Ion sensing based on frequency-dependent physico-chemical processes at electrode/electrolyte interfaces

Domain: physics
Published: 2025-12-03
Editorial outcome: minor_revision

Abstract
Ions play a fundamental role in solid-liquid interface processes, whether as essential or undesirable components, highlighting the need for precise and quantitative real-time monitoring. Electrochemical sensors are identified as promising tools, particularly for field-deployable applications. However, conventional electrochemical sensing is inherently restricted to redox-active species and is often single use, constraining its scope. This study presents electrochemical impedance spectroscopy as an alternative for ion detection, utilizing physico-chemical interactions at the electrode-electrolyte interface. We introduce a first-principles model that describes the interfacial impedance behavior and shows how ion specific processes shape the impedance response. Based on this framework, an extensive dataset is compiled, and a machine learning model is trained to predict electrolyte composition with consistent accuracy, demonstrating detection limits at the parts-per-billion level. The findings indicate that this method has considerable potential as a real-time method for ion sensing, providing a perspective on selectivity and sensitivity beyond traditional electrochemical approaches. This work could serve as a foundation for advanced models of impedance behavior, and development of impedance-based sensors with applicability in complex environments, including biological fluids and industrial liquids.

Introduction
Real-time monitoring of chemical changes in solutions is a crucial aspect for addressing pressing challenges in diverse fields1. Applications such as detecting contaminants in water, analyzing biomarkers in biological fluids, and ensuring the accuracy of processes as well as the safety of consumables require analytical techniques that are not only accurate and sensitive but rapid, cost-effective, and non-invasive2–4. Electrochemical sensors have emerged as promising candidates due to their affordability, simplicity, and suitability for miniaturization5,6. However, conventional amperometric-potentiometric electrochemical sensors primarily depend on redox reactions, making them unsuitable for substances that do not undergo redox processes. Additionally, these sensors involve electron transfer mechanisms that degrade the electrode surface over time, reducing their reusability and shortening their operational lifespan7. Moreover, these sensors carry the risk of altering the solution composition during measurements8,9. However, alternating current (AC) techniques, like electrochemical impedance spectroscopy (EIS), offer deeper insights into electrode-electrolyte interface dynamics. Under small-amplitude conditions that preserve linearity, EIS can probe the interfacial structure with minimal and reversible perturbation. This allows for the characterization and quantification of electrolyte composition while mitigating the possible irreversible compositional changes and limitations often associated with direct current (DC) methods10.

When a solid electrode contacts an electrolyte, an interface known as the electric double layer (EDL), a structured arrangement of ions, counter-ions, and solvent molecules forms11. The structure of the EDL depends on properties of both the electrode, such as roughness and work function, and the electrolyte, including composition and concentration12–15. While significant progress has been made in characterizing the EDL under non-faradaic conditions (i.e., in the absence of any redox reaction), its microscopic structure and its correlation with frequency domain electrochemical signals is not fully understood11,16.

In recent studies, EIS has been increasingly explored for ion detection17. Many of these investigations have employed simplified metrics such as solution conductivity18–20 or EDL capacitance17. To enhance selectivity, strategies involving ion-selective membranes20 or surface functionalization21–23, have been adopted. While these methods can enhance sensing, they also introduce additional complexity and reduce sensor durability. Some approaches also integrate complementary techniques or rely on external calibration to aid in interpreting EIS data18,19,24,25. Recent advancements have begun to explore the use of full-spectrum impedance data in membrane-free systems, signaling progress toward more comprehensive sensing strategies. However, there remains significant potential to further exploit the frequency-dependent characteristics of impedance for richer interpretation of the electrode-electrolyte interface.

EIS provides rich, multidimensional insights into interfacial processes26 enabling the assessment of the electrolyte composition on the EDL. While it does not directly identify chemical species, it contains information on how physicochemical properties, such as ionic mobility, permittivity, and interfacial structure, affect the system’s electrical response27. It is highly convoluted by the complex, coupled EDL responses of the multiple components in the electrified interface. Therefore, the accurate interpretation of EIS data hinges on a comprehensive understanding of the EDL under AC conditions28. Traditional methodologies, which often rely on empirical fitting models such as equivalent electrical circuits10,29, fall short of capturing the actual physical and chemical phenomena occurring at the interface30,31. This lack of knowledge hampers the full exploitation of EIS as a versatile tool for electrochemical analysis and raises concerns about the reliability of its data interpretations, as observed responses often appear without a solid theoretical basis.

To address this gap, a comprehensive theoretical framework for EIS must simultaneously capture the static properties of the electrode-electrolyte interface-such as EDL capacitance-and dynamic behavior, including non-ideal impedance phenomena such as constant phase element (CPE)32. Establishing clear connections between these static and dynamic aspects is essential to unravel the intricate relationships between the structural characteristics of the interface and the impedance responses. In this work, we aim to provide such a framework by developing a continuum-based model that integrates fundamental ion properties-such as ion size, mobility, and adsorption-into a unified description of the electrode-electrolyte interface, allowing explicit linkage of structural interfacial changes induced by electrolyte composition to observed impedance behavior.

Results
Physico-chemical processes at the EDL

Our model is built on the collective behavior of the electrode-electrolyte interface, where ions, counterions, and solvent molecules organize under the influence of electrostatic forces, ion-surface interactions, solvation effects, and thermal motion. Although the exact structure of the EDL remains elusive, computational modeling and experimental analysis14,16,33–35 provide critical insights. Despite its complexity, a well-designed continuum model can capture key EDL electrochemical properties35. To understand its impedance response, we first examine the fundamental interfacial processes that govern charge dynamics. Figure 1 presents the modified Gouy-Chapman-Stern (GCS) model, refined as the basis for this study.

At the electrode surface, the electrostatic potential induces ion accumulation at the interface, forming a depleted region near the electrode known as the Helmholtz (Stern) layer. As illustrated in Fig. 1a, the thickness of this layer is potential-dependent, governed by the competition between electrostatic attraction and hydration effects16. A higher (Volta) potential enhances electrostatic forces, drawing ions closer to the surface while necessitating partial or complete dehydration of their hydration shells. Anions, which exhibit a greater propensity for surface adsorption, undergo significant dehydration under strong electric fields, whereas cations experience only partial suppression of their hydration shells16. This results in a generally thinner Helmholtz layer for anions-determined by their intrinsic ionic radii-compared to cations, whose effective size is dictated by their hydrated radii (more information is provided in the Supplementary Information section S1.2). Additionally, water molecules within the Helmholtz layer align under the influence of the intense local electric field (1–10 V nm−1)33, leading to permittivity saturation in this region (more information is provided in SI section S1.1). The relative permittivity reaches its minimum within the Stern layer. As the distance from the electrode increases, the electric field weakens, leading to a gradual rise in permittivity toward the bulk electrolyte33,36.

Beyond the Helmholtz layer, the interface transitions into a compact layer where ion concentration reaches a maximum, Cmax, constrained by steric effects and determined by the hydration radii of the ions (more information is provided in SI section S1). In this region, the permittivity increases as the electric field weakens, following a trend similar to that of the Helmholtz layer. After the compact layer, a diffuse layer extends into the electrolyte, where ion concentration progressively decreases toward the bulk solution. In these interfacial regions, the electric field declines sharply, and the solvent permittivity recovers to its unsaturated bulk value. Moving away from the interfacial region, the bulk electrolyte is present, where ion concentrations stabilize at their bulk equilibrium value, c0.

Figure 1b illustrates the simulated differential capacitance and surface charge density as functions of the electrode potential. The model successfully reproduces the characteristic camel-shaped differential capacitance curve observed in dilute electrolytes37–39. At low (Volta) potentials, capacitance increases as the electric field enhances ion accumulation near the electrode. As the (Volta) potential rises further, the capacitance reaches a peak before declining, forming the characteristic hump of the camel curve. This behavior arises from the saturation of ion density near the electrode and the associated reduction in the local dielectric constant. Notably, the hump at positive (Volta) potentials is more pronounced than at negative (Volta) potentials, as anions can approach the electrode more closely than cations due to differences in hydration properties.

Building on the ability of the refined GCS model in capturing the steady-state structure of the EDL, we extended our analysis to simulate its impedance response. EIS is performed by introducing a small-amplitude AC perturbation around the steady-state condition, ensuring that the system remains within the linear regime and that the perturbation does not significantly alter the interfacial structure40. Under these conditions, the electrochemical impedance, ZEDL, can be formulated as a one-dimensional series of discrete layers normal to the electrode surface. Each layer contributes to the total impedance through ionic conduction (resistive behavior) and/or displacement conduction (capacitive behavior), represented as a local parallel resistor-capacitor (RC) element. This approach assumes lateral homogeneity and uniform current distribution across the electrode surface, which is justified for small, flat electrodes where spatial heterogeneity is minimal41.

The specific capacitance and ionic conductivity of each interfacial layer are determined by its relative permittivity and ion mobility, respectively. The permittivity values are obtained from the steady-state model, while conductivity depends on both ionic concentration and mobility within each region42,43. As shown in the steady-state modeling, ion concentration varies significantly across the interface. In regions of high ionic concentration, the intense local electric field and reduced intermolecular spacing limit the availability of free ions for conduction, as short-range interactions become dominant44. Furthermore, ion mobility decreases due to ion-ion collisions and other short-range interactions45, leading to a sharp increase in resistance and a decline in conductivity as the concentration rises (see SI section S2.1 for details). Figure 1c presents the simulated ionic conductivity and relative permittivity profiles under different (Volta) potentials. At high (Volta) potentials, permittivity saturation occurs due to the strong electric field, while ionic conductivity drops to zero in the Helmholtz and compact layers, reflecting the absence of mobile ions. At lower (Volta) potentials, neither ionic concentration nor permittivity reaches saturation, aligning with the expected physico-chemical behavior at the interface.

Impedance non-ideality: a revised insight into the origin of the CPE

The electrode/electrolyte interface often exhibits non-ideal capacitive behavior at low frequencies, commonly described by a constant phase element (CPE)32. Despite its ubiquitous presence in electrochemical systems, the fundamental origin of CPE behavior remains a subject of debate. Conventional explanations typically attribute capacitance dispersion to non-uniform current distribution caused by surface roughness, or to spatial variations in interfacial resistance and capacitance arising from surface heterogeneities-including differences in crystallographic orientation, defects, porosity, and even the cell configuration46–48. While these factors may contribute to time-constant dispersion, their influence predominantly manifests at higher frequencies, which does not fully account for the observed CPE behavior. Similarly, spatial variations in charge-transfer kinetics across the electrode surface provide only a minor contribution to impedance dispersion32.

To address this discrepancy, our model attributes CPE behavior to the non-uniform distribution of resistance and capacitance resulting from the formation of compact and diffusion layers that extend into the bulk electrolyte - contrasting with conventional surface-based interpretations. It has been demonstrated that under certain conditions, a distribution of time constants arises as a direct consequence of coupled spatial variations in conductivity and permittivity, leading to non-ideal CPE behavior49,50 in a certain range of frequencies. Note that we excluded ion-surface and ion-solvent interactions governing the distribution of relative permittivity to avoid unnecessary complexity. Although the distribution of resistance and capacitance across the interface may not be the sole cause of CPE behavior, it explains the presence of CPE, even in the case of atomically flat blocking electrodes within the double-layer potential window.

Figure 2a illustrates the characteristic frequency (fc = 1/(R1C1)) as a function of distance from the electrode at various (Volta) potentials. At the electrode surface, fc is initially zero, indicating purely capacitive behavior in the absence of free ions within the Helmholtz layer. Notably, within this region, the relative permittivity is at its lowest due to the highly ordered alignment of water molecules under the intense local electric field. As the system transitions into the compact layer, fc remains near zero, as ion conduction is still negligible due to the scarcity of free ions. In this layer, the relative permittivity gradually increases as the electric field weakens across the Helmholtz and compact layers. Upon reaching the diffusion layer, fc begins to rise due to the increasing presence of mobile ions, peaking in the megahertz range where ionic conduction is most pronounced. Therefore, a CPE behavior can be expected across the frequency range from zero to megahertz due to the coupled distribution of conductivity and permittivity in the compact and diffusion layers. Beyond this peak, fc decreases as ion concentration declines, reducing the number of charge carriers available for conduction. In the bulk electrolyte, fc stabilizes at a value dictated by the ionic conductivity of the electrolyte and the bulk permittivity of the solvent. At frequencies beyond this point, EIS ceases to provide information on interfacial ion dynamics, as the impedance response becomes predominantly governed by the intrinsic dielectric properties of the solvent-water in this case. At low potentials relative to the point of zero charge (PZC), the characteristic distribution of time constants in low frequency is absent. CPE behavior becomes evident only when the (Volta) potential surpasses a critical threshold, leading to the formation of a compact layer.

Figure 2b presents the impedance response calculated using our model across different (Volta) potentials. Near the PZC, CPE behavior is not observed, as neither permittivity nor conductivity exhibit saturation. However, as the potential increases and ion concentration reaches levels where conductivity becomes maximized, the onset of CPE behavior occurs. Figure 2c further illustrates the effect of electrode potential on the CPE parameter. Around the PZC, the system behaves as an ideal capacitor, but as the (Volta) potential increases, the deviation from ideal capacitive behavior grows, leading to a more pronounced CPE response. At sufficiently high potentials, the non-uniformity in conductivity extends further from the electrode due to the thickening of the compact layer, while permittivity saturation remains confined to this region (Fig. 1c). As a result, the spatial separation between the regions of conductivity and permittivity non-uniformity increases, gradually restoring a more ideal capacitive behavior.

The distinctive nature of the CPE lies in its correlation with the formation of the compact layer and the mobility saturation effect caused by the finite size of ions. Figure 2d presents the predicted CPE exponents as a function of the hydration shell radius of cations. The model predicts that larger hydration shell sizes lead to greater deviations from ideal capacitive behavior, as increased ion size enhances spatial heterogeneity in both conductivity and permittivity, reinforcing the CPE effect. This trend is consistent with experimental observations illustrated in the same figure. It can be seen that the non-ideality for lead ions is more pronounced than for cadmium, which, in turn, has a larger hydration shell radius than zinc.

Frequency-dependent behavior of the EDL: influence of the ion-specific fingerprint

As discussed earlier, the structure of the EDL is strongly influenced by the intrinsic properties of ions. While some properties primarily affect the steady-state behavior of the EDL, many others-such as ion mobility-related parameters-manifest predominantly in AC impedance characteristics.

The general behavior of electrochemical impedance exhibits non-ideal capacitive characteristics at low frequencies and resistive behavior at high frequencies27. At low frequencies, the capacitive response arises from the high time constants of the Helmholtz and compact layers, followed by a decreasing time constant in the diffusion layer. This results in a high CPE impedance at low frequencies51. In this regime, the impedance contribution of layers with lower time constants is overshadowed by the dominant effect of the Helmholtz and compact layers, making their influence negligible in the total impedance. On the other hand, at high frequencies, the oscillation period becomes much shorter than the interfacial time constants, causing the interface to behave as a short circuit. As a result, its impedance becomes negligible compared to the bulk electrolyte resistance, which dominates the total impedance, leading to the observed resistive behavior at high frequencies27.

Our model predicts that in the transition region between low and high frequencies, the diffusion layer time constant falls within a range where the distribution of time constants significantly influences the impedance transition. This intermediate frequency range marks the gradual shift from capacitive to resistive behavior, governed by the interplay between interfacial ion dynamics. The nature of this transition is highly dependent on ion properties such as ionic radius, hydration shell radii, and mobility, which dictate how ions respond to the applied AC perturbation.

Figure 3a, b model the impact of the mobility saturation (B) relative to its reference value on the impedance response for ions of the same hydration shell size. While this parameter is closely related to ion size, it is also affected by ion-solvent and ion-ion interactions. By varying this parameter, the steady-state properties remain unchanged, as the collision parameter influences only the dynamic impedance behavior. Therefore, at low frequencies, the impedance response is unaffected by, as this regime primarily reflects the properties of the Helmholtz and compact layers. However, the effect of it becomes evident during the transition from capacitive to resistive behavior, where it influences the time constants in the diffusion region. In the high-frequency regime, again mobility saturation has no impact on the resistive part of the impedance, as this region is dominated by bulk properties.

Experimental results for Pb(NO3)2, Cd(NO3)2 and Zn(NO3)2, provided in Figure 3c, d support these findings. Despite their close ionic radii, lead, zinc, and cadmium exhibit distinct impedance behaviors. This difference cannot be attributed to mobility (μ) alone, as the bulk layer impedance (high-frequency regime) is identical for the ions. Additionally, it is not due to ion adsorption or ion-electrode interactions, since the low-frequency impedance (Helmholtz and compact layers) is also similar.

The consistent trend observed for different ions at the transition frequency, both in modeling and experiments, indicates that factors beyond size and basic mobility play a crucial role in shaping the overall impedance response. Variations in ion-solvent interactions, along with differences in how ions engage with the solvent and other ions in solution, directly impact effective mobility. These interactions profoundly influence impedance behavior, particularly in the transition region. While ion-dependent behavior is not entirely unique to each individual ion, the evidence clearly demonstrates that the “ion-specific fingerprint" significantly dictates the interfacial response in the frequency domain. This underscores the capability of impedance response in distinguishing ion types and concentrations with high sensitivity.

Machine learning-assisted EIS for ion detection and quantification

Building on our model’s findings, we expect the dynamic interactions of ions to be reflected in their impedance behavior. To investigate this, we selected Zn2+, Cd2+, and Pb2+-ions with the same charge and similar sizes, yet crucial for environmental monitoring. A comprehensive dataset of over 500 EIS measurements was gathered, encompassing a wide range of compositions, counterions, concentrations, and their combinations (more detail can be found in the methods section and SI section S3 and S4).

While our physicochemical model provides mechanistic insight into how ion properties shape the impedance response, extracting compositional information from measured spectra remains complex. This complexity arises because relevant compositional signatures are embedded within the intricate spectral features, particularly in the presence of multiple ions, making direct interpretation difficult. Inspection of the raw impedance spectra reveals that mixed-ion solutions deviate non-linearly from a simple superposition of the corresponding single-ion responses, with the most informative differences concentrated in the transition-frequency regime. These observations motivate a data-driven approach capable of integrating subtle, distributed cues across the entire spectrum. We therefore developed a machine learning (ML)-based framework to resolve ion identity and concentration directly from full-spectrum EIS measurements.

To expose these discriminative features to the model, we implemented a targeted preprocessing pipeline (further details in Supplementary Information, Section S4.2) designed to amplify composition-dependent structure while suppressing nuisance variance. First, a logarithmic mapping of the real and imaginary impedance compresses the several orders of magnitude dynamic range. This step, commonly employed to visualize impedance spectra, renders ion-specific modulations more apparent across frequency. Next, the real and imaginary parts of the spectra were resampled onto a uniform frequency grid and concatenated into a single vector, ensuring strict comparability between measurements (Fig. 4a shows representative spectra for 10 mmol L−1 Zn(NO3)2, Pb(NO3)2, and their combination). A variance-stabilizing power transform was then applied to improve feature normality and reduce skewness, effectively sharpening feature separation - particularly in the transition-frequency region where differences between mixed-ion and single-ion spectra are most pronounced (Fig. 4b). Finally, principal component analysis (PCA) was used to concentrate ion-specific variance while attenuating noise; retaining six components preserved 98% of the variance while yielding a compact data representation. Together, these steps increase the signal-to-overlap ratio in the impedance data, enabling the neural network to identify and quantify ions from full-spectrum EIS with high fidelity.

Figure 4c presents the aggregated distribution of prediction errors, together with the confusion matrices for the test datasets aggregated over all folds and random seeds in repeated cross-validation underscoring the model’s robustness against partitioning bias and experimental variability. d Boxplots of prediction accuracy vs. concentration, comparing the aggregate of all folds/seeds (repeated cross-validation) with the top-five performing folds. e Boxplots of prediction accuracy by ion type, comparing the aggregate of all folds/seeds (repeated cross-validation) with the top-five performing folds. For boxplots in (d, e): the center line represents the median, box limits denote upper and lower quartiles and whiskers indicate 1.5× the interquartile range. f Sensor stability metrics: reusability error (Milli-Q references before/after each sample) remained below 10% and repeatability error (three back-to-back measurements) below 3%, with no detectable degradation after 250 days of operation.

Beyond capturing ion-specific impedance signatures, our approach offers a key advantage over conventional DC methods-enhanced stability over extended measurement periods. The absence of redox reactions in our AC-based sensor prevents electrode degradation, ensuring consistent results across independent measurements for each sample. This is reflected in the low reusability error (deviation of Milli-Q (MQ) water reference spectra measured before and after each sample), which remained below 10% across the measurement campaign (Fig. 4f). The repeatability error, calculated from three consecutive back-to-back measurements on the same solution, was below 3%, confirming high short-term consistency. Even after 250 days of operation with only routine rinsing in MQ water, no significant degradation or fouling was observed, underscoring the sensor’s durability. This long-term stability makes it suitable for continuous monitoring applications, where reliability and minimal maintenance are essential.

This study extends electrochemical impedance spectroscopy from a largely empirical method to a mechanistically grounded, predictive platform for real-time ion sensing. Through a first-principles continuum model that explicitly links ion-specific physico-chemical properties-such as ionic radius, hydration shell structure, ion mobility (including mobility saturation), and ion-solvent interactions-to frequency-dependent impedance, we identify the key interfacial processes shaping the observed spectra. In particular, variations in the constant phase element and transition frequency arise from differences in interfacial heterogeneity and the distribution of relaxation times, which are governed by ion-specific properties such as hydration shell structure, mobility, and adsorption behavior within the compact and diffuse layers. These coupled mechanisms-especially how ions interact with the solvent and reorganize the EDL-are responsible for the distinct spectral fingerprints observed across ion types and concentrations. Our results show that non-ideal features in EIS, including but not limited to CPE behavior, are intrinsic signatures of interfacial structure and dynamics, not measurement artifacts. Recognizing and modeling these features enables selective, stable, and reproducible ion detection across a wide concentration range. Coupled with AI-assisted interpretation, this approach achieves detection limits down to the ppb range and remains robust over months of operation, making it promising for applications in environmental monitoring, biomedical diagnostics, and industrial process control.

Methods
Model development

The EIS model was developed using a steady-state/perturbation approach. A modified GCS model was derived for electrified electrode-electrolyte interfaces using continuum models based on local free energy functionals. These models account for non-uniform dielectric constants ϵr(ϕ), ion size effects, and variable ion-surface interactions ψ(x).

The GCS model is driven by minimizing the local free energy, expressed as:

F[ρions(x), ϕ(x), ψ(x), ci(x)] = ∫ [ (ϵr/8π) |∇ϕ(x)|2 + ρions(x)ϕ(x) + ∑i=1p ci(x)ψi(x) + ∑i=1p (μi ci(x)) c0i(x) + Ts[ci(x)] - Ts[c0i(x)] ] dx

Here, x represents the distance from the electrode surface. The first two terms describe the electrostatic interactions created by the electric potential ϕ(x) and the ionic charge density ρion(x) = ∑i=1p ci(x)zi, where zi and ci denote the ion charge and concentration, respectively. The third term captures the interaction of the external potential ψi(x) with the ions, which can simulate repulsive forces (e.g., Helmholtz layer) or attractive forces (e.g., ion-surface interactions).

The fourth term introduces a grand canonical description of the ions by incorporating their chemical potential μi. The final term represents the entropic contribution to the free energy, where s is the entropy density.

By inserting the entropy density from a lattice gas model (more details in SI S1), ion size effects are introduced, with the maximum ion density defined by cmax, determined by the ion’s hydration shell size.

Minimizing the free energy F with respect to ϕ(x) yields the modified Poisson-Boltzmann equation:

∇(ϵr ∇ϕ(x)) + 4π ∑i=1p zi ci(ϕ(x)) = 0

This second-order differential equation is solved numerically for varying electrode potentials. Numerical solutions provide the electric potential, electric field, dielectric constant, and ion distribution as functions of the distance from the electrode. The model’s results depend on the parameters defined in the free energy expression, with detailed parameter information provided in the supplementary table S3.

The differential capacitance can be calculated based on electrode potential and charge density on the surface using the Gauss law as follow:

Q = ϵE(x) dA

To simulate the EIS response of the interface, the DC permittivity profile was extracted from the mean-field model, which relates to the electric field strength and solvent molecule alignment at varying distances from the electrode. Using the relative permittivity and ion concentration from the GCS model, impedance was calculated based on displacement and ionic conductivity.

In dilute solutions, the electrolyte solution conductivity is the sum of individual ion conductivities, expressed as:

σ = ∑ μi m exp(-m/B)

Here, σ denotes conductivity, m for ion concentration, and μi is the ion mobility. In highly concentrated regions, high electric fields and close ion proximity reduce the number of free ions contributing to conduction. Beside, ion mobility, the average ion speed per unit electric field, results from the balance between external electric field forces and ion movement resistance, including ion-ion, ion-solvent, and solvent-solvent interactions. As electrolyte concentration increases, molecular distances shrink, intensifying short-range interactions and increasing resistance, thus reducing ion mobility. This behavior is captured by the permittivity profile and conductivity. From Eqs. (4), an RC model was employed to extract the EIS response. The interface impedance is expressed as:

Z = ∫01 dx / (σ(x) + jωϵ(x))

Completed details on model parameters and functional forms are provided in the supplementary information.

EIS measurement

Experimental EIS measurements were conducted using a custom-designed sensor. The system consisted of a pair of platinum interdigitated electrodes for impedance measurement and a rectangular platinum electrode serving as a pseudo-reference. The pseudo-reference electrode was included solely to monitor the working electrode’s potential, enabling accurate tracking of electrode fouling, contamination, and overall system stability over time. The impedance was strictly measured between the working and counter electrodes. All electrodes were fabricated on a silicon chip with a silicon nitride isolation layer. Platinum was deposited via physical vapor deposition (PVD), resulting in a flat surface with a roughness of approximately 5 nm. The interdigitated design increased the effective surface area, and the 10 μm spacing between electrode fingers was optimized to minimize bulk impedance contributions. The fabricated chips were cleaned with isopropanol and ultrapure Milli-Q water, dried, and stored in gel boxes at controlled room temperature (21±1°C). During measurements, if the reusability error exceeded 10%, the chips were re-cleaned by sequential rinsing with Milli-Q water followed by isopropanol.

Electrolytes were prepared by dissolving lead, cadmium, and zinc salts (Pb(NO3)2, Cd(NO3)2, Zn(NO3)2, PbCl2, CdCl2, ZnCl2, CdSO4, and ZnSO4 ≥99%, Sigma-Aldrich) in MQ water, yielding concentrations of 100 nmol L−1, 10 μmol L−1, and 10 mmol L−1. EIS measurements were conducted under open-circuit potential (OCP) conditions using a potentiostatic sinusoidal excitation (10 mV amplitude, 20 points per decade; 171 data points in total), with a VSP300 potentiostat (Bio-Logic) housed within a Faraday cage equipped with a temperature control unit to minimize environmental noise. All experiments were performed at a controlled temperature of (21±1°C). Prior to each measurement, a 15-minute stabilization period at OCP was employed to ensure steady-state conditions. MQ water EIS responses were recorded before and after each measurement to verify electrode integrity and confirm the absence of contamination or surface modification. Detailed measurement procedures are provided in the Supplementary Information. All EIS measurements reported in this work were performed using a single fabricated chip. This choice was motivated by the demonstrated long-term stability and reusability of the device, which allowed us to carry out all experiments on the same platform.

Electrochemical measurements for CPE behavior as a function of electrode potential were performed using an SP-200 potentiostat (Bio-Logic). A vertical electrochemical cell with a 3.5 cm2 opening area (Redox.me) was employed. The working electrode was confined to a 1 mm2 exposed area, ensuring precise control over the active electrochemical surface. The working electrode consisted of a polycrystalline gold electrode with a (111) orientation (1.1×1.1 cm2, Arrandee). Prior to use, the Au electrodes were annealed with a butane flame for 2 min and cooled in a nitrogen atmosphere. They were subsequently immersed in HCl solution (10 mM) at open-circuit conditions for approximately 10 min to remove surface reconstruction and contamination. Finally, the electrodes were extensively rinsed with ultrapure water (18.2 MΩ⋅cm, Milli-Q) to eliminate residual Cl− ions. A platinum wire served as the counter electrode (redox.me), and a saturated Ag/AgCl leakless electrode (ET072, Edaq) was used as the reference electrode.

The working and counter/reference electrodes were housed in separate compartments of the electrochemical cell. The electrolytes for CPE measurements were prepared by dissolving sodium fluoride (NaF, ≥99%, Sigma-Aldrich) in ultrapure water (≥18.2 MΩ, Milli-Q). Since the adsorption of hydrated ions such as Na+ and F− on the electrode surface is limited, NaF has been chosen for the analysis. Prior to use, the electrochemical cell was cleaned by sonication in isopropanol (IPA) for 15 minutes, followed by thorough rinsing with ultrapure water. EIS measurements were conducted using single potential electrochemical impedance spectroscopy (SPEIS) within a potential range from −0.1 V to 0.8 V versus Ag/AgCl, on a single Au electrode in one experimental series. The measurements were performed over a frequency range of 0.5 Hz to 1 MHz using a potentiostatic sinusoidal excitation (10 mV amplitude, 20 points per decade) under the quasi-stationary potential determined by the SPEIS potential step. CPE values were obtained by fitting the impedance response incrementally, starting from the lowest frequency with the CPE impedance expression 1/[Q(jω)n] and extending the fit frequency by frequency until the relative error is below 3%.

AI-assisted ion detection

A supervised machine learning framework was developed to infer ion identity and concentration directly from full-spectrum electrochemical impedance measurements. Raw spectra were preprocessed to enhance composition-dependent features and suppress nuisance variance: the real and imaginary components were logarithmically transformed to compress the several orders of magnitude dynamic range, resampled onto a uniform frequency grid to ensure comparability across experiments, concatenated into a single feature vector, and variance-stabilized using a power transform. Dimensionality was then reduced via principal component analysis, with components retained to preserve 98% of the variance while concentrating ion-specific information. The resulting low-dimensional feature set was provided as input to an ensemble of fully connected neural networks, with dropout regularization incorporated to mitigate overfitting. Training was performed using a composite loss function that combined mean-squared error with a soft constraint enforcing overall charge neutrality.

Model performance was assessed using 5-fold cross-validation repeated across multiple random seeds to account for partitioning bias, which is particularly important for limited datasets. This procedure ensured that the reported performance reflected both the intrinsic capability of the model and its robustness to variations in training/test composition. Accuracy was quantified using the coefficient of determination (R2) and relative error distributions across ion species and concentration regimes.

Further methodological details, including network architecture, hyperparameters, and preprocessing rationale, are provided in the Supplementary Information (Section S4).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is an interesting, innovative and very well-written contribution to better understand the meaning of impedance spectra and how to extract meaningful information. The paper attributes “CPE” behaviour not only to non-uniformity of the electrode “surface” but also of the interfacial region contacting with the surface which is then explored in relation to ion sensing. Illustrations of this are given with three different nitrate salt solutions. AI-assisted modelling seems to be an excellent approach but whether it represents a significant advance in practice is not yet clear; hence this is a communication. More results and examples are needed to show if the approach is as valuable as it potentially appears to be. The work supports the claims and the methodology is spound. Sufficient details is provided to enable reproduction of the work.\nI recommend publication after attention to the minor points below.\n1. Introduction Paragraph 1. It is stated implicitly that EIS, as an AC technique, does not alter the composition of the ED whereas DC techniques do. This is, of course, not strictly correct as the applied potential is changes and is why, to minimise such effects, small ac perturbations are used to elicit a linear response and to minimise changes.\n2. Introduction Paragraph 3. EIS is an electrical technique and cannot be used by itself to fully understand changes to chemical species, as the text appears to imply, unless it is known what they are. It will never be able to do this, whatever the theoretical framework. It relies on fitting data to models that (may) reflect movements etc. of chemical species.\n3. Fig 1a shows RC elements in series between the anode and cathode, each of which represents the “layer” referred to in the manuscript. This assumes that they are independent of where the current paths start on the anode (or cathode) surface. Fig.1 caption says “modeled as a series of parallel RC circuits” which is an ambiguous expression. Please state more clearly that it is parallel RC circuits that are in series. This is clearly crucial to the model.\n4. The authors seem to use the words “empirical” and “experimental” interchangeably. They do not mean exactly the same. For example, on p.9 it should say “Experimental” rather than “Empirical”.", "reviewer_2": "The work presents a valuable and rare case of ML EIS. Big EIS data collected can promote further following work like physics-based EIS modeling, which is not performed in this work.\nThe analysis on CPE behavior was done using the other sets of EIS. Why? The experimental data are not provided.\nWhat are the 50 features is not clear. In Supplementary, ....\nfrequency range \"1 MHz to 100 MHz\" and consists of 50 equally spaced features. It appears to the experimental frequency range. State it clearly if they are (part of) the logarithmic frequency values. In the code start_freq= -2, end_freq=15...\nRelatedly, EIS and transformed EIS are already in the frequency domain. What kind of Fourier transform is performed?\nImpedance presentation is not very informative. Capacitance spectra are more gaussian-like as desired. The character of Power transformation used in this work is not clearly understood. What kind of the data deformation and the effect needs to be clarified. Many data exhibits the AC noise around 50Hz, which becomes pronounced in the Power or Fourier transform in Fig. 12. The data removal would improve the results.\nProvide more details of PCA. The contributions of each PC and what are the most contributing frequency features. They may be discussed together with the experimental data in Fig. 3 (or in different representations).\nAccording to the EDL model, what is the effect of the mixed composition? How do they contribute to the layers? This should be related to the impedance characteristics, which is revealed by ML as in the above discussion.\nI checked the codes, but did not run at the present since PyEIS and torch need to be installed. They look OK. I hope they will be updated in revision.", "reviewer_3": "- The novelty of the work is to monitor ions using EIS without an ion-selective membrane with the help of AI by looking at the interface CPE. For integrity, I recommend citing publications employing EIS instead of potentiometry for ion detection, and highlighting the new approach of this submission, e.g.:\no A novel thin film impedance Ca ion sensor for drinking water https://doi.org/10.1016/j.snb.2017.01.087\no Improved Selectivity of Impedimetric K+ Sensors, DOI: 10.1109/SENSORS60989.2024.10784744\no Textile-Integrated Organic Electrochemical Transistor for Selective Ion Detection via Electrical Impedance Spectroscopy\nDOI: 10.1109/LSENS.2024.3414851\no Impedance-based sensor for potassium ions, https://doi.org/10.1016/j.aca.2018.06.044\n- Some of these publications already employ the CPE for ion detection, and one works without an ion-selective membrane, but to my knowledge, there is no publication on impedimetric sensors without ionophores using AI for improved results. Therefore, this work has the potential to significantly reduce sensor complexity and costs while increasing stability.\n- Why is a three-electrode setup required? Two electrodes would further reduce sensor complexity and improve stability.\n- How about surface contamination of the electrode influencing the CPE quality? How were the electrodes stored? Would a cleaning cycle be necessary prior to every measurement in an application?\n- How can one (non-specific) sensor extract information on the concentrations of various ions in mixed solutions? Why do you not rely on multiple sensors with (low) specificity? It would help to see an EIS curve in a mixed solution to see how you are able to distinguish between different ions in one measurement.\n- The concentration steps are rather high: can you estimate the sensitivity of your approach? Are you able, e.g., to detect 100nM Zn2+ in 10mM Pb2+?\n- What is the influence of temperature changes on the data quality? The electrical double layer is temperature-dependent (e.g. Eq.(1)).\n- Is there an influence of the solvent?\n- More citations needed in some paragraphs (e.g., last 2 paragraphs in section physico-chemical processes at the EDL, 3rd paragraph in Frequency-Dependent Behavior)\n- In the conclusion: Present in more detail/write more clearly, which characteristic physico-chemical effect is responsible for the differentiations in CPE\n- Fig. 2(c) and (d): Meaning of CPE Value (a.u.)? Does this refer to the exponent of the CPE? Clarify in text.\n- Fig. 2(c) and (d): explain deviations between Model and Experiment\n- Fig. 3(a) and (b): explain the legend “dB/B” in the text. Are these graphs valid for anions?\n- Clarify Fig. 4(d): How are reproducibility and repeatability calculated? Reproducibility should compare the results of different sensors. Why is the reproducibility error lower than the repeatability error? Why is reproducibility shown over days? Why is the stability error >5% if you claim in the motivation that your sensors reveal improved stability due to no leakage? Explain what the single dots mean.\n- The prediction errors of the analyte concentration are rather high, with average errors of 5-10%. However, a new approach to ion sensing is demonstrated. To underscore its advantage of stability and reusability, this data should be more understandable.\n- There are differences in the methodology in the publication and supplementary information that should be corrected (e.g., EIS Measurements stabilization period, frequency range).\n- How many sensors were manufactured/tested? How many measurements per sensor?\n- Otherwise, there are enough details provided in the EIS methods for the work to be reproduced. However, I am not an expert in the AI field to evaluate the reproducibility of the AI methods."}, "author_response": "Response to Reviewers\nPeer Reviewer 1:\nRemarks to the Author: Thisisaninteresting, innovativeandverywell-writtencontri-\nbution to better understand the meaning of impedance spectra and how to extract mean-\ningful information. The paper attributes “CPE” behaviour not only to non-uniformity\nof the electrode “surface” but also of the interfacial region contacting with the surface\nwhich is then explored in relation to ion sensing. Illustrations of this are given with three\ndifferent nitrate salt solutions. AI-assisted modelling seems to be an excellent approach\nbut whether it represents a significant advance in practice is not yet clear; hence this is a\ncommunication. More results and examples are needed to show if the approach is as valu-\nable as it potentially appears to be. The work supports the claims and the methodology\nis spound. Sufficient details is provided to enable reproduction of the work.\nI recommend publication after attention to the minor points below.\nResponse: We thank the reviewer for the positive and insightful evaluation of our work.\nWe are particularly encouraged by the recognition of the conceptual advance our study\noffersinattributingCPEbehaviornotjusttoelectrodesurfaceinhomogeneities,buttothe\nion-specific structure and dynamics of the entire interfacial region. This reinterpretation\nchallenges long-standing assumptions in impedance analysis and opens a new path toward\nextracting chemically meaningful information from electrochemical spectra. We fully\nstand behind the practical significance of the AI-assisted modeling presented. While this\nis the first demonstration of its kind, we have shown that the model, trained on physically\ngroundedfeatures, canquantitativelypredictioncompositionandconcentrationwithhigh\naccuracy across multiple systems. This represents a major shift from conventional EIS\ninterpretation, where such predictive capabilities have not been possible. We consider\nthis not only a proof of concept, but a foundation for a new class of real-time, data-driven\nsensing approaches. We are grateful for the reviewer’s recommendation for publication\nand have addressed the points raised below with careful attention.\nComment 1: Introduction Paragraph 1. It is stated implicitly that EIS, as an AC\ntechnique, does not alter the composition of the ED whereas DC techniques do. This is,\nof course, not strictly correct as the applied potential is changes and is why, to minimise\nsuch effects, small ac perturbations are used to elicit a linear response and to minimise\nchanges.\nResponse: We thank the reviewer for the clarification. We fully agree that EIS, although\nsignificantly less perturbative than DC techniques, can still influence the interfacial struc-\nture. Our original intention was not to suggest that EIS is entirely non-invasive, as\nthe reviewer rightly notes. Rather, our aim was to emphasize that, when applied with\nsmall-amplitude AC perturbations, EIS enables the characterization of interfacial pro-\ncesses with minimal and reversible disruption, assuming the system remains within the\nlinear regime. We have carefully revised the relevant sentence in the Introduction (Page\n3, Paragraph 1) to ensure that the description is now scientifically accurate. The revised\ntext explicitly acknowledges that EIS introduces perturbations, although in a controlled\nand non-destructive manner, thereby eliminating any unintended implication that the\nmethod is inherently non-invasive.\nComment 2: Introduction Paragraph 3. EIS is an electrical technique and cannot be\nused by itself to fully understand changes to chemical species, as the text appears to\nimply, unless it is known what they are. It will never be able to do this, whatever the\ntheoretical framework. It relies on fitting data to models that (may) reflect movements\netc. of chemical species.\nResponse: We appreciate this critical observation. We fully agree that EIS, as an\nelectrical measurement technique, does not directly identify specific chemical species.\nRather, its strength lies in probing the dynamic response of the interfacial system, from\nwhichinformationaboutunderlyingphysicochemicalprocessescanbeinferred. Ourintent\nwas not to suggest that EIS alone can unambiguously determine chemical identity, but\nto show that, when combined with a mechanistic model based on known ion-specific\nparameters (e.g., size, mobility), it can be used to differentiate and quantify species whose\ncharacteristics are already defined.\nTo eliminate this possible overstatement, we have revised the relevant section in the\nIntroduction (Page 3, Paragraph 4).\nComment 3: Fig 1a shows RC elements in series between the anode and cathode, each\nof which represents the “layer” referred to in the manuscript. This assumes that they\nare independent of where the current paths start on the anode (or cathode) surface.\nFig.1 caption says “modeled as a series of parallel RC circuits” which is an ambiguous\nexpression. Please state more clearly that it is parallel RC circuits that are in series. This\nis clearly crucial to the model.\nResponse: We thank the reviewer for this insightful observation. Indeed, our model\nassumes lateral homogeneity of the electrode–electrolyte interface and uniform current\ndistribution across the electrode surface. Each RC element in Fig. 1a represents a dis-\ncrete layer normal to the surface, and the series connection reflects the one-dimensional\nrepresentation of ion transport and dielectric response across the interfacial region. This\nis a commonly adopted approximation in EDL modeling[1, 2, 3], where lateral variations\nareneglectedandcurrentpathsaretreatedasuniformandindependentoflateralposition.\nThis assumption holds for small, flat electrodes where spatial heterogeneity is minimal.\nIn this work, we adopt a 1D framework to isolate and analyze the influence of ion-specific\nproperties on impedance behavior. We have revised the figure caption and main text\n(page 6, paragraph 3) to explicitly state the modeling assumption.\nComment 4: The authors seem to use the words “empirical” and “experimental” in-\nterchangeably. They do not mean exactly the same. For example, on p.9 it should say\n“Experimental” rather than “Empirical”.\nResponse: Wethankthereviewerforthiscorrection. Intheinstancenoted(page10),the\nintended meaning was indeed “experimental.” We have carefully revised the manuscript\nto replace “empirical” with “experimental” wherever appropriate and ensured consistent\nand correct terminology throughout the text.\nPeer Reviewer 2:\nRemarks to the Author: The work presents a valuable and rare case of ML EIS. Big\nEIS data collected can promote further following work like physics-based EIS modeling,\nwhich is not performed in this work.\nResponse: We sincerely thank the reviewer for recognizing the value of our work,\nparticularly its contribution to the emerging area of machine learning (ML) applied to electro-\nchemical impedance spectroscopy (EIS). We agree that large-scale EIS data generation,\nas demonstrated here, offers a foundation for future studies in physics-based EIS model-\ning. While our focus in this communication is on data-driven predictive modeling, we are\nactively exploring hybrid frameworks that incorporate physical constraints into the ML\npipeline in ongoing and future work. Below, we address the reviewer’s specific comments\nand have revised the manuscript and supplementary materials accordingly to enhance\nclarity and transparency.\nComment 1: The analysis on CPE behavior was done using the other sets of EIS. Why?\nThe experimental data are not provided.\nResponse: We thank the reviewer for the opportunity to clarify this point. Only for\nFigure 2(c) we did use a separate dataset obtained from EIS measurements in a NaF\nsolution. The reason is that in this part of the study we aimed to demonstrate the effect\nof CPE behavior as a function of working potential. For this purpose, it was essential\nto use an electrolyte that provided a wide double-layer potential range and an ion with\nminimal specific attraction or repulsion to the electrode surface, in order to minimize\nother phenomena that could influence the CPE response. NaF meets these requirements,\nas mainly use in other fundamental studies[2, 4, 5, 6], and allowed us to isolate the\nworking-potential dependence of the CPE. Also, these measurements were performed\nusing a single-crystal gold electrode, as described in the Methods section (page 16), to\nensure a well-defined and reproducible interfacial structure.\nThe complete raw experimental data for this and all other datasets used in the manuscript\nare provided in the public repository\nComment 2: What are the 50 features is not clear. In Supplementary, .... frequency\nrange ”1 MHz to 100 MHz” and consists of 50 equally spaced features. It appears to\nthe experimental frequency range. State it clearly if they are (part of) the logarithmic\nfrequency values. In the code start freq= -2, end freq=15...\nResponse: We thank the reviewer for pointing out the ambiguity. We have clarified\nthe definition and construction of the 50 features in the revised Supplementary Informa-\ntion (section 4.2, page 16). Specifically, the 50 features correspond to impedance values\nuniformly sampled over the full experimental frequency range in logarithmic space, from\nlog f = −1.67 (0.02 Hz) to log f = 6.85 (7 MHz). These 50 points are evenly spaced\n10 10\nin log f with a step size of 0.174. For each selected frequency, both the log-transformed\n10\nreal and imaginary parts of the complex impedance are included, yielding a total of 100\ninput features. We also corrected inconsistencies in variable naming in the code and\ndocumentation, where placeholder values such as start freq = -2 and end freq = 15\ndid not reflect the actual experimental frequency range. These have now been updated\nto match the correct range of −1.67 to 6.85 in log scale. For improved clarity and\n10\nreproducibility, we have corrected and revised our code and algorithm in the updated\nmanuscript as follows:\n• We cleaned the dataset to ensure that all experiments share the same starting and\nending frequencies, eliminating the need to handle inconsistent frequency ranges\nduring preprocessing.\n• We replaced the natural logarithm with base-10 logarithm in the updated version.\nAs a result, the log-transformed frequency range is now correctly specified as −1.67\nto 6.85, rather than the previous placeholder values of −2 to 15.\n• We revised the Supplementary Information to explicitly state that the 50 frequency\npoints are uniformly spaced in log f, covering the range from 0.02 Hz to 7 MHz.\n10\n(SI section 4.2, page 16)\n• We updated both the main manuscript (Methods section) and Supplementary Sec-\ntion 4 to clearly describe the construction of the 100-dimensional feature vector\nderived from the 50 complex impedance points.(Manuscript page 16)\nThese revisions ensure consistency and clarify how the feature vectors used in training\nare derived from the experimental data.\nComment 3: Relatedly, EIS and transformed EIS are already in the frequency domain.\nWhat kind of Fourier transform is performed?\nResponse: We thank the reviewer for this insightful comment. The reviewer is cor-\nrect that standard EIS data are already acquired in the frequency domain, and thus a\nconventional Fourier transform is not required to convert time-domain data to frequency-\ndomainrepresentations. Inmachinelearning, werefertothisoperationasa”feature-space\ntransformation” or ”neural embedding” instead of using the potentially misleading term\n“Fourier-transformed EIS.” In our updated ML framework, we removed this operation and\nachieved comparable results to those obtained previously. This adjustment is expected to\neliminate any potential confusion.\nComment 4: Impedance presentation is not very informative. Capacitance spectra are\nmore gaussian-like as desired.\nResponse: We thank the reviewer for this suggestion. While impedance magnitude and\nphase plots are widely used for EIS data interpretation, we agree that they may not\nalways clearly reveal the differences between spectra of various solutions. To address this,\nwe have added two new panels (a and b) to Figure 4 with corresponding explanations.\nThe EIS spectra are shown both in their conventional representation and after power\ntransformation, which enhances subtle spectral variations, emphasizing the differences\nbetween solutions more visible and interpretable.\nComment 5: The character of Power transformation used in this work is not clearly\nunderstood. What kind of the data deformation and the effect needs to be clarified.\nMany data exhibits the AC noise around 50Hz, which becomes pronounced in the Power\nor Fourier transform in Fig. 12. The data removal would improve the results.\nResponse: We thank the reviewer for raising this important point. In our work, the\n“Power transformation” refers specifically to the Box-Cox transformation, a statistical\ntechnique used to improve the normality and reduce the skewness of each input feature\nin the real-valued impedance vector:\n xλ −1\n , if λ ̸= 0,\nF[x] =\nλ\n(1)\n log(x), if λ = 0,\nwherexis a strictlypositive input feature andλis determinedvia maximum likelihood es-\ntimation for each feature. This transformation is applied independently to each of the 100\ninput features (real and imaginary parts of impedance at 50 frequencies). The purpose of\nthe Box-Cox transformation is to stabilize variance and make the features more Gaussian-\nlike, which benefits the performance and convergence of the machine learning model.\nThe transformation is implemented using the PowerTransformer(method=\"box-cox\")\nin scikit-learn.\nRegarding the 50 Hz AC noise, we thank the reviewer for bringing this to our attention.\nThis noise is present only in a few spectra within the dataset, originating from rare cases\nwhere the Faraday cage did not fully suppress environmental interference. While it could\nbe removed by applying smoothing filters, we chose not to do so in order to preserve the\noriginal spectral features and avoid introducing artifacts that could bias the analysis. In\nthe revised analysis, the frequency down-sampling inherently removes this noise, as the\nclosest sampled frequencies are 40 Hz and 60 Hz.\nComment 6: Provide more details of PCA. The contributions of each PC and what\nare the most contributing frequency features. They may be discussed together with the\nexperimental data in Fig. 3 (or in different representations).\nResponse: We appreciate the reviewer’s suggestion to clarify and elaborate on the Prin-\ncipal Component Analysis (PCA) used in our study. In the revised SI, we have added a\ndetailed explanation of the PCA results, including the individual and cumulative variance\nexplained by the top principal components. We also discuss the frequency-domain contri-\nbutions of each component. (SI section 4.2.5, Principal Component Analysis) To support\nthis analysis, we include a supplementary figure (Fig. 13 in the SI), which visualizes the\nexplained variance (scree plot) as well as the loading vectors of the principal components\nacross the frequency spectrum. This provides insight into which frequency ranges con-\ntribute most strongly to each PC and how the PCA captures underlying patterns in the\nexperimental data. It can be found that PC1 remains relatively flat with weak correlation\nacross all frequencies, indicating it captures broad trends rather than frequency-specific\nbehavior. PC3 shows higher correlation in low frequencies while dips negative in high\nfrequencies. PC4 shows strong peak in high-frequency region. This suggests different\nPCs represent patterns localized in distinct frequency domains. We believe this addition\nstrengthens the interpretation of our feature space.\nThis additional discussion is now supported by a new discussion and new panels (a and\nb) in figure 4 (manuscript page 11 and 12) on data pre-processing, which explains how\nimpedance features—particularly those highlighted by the PCA loadings—can be ex-\ntracted, enhanced, and used to determine ion composition. This section also illustrates\nhow these processed features are fed into the ML model, linking the most contributing\nfrequency regions directly to predictive performance.\nComment 7: According to the EDL model, what is the effect of the mixed composi-\ntion? How do they contribute to the layers? This should be related to the impedance\ncharacteristics, which is revealed by ML as in the above discussion.\nResponse: We thank the reviewer for raising this important point. To the best of our\nknowledge, a clear theoretical or experimental understanding of the EDL structure in\nmulti-ion systems is still lacking, primarily due to the complex ion–ion and ion–surface\ninteractions involved. What is evident from both our experimental results and our EDL-\nbased theoretical framework is that the impedance spectrum of a mixed-ion solution is\nnot a simple superposition of the spectra of the individual ions.\nIn mixed systems, ions interact through competition for adsorption sites, modification\nof each other’s hydration shells, and changes to local mobility and permittivity within\nthe compact and diffuse layers. These coupled effects alter the spatial and frequency-\ndependent conductivity and permittivity profiles of the EDL, leading to non-linear spec-\ntral changes, particularly in the transition-frequency region.\nItisclearthatsuchcomposition-dependentfeaturesarepresentintheEISdata, asdemon-\nstrated by both our theoretical model and experimental results. This is precisely why AI\ncan extract these features and use them for accurate prediction. For better clarity, we\nhave added a new discussion (manuscript page 11) on data preprocessing, showing an\nexample of a multi-ion EIS spectrum, how we enhance the feature differences, and how\nthese processed features are fed into the ML model for improved predictive performance.\nRemarks on code availability:\nI checked the codes, but did not run at the present since PyEIS and torch need to be\ninstalled. They look OK. I hope they will be updated in revision.\nResponse: We thank the reviewer for taking the time to inspect our code. In the\nrevised version, we have updated the repository to ensure better clarity and ease of use.\nSpecifically:\n• WeaddeddetailedinstallationinstructionsintheREADME.md,includingenvironment\nsetup for PyEIS, torch, and other dependencies.\n• We cleaned and reorganized the code for reproducibility, including data loading,\npreprocessing, and model inference.\nWe will continue to maintain the repository and keep it up-to-date to support repro-\nducibility and further development by the community.\nPeer Reviewer 3:\nRemarks to the Author: The novelty of the work is to monitor ions using EIS without\nan ion-selective membrane with the help of AI by looking at the interface CPE. For\nintegrity, I recommend citing publications employing EIS instead of potentiometry for ion\ndetection, and highlighting the new approach of this submission, e.g.:\nA novel thin film impedance Ca ion sensor for drinking water\nhttps://doi.org/10.1016/j.snb.2017.01.087\nImproved Selectivity of Impedimetric K+ Sensors\nDOI: 10.1109/SENSORS60989.2024.10784744\nTextile-IntegratedOrganicElectrochemicalTransistorforSelectiveIonDetectionviaElec-\ntrical Impedance Spectroscopy\nDOI: 10.1109/LSENS.2024.3414851\nImpedance-based sensor for potassium ions\nhttps://doi.org/10.1016/j.aca.2018.06.044\nSome of these publications already employ the CPE for ion detection, and one works\nwithout an ion-selective membrane, but to my knowledge, there is no publication on\nimpedimetric sensors without ionophores using AI for improved results. Therefore, this\nwork has the potential to significantly reduce sensor complexity and costs while increasing\nstability.\nResponse: We appreciate the reviewer’s recognition of our work’s potential to sim-\nplify sensor design and reduce costs while enhancing stability. This study represents\nthe first demonstration combining a first-principles model with AI-assisted analysis of\nfull-frequency EIS data for the detection and quantification of multiple ions without\nionophores or membranes. Our integrated approach addresses significant limitations in\npreviousresearchandholdspromiseforadvancingimpedance-basedsensorswithlowcom-\nplexity and high stability.\nIn response to the reviewer’s suggestion, we have added a new paragraph to the Intro-\nduction (page 3, paragraph 3) that reviews previous studies utilizing EIS for ion sensing,\nincorporating the recommended references. These studies encompass various approaches,\nsuch as ion-selective membranes, functionalized surfaces, and simplified metrics like con-\nductivity or capacitance. While some methods have achieved selectivity or membrane-free\noperation, they often rely on surface modifications or supplementary techniques and cal-\nibration, which may compromise stability and scalability.\nIt is important to clarify that our sensing method does not solely rely on CPE. The\ninclusion of the CPE section serves to validate our continuum-based theoretical model\nrather than acting as the sole detection metric. Our approach utilizes the full-spectrum\nimpedance response to capture ion-specific interfacial behavior, enabling robust and scal-\nable multi-ion detection without the use of membranes.\nComment 1: Why is a three-electrode setup required? Two electrodes would further\nreduce sensor complexity and improve stability.\nResponse: We appreciate the reviewer’s critical and practical observation. We fully\nagree that a two-electrode configuration can reduce sensor complexity and is well-suited\nfor practical deployment, whereas the inclusion of the reference electrode in this work\nserved a deliberate and critical diagnostic purpose, without adding complexity to the\nimpedance measurement itself.\nWe intentionally employed a three-electrode setup in this study to enable precise track-\ning of the working electrode potential across different measurements, which is essential\nfor monitoring electrode fouling, contamination, and ensuring overall system stability\nthroughout open circuit potential measurements. The reference electrode plays a crucial\nrole in maintaining the integrity of the sensing system, particularly during repeated ex-\nperiments and long-term operation.\nImportantly, we emphasize that impedance was always measured exclusively between\nthe working and counter electrodes and the reference electrode was not involved in the\nimpedance path. As such, the sensing mechanism remains functionally equivalent to a\ntwo-electrode system. This distinction has been clarified in the revised Methods section\nof EIS Measurement.\nComment 2: How about surface contamination of the electrode influencing the CPE\nquality? How were the electrodes stored? Would a cleaning cycle be necessary prior to\nevery measurement in an application?\nResponse: We thank the reviewer for raising this important point regarding electrode\nsurface contamination and its potential influence on impedance behavior.\nIn our study, we took extensive measures to ensure surface cleanliness and stability\nthroughout all measurements. The electrodes were fabricated with a flat, inert plat-\ninum surface and stored dry in clean gel boxes at room temperature. Before and between\neach measurement, Milli-Q (MQ) water was used as a reference solution to verify that the\nelectrode remained uncontaminated and the baseline impedance was stable. No chemical\ncleaning or electrochemical cycling was applied between successive measurements, in or-\nder to simulate realistic reusability in practical applications.\nIf the measured impedance in MQ deviated by more than 10%, the chip was rinsed with\nMQ followed by isopropanol (IPA), which proved sufficient throughout the duration of\nour study. For more demanding applications, we note that the fabricated chips have been\ncleaned after fabrication, and they are fully compatible with standard RCA-1 and RCA-2\nclean room cleaning procedures, if regeneration is required.\nTo further ensure reliability, baseline EIS measurements in MQ water were recorded be-\nfore and after each experiment. The impedance response remained consistent across more\nthan 250 independent measurements, confirming that no significant fouling or drift oc-\ncurred (see Figure 4f). This demonstrates the long-term stability of the sensor without\nrequiring routine regeneration.\nIn practical applications, we therefore anticipate that no aggressive or frequent cleaning\ncycles would be necessary, especially when used in clean aqueous media. If long-term\ndeployment is envisioned in fouling-prone environments, simple rinsing or occasional re-\ngeneration (e.g., DI water and IPA rinse, or brief voltage sweeps over a demi electrode)\ncouldbeemployedwithoutcompromisingthelow-complexityandreusabilityofthesensor.\nComment 3: How can one (non-specific) sensor extract information on the concentrations\nof various ions in mixed solutions? Why do you not rely on multiple sensors with\n(low) specificity? It would help to see an EIS curve in a mixed solution to see how you\nare able to distinguish between different ions in one measurement.\nResponse: We appreciate the reviewer’s critical question regarding the ability of a non-\nspecific sensor to resolve the concentrations of multiple ions in mixed solutions.\nOur approach is fundamentally different from conventional ion sensing strategies that rely\non chemically selective sensors. Instead of using specific recognition elements, we leverage\nthe fact that different ions induce distinct frequency-dependent alterations in the struc-\nture and dynamics of the EDL at the electrode/electrolyte interface. These effects are\ncaptured in the full-spectrum impedance response, which reflects complex nonlinear in-\nteractions governed by ion size, hydration behavior, mobility, and interfacial structuring.\nUnlike prior EIS-based methods that focus only on simplified metrics like bulk conduc-\ntivity or double-layer capacitance, we analyze the entire impedance spectrum, including\nthe transitional frequency regions where capacitive and resistive behaviors overlap, re-\ngions that are highly sensitive to ion-specific physicochemical properties. These nuanced\nspectral features form an ion-specific impedance fingerprint, enabling our AI model to\naccurately resolve the concentrations of multiple ions using a single, non-functionalized\nsensor.\nUsing an electrode array with variant electrode material compositions and morphologies\nas well as functionalization, could further enhance selectivity and sensitivity of our ap-\nproach. Indeed, electrode material strongly influences the EDL structure, and extending\nthis work to sensor arrays with different materials or surface functionalizations, each tar-\ngeting the detection of particular ions, would add an information-rich dimension to the\ndataset. This is a key focus of our ongoing and future research after the current proof\nof concept work demonstrating the untapped potential of impedance spectroscopy itself,\nnot as a supporting measurement, but as a standalone technique for multi-ion detection.\nTo provide better clarity on how mixed ion solutions can be resolved, we have added a\nnew discussion (figure 4) in the main manuscript detailing the machine learning pipeline,\nfrom raw impedance data through data transformation to concentration prediction. This\naddition is intended to give the reader a transparent understanding of how the model\nextracts and utilizes spectral information to distinguish ions in complex mixtures.\nComment 4: The concentration steps are rather high: can you estimate the sensitivity\nof your approach? Are you able, e.g., to detect 100nM Zn2+ in 10mM Pb2+?\nResponse: We appreciate the reviewer’s thoughtful comment regarding sensitivity. In\nthis work, our primary objective is to demonstrate the applicability of the proposed ap-\nproach across a broad concentration range—including both high and trace levels—rather\nthan to optimize for the lowest achievable detection limits. The study aims to introduce\nand validate a fundamentally new method; the development of a product-grade chip with\nmaximized sensitivity and selectivity lies beyond the current scope.\nNonetheless, to illustrate the sensor’s capability in its present form, we conducted ad-\nditional measurements on Zn2+/Cd2+ mixtures (ZnSO /CdSO ) at molar ratios ranging\n4 4\nfrom 1:1 to 99:1, maintaining a total concentration of 10 mM. (The raw data are available\nin the repository - please refer to the Data Availability section). As shown in Figure R1,\nthe resulting impedance spectra exhibit distinguishable differences even at minor compo-\nsitional shifts (1–5% or 100–500 µM in 10 mM), remaining well above the experimental\nnoise level.\nThis demonstratesthe method’s capability to detectsubtle changesin mixed-ion composi-\ntions with the current configuration, although it does not represent the ultimate detection\nlimitofthetechnique. Asthereviewersuggested, furtherdevelopmentcouldenhanceboth\nsensitivity and selectivity. Notably, the electrochemical impedance spectroscopy frame-\nwork offers inherently high measurement stability, providing a solid foundation for future\noptimization toward ultra-trace detection.\n90°\n120° 60°\n6%\n150° 4% 30°\nZn:Cd 1:1\nZn:Cd 3:1\n2%\nZn:Cd 9:1\nZn:Cd 19:1\nZn:Cd 99:1\n180° 0 0°\n210° 330°\n240° 300°\n270°\nFigure R1: Polar representation of impedance spectral differences compared to Zn sin-\ngle ion solution spectra for Zn2+/Cd2+ mixtures with molar ratios from 1:1 to 99:1\n(ZnSO /CdSO ) with total concentration of 10mM\n4 4\nComment 5: What is the influence of temperature changes on the data quality? The\nelectrical double layer is temperature-dependent (e.g. Eq.(1)).?\nResponse: We appreciate the reviewer’s observation regarding the temperature depen-\ndenceoftheelectricaldoublelayerandEISmeasurements. Indeed, likeallelectrochemical\nprocesses, parameters such as diffusion coefficients, reaction kinetics, ion mobility, and\ndouble-layer structure are inherently temperature-sensitive to different extents.\nTo address the reviewer’s point, we performed additional measurements to directly eval-\nuate temperature effects on our EIS spectra. We conducted EIS experiments on a sample\nsolution (Zn(NO ) 10mM) over the temperature range of 21–40 ◦C (total 6 measurement,\n3 2\navailable in data repository). Two complementary analyses are presented in Figure R2 a\nand b described as follows:\na. Frequency-resolved sensitivity (%/°C): For each frequency, we calculated the\nimpedance magnitude\n√\n|Z| = Z′2 +Z′′2\nacross all measured temperatures and fitted a linear model\n|Z|(T) = a+bT.\nTheslopebwasnormalizedbythemean|Z|atthatfrequencytoyieldthepercentage\nchange per °C:\nb\nS(f) = ×100% / ◦C.\n|Z|\nThis produces a curve highlighting the frequency regions most sensitive to temper-\nature variation.\n0\n-0.2\n-0.4\n-0.6\n-0.8\n-1\n-1.2\n10-2 100 102 104 106 108\nFrequency (Hz)\n)C°\n/\n%(\nytivitisneS\nTemperature Sensitivity of |Z| Across Frequency Frequency-resolved Temperature Effect on |Z|\n40\n38\n36\n34\n32\n30\n28\n26\n24\n22\n-2 0 2 4 6\nlog10 Frequency (Hz)\n)C°(\nerutarepmeT\n2\n0\n-2\n-4\n-6\n-8\n-10\n-12\n-14\nC°52\nsv\negnahc\n%\na b\nFigure R2: Temperature dependence of impedance magnitude for Zn(NO ) between 21\n3 2\nand40◦C.(a)Frequency-resolvedtemperaturesensitivity, expressedaspercentagechange\nin |Z| per ◦C, calculated by fitting a linear model at each frequency and normalizing the\nslope b by the mean |Z|. (b) Percent-change heatmap relative to 25 ◦C, showing across\nfrequency and temperature. In the frequency range most relevant to our AI model for ion\nprediction, the temperature sensitivity remains below 1%, indicating minimal impact on\npredictive performance under controlled thermal conditions.\nb. Percent-change heatmap: Using 25 ◦C as a reference, we computed the relative\nchange in impedance magnitude at each frequency and temperature:\n|Z|(f,T)−|Z|(f,25◦C)\n%∆|Z|(f,T) = ×100%.\n|Z|(f,25◦C)\nThese values were plotted as a frequency–temperature heatmap, providing a visual\nrepresentation of the spectral regions most affected by temperature.\nThe results show that, in the frequency range most relevant to our AI model for ion pre-\ndiction, the temperature sensitivity remains below 1%, indicating minimal impact on data\nquality for the purposes of this study. Nevertheless, all main experiments were conducted\nunder well-controlled thermal conditions to eliminate even minimal temperature-related\ninfluences on the reported results.(SI section 3, page 13)\nComment 6: Is there an influence of the solvent?\nResponse: We thank the reviewer for raising this important point. The solvent can\nindeed influence electrochemical impedance by affecting parameters such as permittivity,\nviscosity,ionpairing,conductivity,and,consequently,thestructureoftheelectricaldouble\nlayer.\nIn this study, we carefully controlled these effects by performing all measurements in the\nsame aqueous solvent matrix with fixed ionic strength and pH, ensuring that solvent-\nrelated variations remained constant across the dataset. This allowed us to attribute the\nobserved spectral differences to analyte composition rather than solvent changes.\nWe also recognize that this is an area where AI can be particularly beneficial. In systems\nwhere the solvent composition is steady, its influence can be effectively mitigated by\ntraining the model on representative system data. In cases where the solvent composition\nmay vary, selectivity could be enhanced to decouple solvent effects from analyte signals,\nand AI models trained on datasets that include solvent variability can provide a robust\nmeans of compensating for such effects.\nComment 7: More citations needed in some paragraphs (e.g., last 2 paragraphs in\nsection physico-chemical processes at the EDL, 3rd paragraph in Frequency-Dependent\nBehavior)\nResponse: We thank the reviewer for this observation. We have revised the manuscript\nto include additional citations (page 6 and 8) supporting the discussed concepts in the\nindicated sections.\nComment 8: In the conclusion: Present in more detail/write more clearly, which char-\nacteristic physico-chemical effect is responsible for the differentiations in CPE\nResponse: We thank the reviewer for this valuable suggestion. In the revised conclu-\nsion, we have now explicitly described the characteristic physico-chemical effects respon-\nsible for the observed variations in impedance spectra. Specifically, we clarify that these\ndifferentiations arise from differences in interfacial heterogeneity and the distribution of\nrelaxation times within the electrode–electrolyte interface. These, in turn, are governed\nby ion-specific properties such as hydration shell structure, ion mobility (including mo-\nbility saturation effects), and adsorption behavior within the compact and diffuse layers.\nWe have also emphasized that such non-idealities are intrinsic signatures of interfacial\nstructure and dynamics rather than experimental artifacts. The revised conclusion now\ndirectly links the impedance variations to their underlying physico-chemical origins, as\nsuggested.\nComment 9: Fig. 2(c) and (d): Meaning of CPE Value (a.u.)? Does this refer to the\nexponent of the CPE? Clarify in text.\nResponse: We thank the reviewer for pointing out the need for clarification. In Fig-\nures 2(c) and 2(d), the “CPE Value (a.u.)” indeed refers to the exponent n of the CPE\nobtained from the equivalent circuit fitting. This exponent quantifies the deviation from\nideal capacitive behavior, with n = 1 representing an ideal capacitor and lower values in-\ndicating increased dispersion due to interfacial heterogeneity or non-uniform current dis-\ntribution. We have revised the figure captions and the relevant section of the manuscript\nto explicitly state that these panels present the CPE exponent n (dimensionless), rather\nthan the magnitude parameter Q.\nComment 10: Fig. 2(c) and (d): explain deviations between Model and Experiment\nResponse: We thank the reviewer for noting the discrepancy between the model pre-\ndictions and the experimental CPE exponent values in Figures 2(c) and 2(d). Please\nnote that our model incorporates major parameters, i.e. potential-dependent conduc-\ntivity and permittivity distributions, compact-layer formation, and mobility saturation\neffects. However, the underlying origin of the CPE may not solely be mobility saturation,\nas clarified in the manuscript (page 7). It also reflects ion-specific differences in hydration\nshell structure, ion–solvent interactions, adsorption behavior, and spatial heterogeneity\nin the compact and diffuse layers. These effects are further influenced by surface rough-\nness, grain boundaries, and localized variations in current distribution, which are not fully\ncaptured in the model. Additionally, small experimental errors—such as potentiostat res-\nolution limits, minor temperature fluctuations, and residual electrolyte impurities—can\ncontribute to the observed discrepancies. Nevertheless, the model reproduces both the\ntrend and magnitude of the potential- and ion-dependent CPE variations, indicating that\nthe dominant physico-chemical mechanisms are well represented.\nComment 11: Fig. 3(a) and (b): explain the legend “dB/B” in the text. Are these\ngraphs valid for anions?\nResponse: We thank the reviewer for this comment and have clarified the description in\nthe revised manuscript. Specifically, we now explicitly define “dB/B” in Figures 3a and\n3b as the fractional change in the mobility-saturation (collision) parameter B relative to\nits reference value B , given by ∆B/B = (B −B )/B .\n0 0 0\nNegativevalues(e.g.,-40%)indicatestrongermobility-saturationeffects(smallerB),which\nshift and reshape the transition from capacitive to resistive behavior in the Bode magni-\ntude and phase plots. We clarified this definition explicitly in the main text and figure\ncaption.\nRegardingapplicabilitytoanions,thegraphsillustratethegeneralinfluenceofthemobility-\nsaturation parameter on interfacial impedance and are, in principle, also valid for an-\nions—provided that anion-specific parameters (e.g., hydration shell size, diffusion coef-\nficient, mobility, and specific adsorption or repulsion in the compact layer) are used.\nWhile the qualitative trends—such as modulation of the transition-frequency region and\nphase—remain consistent, the quantitative curves differ for anions due to their distinct\nhydration and adsorption characteristics.\nComment 12: Clarify Fig. 4(d): How are reproducibility and repeatability calculated?\nReproducibilityshouldcomparetheresultsofdifferentsensors. Whyisthereproducibility\nerror lower than the repeatability error? Why is reproducibility shown over days? Why\nis the stability error 5% if you claim in the motivation that your sensors reveal improved\nstability due to no leakage? Explain what the single dots mean.\nResponse: We thank the reviewer for this comment and have revised the terminology\nfor accuracy. In the updated manuscript, “reproducibility error” is now referred to as\nrepeatability error, and “stability error” is renamed reusability error.\n• Repeatability error: calculated as the relative standard deviation (RSD) of three\nconsecutive back-to-back measurements on the same solution using the same sensor.\nAcross all solutions tested, the repeatability error remained below 3%.\n• Reusability error: calculatedasthedeviationbetweentheMilli-Qwaterreference\nspectra recorded before and after each sample measurement, quantifying baseline\nchange when the same sensor is reused. In all cases, the reusability error remained\nbelow 10%.\nThehighervalueofthereusabilityerrorcomparedtotherepeatabilityerrorarisesbecause\nthereusabilitymetricreflectscumulativevariationsintroducedbyrinsing,handling,minor\ntemperature changes, and mainly the conductivity change of MQ water (e.g., adsorption\nof gases like CO2). Our good reusability is achieved because the sensing method uses only\na small AC excitation signal, which does not trigger irreversible electrochemical reactions\nand thus preserves the electrode surface over multiple cycles. The errors are shown over\ndays to present performance consistency across the full measurement campaign, rather\nthan as a long-term aging or degradation study. Each single dot in Fig. 4d represents the\ncalculated error for one individual solution measurement.\nComment 13: The prediction errors of the analyte concentration are rather high, with\naverage errors of 5-10%. However, a new approach to ion sensing is demonstrated. To\nunderscoreitsadvantageofstabilityandreusability, thisdatashouldbemoreunderstand-\nable.\nResponse: Weappreciatethereviewerforthisvaluableobservationandpositivefeedback\non the novelty of this work. Following the suggestion of Reviewer 2, we have implemented\nadditional model refinements that increase the robustness of our AI-based concentration\nestimation. Specifically, these refinements involved improved feature selection, optimized\npreprocessing, and additional cross-validation, which improved the model’s robustness\nwhile maintaining generalization.\nIn the revised manuscript, we now report performance across multiple random seeds and\nfoldconfigurations—adeliberatelystringentvalidationapproachintendedtoensuretrans-\nparency rather than to highlight only the best-performing model. This strict approach\ninevitably exposes variability, particularly for a small dataset where certain splits may,\nfor example, omit high-concentration cadmium from the training set and evaluate it only\nin the test set, leading to locally higher errors. Despite these constraints, the results\nconsistently demonstrate strong correlation between predicted and actual concentrations,\nunderscoring the robustness of the methodology and the novelty, stability, and reusability\nof the sensing concept.\nWebelievethatexpandingthedataset, incorporatingstrongerphysicalconstraintsderived\nfrom fundamental understanding, and acquiring cleaner datasets from more sensitive and\nselective electrochemical setups (e.g., hardware, design and material of the electrodes) will\nsubstantially enhance predictive accuracy and further improve model generalizability.\nTo highlight the advantages of our approach in terms of stability and reusability, we have\nrewritten the corresponding section(page 13) of the manuscript. We now present the\nreusability and repeatability metrics alongside the prediction performance, showing that\nthe sensor achieves repeatability errors below 3% and reusability errors below 10% over\nthe entire measurement campaign. These metrics confirm that the sensing platform de-\nlivered consistent and reusable measurements, which is a key advantage over conventional\napproaches that often suffer from electrode degradation or drift. The improved clarity\nand organization of the data should make the stability and reusability benefits of our\napproach more evident to the reader.\nComment 14: There are differences in the methodology in the publication and sup-\nplementary information that should be corrected (e.g., EIS Measurements stabilization\nperiod, frequency range).\nResponse: We thank the reviewer for this. We have carefully reviewed both the\nmainmanuscriptandthesupplementaryinformationandidentifiedtheinconsistencies\nin the reported methodology, including the EIS measurement stabilization period and the\nspecifiedfrequencyrange. Intherevisedversion, themethodologyisnowconsistentacross\nthe main text and supplementary information.\nComment 15: How many sensors were manufactured/tested? How many measurements\nper sensor?\nResponse: Allmeasurementsreportedinthisstudywereperformedusingasinglesensor.\nThe focus of this work is not on evaluating the manufacturing process or device-to-device\nreproducibility, but rather on introducing and validating a new measurement methodol-\nogy for ion sensing. Using one sensor allowed us to isolate and study the fundamental\nmeasurement principle without additional variability from fabrication differences. Over\nthe course of the study, this single sensor was used for the entire measurement campaign,\nincluding more than 500 individual EIS measurements across more than 150 different\nsolutions and conditions.\nComment 16: Otherwise, there are enough details provided in the EIS methods for\nthe work to be reproduced. However, I am not an expert in the AI field to evaluate the\nreproducibility of the AI methods.\nResponse: We thank the reviewer for acknowledging that the EIS methodology is suffi-\nciently detailed for reproducibility. To ensure the same level of transparency for the AI\nmethods, we have expanded the description of the data pre-processing, model training,\nand validation procedures in the Methods section and Supplementary Information. These\nadditions include the full list of model parameters, pre-processing steps, cross-validation\nstrategy, and evaluation metrics. Furthermore, we have made the processed dataset and\nanalysis scripts available in an open-access repository, enabling other researchers to fully\nreproduce and validate the AI-based results.\nReferences\n[1] Katharina Doblhoff-Dier and Marc T. M. Koper. Modeling the gouy–chapman diffuse\ncapacitancewithattractiveion–surfaceinteraction. The Journal of Physical Chemistry\nC, 125(30):16664–16673, 2021.\n[2] Seung Joon Shin, Dong Hoon Kim, Gwanghyun Bae, et al. On the importance of the\nelectric double layer structure in aqueous electrocatalysis. Nature Communications,\n13:174, 2022.\n[3] K.Ojha,K.Doblhoff-Dier,andM.T.M.Koper. Double-layerstructureofthept(111)–\naqueous electrolyte interface. Proceedings of the National Academy of Sciences of the\nUnited States of America, 119(3):e2116016119, 2022.\n[4] S. Wang, J. Zhang, O. Gharbi, et al. Electrochemical impedance spectroscopy. Nature\nReviews Methods Primers, 1:41, 2021.\n[5] Christian M. Schott, Peter M. Schneider, Kun-Ting Song, Haiting Yu, Rainer Go¨tz,\nFelix Haimerl, Elena Gubanova, Jian Zhou, Thorsten O. Schmidt, Qiwei Zhang, Vi-\ntaly Alexandrov, and Aliaksandr S. Bandarenka. How to assess and predict elec-\ntrical double layer properties. implications for electrocatalysis. Chemical Reviews,\n124(22):12391–12462, 2024.\n[6] Xueting Cao, Shuangshuang Cha, and Ming Gong. Interfacial electrical double layer\nin electrocatalytic reactions: Fundamentals, characterizations and applications. Acta\nPhysico-Chimica Sinica, 41(5):100041, 2025.\n16"}, {"round": 2, "reviewer_comments": {"reviewer_2": "The authors addressed my comments adequately. The manuscript is now recommended for publication.", "reviewer_3": "All comments were carefully implemented in the manuscript.\nNo additional comments from my side.\nThe works describes an interesting and important new sensing approach using EIS. My only doubt is that all measurements were carried out with only one sensor. However, this sensor was tested more than 500 times showing high repeatability.\nI therefore recommend publishing the article as a first proof of concept for a new measurement methodology for ion sensing."}, "author_response": ""}]

Decision letter