Electrical signal transmission across electrolyte junctions separated by atomically-thin graphene

Abstract

Signal transmission across membranes is usually mediated by the permeation of molecular species. Here we show that atomically thin graphene crystals, although impermeable to any ions or molecules, can transmit interfacial electrical potentials across electrolyte junctions without significant disruption. In monolayer graphene, applying an electrical potential at one graphene-electrolyte interface induces a similar responsive potential at the opposite side, with the magnitude governed by ionic sizes. By increasing the number of graphene layers, the response decays and vanishes at ~ 5 layers. Theoretical analysis attributes these observations to graphene’s tunable charge-carrier concentration combined with its extreme thinness. This capability of transmitting activation stimuli without mass transport may find its applications in artificial synapses and other neuromorphic junctions.

This study shows that atomically thin graphene can transmit electrical signals between separated liquids without allowing ions or molecules to pass, enabling communication across otherwise impermeable membranes.

Introduction

In nature, membranes are ubiquitously used to separate electrolytes into distinct compartments while enabling communication between them. Such communication typically relies on the transport of signaling species¹, such as Na⁺ and K⁺ ions that regulate membrane potentials², and neurotransmitters that transmit neuronal signals³. Similar functions have also been reproduced in artificial membranes^4–6. Beyond that, however, biological membranes can also conduct signals carried by species that are impermeable to the membrane^7,8. This mode of signaling, which avoids mass transport yet underpins important processes such as vision, olfaction and gustation⁹, remains far less studied in artificial systems. Some pioneering efforts have employed conformational changes of biomimetic molecules embedded in membranes to transmit information^10,11, but other mechanisms for transmembrane communication are still largely unknown. That leaves open the possibility of alternative routes, such as those enabled by atomically thin materials, to be discovered.

We hypothesis that atomically thin membranes could transmit interfacial double layer potential signals without mass transport, a function that is currently inaccessible to thicker membranes. At the membrane-electrolyte interfaces, direct exchange between carriers (e.g., between electrons in the solid and ions in the electrolytes) is blocked by energy barriers, and the potential drop across the electrical double layer penetrates only a few atomic layers into the membrane’s bulk¹². Therefore, in thick membranes, this potential has negligible influence on the opposite side behind the membrane, which constraint, though, may not hold at atomic thickness. Few-layer graphene provides us an ideal test system, due to its impermeability to all ions and molecules^13,14 and, importantly, its limited carrier concentrations near the Fermi levels that cannot effectively screen perpendicular electric fields¹⁵. Therefore, applying a potential at one graphene-electrolyte interface may promote the redistribution of ions in the opposite double layer and induce a measurable potential variation. In this work, we study such responses across electrolyte junctions separated by graphene, where the results reveal a previously unexplored route of transmembrane communication, enabling transparent signal transmission without mass transport.

The schematic of our devices is described in Fig. 1a. Mechanically exfoliated graphene crystals (with various numbers of layers) were suspended over a micro-meter-sized aperture prepared on silicon nitride wafers, using the methods as described in previous works^16,17. Two electrodes were also deposited on graphene to monitor its electrical conductance G_e. The graphene was encapsulated with inert polymers to expose only the suspended area. The wafer was then used to separate two reservoirs filled with equal concentrations of KCl solutions so that the ions from different reservoirs can interact only via the graphene. Details of device fabrication and characterization of graphene thickness can be found in Supplementary Note 1 and Supplementary Figs. S1 and S2.

Fig. 1. Measurements of cross-membrane potential.

a Schematic of devices used in this work. b The electrical conductance of a monolayer graphene device, where the gate potential shifts the Fermi level of graphene with respect to the neutrality point (yellow). c Measurements of the output I_b (at V_b = 0) and d the V_b (at I_b = 0) under the applied input potential V_t. The I_b⁰ and the V_b⁰ are the saturated output currents and voltages, as defined by the black dashed lines in (c, d), respectively. In (c, d), the bottom insets show schematics of the gate potential (Φ) as a function of the distance from the graphene for different gate configurations (c, V_b = 0; d, V_b = V_b⁰). Note that the applied V_t or V_b is relative to the Fermi surface of graphene defined as Φ = 0 in the energy scale. The interfacial Φ_int experienced by electrolytes measures the difference between V_t (or V_b) relative to the neutrality point of graphene indicated by the dashed lines. The V_t and V_b shift the Fermi level of graphene with respect to the neutrality points (yellow). For simplicity, only positively charged ions (green sphere) are shown to indicate ion transport direction. Analogous analysis is applicable to anions. Hydration shell of ions is omitted for clarity. The dark gray balls represent carbon atoms. e V_b⁰ and I_b⁰ modulated by V_t in a representative monolayer graphene device. The black line indicates the relationship when V_b⁰ = V_t. f The relation between I_b⁰ and V_b⁰. The red solid line is the best linear fit. In all experiments, both the top and bottom reservoirs were filled with 0.01 M KCl of pH ≈ 6.5. The slight deviation from neutral can be attributed to dissolved CO₂ from environment. Error bars in (e, f) are the uncertainties due to signal noise.

Results and disscussion

To generate an interfacial electrical potential, a gate voltage V_t was applied between the graphene and an Ag/AgCl electrode in one of the reservoirs (the top reservoir, Fig. 1a). Here, graphene was electrically grounded. Therefore, a positive V_t means that the top electrolyte/electrode is biased positively relative to graphene, or equivalently that graphene is negatively biased relative to the top electrolyte. The applied V_t was kept within ±0.6 V to avoid any electrochemical reactions at the graphene electrodes, including water electrolysis, which typically occurs at potentials above ~1.2 V. Under these conditions, a small but non-zero current I_t in the picoampere range was observed between graphene and the Ag/AgCl electrode. Such currents have been systematically investigated in previous work¹⁸, where I_t was attributed to the dissolution and migration of trace amounts of Ag/AgCl species and/or particles from the bulk electrode that become deposited on the pristine graphene surface under an applied bias. This process enables a direct ionic current to flow at the graphene-electrolyte interface via the reversible electrochemical equilibrium AgCl + e⁻ ↔ Ag + Cl⁻. In Supplementary Fig. S3, we further show that encapsulating the Ag/AgCl electrode with a salt bridge to suppress the migration of Ag/AgCl nanoparticles reduces I_t to only a few picoamperes. The extremely small magnitude of I_t indicates that the potential drop across the bulk electrolytes is less than 0.1% of V_t and can therefore be negligible (see Supplementary Note 2). Likewise, the potential drop at the Ag/AgCl electrode is also negligible, as the picoampere current is insufficient to polarize the macroscopic electrode or to measurably bias the reversible equilibrium between the electrode and the Cl⁻ ions¹⁹. Therefore, the applied potential V_t drops predominantly at the graphene-electrolyte interface. This conclusion is further supported by the bipolar G_e-V_t characteristics observed in monolayer graphene (Fig. 1b), which reflect electrolyte double-layer gating. The minimum of G_e occurs at positive V_t, a sign of electron doping of graphene induced by the electrolyte.

Interestingly, under an applied V_t, we also observed a finite negative I_b = I_b⁰ of a few picoamperes in the bottom reservoir under short-circuit conditions (Fig. 1c). This observation indicates that the electrical potential applied at one graphene-electrolyte interface is effectively transmitted across the graphene membrane and modulates the interfacial currents at the opposite side. To quantify the transmitted potential, a compensating voltage V_b was applied such that the bottom current vanished (I_b = 0, Fig. 1d). The responding V_b reaches its equilibrium value of V_b⁰ within tens of seconds and remains stable for hours (Supplementary Fig. S4). Under this condition, V_b⁰ corresponds to the transmitted interfacial potential, with equal magnitude and opposite sign. Both I_b⁰ and V_b⁰ were found to vary systematically with V_t (Fig. 1e), and the linear relationship between I_b⁰ and V_b⁰ confirms that the transmitted potential acts as the driving force for I_b⁰ (Fig. 1f). We note that the finite I_b⁰ is likely supported by Ag/AgCl-related interfacial redox species at the bottom graphene interface. Replacing the Ag/AgCl electrode with other metal electrodes leads to unstable interfacial electrochemical readout (Supplementary Fig. S5). While local field inhomogeneities near isolated Ag/AgCl-related particles cannot be fully excluded, such local effects are proven do not produce a measurable change in the transmitted potential (Supplementary Fig. S6).

For monolayer graphene, we find that V_b⁰ ≈ V_t (Fig. 1e), indicating that the interfacial potential is transmitted through graphene without any loss in magnitude, despite the presence of the membrane. Device-to-device variations in the intrinsic charge-neutrality point of monolayer graphene, as well as the trace amount of Ag/AgCl species, do not measurably change this near-unity V_b⁰-V_t relation within our experimental uncertainty (Supplementary Fig. S7). Importantly, this transmission occurs in the absence of any mass transport. The impermeability of mono- and few-layer graphene to ions and molecules, when prepared by the same mechanical exfoliation technique as use here, has been systematically demonstrated in previous studies^13,14,16,17. Consistently, post-measurement Raman and electron microscopy show no detectable permanent damage or pinhole formation in graphene after the signal-transmission experiments (Supplementary Fig. S8). In addition, direct measurements of the cross-membrane ionic current (Supplementary Fig. S8) reveal values no larger than the background current level measured in control devices fabricated on aperture-free silicon substrates, and substantially smaller than the observed I_b⁰ and I_t. Further evidence of mass-transport-free signal transmission is provided in Supplementary Note 5 and Supplementary Fig. S9 and S10. To understand the origin of the observed transmission, we recall that applying V_t shifts the Fermi level of graphene relative to its charge-neutrality point, thereby generating an electric field at the bottom graphene-electrolyte interface even when V_b = 0 (Fig. 1c, bottom inset). When a compensating voltage V_b (= V_b⁰) ≈ V_t is applied, the chemical potentials of the Ag/AgCl electrodes are aligned with graphene’s neutrality point, eliminating potential drops in both the top and bottom electrolytes (Fig. 1d, bottom inset). Under these conditions, the bottom current vanishes (I_b = 0) and the top current I_t simultaneously approaches zero (Supplementary Fig. S10), consistent with complete electrostatic compensation.

To elucidate the mechanism underlying the transmitted signals and to examine the role of ions in the electrolytes, we varied the electrolyte in the top reservoir using chloride solutions of alkaline metal cations M⁺ (Li⁺, Na⁺, K⁺ and Cs⁺). These cations share the same valence but possess different hydration diameters d_H. The electrolyte in the bottom reservoir was kept unchanged as KCl. For monolayer graphene and positive V_t, we found that the compensating voltage V_b⁰ depends on the identity of the cations in the top reservoir (Fig. 2a). Specifically, V_b⁰ decreases with increasing hydration diameter d_H of M⁺. For example, similar values of V_b⁰ are observed for K⁺ and Cs⁺, which have comparable d_H, whereas Li⁺ yields a V_b⁰ that is about 30% smaller. Note that under this voltage convention, positive V_t drives cations such as Li⁺, Na⁺, K⁺ and Cs⁺ toward the graphene surface, because graphene is effectively negative relative to the top electrolyte. Therefore, these results demonstrate that modifying the ionic environment at one graphene-electrolyte interface effectively controls the electrical responses at the opposite interface. In contrast, at negative V_t, we obtain V_b⁰ ≈ V_t for all electrolytes, consistent with the accumulation of Cl^- ions at the graphene surface regardless of the accompanying cations. This behavior indicates a strong electrostatic coupling between the electrical double layers on the two sides of graphene.

Fig. 2. Transmitted signals tuned by the size of ions.

a The V_b⁰-V_t dependence in monolayer graphene obtained using various cations in the top reservoir. The bottom reservoir was filled with KCl. All solutions used were 0.01 M. The solid line is a guide to the eye, indicating the relationship of V_b⁰ = V_t. Error bars are S. T. D. Inset shows statistic results from 4 monolayer devices, where each bar represents one device. The grey bars are the ratio of V_b⁰ between using Li⁺ and K⁺ ions in the top reservoir, taken at V_t = −0.6 V. The red bars are the same ratio, but taken at V_t = +0.6 V. b The variation of V_b⁰ as a function of cations’ hydration sizes 1/d_H, taken from (a) at V_t as indicated. The dashed lines are the predictions using V_b⁰ = V_t d_H^K+/d_H, with d_H^K+ = 6.6 Å.

Figure 2b further suggests an approximately linear relationship between V_b⁰ and 1/d_H, such that V_b⁰ ≈ V_t d_H^K+/d_H^M+. This scaling immediately links the transmitted potential to the strength of the electrical field within the electrical double layer and, consequently, to the effective Stern layer thickness d_S, which is governed by the hydrated ion size. Accordingly, the electric fields at the top and bottom graphene-electrolyte interface can be expressed as E_t = αV_t/ε_Sd_H^M+ and E_b = αV_b⁰/ε_Sd_H^K+, respectively. ε_S is the effective dielectric constant of the Stern layer, and α is a dimensionless factor accounting for possible deviations between the actual interfacial potential drop and the experimentally measured values, as well as between d_S and d_H. Independent experimental estimates of α and its physical origin are provided in Supplementary Note 6 and Supplementary Fig. S11 and S12, yielding values close to unity. At equilibrium, continuity of the displacement field requires ε_SE_t = ε_SE_b, which leads to V_b⁰ = V_t d_H^K+/d_H^M+, in agreement with the experimental observations in Fig. 2b.

We next investigate the screening of the transmitted signal in thicker graphene crystals (Fig. 3a, b). As the number of graphene layers increases, both V_b⁰ and I_b⁰ decrease gradually. For four-layer graphene, V_b⁰/V_t remains measurable but is already strongly reduced to approximately 9%. For five-layer graphene and beyond, V_b⁰/V_t decreases to approximately 5% and saturates at values characteristic of bulk graphite. In this limit, V_b⁰ falls below our detection limit (less than 1% of V_t) and shows no measurable dependence on V_t. This layer-dependent suppression is also inconsistent with a leakage-based origin of the transmitted signal, because parasitic leakage through the SiN_x surface or device periphery would not be expected to depend systematically on the number of graphene layers. Despite the absence of direct contact between the two electrolytes, the persistence of signal transmission reproducibly through few-layers graphene (Supplementary Fig. S7) implies incomplete electrostatic screening, an intrinsic property of atomically thin conductors. To further verify that the observed potential transmission is not a general property of conductive electrodes, we performed control experiments using conventional thick metal electrodes. When graphene was replaced by either copper or gold films with thickness down to tens of nanometers, no measurable transmitted potential was detected under otherwise similar measurement conditions (Supplementary Fig. S13). Previous studies have shown that the doping-induced charge density in gated multilayer graphene decays from the surface layer into the bulk, with a screening length of about 4-5 monolayers^20,21. Consistent with this picture, Raman spectroscopy of a bilayer device reveals a characteristic G-peak splitting upon application of V_t (Supplementary Fig. S14), suggesting asymmetric electrical doping²². The graphene thickness at which V_b⁰ vanishes (about 4–5 layers) agrees well with the reported screening length.

Fig. 3. Mechanism of the potential distribution at atomically-thin graphene interfaces.

a V_b⁰ responses as a function of V_t applied for multilayer graphene with various numbers of layers as indicated in the figure. Both reservoirs were filled with 0.01 M KCl. The empty symbols are the experimental data. The solid lines are the predictions using V_b⁰ = V_t/[1 + (ε_S/ε_g)·(d/d_H^K+)] with different ε_S as the fitting parameters. For simplicity, only the fittings at positive V_t are shown. Inset shows the best ε_S being used, with the error bars representing the uncertainty. Note that the effective thickness of monolayer graphene is assumed zero as defined in the text. Therefore, no ε_S is needed to fit the monolayer graphene data. The arrow indicates the dielectric constant ~80 of bulk water. b The decay of I_b⁰ and V_b⁰ with increasing number of graphene layers. Error bars are S.T.D., estimated from at least three different devices in each thickness. c Schematic of the potential drop Φ at the top and bottom interfaces, in the case when I_b = 0. For simplicity, only the Stern layers are shown, with their boundaries indicated by the green dashed lines. The slopes of Φ in the two Stern layers are equal (in their absolute values) and are different than that in graphite, depending on the ratio of dielectric constant ε_S/ε_g. The purple and green balls represent ions of different hydration sizes, while the dark gray balls represent carbon atoms. The sizes of the blurred blue spheres around the ions indicate the relative sizes of hydrated ions.

These observations allow us to model multilayer graphene as a capacitor with unequal surface charge densities induced by V_t on its two outermost layers, separated by a distance d = a (N - 1), where a is the interlayer spacing of graphite and N is the number of layers (Fig. 3c). Detailed potential drop profiles for multilayer graphene at V_b = 0 and V_b = V_b⁰ can be found in Supplementary Fig. S15. As derived in Supplementary Note 7, the transmitted potential can be expressed as V_b⁰ = V_t ·(d_H^K+/d_H^M+)/[1 + (ε_S/ε_g)·(d/d_H^M+)]. In this formula, ε_g ≈ 3 is the effective dielectric constant of graphite, which is independent of N at low electric fields²³. Therefore, ε_S can be used as the only fitting parameter for the thickness-dependence data in Fig. 3a. For monolayer graphene (d = 0), the equation reduces to V_b⁰ = V_t ·(d_H^K+/d_H^M+), consistent with the experimental results. Fitting the data yields an effective Stern layer dielectric constant ε_S that is markedly reduced compared with its bulk water value ~80. For few-layer graphene, ε_S ≈ 2, comparable to values reported for two-dimensional confined water (~2.1)²⁴ and for water at optical frequencies (~1.8)²⁵, where polarization arises predominantly from electronic rather than orientational contributions. This reduced dielectric response indicates that rotational freedom of water dipoles is strongly suppressed in the direction perpendicular to the graphene surface. In thicker graphite, ε_S raises rapidly, which we attribute to the orders-of-magnitude smaller transmitted V_b⁰, insufficient to significantly polarize interfacial water molecules.

To conclude, we demonstrate that atomically-thin graphene is transparent to the transmission of electrical double layer potential signals, a property that arises from its extreme thinness combined with its tunable charge-carrier concentrations. Additional measurements using monolayer MoS₂ show that transmembrane potential transmission is not exclusive to graphene, although the transmitted signal is weaker and strongly dependent on the electronic structure and electrochemical stability of the membrane material (Supplementary Fig. S16). The ability to transmit interfacial electrical potentials without cross-membrane mass transport may be useful in systems where two electrolyte compartments must remain chemically isolated while still communicating electrically. Potential application scenarios include membrane-based chemical sensing, iontronic signal processing, artificial synaptic junctions, and membrane electronics. As preliminary proof-of-concept demonstrations, we show that a charged molecular stimulus introduced at one graphene-electrolyte interface can be detected electrically from the opposite side (Supplementary Fig. S17), and that pulsed electrical inputs can be dynamically transmitted across the graphene junction with frequency-dependent attenuation and history-dependent signal accumulation (Supplementary Fig. S18). Further studies will be required to evaluate selectivity, sensitivity, long-term stability, integration, and scalability for optimized device performance. More broadly, the demonstrated double-gating approach allows independent control of the electrolyte environments at two otherwise identical solid-liquid interfaces, creating a platform for the direct comparison of interfacial effects, such as ion-specific interactions demonstrated here. Therefore, beyond device implications, our approach offers an experimental tool for probing the structure of electrical double layers and related interfacial electrostatic and electrochemical phenomena under well-controlled and asymmetric boundary conditions.

Methods

Devices fabrication

The micrometer-sized apertures were etched through silicon substrates (with double-side coated 500 nm silicon nitride layers) using a combination of photolithography, wet etching, and reactive ion etching techniques, following the fabrication procedures as being previously reported¹⁶. After that, metal electrodes (20 nm Au and 3 nm Cr) were patterned and deposited using photolithography and electron-beam evaporation techniques, respectively. Subsequently, mechanically exfoliated graphene crystals were transferred to cover the apertures as well as the electrodes (Fig. S1). A SU-8 washer was further transferred, with the hole in the washer being precisely aligned with the aperture in the silicon nitride substrate; as such, only the working area in graphene was exposed in electrolytes. Other parts of the flakes and the electrodes were fully encapsulated to avoid leakage and/or electrochemistry occurring at the metal electrodes (Fig. S1b). Electron microscopy clearly resolves the boundary of the monolayer graphene flake and confirms that the graphene fully covers the SiN_x aperture, as shown in Fig. S1c, d. Atomic force microscopy performed over the suspended region further shows a continuous membrane morphology, with no visible cracks or holes (Fig. S1e). Within the spatial resolution of these measurements, we did not observe defective pinholes in the suspended graphene region.

Interfacial signal measurements

Dual-channel Keithley 2636B sourcemeters were used for electrical measurements. Gate voltages of V_t and V_b in the range of ±0.6 V was applied between the graphene and the Ag/AgCl electrodes in the top and bottom reservoirs, respectively. For measuring the electrical conductance of graphene, a constant bias voltage V_SD = 1 mV was applied to obtain the current I_SD as a function of V_t. To limit the redeposition of Ag and/or AgCl particles onto the graphene electrodes, we placed the Ag/AgCl electrodes inside a salt bridge that was filled with the same electrolytes as that of bulk. The opening of the salt bridge was covered with a nanoporous membrane that allowed ion transport but sterically block the migration of any large particles into the bulk electrolyte. That leads to a significant reduction of I_t (Fig. S3). On the other hand, such reduction also supports the origin of I_t as Ag/AgCl redeposition. In the latter case, the current exchange between the electrically conductive graphene and the ionically conductive electrolytes is allowed at the interface via the spontaneous electrochemical equilibrium of AgCl + e^- ↔ Ag + Cl⁻. Analogous analysis is applicable to the V_b and I_b.

Theoretical prediction of the V_t and V_b⁰ relationship

Figure S15 shows the potential distributions in the Stern layers as well as in the few-layer graphene. The electric displacement field D must satisfy the following boundary condition at z = 0:

$$D_{z>0}-D_{z<0}=-{\sigma }_0$$ 1

where σ₀ is the graphene’s surface charge. Thus,

$$D_{z<0}=\frac{{\sigma }_0}{2}$$ 2

$$D_{z>0}=-\frac{{\sigma }_0}{2}$$ 3

The electric field then reads:

$$E=\left\{\begin{array}{c}\hfill \frac{{\sigma }_0}{2{\epsilon }_0{\epsilon }_{\mathrm{s}}},z<0\hfill \\ \hfill -\frac{{\sigma }_0}{2{\epsilon }_0{\epsilon }_{\mathrm{g}}},0<z\le d\hfill \\ \hfill -\frac{{\sigma }_0}{2{\epsilon }_0{\epsilon }_{\mathrm{s}}},z>d\hfill \end{array}\right)$$ 4

Here, the ε_S and the ε_g are the dielectric constants of the Stern layer and graphite in the vertical direction, respectively. By switching on the top gate voltage V_t, the potential on the bottom side is reduced by the value

$$△V=\frac{{\sigma }_{0}d}{2{\epsilon }_0{\epsilon }_{\mathrm{g}}}$$ 5

where d is the thickness of graphene given by d = a (N - 1), with a the out-of-plane lattice constant of graphite, N the number of layers. The voltage that is applied to compensate the interfacial potential at the bottom side is then given by:

$$V_{\mathrm{b}}^0=\frac{{\sigma }_0{d}_{\mathrm{S}}^{\mathrm{K}+}}{2{\epsilon }_0{\epsilon }_{\mathrm{s}}}$$ 6

$$V_{\mathrm{t}}=\frac{{\sigma }_{0}d}{2{\epsilon }_0{\epsilon }_{\mathrm{g}}}+\frac{{\sigma }_0{d}_{\mathrm{S}}^{\mathrm{M}+}}{2{\epsilon }_0{\epsilon }_{\mathrm{s}}}$$ 7

Here, d_S^M+ is the Stern layer thickness for a given cation M⁺. Even though σ₀ may strongly depend on the number of graphene layers, it can be excluded from the equations. The relation between V_b⁰ and V_t then reads:

$$V_{\mathrm{b}}^0=V_{\mathrm{t}}\frac{d_{\mathrm{S}}^{\mathrm{K}+}}{d_{\mathrm{S}}^{\mathrm{M}+}}\frac{1}{1+\frac{d}{d_{\mathrm{S}}^{\mathrm{M}+}}\bullet \frac{{\epsilon }_{\mathrm{s}}}{{\epsilon }_{\mathrm{g}}}}$$ 8

To the first approximation, considering the correction factor α ≈ 1, we have the following formula without losing generality:

$$V_{\mathrm{b}}^0=V_{\mathrm{t}}\frac{d_{\mathrm{H}}^{\mathrm{K}+}}{d_{\mathrm{H}}^{\mathrm{M}+}}\frac{1}{1+\frac{d}{d_{\mathrm{S}}^{\mathrm{H}+}}\bullet \frac{{\epsilon }_{\mathrm{s}}}{{\epsilon }_{\mathrm{g}}}}$$ 9

If the top and bottom reservoirs are filled up with the same solution (e.g., KCl), then we have a single d_S given by the hydrated diameter of K⁺ that describing both the interfaces.

Author contributions

S.H. initiated and directed the project with M.T. and K.S.N.; C.W., J.Z., and J.L. fabricated the devices; C.W., M.X. and J.Z. performed measurements and analyzed the data; M.T. carried numerical simulations and theoretical analysis; S.H., M.T., and K.S.N. wrote the manuscript. All authors contributed to discussions.

Peer review

Peer review information

Nature Communications thanks Wen-Bin Cai, Zheng Liu and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was supported by the National Key Research and Development Program of China (2024YFA1210804), the National Natural Science Foundation of China (22021001, 22472140), the Singapore Ministry of Education Research Centre of Excellence award to the Institute for Functional Intelligent Materials (I-FIM, Project No. EDUNC-33-18-279-V12), and the Discipline Development Funds from the Science and Technology on Surface Physics and Chemistry Laboratory (XKFZ202302).

Data availability

The relevant data generated in this study are provided in the Source Data file. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-78067-x.