groups protonate at a low pH value, resulting in positively charged -NH₃⁺ groups. Therefore, the modified surface is positively charged (Stein et al., 2004). This universal strategy can be applied to other materials. Ji et al. developed a two-step scheme to fabricate positively charged GO membranes, where carbodiimide was created on the GO membrane in the first step and 1-aminopropyl-3-methylimidazolium bromide (APMIB) was conjugated subsequently. The APMIB was positively charged, which caused the GO membrane to carry positive charges (Ji et al., 2017).

For PET nanopores, several chemical modification methods have been proposed to control the surface charge density, including layer-by-layer deposition of polyelectrolytes (Ali et al., 2010), 1-(3-Dimethylaminopropyl)-3-ethylcarbodiimide (EDC) solution treatment (Vlassiouk and Siwy, 2007), succinic anhydride solution treatment (Vlassiouk and Siwy, 2007), and cetyl trimethyl ammonium bromide (CTAB) treatment (Xie et al., 2009). Layer-by-layer deposition of polyelectrolytes first deposits poly-(allylamine hydrochloride) (PAH) molecules to PET nanopores through electrostatic adsorption. Because PET nanopores carry anionic carboxylate groups and PAH molecules have many positively charged -NH₃⁺ groups, the resulting assemblies provide excessive positively charged -NH₃⁺ groups, which make the modified surface positively charged. Upon the positively charged PET surface, poly (styrenesulfonate) (PSS) treatment can be applied to reverse the surface polarity. PSS molecules have abundant negatively charged -SO₃^- groups and they electrostatically assemble to -NH₃⁺ groups. This leads to a -SO₃^--group-terminated surface, which is negatively charged. EDC solution treatment aminates PET nanopore surfaces and the resulted -NH₃⁺ groups make the surface positively charged. The PET nanopore surfaces bonding with -NH₃⁺ can be transformed back to carboxylate-group-terminated surfaces by succinic anhydride solution treatment, which exhibit negatively charged. The modification method using cetyl trimethyl ammonium bromide (CTAB) can make the surface charge density of PET nanopores chemical concentration-dependent. When PET nanopores are modified by a low-concentration CTAB solution, cetyltrimethylammonium ions (CTA⁺) are absorbed onto the pore surface due to strong electrostatic effects and the surface is mildly charged. When the CTAB solution concentration is increased, more CTA⁺ groups attach onto the surface, changing the surface from a negatively charged state to a neutral state. If the CTAB solution concentration becomes sufficiently high, CTA⁺ groups accumulate on the surface, which can reverse the surface polarity and cause the surface to be positively charged.

Surface modifications under a gaseous environment have been reported as well. Emmerich et al. developed an activation method for graphite. The first step was to etch the graphite in a water-reactive environment inside a scanning electron microscope (SEM) chamber, and the second step was to etch it in an oxygen (O₂) plasma environment in a reactive ion etching (RIE) chamber. Graphite with extremely strong surface charge densities from −2000 to −340 mC m^-2 were achieved using this approach. The activation phenomenon for these two configurations were explained by highly reactive radicals and crystalline structure defects (Emmerich et al., 2022). Oxygen plasma treatment is also feasible for graphene nanopores (Shan et al., 2013) and PMMA nanofluidic systems (Uba et al., 2015).

2.3 Surface charge tuning by external fields

The surface charge polarity and density can also be modified by various external fields. Figure 2 illustrates three methods. The first method is through altering chemical concentrations. Changing the concentration of H⁺, or pH value, is one of the most common and effective approaches. Zhang et al. reported that porous anodic alumina membrane’s surface charge polarity and density varied under pH stimuli, as shown in Figure 2A. The porous anodic alumina surface experienced a protonation process and gradually exhibited neutral and then positively charged characteristics when the pH value of the electrolyte solution was decreased. When the pH value was increased, a deprotonation process occurred, and the surface became neutral, then negatively charged from a positively charged state (Zhang et al., 2016). It has also been shown that Poly (acrylic acid) (PAA) and poly (4-vinylpyridine) (PVP) can be employed for polydimethylsiloxane (PDMS) nanochannels to achieve a similar pH-responsive surface charge density. Figure 2B shows such a case containing PDMS channels. When pH=3, the PAA-coated PDMS surface was neutral. However, the PVP-coated PDMS surface was positively charged. At pH=11, the PAA-coated surface became negatively charged, while the PVP-coated surface was neutral (Li et al., 2022). Figure 2C depicts another concentration-responsive scheme for changing the surface charge properties, i.e., through adjusting the concentration of fluoride. Upon the increase of fluoride concentration in the solution, 4-aminophenylboronic-acid (APBA) molecules on the modified nanochannels experienced a transformation from a neutral state to negatively charged monofluoride adducts (RB(OH)₂F⁻), difluoride adducts (RB(OH)F₂⁻), and trifluoride adducts (RBF₃^-). Meanwhile, the transformation was reversible, i.e., the modified surface could resume the neutral state upon reducing the fluoride concentration (Liu et al., 2014).

FIGURE 2

FIGURE 2. Nanofluidic systems with surface charges tuned by external fields. (A–C) Surface charge tuned by chemical concentrations. From left to right: Adapted with permission (Zhang et al., 2016). Copyright 2015, John Wiley and Sons. Adapted with permission (Li et al., 2022). Copyright 2022, American Chemical Society. Adapted with permission (Liu et al., 2014). Copyright 2014, American Chemical Society. (D–F) Surface charge changed by electric fields. From left to right: Adapted with permission (Karnik et al., 2005). Copyright 2005, American Chemical Society. Adapted with permission (Ren et al., 2018). Copyright 2018, American Chemical Society. (G–J) Surface charges regulated by light. From left to right: Adapted with permission (Su et al., 2021). Copyright 2021, American Chemical Society. Adapted with permission (Zhang et al., 2014). Copyright 2013, John Wiley and Sons. Copyright 2019, Nature Publishing Group. Copyright 2020, Oxford University Press.

The second method uses external electric fields. Karnik et al. demonstrated a nanofluidic transistor consisting of a source reservoir, a drain reservoir, a gate metal coating, and a nanotube or several parallel nanochannels, as shown in Figure 2D. Analogous to electronic metal-oxide-field-effect-transistors (MOSFETs), where the electronic current can be tuned by a gate voltage, the nanofluidic transistor enabled the control of ionic currents by electric gating. This phenomenon was caused by the charge density variance induced by the external electric field and surface charge-governed ionic flows. Quantitative investigations showed that the achievable surface charge density ranged from −100 to −2 mC m^-2 for parallel nanochannels and from −20 to −10 mC m^-2 for nanotubes (Karnik et al., 2005). Guan et al. developed a nanofluidic system, which contained two electric gates above nanochannels, as shown in Figure 2E. With this electric gate arrangement, gating voltages in opposite polarities were applied to different parts of the nanochannels simultaneously. Hence, the nanochannels simultaneously owned positively and negatively charged regions, resulting in diverse functions (Guan, 2013). Figure 2F illustrates the case, where an electric gate was applied to MXene Ti₃C₂T_x membranes. The ion permeation in this case was enhanced, indicating that the surface charge densities of the membranes were increased.

The third way to tune surface charge is using light. Su et al. observed that the ionic conductivity of MoS₂ membranes could be enhanced under the illumination of UV light, which was caused by the light-enhanced surface charge density (Su et al., 2021), as demonstrated in Figure 2G. Zhang et al. reported a fabrication method to make membranes with heterogeneous surface charge distribution through TiO₂-assisted photochemical reactions. As shown in Figure 2H, TiO₂/Al₂O₃ heterogeneous nanochannels were coated with OTS molecules before light modification. Then, UV irradiation was applied to the as-prepared nanochannels, which caused the OTS molecules on the TiO₂ surface to decompose, and eventually carboxylic groups were created on the surface, making the surface negatively charged. In contrast, the OTS molecules on the Al₂O₃ surface remained unchanged. This resulted in heterogenous surface charge properties. In this strategy, the decomposition reactions of OTS molecules were irreversible. Therefore, the surface charge distribution would not change after the removal of UV irradiation (Zhang et al., 2014). Reversible surface charge tuning is achievable by using photo-responsive materials, such as semiconductors or semiconductor heterojunctions. Kai et al. proposed a photo-driven ion pump using a semiconducting carbon nitride nanotube membrane. Under light illumination, photo-induced holes moved to the illuminated side and photo-induced electrons moved to the unilluminated side, resulting in an asymmetrical charge distribution, as shown in Figure 2I. The photo-induced charge gradient caused a surface charge density gradient on the nanochannel wall. Once the light irradiation was removed, the photo-induced charge separation disappeared and the uneven surface charge distribution vanished (Xiao et al., 2019). A similar idea was applied to TiO₂/C₃N₄ heterojunction nanotubes, as shown in Figure 2J, where the as-fabricated nanofluidic system had a surface charge gradient on the nanochannel wall (Xiao et al., 2021).

3 Surface charge characterizations

3.1 Estimated by ionic conductance

A theory describing ion transport in nanochannels has been developed by Stein et al. (Stein et al., 2004). The theory divides the transport problem into two scenarios, based on the quantitative relationship between the Debye screening length, κ ⁻¹ (${\kappa }^2=\frac{2e^{2}n}{\epsilon {\epsilon }_0{k}_{B}T}$) and the channel height, h. If the notations for a nanochannel in Figure 3 are used, for the first scenario, at high ion concentrations, where $\kappa h\gg 1$ and the surface charge density, σ, is small, i.e., $\left|\sigma \right|\ll enh$, where e is the elementary charge and n is the number density of ions, the ionic conductance, G, is approximately given by (Li, 2018)

$G\approx \frac{2ne\mu hw}{L}(1)$

where μ is the bulk mobility of ions, w, and L are the channel width and length, respectively (see Figure 3). Eq. 1 shows that the ionic conductance directly depends on the ion concentration and channel dimensions and appears to be independent of the surface charge density, which is consistent with the classic model.

FIGURE 3

FIGURE 3. Schematic and notations for a nanochannel for ionic conductance analysis.

At low ion concentrations, however, the surface charge plays an important role in affecting G. In this case, $\kappa h\ll 1$ and $\left|\sigma \right|\gg enh$, and G is given by

$G\approx \left|\sigma \right|\frac{\mu w}{L}\left(1+\frac{4\epsilon {\epsilon }_0{k}_{B}T}{e\mu \eta }\right)(2)$

where ε is the dielectric constant of water, ε₀ is the permittivity of free space, k_B is the Boltzmann constant, T is temperature, and η is the fluid viscosity. Eq. 2 indicates that G is independent of the ion concentration, but strongly depends on σ.

Eq. 2 provides a practical protocol for estimating σ of a nanofluidic system. For an experimental setup illustrated in Figure 4, G can be obtained based on the ionic current measured and the voltage applied. By changing the electrolyte concentration, a relationship between G and the ion concentration of the electrolyte is determined. G at the low ion concentration limit (e.g., 10⁻⁶–10^–4 M) can be used to predict σ using Eq. 2. To ensure the accuracy of σ estimation, the measurements of G can be repeated by altering the nanochannel height from tens of nanometers to hundreds of nanometers.

FIGURE 4

FIGURE 4. Experimental setup for ionic conductance measurement. It contains a slit-like nanochannel, a power supply, and a current meter. Reprinted with permission (Stein et al., 2004). Copyright 2004, American Physical Society.

An example is depicted in Figure 5, where fused silica nanoslit channels were modified by 1 mM and 3 mM OTS solutions. σ was determined using Eq. 2. It was found that σ for the surfaces treated by 1 mM and 3 mM OTS solutions was reduced by 35% and 18% compared with the untreated channels, respectively (Stein et al., 2004).

FIGURE 5

FIGURE 5. Ionic conductance as a function of KCl concentration in fused silica nanoslit fluidic systems. The data can be used to estimate the surface charge density, σ, of the untreated fused silica channels and channels modified by 1 mM and 3 mM OTS. Reprinted with permission (Stein et al., 2004). Copyright 2004, American Physical Society.

3.2 Electroosmotic flow method

The surface charge density σ can also be assessed using electroosmotic flows. For a nanofluidic system containing nanoslit channels, if fluid properties are assumed to be uniform and under the stick boundary condition, the electroosmotic flow velocity, V_EOF, should increase linearly with increasing electric field, E, applied to the system. According to the Smoluchowski equation, V_EOF is given as

$V_{EOF}=-\left(\frac{\epsilon {\epsilon }_0\varsigma }{\eta }\right)E(3)$

where ζ is the zeta-potential. If the channel height is relatively large, it can be assumed that ζ is approximately equal to the surface potential ψ_s. Then, σ can be estimated by the Grahame equation

$\sigma =\sqrt{8\epsilon {\epsilon }_0{k}_{B}Tn}\mathit{sin}h\left(\frac{q{\psi }_s}{2k_{B}T}\right)(4)$

where n is the number density of ions.

Figure 6 shows an experiment setup to determine σ by analyzing the data obtained from electroosmotic flow measurements, which was reported by (Cheng and Guo, 2009; Cheng, 2008.). The experimental system comprised a microfluidic chamber, two electrodes, a power supply, and a camera. The microfluidic chamber consisted of two pieces of glass slides coated with films of interest. The height, width, and length of the microchannel were 80 μm, 0.5 cm, and 1 cm, respectively. An electrolyte (0.1 mM KCl solution) and 1-μm diameter polystyrene beads, which were used to display the flow velocity, were filled into the chamber. Figure 7 plots V_EOF as a function of the electric field for various coatings. The slope of the data points equals to $-\epsilon {\epsilon }_0\varsigma /\eta$, which was used to calculate σ. By this method, the surface charge densities of SiO₂, Al₂O₃, MgO, and NiO were determined as −4.24, 2.10, 1.36, and 3.77 mC m^-2, respectively.

FIGURE 6

FIGURE 6. An experimental setup for electroosmotic flow measurement.

FIGURE 7

FIGURE 7. Electroosmotic flow velocity as a function of electric field for different surface coatings. Adapted with permission (Cheng and Guo, 2009). Copyright 2009, American Chemical Society.

3.3 Estimation based on streaming currents

The surface charge density σ can also be determined using the streaming current of a nanofluidic system. A theory describing the streaming current (I_str) in a single nanochannel has been developed by (van der Heyden et al., 2005). Figure 8 depicts an experimental setup for measuring the streaming current. It consisted of a nanochannel, a pressure chamber, where high-pressure air was used to change the fluid pressure inside the channel, a pressure sensor (P-sensor), and an ammeter for measuring the streaming current through the nanochannel. With this setup, a relationship between the streaming current I_str and the applied pressure difference ΔP, can be obtained. The streaming conductance, S_str, is then calculated as

$S_{str}=\frac{d{I}_{str}}{d\Delta P}(5)$

where, with the notations in Figure 3, I_str, is calculated as

$I_{str}=w{\displaystyle \underset{-\frac{h}{2}}{\overset{\frac{h}{2}}{\int }}}{\rho }_e\left(y\right)u\left(y\right)dy(6)$

where ρ_e is the ion density. It is given by Poisson’s equation,

${\rho }_e\left(y\right)=-\frac{\epsilon {\epsilon }_0{k}_{B}T}{e}\cdot \frac{d^2\psi \left(y\right)}{d{y}^2}(7)$

where the electrical potential $\psi \left(y\right)$ is described by the Poisson-Boltzmann equation,

$\frac{d^2\psi \left(y\right)}{d{y}^2}=\frac{k_{B}T{\kappa }^2}{e}\mathit{sin}h\left(\frac{e\psi \left(y\right)}{k_{B}T}\right)(8)$

FIGURE 8

FIGURE 8. Schematic of a nanofluidic system for I_str measurement. Reprinted with permission (van der Heyden et al., 2005). Copyright 2005, American Physical Society.

The analytical solution of Eq. 8 gives $\psi \left(y\right)$,

$\psi \left(y\right)={\psi }_0+\frac{2k_{B}T}{e}\mathit{ln}\left(\text{JacCD}\left(z\left|m\right.\right)\right)(9)$

where ${\psi }_0$ is the potential at the centerline of the channel and JacCD (z|m) is the Jacobi elliptic function ($z=\frac{\kappa y}{2}{e}^{-e{\psi }_0/2k_{B}T}$ and $m=e^{2e{\psi }_0/k_{B}T}$). To obtain ${\psi }_0$, a boundary condition regarding σ is employed by Gauss’s law,

$\sigma =\pm \epsilon {\epsilon }_0{E}_e\left(x=\mp \frac{h}{2}\right)(10)$

where the electric field, $E_e\left(y\right)$, is given by

$E_e\left(y\right)=-\frac{d\psi \left(y\right)}{dy}(11)$

The velocity distribution u(y) in Eq. 6 is given by Poiseuille’s law,

$u\left(y\right)=\frac{\Delta P}{8L\eta }\left(h^2-4y^2\right)(12)$

Plug Eqs 7, 12 into Eq. 6, it is obtained that

$I_{str}=-\frac{w\Delta P}{8L\eta }{\displaystyle \underset{-\frac{h}{2}}{\overset{\frac{h}{2}}{\int }}}{\rho }_e\left(y\right)\cdot \left(h^2-4y^2\right)dy(13)$

Then, S_str reads

$S_{str}=-\frac{w}{8L\eta }{\displaystyle \underset{-\frac{h}{2}}{\overset{\frac{h}{2}}{\int }}}{\rho }_e\left(y\right)\cdot \left(h^2-4y^2\right)dy(14)$

Equations 6–14 show that S_Str is related to σ, which can be estimated based on the value of S_Str. Details regarding the determination of σ using the streaming current can be found in the literature (van der Heyden et al., 2005; van der Heyden et al., 2006; van der Heyden et al., 2007). An example of this method is shown in Figure 9, where σ of modified PET nanopores was obtained (Xie et al., 2009). In this work, S_str for the flow through the PET nanopores was measured. The method employed CTAB solutions with different concentrations, which enabled different molecular assemblies attached onto the modified nanopore surfaces and caused the surface to carry different charges. I_str was measured under various pressure drops (Figure 9A). The slopes of the I_str-ΔP curves were obtained as S_str, which is plotted versus the CTAB solution concentration in Figure 9B. Eventually, σ for the nanopores was calculated as a function of the CTAB solutions, as shown in Figure 9C.

FIGURE 9

FIGURE 9. Theoretical estimation of surface charge density, σ, by measuring the streaming current, I_str. (A) I_str as a function of pressure difference, ΔP. (B) Streaming conductance S_str as a function of the modification concentration, C_s. (C) σ as a function of C_s. Adapted with permission (Xie et al., 2009). Copyright 2009, American Chemical Society.

3.4 Estimation using functional groups

For surfaces modified by functional groups, the surface charge polarity can be estimated based on the structure and polarity of the functional groups. Ji et al. fabricated a negatively charged GO membrane by assembling carboxylic acid groups on the surface (Ji et al., 2017). X-ray photoelectron spectroscopy was employed to determine the density of surface functional group of the as-prepared surface, indicating that carboxylic acid group took up ∼2.0% of the total carbon content on the membrane surface. Then, the surface charge density was calculated by multiplying the density and the charges of the functional groups, which showed a result of −123 mC m^-2. This method has also been applied to determine the surface charge density of MOF-based membranes (Lu et al., 2021) and chemical-modified PET nanopores (Ali et al., 2010).

4 Applications

4.1 Nanofluidic ionic diodes

Various nanofluidic ionic diodes have been developed and reported in the literature. The concept of nanofluidic ionic diodes is analogous to electronic semiconductor diodes. A nanofluidic ionic diode allows ion transport in a favorable direction when a forward bias is applied (open state) while hindering the ion migration in the opposite direction when a backward bias is applied (close form). The underlying mechanism is the appearance of an ion depletion region, which is similar to the charge depletion region in a semiconductor p-n junction diode. Under a forward bias, the depletion region does not appear inside the nanochannel, and the transport of ions is allowed. Under a backward bias, the depletion region is created, where the ion concentration is low. Ions can hardly move across the depletion region. The key to achieving the ion depletion region under a backward bias is asymmetry, either in geometry or surface charge distribution. Cheng et al. proposed an ionic diode by creating counter-charged regions in a nanochannel array (Cheng and Guo, 2009). An SEM image of the diode is shown in Figure 10A and the structure of the diode is schematically depicted in Figure 10B. For the nanochannels, half of the surfaces were coated with Al₂O₃, which was positively charged, while the other half was coated with SiO₂, which was negatively charged. Figure 11 summarizes the device’s performance with electrolytes of different concentrations. When a negative bias was applied at low concentrations (0.01–100 mM), the ionic current did not change and remained low. However, when a positive bias was imposed, the ionic current increased with increasing bias. The rectification factor, which is the ratio of the ionic currents under the forward and the backward bias, reached the maximum value of 321. The synergy effect of the highly charged surface and asymmetric geometry caused the enhancement of the rectification factor and improved the performance of the diode. A numerical study by Pal Singh et al. revealed that a high surface charge density increases the electrolyte’s unipolar character in a bipolar nanochannel-based fluidic diode. Specifically, the ion depletion was enhanced and the ion current decreased when a backward bias was applied, which resulted in a promoted ion current rectification (Pal Singh et al., 2011). Moreover, a more significant current rectification effect could be generated by combining geometry asymmetry and surface charge asymmetry, as reported by Xiao et al. (Xiao et al., 2016), where untreated funnel-shaped nanochannels with a uniform surface charge distribution were employed and the highest rectification ratio was about 13.5. For the treated funnel-shaped nanochannels with surface charge asymmetry, i.e., the conical segment of the funnel was positively charged and the cylindrical segment of the funnel was negatively charged, the rectification ratio reached 553. The enhanced ionic rectification was due to the accumulation and depletion of ions at the cylindrical segment, which was caused by the asymmetric surface charges.

FIGURE 10

FIGURE 10. A nanoscale ionic diode. (A) SEM image of the fluidic system with asymmetric surface charges due to heterogeneous coatings. (B) Schematic of the charge distribution and nanochannel structure. Adapted with permission (Cheng and Guo, 2009). Copyright 2009, American Chemical Society.

FIGURE 11

FIGURE 11. Performance of the ionic diode shown in Figure 10. (A–F) I-V curves at various concentrations. (G) Ionic conductance and rectification factor as a function of KCl concentration. Adapted with permission (Cheng and Guo, 2009). Copyright 2009, American Chemical Society.

4.2 Osmotic power generator

Nanofluidic osmotic power generators are devices that convert the energy from cation or anion flows through nanochannels/pores into electrical energy. Such a device usually consists of two chambers separated by an array of nanochannels or a thin membrane with nanoscale pores. One chamber contains a salt solution with a high concentration, while the other one is filled with a low-concentration solution. When the two solutions are brought into contact, the salinity gradient drives the ions to migrate from the high concentration end to the low concentration end. Due to the sieving effect of the charged nanochannels/pores, only ions with specific charges (either cations or anions) can pass through, which creates an osmotic voltage and osmotic current across the two chambers. The sieving effect of the nanochannels/pores depends on the surface charge. Therefore, the surface charge density plays a critical role in osmotic power generation. Numerous studies have been conducted to improve the conversion efficiency of osmotic power generators by enhancing the surface charge density of the nanochannels/pores. Hong et al. reported an osmotic power harvesting system using MXene Ti₃C₂T_x membranes (Hong et al., 2019). The ionic conductance, G, of the system as a function of the salt concentration is shown in Figure 12. It is seen that G is higher than that for the system containing neutral membranes. The enhancement was caused by the highly charged MXene membrane surfaces.

FIGURE 12

FIGURE 12. Ionic conductance of MXene membranes (red circles) as a function of salt concentration. The dashed line represents the case of neutral membranes. The solid line represents the predictions for a constant surface charge density of 0.1 mC m^-2. The inset shows the surface charge density as a function of salt concentration. Adapted with permission (Hong et al., 2019). Copyright 2019, American Chemical Society.

Regulating counter-ion transport from the high salinity chamber to the low salinity chamber by counter-charged nanochannels is another way to achieve high electrical outputs. Gao et al. developed and fabricated a heterogenous membrane with positively charged pores on one side and negatively charged pores on the other side (Gao et al., 2023). The positively charged pores were achieved by an ordered alumina nanochannel membrane (ANM), which had a surface charge density of 7.18 mC m^-2 and a pore size of 100 nm. The negatively charged pores were achieved by the β-ketoenamine-linked two-dimensional covalent-organic framework (COF) membrane with a surface charge density of −5.14 mC m^-2 and a pore size of 1.1 nm. The proposed heterogeneous membrane reached an osmotic power density of 27.8 W m^-2 when salt gradient was created by artificial salt-lake and river water. Similar heterogenous membranes with positively and negatively charged pores for power generation have been reported by several groups as well (Zhou et al., 2021; Cao et al., 2022; Fauziah et al., 2023; Wang et al., 2023). Ji et al. reported an osmotic power generator with a pair of positively and negatively charged GO membranes, as shown in Figure 13 (Ji et al., 2017). It achieved an output power density of 0.77 W m^-2 when artificial seawater and river water were added to the high and low salinity sides, respectively. The configuration with positively and negatively charged membranes can be achieved by stacking positively and negatively charged nanoparticles as well (Wang et al., 2018). The positively charged membranes were fabricated by packing aminated silica-coated iron oxide nanoparticles and negatively charged ones were fabricated by hydroxyl-group-bonded silica and polystyrene nanoparticles. Each full cell consisted of a positively charged membrane and a negatively charged membrane. When 20 full cells were connected in series, the device achieved an output voltage as high as 1 V.

FIGURE 13

FIGURE 13. An osmotic power generator with a pair of positively and negatively charged graphene oxide membranes. Adapted with permission (Ji et al., 2017). Copyright 2016, John Wiley and Sons.

4.3 Ion transport enhancement

Ion transport in nanochannels can be enhanced by changing the surface charge density. Several studies have demonstrated superior ionic conductance in highly charged nanochannels. As shown in Figure 14, Emmerich et al. demonstrated that the ionic conductance in activated nanochannels could be enhanced by 10,000 times compared with the bulk value. They attributed such a significant improvement to one to two orders of magnitude increase in the surface charge density during the activation process (Emmerich, 2021). Fast ion transport was also observed in nanochannels consisting of mica and graphite, as reported by Jiang et al. (2023). The mica surface showed a very high surface charge density, which was around −200 mC m^-2. This highly charged mica surface absorbed a large number of cations, forming a cation stack with a packing density close to the 2D dense packing limit. The highly packed cation stack migrated under an electric field, which demonstrated an ionic conductivity orders of magnitude higher than the bulk value.

FIGURE 14

FIGURE 14. Conductivity enhancement for pristine and activated nanochannels at different concentrations (Emmerich, 2021). (A) Pristine nanochannel with a height of 10 nm. (B) Pristine nanochannel with a height of 15 nm. (C) Activated nanochannel with a height of 8 nm. (D) Activated nanochannel with a height of 10 nm. Symbols represent experimental data. Solid and dashed lines are theoretical predictions with different assumptions.

Recently, a new strategy for enhancing ion transport in nanofluidic systems was proposed by using counter-charged nanochannels, where half of the nanochannels were positively charged and the other half of the nanochannels were negatively charged (Zhou et al., 2023). Figure 15 illustrates the design of the system. Positively charged nanochannels were achieved by coating surface with Al₂O₃ and negatively charged nanochannels were pristine SiO₂. In such a fluidic system, cations and anions moved in different channels, which avoided opposite-directional migration of ions in the same channel under an electric field and boosted the velocity of ions. Numerical simulations showed that the ionic current could be enhanced by a factor up to 5.8 at a proper surface charge density. In experiments, the maximum current was 1.8 times the bulk value, which is lower than numerical results due to a relatively low surface charge density.

FIGURE 15

FIGURE 15. Schematic of a nanofluidic system with counter-charged nanochannels. Reprinted with the permission of AIP Publishing (Zhou et al., 2023).

5 Summary and outlook

In conclusion, we have reviewed the recent progress in nanofluidic systems with tunable surface charges for ion transport. Surface fabrications, surface charge characterizations, and applications are discussed. For surface fabrications, pristine surfaces and surface charge properties under various fabrication methods in the literature are summarized. Furthermore, various surface modification methods that can be used to tune surface charge polarity or density by chemical solutions or in gaseous environments are introduced. External fields including chemical concentration, electric field, and light for altering the surface charge density are also discussed. Materials, techniques, and underlying mechanisms for surface charge modifications are elaborated.

Primary methods for surface charge characterizations are presented in the second part. Theoretical estimations can be performed using ionic conductance, electroosmotic flows, streaming currents, and the density of functional groups. Necessary theories for characterization analysis are described. Experimental setups and nanofluidic system configurations involved in these characterization methods are provided. Examples from the literature are presented for reference.

The third part of this review deals with the applications of surface charge-dominated ion transport in nanofluidic systems. Three major applications are discussed. Nanofluidic ionic diodes, which take advantage of asymmetric geometry and/or surface charge distribution of nanochannels, allow ion transport in a particular direction and suppress the ionic current in the reverse direction. Osmotic power generators convert energy of osmotic flows to electricity. Their efficiency can be enhanced by increasing the surface charge density or regulating ionic flows through oppositely charged membranes. Counter-charged nanochannels can be utilized to boost ion transport in nanofluidic systems and the ionic current enhancement can be adjusted by varying the surface charged density.

For future developments, several issues need to be investigated and addressed. First, various pristine surfaces show negative charges, but few carry positive charges. More efforts can be made to explore the possibility of making pristine surfaces positively charged. This will provide flexibility for nanofluidic system fabrication in terms of material selection. Second, regarding the surface charge tuned by external fields, nanochannels with surface charges being tuned through a joint method (e.g., tuned simultaneously by an electric field and light) can be studied, which may shed light on more powerful nanofluidic systems. Third, the results about surface charge characterizations in the literature are based on different methods. It is difficult to compare them. It would be convenient for data comparison if a standard protocol for surface charge characterizations can be developed.

Regarding the potential applications, topics such as nanofluidic memristors and nanofluidic membranes for salt-lake lithium mining can be considered. Nanofluidic memristors are a type of memory resistors achieved in nanofluidic systems that have an internal state which can be altered based on the voltage history of the system, resulting in a change in their conductance (Robin et al., 2023). If nanofluidic systems with voltage-responsive hysteretic surface charge can be developed, nanofluidic memristors facilitating this mechanism can be achieved. Salt-lake lithium mining is proposed as a solution to meet the increasing demand for lithium ions in battery industry. The surface charge properties of nanofluidic membranes are of great importance in this application, as they can control the behavior of Li⁺ inside nanopores (Razmjou et al., 2019; Hou et al., 2021). However, limited surface charge tuning techniques have hindered the progress in this area. With the advances in nanofluidic systems with tunable surface charges, the selective transport of Li⁺ is expected to be enhanced.

Author contributions

DS: Conceptualization, Data curation, Formal Analysis, Writing–original draft. LZ: Conceptualization, Data curation, Formal Analysis, Writing–original draft. ZL: Conceptualization, Funding acquisition, Project administration, Supervision, Writing–review and editing.

Funding

The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This work was supported by the General Research Fund (16208422 and 16207323) and Collaborative Research Fund (C6020-22G) of the Hong Kong Special Administrative Region.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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