Electric double layer structure in concentrated aqueous solution

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Kim, Dong Hyun Kim, Junsic Cho, Seung-Jae Shin, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7166816/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Mar, 2026 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Toward tailored electrocatalysis, significant attention has been directed to the electrode-electrolyte interface. The electric double layer (EDL) provides a crucial microenvironment for electrochemical reactions. However, its atomic-scale structure remains unresolved, particularly for non-dilute electrolyte concentrations relevant to practical systems. A notable example is the camel-to-bell shape transition in the capacitance curve, where two peaks merge as the concentration increases, which is still poorly understood at the molecular level. Herein, using all-atom simulations, we elucidate the EDL structures and their phase transitions which give rise to capacitance peaks. The predicted transition potentials match the experimental peak positions. We observe collective water reorientation in the cathodic region and anion surface condensation in the anodic region, which are further validated by in situ spectroscopy. Finally, we construct an EDL structural phase diagram to provide detailed insight into the EDL microenvironment. This work presents a valuable framework for design of improved interfaces. Physical sciences/Chemistry/Electrochemistry/Electrocatalysis Physical sciences/Chemistry/Theoretical chemistry/Computational chemistry Physical sciences/Chemistry/Surface chemistry/Surface spectroscopy Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 INTRODUCTION The electric double layer (EDL), which is formed at electrochemical interfaces when the electrolyte region screens a charged electrode, is one of the most fundamental concepts in electrochemistry 1 , 2 . Because electrochemical reactions occur within the EDL, understanding its structure and behaviour is directly relevant to the electrocatalytic performance. In particular, optimisation of the EDL structure for tuning of the local microenvironment has gained significant attention as a strategy for the development of high-performance electrocatalysts, especially for key reactions related to sustainable technologies, such as electrochemical CO 2 reduction and hydrogen evolution 3 – 25 . Nevertheless, the atomic-scale structure of the EDL remains largely elusive, particularly under a finite bulk concentration (e.g., 0.1−1 M), which is the condition most representative of practical electrochemical operations. The EDL structure is primarily defined by water orientation and local ion concentration (Fig. 1 a), both of which contribute to charge storage at the interface in response to an applied potential difference across the EDL, E . Consequently, the change in the stored interfacial charge density, σ , with respect to the changes in E reflects the underlying structural details of the EDL, while the differential capacitance, defined as \(\:C=\partial\:\sigma\:/\partial\:E\) , serves as a sensitive fingerprint of EDL structure. The camel-to-bell shape transition is a characteristic feature observed in the EDL capacitance curve when the bulk electrolyte concentration is increased from the very dilute to finite regime 26 – 30 . When measuring the capacitance of an interface composed of a single-crystal electrode (e.g. silver) and an aqueous electrolyte containing non-specifically adsorbing ions (e.g. NaF electrolyte), a two-peak ( camel-shaped ) curve shifts to a single-peak ( bell-shaped ) curve with increasing concentration. Starting with the traditional Gouy-Chapman-Stern (GCS) theory 31 – 33 , various theories have been proposed to explain this transition. However, these theories have failed to explain the peak behaviour (Supplementary Fig. 1), and have been mostly based on mesoscopic to macroscopic models 30 , 34 – 36 . For example, Kornyshev introduced a lattice gas model that accounts for the steric effects among ions 34 . This model predicts the merging of the two peaks when the capacitance decreases owing to ion saturation at high bias potentials; however, it is mainly applicable to highly concentrated electrolytes with large ion sizes, such as ionic liquids, rather than to aqueous electrolytes. Modern atomic-level simulations serve as computational microscopes for EDL structure exploration. Using ab initio molecular dynamics (AIMD) simulations of the Pt(111)-water interface, Cheng et al. proposed that the bell-shaped Helmholtz capacitance curve originated from water adsorption 37 . Later, the Koper group combined their simulation results with the Gouy-Chapman (GC) model to reproduce the camel-to-bell shaped transition at the Pt(111)-electrolyte interface 30 . However, this combined model does not include atomic-level details beyond the Helmholtz layer region (mostly due to the size limitations of the computationally expensive AIMD simulations); thus, the full atomic-scale origins of the camel-to-bell shape transition remain elusive. Using mean-field quantum mechanics/molecular mechanics (QM/MM) simulation framework, known as density functional theory in classical explicit solvents (DFT-CES) 38 – 40 , we recently reproduced a characteristic camel-shaped curve of an aqueous EDL in the dilute limit 41 . However, this study was limited to the dilute regime in which only a minimal number of counterions were included to screen the electrode charge. Thus, this approach cannot capture the full complexity of the EDL structural responses under practical, non-dilute conditions, thereby limiting the comprehensive understanding of its potentiodynamic behaviour. In this study, we investigate the EDL atomic structure as a function of the bulk electrolyte concentration by developing a constant-concentration simulation method, termed Chemostat , which is essential for capturing realistic interfacial behaviours where ion and bulk concentrations can differ by up to 80-fold 42 . Our simulations revealed that the capacitance peaks arise from EDL phase transitions, with a concentration-independent cathodic peak linked to water reorientation at the inner Helmholtz layer (IHL) and a concentration-dependent anodic peak due to anion condensation. A full EDL phase diagram was constructed, connecting these transitions to the camel-to-bell shape transition of the capacitance curves, and the predicted water structures were confirmed by in situ attenuated total reflectance-surface-enhanced infrared absorption spectroscopy (ATR-SEIRAS). We expect that our work will provide a comprehensive picture of the interfacial microenvironment at potentials relevant to practical electrocatalytic applications. RESULTS DFT-CES simulations on the interfaces of Ag(100) and Ag(111) electrodes with the NaF electrolyte are performed by varying σ to evaluate E (Fig. 1 a and Supplementary Note 1). Here, the results for the Ag(100) electrode are presented unless stated otherwise. During the simulation, the bulk concentration of the electrolyte was controlled using the Chemostat method (Supplementary Note 2 and Supplementary Fig. 2), producing smoothly varying ion concentration profiles at various electrode potentials (Supplementary Figs. 3–5). Furthermore, the simulation results for finite concentrations are quantitatively consistent with the available experimental data on the potential of zero charge (PZC; −0.63 V SHE for both simulation and experiment) and the interfacial water profile (Supplementary Fig. 6) 43 – 45 . EDL charging curves ( σ - E curves) are calculated for bulk concentrations in the dilute limit (only counter-ions included to neutralise σ ), and in the finite value of 0.1 and 0.2 M (Fig. 1 b). These curves reveal two noticeable features: a concentration-independent S -shaped region in the negative σ (cathodic) region and a concentration-dependent S -shaped region in the positive σ (anodic) region. In the S -shaped region, a thermodynamic instability exists (refer to Supplementary Note 3), causing σ to change along the Maxwell construction line at equilibrium (dashed red line in Fig. 1 c), where two phases coexist. This implies the presence of a first-order phase transition, described using the order parameter σ , which results in capacitance divergence as the potential remains fixed, yielding a capacitance peak (Fig. 1 d). Considering EDL charging as a thermodynamic process in which entropy decreases due to electric work (defined by w = σE ), the peak in \(\:C=\partial\:\sigma\:/\partial\:E\) is analogous to the divergence of the isothermal compressibility \(\:\kappa\:\sim\:\partial\:V/\partial\:p\) during a liquid-gas phase transition, which is another entropy-decreasing thermodynamic process that is driven by pressure-volume ( w = pV ) work. Thus, our simulation results indicate the emergence of two capacitance peaks, each associated with a distinct phase transition in the cathodic and anodic regions, respectively. Similarly, the Rotenberg group reported an anomalous capacitance peak driven by structural changes in ionic-liquid-based EDLs 46 . Using the potential corresponding to the Maxwell construction line (i.e., the phase transition potential), we predict the theoretical peak positions at different concentrations and find that they are consistent with experimental values (Fig. 1 e), with an error of less than ~ 0.1 V (Table 1 ). In the cathodic region, the peak position remains relatively unchanged, whereas in the anodic region, it shifts to lower E values as the bulk concentration increases. Notably, the anodic peak shift is attributed to the development of a more pronounced S -shape in the σ - E curve (Fig. 1 b), suggesting that stronger thermodynamic instability is induced at higher concentrations (its microscopic origin will be discussed below). Finally, the two peaks merge at high concentrations, resulting in the camel-to-bell shape transition. Same trends were observed for the Ag(111) electrode (Supplementary Fig. 7 and Supplementary Table 1). To the best of our knowledge, this is the first study that reproduces the camel-to-bell shape transition in aqueous EDLs using all-atom simulations. Table 1 Comparison of phase transition potentials predicted from all-atom simulations with experimental capacitance peak positions. Theoretical phase-transition potentials are determined using Maxwell construction lines on the S -shaped curves in Fig. 1 b, while experimental peak positions are extracted from the capacitance curves in Fig. 1 e. V SHE Cathodic peak Anodic peak Simulation Experiment Simulation Experiment 5 mM (Dilute in simulation) −0.78 −0.84 −0.47 −0.34 100 mM −0.78 −0.78 −0.56 −0.49 200 mM −0.77 −0.78 −0.70 −0.59 Water structure reorientation at the cathodic interface The local charge profiles of cations—the dominant ionic species near the electrode under cathodic potential—reveal the formation of two compact cation layers located at the distances of 5.1 and 7.4 Å from the electrode (Figs. 2 a,b and Supplementary Figs. 3–5). These layers are referred to as OHL 1 (the outer Helmholtz layer 1) and OHL 2 (outer Helmholtz layer 2), respectively. The formation of the two OHLs is attributed to the short-range correlation between the solvated cations. Beyond these OHLs, the local cation concentration decays exponentially, which is a typical characteristic of diffuse layers. Thus, our findings suggest the formation of two OHLs and a diffuse layer—distinct from the conventional view based on the GCS model which simplifies the EDL structure by ignoring atomic-level details and ion-ion correlations. Surprisingly, the net charge profile (including both cationic and anionic contributions) was found to be almost independent of bulk concentration. The net ionic charges that accumulated in OHL 1 and OHL 2 remained nearly the same across different bulk concentrations (Supplementary Note 4). Furthermore, the fitted exponent of the net charge profile in the diffuse layer, that is the Debye length, was consistently 5.6 Å under all concentration conditions (Supplementary Fig. 8). The small Debye length suggests substantial electric field screening between the electrode and OHL 1 where a water adlayer exists. This is correlated with the conclusions reached by the Willard group who suggested that water molecules can mute the dependence on ionic strength 47 . The water adlayer effectively screens the field of σ , leading to a similar E . Thus, the capacitance becomes concentration-independent at the cathodic potential. To quantify the water-screening effect, we develop a multi-layer capacitor model consisting of three dielectric layers— ε 1 , ε 2 , and ε DifL —corresponding to the OHL 1 , OHL 2 , and diffuse layers, respectively (Fig. 2 a). This model can be considered an extended GCS model with additional OHLs. Using the amounts of ions stored in each region obtained from our all-atom simulation, ε 1 and ε 2 are adjusted to reproduce the E values obtained by the simulations (Supplementary Note 4). This yields a positive ε 1 and a negative ε 2 (Fig. 2 c), consistent with previous work 48 . Moreover, ε 1 exhibits σ -dependent behaviour, reaching a maximum at − 13 µ C cm −2 within the S -shape region, indicating the crucial role of water adlayer screening in shaping the cathodic capacitance peak. As orientational polarisation is the major field-screening mechanism for water, we analysed the orientation of water in the adlayer region at different electrode potentials (Supplementary Fig. 9). At PZC, two distinct peaks are observed in the probability distribution of φ (the angle between the water bisector and the surface normal). The distribution of θ (the angle between the O − H bond and the surface normal) further shows that two water orientations are possible at PZC: (1) both O − H bonds are parallel to the surface, “ parallel state”, and (2) one parallel O − H bond with the other bond pointing toward the bulk region, “ H-up state”. Under a more negative potential, the water orientations converge into a single state, characterised by φ = ~140°, corresponding to a configuration where one O − H bond is parallel and the other points toward the electrode, “ H-down state”. Based on this three-state classification of the water orientation, which is also consistent with previous studies (see the water configurations in Fig. 2 d) 37 , 41 , 49 , we observed the coexistence of parallel and H-up states at the PZC, stabilised by favourable metal-O(water) interactions and the maximum number of hydrogen bonds. As the electrode potential decreased, a transition to the H-down state was induced (Fig. 2 d), driven by the strong interaction between the OH bond dipole and the electric field from the electrode. As this interaction must overcome the energetic penalty of forming a dangling hydrogen bond by restructuring the hydrogen-bond network (Supplementary Fig. 10), the phase transition occurs collectively in a first-order manner (similar to the 2D spin-1 Ising model; Supplementary Note 5). This leads to the non-monotonic behaviour of E as a function of σ (Fig. 2 e), giving rise to the capacitance peak 41 . Concentration-dependent anion condensation at the anodic interface Notably different from the cathodic interface, many anions are adsorbed on the electrode under anodic bias (Fig. 3 a) 41 while no dramatic change in the water structure with parallel or H-up state in the IHL is observed (Supplementary Fig. 9). The anion adsorption process is accompanied by the partial desolvation of anions to develop a direct electrostatic interaction with the positively charged electrode, which is facilitated by the dispersion interaction (Supplementary Fig. 11). The total charge of the adsorbed anions in the IHL ( σ IHL ) screens σ . Surprisingly, we observe a transition from underscreening (| σ IHL | < σ ) to either complete screening or overscreening (| σ IHL | ≥ σ ) as σ increases (Fig. 3 c), with the tendency for overscreening becoming more pronounced at higher bulk concentrations. Consequently, the net charge of the anion-adsorbed electrode ( σ + σ IHL ) decreases with increasing σ , yielding the S -shaped curve and thereby producing a concentration-dependent peak at the anodic potential. In addition, overscreening causes the net electrode charge to become negative, leading to the formation of two cationic OHLs and a diffuse layer, similar to the structure in the cathodic region (Fig. 3 b). This behaviour was also modelled using a multilayer capacitor model consisting of the IHL, OHL 1 , OHL 2 , and diffuse layers, as described in Supplementary Note 4. Although previous studies ascribed the origin of the capacitance peak to ion saturation at the interface (i.e., as a result of repulsion) 34 , 35 , our all-atom simulations showed no evidence of such ion saturation behaviour (Fig. 3 c). Rather, the adsorbed anions are closely and quasi-regularly spaced on the electrode surface (Fig. 3 d). This unexpected two-dimensional (2D) dense ionic structure was observed even at dilute concentrations, implying the presence of an effective attraction that overcomes the strong Coulomb repulsion among the anions. Further analysis reveals that water monomers or dimers bridge adjacent anions in the IHL, maintaining their separation at 3.9 or 6.4 Å, respectively (Fig. 3 a). Since the formation of a 2D dense ionic structure is enabled by effective attraction mediated by water molecules, the anion adsorption process involves anionic condensation, similar to the “surface condensation” of gas. From this perspective, increasing the bulk concentration lowers the entropy of the gas-like free anions; thus, their condensation into a liquid-like 2D anion layer incurs a lower entropic cost, reducing the work required for the phase transition (Fig. 3 e). Consequently, the phase transition potential decreases with increasing concentration. Phase diagram of EDL structure Using the aforementioned multi-layer capacitor models fine-tuned to reproduce our all-atom simulation results, we inter- and extrapolate the simulated E-σ curves originally obtained at 0, 0.1, and 0.2 M to cover the c range from 0 to 0.3 M (Fig. 4 a). This enabled us to construct a full E-c phase diagram of the EDL structure (Fig. 4 b). The phase diagram of the EDL structure consists of three major phases: the H-down water phase, parallel + H-up water phase, and condensed anion phase (Fig. 4 c). At low concentrations (0–0.24 M), increasing the potential from − 0.5 to + 0.5 V PZC induces two phase transitions: first from the H-down water to the parallel + H-up water phase, and then from the parallel + H-up water phase to the condensed anion phase. These transitions give rise to cathodic and anodic peaks, defining the camel-shaped capacitance curve, and the phase boundary between the parallel + H-up water and condensed anion phases is concentration-dependent, accounting for the anodic peak shift with increasing concentration c . For c > 0.24 M (triple point), the phase transition occurred directly from the H-down water phase to the anion-condensation phase, resulting in a single peak in the capacitance curve, corresponding to the transition from the camel shape to the bell shape. Spectroscopic features supporting the EDL phase transition To identify the spectroscopic features supporting the proposed EDL structural phase transitions, we simulated the infrared (IR) spectra of the interfacial water molecules in the first two layers using DFT calculations (Supplementary Note 6). At PZC (approximately − 0.6 V SHE ), the IR spectra for both the dilute and 0.2 M concentrations are dominated by the contributions from the 2nd layer water (~ 3390 cm − 1 ) and the parallel + H-up water phase in the adlayer (~ 3380 cm − 1 ; Supplementary Fig. 12 and Supplementary Tables 2,3). Using these as references, we observed a reduction in the intensity of the O–H vibrational mode under a cathodic bias (Figs. 5 a,b), which is attributed to a decreased population of the parallel + H-up water phase (Fig. 5 c), whereas the signals from the 2nd water layer remained largely unchanged. Notably, although the formation of H-down water phase under cathodic bias contributes a signal near ~ 3340 cm⁻ 1 (Supplementary Fig. 13), its intensity is weaker due to both a smaller population and the lower transition dipoles (Supplementary Fig. 14). Consequently, this signal is obscured by a more pronounced intensity reduction in the same frequency range. Under anodic bias, we observe increases in the intensities of two characteristic IR bands at ~ 3400 and ~ 3300 cm⁻ 1 (Figs. 5 a,b). These features are attributed to the asymmetric and symmetric stretching modes of water molecules coordinated with F⁻ anions at the IHL, indicating the formation of the anion-condensed phase. Notably, these spectral increases are more pronounced and emerge at lower bias potentials for the 0.2 M case compared to the dilute regime, reflecting a lower phase transition potential at higher electrolyte concentrations. These simulated spectral features are supported by the experimental results. In situ ATR-SEIRAS measurements, conducted using an Ag-coated Ge ATR electrode and referenced to the spectrum obtained at − 0.6 V SHE , show a decrease in the spectral intensity at approximately 3400 cm⁻ 1 under cathodic bias in both dilute (5 mM) and concentrated (200 mM) NaF electrolytes (Fig. 5 d). Conversely, two IR band intensities increased with anodic bias. Despite broader spectral features—likely resulting from the multi-faceted surface—and the associated uncertainty in spectral deconvolution, the experimentally observed trends are in good agreement with our simulated results within a reasonable error margin (~ 100 cm⁻ 1 ). More importantly, the experiments also reproduced the trend of stronger anodic spectral features at higher electrolyte concentrations, validating the EDL phase transitions predicted by DFT-CES calculations. CONCLUSION In summary, our study reveals the molecular origins of the capacitance behaviour at electrode-electrolyte interfaces under practical, non-dilute ion concentrations. Using predictive all-atom simulations, we identify two distinct phase transitions: concentration-independent water reorientation in the cathodic region and concentration-sensitive anion condensation in the anodic region. These transitions, whose spectroscopic signatures were also captured in our in situ experiments, give rise to the characteristic camel-to-bell shape evolution of the capacitance curve with increasing ion concentration, a long-standing unresolved phenomenon in the study of EDL. By constructing the EDL phase diagram, we provide a unified framework that relates the interfacial structure, potential, and concentration. These insights deepen our understanding of the EDL microenvironment and offer guiding principles for the rational design of next-generation electrocatalysts and energy-conversion systems. METHODS DFT-CES simulations The mean-field QM/MM simulations were performed using the DFT-CES approach developed by our group, with the incorporation of the Chemostat method. DFT-CES enables accurate sampling of all-atomic information of the EDL. The Chemostat method was developed in this study to maintain the bulk concentration of the non-dilute EDL. The method is described in detail in Supplementary Notes 1–2. Electrochemical measurements Electrochemical measurements were performed using an SP-150 potentiostat (BioLogic) in a custom-made (polyetheretherketone) H-type electrochemical cell. Prior to each measurement, the cell was cleaned by sequential boiling in 0.5 M H 2 SO 4 (98%, Daejung) and deionised (DI) water (> 18.2 MΩ·cm, Arium® Pro, Sartorius) over 3 h. Single-crystalline Ag foils with (111) and (100) orientations (1 × 1 cm 2 , 99.999%, MTI) were used as working electrodes. The Ag electrodes were chemically polished using a previously reported procedure 50 – 52 . Briefly, each electrode was immersed in a mixed solution of 0.3 M KCN (≥ 96%, Sigma-Aldrich) and H 2 O 2 (29–32%, Alfa Aesar) at a volume ratio of 1.5:1 for 3 s, during which vigorous gas evolution occurred. The electrode was then exposed to air for an additional 3 s, followed by immersion in a 0.55 M KCN solution until gas evolution ceased. The electrode was then thoroughly rinsed with DI water. This polishing cycle was repeated 8–12 times to obtain a highly reflective surface. Prior to use, the polished Ag surface was protected using a water droplet. The differential capacitance was measured using staircase potentiostatic electrochemical impedance spectroscopy (SPEIS). A graphite rod and saturated Ag/AgCl electrode (RE-1A, EC-Frontier) served as the counter and reference electrodes, respectively. The geometric area of the working electrode exposed to the electrolyte was limited to 0.16 cm 2 . Electrolytes were prepared by dissolving NaF (~ 99%, Sigma-Aldrich) in deionised (DI) water. To prevent unexpected contamination, the working electrode was spatially separated from the counter and reference compartments using a Nafion 115 membrane (DuPont). Measurements were conducted over a potential range from − 1.1 to 0 V SHE at a frequency of 20 Hz with a potential amplitude of 10 mV. All measurements were carried out in a deaerated electrolyte under continuous Ar (99.999%, Donghae Gas Ind.) flow. The ohmic drop was manually compensated by 85% during the SPEIS experiments. In situ ATR-SEIRAS measurements Chemically deposited Ag films were prepared by immersing a Ge substrate (60° angle, 20 mm radius; PIKE Technologies) into a mixed solution consisting of a hydrazine solution (50 µL, 0.02 M) and a silver nitrate solution (10 mL, 0.01 M) containing ammonium hydroxide (0.46 M) and EDTA (0.14 M). 53 The deposition was conducted for 150 s. Following the deposition, the substrate was thoroughly rinsed with DI water and dried under Ar atmosphere. In situ ATR-SEIRAS measurements were performed using a Nicolet iS50 FTIR spectrometer (Thermo Fisher Scientific) equipped with a liquid-nitrogen-cooled mercury cadmium telluride (MCT) detector. To eliminate interference from ambient water vapour and CO 2 , the entire optical path was purged with high-purity N 2 (99.999% purity, Donghae Gas Ind.). Spectra were collected using a specular reflection unit (VeeMax III, PIKE Technologies) equipped with a Ge attenuated total reflection (ATR) prism and a light polariser, with the incident angle fixed at 60°. The measurements were performed at a spectral resolution of 8 cm⁻ 1 by averaging 128 scans per spectrum. A spectrochemical flow-type cell was mounted on the Ge prism, with the Ag-coated Ge surface serving as the working electrode (exposed geometric area of 0.5 cm 2 ). A silver wire and saturated Ag/AgCl electrode were used as the counter and reference electrodes, respectively. Electrolytes were 5 and 200 mM NaF. All spectra are presented relative to a reference spectrum recorded at − 0.6 V SHE , a potential close to the PZC. Declarations COMPETING INTERESTS The authors declare no competing interests. AUTHOR CONTRIBUTIONS H.K. and S.-J.S. conceived the initial idea and H.K., C.H.C., and S.-J.S. supervised the project. M.M.K. performed the DFT-CES simulations and analysed the data. D.H.K. and J.C. performed the SPEIS and ATR-SEIRAS experiments, respectively. M.M.K., D.H.K., and J.C. contributed equally. All authors have written and revised the manuscript. ACKNOWLEDGEMENTS This research was supported by the Samsung Science and Technology Foundation (Grant No. SSTF-BA2101-08 (H.K. and C.H.C.), and National Research Foundation of Korea funded by the Korean government (Grant Nos. RS-2024-00450102 and 2021R1A5A1030054). References Helmholtz H (1853) Ueber einige Gesetze der Vertheilung elektrischer Ströme in körperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche. Ann Phys 165:211–233 Schmickler W (2020) Double layer theory. J Solid State Electrochem 24:2175–2176 Ringe S et al (2019) Understanding cation effects in electrochemical CO 2 reduction. 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Phys Chem Chem Phys 17:16682–16687 Kasina A, Cocklin E, Horswell S, Grunder Y, Lucas CA (2024) Structure of the electrochemical interface: Ag(hkl) in an alkaline electrolyte. J Phys Chem C 128:13318–13332 Merlet C et al (2014) The electric double layer has a life of its own. J Phys Chem C 118:18291–18298 Limaye A, Suvlu D, Willard AP (2023) Water molecules mute the dependence of the double-layer potential profile on ionic strength. Faraday Discuss 249:267–288 Tran B, Zhou Y, Janik MJ, Milner ST (2023) Negative dielectric constant of water at a metal interface. Phys Rev Lett 131:248001 Le J, Cuesta A, Cheng J (2018) The structure of metal-water interface at the potential of zero charge from density functional theory-based molecular dynamics. J Electroanal Chem 819:87–94 Jovićević JN, Jović VD, Despić AR (1984) The influence of adsorbing substances on the lead UPD onto (111) oriented silver single crystal surface—I. Electrochim Acta 29:1625–1638 Bewick A, Thomas B (1975) Optical and electrochemical studies of the underpotential deposition of metals Part I. Thallium deposition on single crystal silver electrodes. J Electroanal Chem 65:911–931 Adzic RR, Hanson ME, Yeager EB (1984) Structure of silver (100) and (111) single-crystal surfaces obtained by chemical polishing. J Electrochem Soc 131:1730–1731 Delgado JM, Orts JM, Rodes A (2005) ATR-SEIRAS study of the adsorption of acetate anions at chemically deposited silver thin film electrodes. Langmuir 21:8809–8816 Additional Declarations There is NO Competing Interest. Supplementary Files EDLstructureSIfinal.docx Supplementary notes, figures and tables Cite Share Download PDF Status: Published Journal Publication published 07 Mar, 2026 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7166816","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":489135504,"identity":"9c2277cd-2996-40a8-aa35-5db1320fa37f","order_by":0,"name":"Hyungjun Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYBACPmYQaWAjJ8HA2AAR4iGghQ2spSDNGKzlAFFawOSHQ4kzQDRxWth5j0n+MDiQPrP9cPPnDwx28gw8Zx8QcBhfmjSPwZ3c2TyJbRIHGJING3jbDQho4TGTZjB4ljuPIbEN6DDmBAZ+NgIOA2oBOuxwuhz/w+YPBxjqidMiwWNwOEFaIrEB6LDDCQy8bQS1GFvzGKQZzpzxsE3ijMFxwzaeY/i18POfMbz544+NvMT59McfKiqq5fl50vBrQQMGsJgaBaNgFIyCUUARAABDejkjsI0B5wAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-8261-9381","institution":"Korea Advanced Institute of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Hyungjun","middleName":"","lastName":"Kim","suffix":""},{"id":489135505,"identity":"c38b3d30-2991-41a6-a698-e94587b3d21c","order_by":1,"name":"Minho M. Kim","email":"","orcid":"https://orcid.org/0000-0002-3960-8908","institution":"Korea Advanced Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Minho","middleName":"M.","lastName":"Kim","suffix":""},{"id":489135507,"identity":"8122ad97-f48e-4c3f-85fa-ed10fd406a00","order_by":2,"name":"Dong Hyun Kim","email":"","orcid":"https://orcid.org/0000-0002-3364-4991","institution":"Pohang University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Dong","middleName":"Hyun","lastName":"Kim","suffix":""},{"id":489135509,"identity":"8aa29b32-d747-4470-91f2-3f7d34b19c20","order_by":3,"name":"Junsic Cho","email":"","orcid":"https://orcid.org/0000-0002-4875-0287","institution":"Pohang University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Junsic","middleName":"","lastName":"Cho","suffix":""},{"id":489135512,"identity":"9d1c82ab-c06f-4189-9175-6a475ee53189","order_by":4,"name":"Seung-Jae Shin","email":"","orcid":"https://orcid.org/0000-0002-5530-4453","institution":"UNIST","correspondingAuthor":false,"prefix":"","firstName":"Seung-Jae","middleName":"","lastName":"Shin","suffix":""},{"id":489135518,"identity":"b7d3fb18-b98c-4736-8535-26b148e31fbf","order_by":5,"name":"Chang Hyuck Choi","email":"","orcid":"https://orcid.org/0000-0002-2231-6116","institution":"Pohang University of Science and Technology (POSTECH)","correspondingAuthor":false,"prefix":"","firstName":"Chang","middleName":"Hyuck","lastName":"Choi","suffix":""}],"badges":[],"createdAt":"2025-07-19 23:50:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7166816/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7166816/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-026-70322-5","type":"published","date":"2026-03-07T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":88299878,"identity":"b64b5b43-d61d-48ed-816c-bf2e449c764d","added_by":"auto","created_at":"2025-08-05 04:15:25","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":405240,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePhase transitions predicted from all-atom EDL simulations and their connection to capacitance peaks. a, \u003c/strong\u003eSnapshot of the simulation system for the Ag(100) electrode–NaF electrolyte interface. \u003cstrong\u003eb,\u003c/strong\u003e Curves for surface charge density (\u003cem\u003eσ\u003c/em\u003e)versus electrode potential (\u003cem\u003eE\u003c/em\u003e) predicted from all-atom simulations at different bulk electrolyte concentrations. Red ovals indicate \u003cem\u003eS\u003c/em\u003e-shaped regions associated with phase transitions. \u003cstrong\u003ec, \u003c/strong\u003eSchematic diagrams showing the \u003cem\u003eS\u003c/em\u003e-shaped curve on the \u003cem\u003eσ\u003c/em\u003e-\u003cem\u003eE\u003c/em\u003e plane, with the red dashed line indicating the phase transition path. \u003cstrong\u003ed,\u003c/strong\u003e Corresponding schematic of the capacitance peak. \u003cstrong\u003ee,\u003c/strong\u003e Experimental capacitance curves for the Ag(100) electrode in NaF electrolytes, showing the \u003cem\u003ecamel-to-bell\u003c/em\u003e shape transition with increasing electrolyte concentration.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7166816/v1/47fdc0d4a27c2d7243d33d3d.png"},{"id":88299880,"identity":"0b3e13a5-2481-4fe9-866a-43941658fd0d","added_by":"auto","created_at":"2025-08-05 04:15:25","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":515691,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCollective reorientation of water molecules driven by cathodic bias. a, \u003c/strong\u003eRepresentative snapshot of the cathodic interface. Hydrogen, sodium, and silver atoms are shown in white, magenta, and blue, respectively. Oxygen atoms in the adlayer are color-coded according to their water orientation state (refer to Fig. 2d), while the other oxygen atoms are shown in red. \u003cstrong\u003eb,\u003c/strong\u003e Local cationic (solid lines) and anionic (dashed lines) charge profiles along the surface normal direction at varying bulk electrolyte concentration (\u003cem\u003eσ \u003c/em\u003e= −13.9 \u003cem\u003eμ\u003c/em\u003eC cm\u003csup\u003e-2\u003c/sup\u003e). \u003cstrong\u003ec,\u003c/strong\u003e \u003cem\u003eσ\u003c/em\u003e-dependent changes in the dielectric constants, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e for the water between electrode and OHL\u003csub\u003e1\u003c/sub\u003e, and \u003cem\u003eε\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e for the water between OHL\u003csub\u003e1\u003c/sub\u003e and OHL\u003csub\u003e2\u003c/sub\u003e, obtained by fitting the multilayer capacitor model to the all-atom simulation results. \u003cstrong\u003ed,\u003c/strong\u003e Populations of water orientation states and their configurations (dilute case). As \u003cem\u003eσ\u003c/em\u003e becomes more negative, the populations of the \u003cem\u003eparallel\u003c/em\u003e and \u003cem\u003eH-up\u003c/em\u003e states decrease, while the population of the \u003cem\u003eH-down\u003c/em\u003e state increases. \u003cstrong\u003ee,\u003c/strong\u003e Potential drops between regions: \u0026nbsp;between electrode and OHL\u003csub\u003e1\u003c/sub\u003e, \u0026nbsp;between OHL\u003csub\u003e1\u003c/sub\u003e and OHL\u003csub\u003e2\u003c/sub\u003e, and \u0026nbsp;between OHL\u003csub\u003e2\u003c/sub\u003e and the diffuse layer. This partitioning is achieved by fitting the multi-layer capacitor model to the all-atom simulation results. Note that the sum of , , and \u0026nbsp;corresponds to the total potential drop across the interface, i.e., the electrode potential from the DFT-CES simulation, \u003cem\u003eE\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7166816/v1/bedfba25c2abf12f246bf447.png"},{"id":88300205,"identity":"bec027ad-0402-43b5-af38-4fbe19cf4a11","added_by":"auto","created_at":"2025-08-05 04:23:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":736812,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAnion surface condensation driven by anodic bias. a, \u003c/strong\u003eRepresentative snapshot of the anodic interface. Hydrogen, oxygen, fluoride, sodium, and silver atoms are shown in white, red, cyan, magenta, and blue, respectively. Red dashed ovals highlight water-bridging configurations of anions in the IHL. \u003cstrong\u003eb,\u003c/strong\u003e Local cationic (solid lines) and anionic (dashed lines) charge profiles along the surface normal direction at different bulk electrolyte concentrations (\u003cem\u003eσ \u003c/em\u003e= 18.5 \u003cem\u003eμ\u003c/em\u003eC cm\u003csup\u003e-2\u003c/sup\u003e). \u003cstrong\u003ec,\u003c/strong\u003e \u003cem\u003eσ\u003c/em\u003e-dependent variation of the charge difference between the adsorbed anions in the IHL (\u003cem\u003eσ\u003c/em\u003e\u003csub\u003eIHL\u003c/sub\u003e) and \u003cem\u003eσ\u003c/em\u003e. The black solid line indicates the condition |\u003cem\u003eσ\u003c/em\u003e\u003csub\u003eIHL\u003c/sub\u003e| = \u003cem\u003eσ\u003c/em\u003e, corresponding to complete screening. \u003cstrong\u003ed, \u003c/strong\u003eRadial distribution function (RDF) between anions in the IHL shows intermediate-range ordering among adsorbed anions and is indicative of anion condensation (\u003cem\u003eσ \u003c/em\u003e= 18.5 \u003cem\u003eμ\u003c/em\u003eC cm\u003csup\u003e-2\u003c/sup\u003e). \u003cstrong\u003ee,\u003c/strong\u003e Schematic free energy diagrams of phase transitions at the anodic interfaces as different bulk concentration. At higher concentrations, the entropy of free (non-adsorbed) ions decreases, destabilising the “pre-condensation” phase. As a result, the required phase transition potential shifts to a lower value.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7166816/v1/0b28d1e59eb65d3189ae4cde.png"},{"id":88300208,"identity":"209656d1-4ac8-4e53-b266-a9fdd052ac53","added_by":"auto","created_at":"2025-08-05 04:23:25","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":504534,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePhase diagram of EDL structure and phase transitions. a, \u003c/strong\u003e\u003cem\u003eE-σ\u003c/em\u003e diagram extended using the multilayer capacitor model fitted to reproduce the all-atom simulation results. \u003cstrong\u003eb,\u003c/strong\u003e \u003cem\u003eE\u003c/em\u003e-\u003cem\u003ec\u003c/em\u003e phase diagram of EDL structure. The number of phase boundary crossings along a vertical line corresponds to the number of phase transitions induced by sweeping the electrode potential, which determines the number of capacitance peaks. \u003cstrong\u003ec,\u003c/strong\u003eSchematic illustration of the phase transitions between the three EDL structural phases: \u003cem\u003eH-down water\u003c/em\u003e phase, \u003cem\u003eparallel+H-up water\u003c/em\u003e phase, and \u003cem\u003econdensed anion\u003c/em\u003e phase.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7166816/v1/ade84a35a2c1425720e13de6.png"},{"id":88299888,"identity":"4a707a51-8fcb-4a78-8754-e5c15b0a22d1","added_by":"auto","created_at":"2025-08-05 04:15:25","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":496012,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpectroscopic features relevant to the formation of the phases. \u003c/strong\u003eCalculated IR spectra of interfacial water molecules obtained from DFT-CES trajectories at different bias potentials for \u003cstrong\u003ea,\u003c/strong\u003e dilute, and \u003cstrong\u003eb,\u003c/strong\u003e 0.2 M bulk concentration conditions. Solid lines show total IR spectra referenced to the spectra at the PZC. Dashed lines indicate the phase transition potentials, with the corresponding phases labelled. Characteristic molecular structures responsible for emerging and disappearing peaks are shown in the inset of (a); the same structures also explain the spectral features in (b). \u003cstrong\u003ec,\u003c/strong\u003e Integrated peak area for different molecular structures in dilute (top) and 200 mM (bottom) bulk concentration conditions. \u003cstrong\u003ed,\u003c/strong\u003e Experimental ATR-SEIRAS data measured on Ag in 5 and 200 mM NaF electrolytes. All experimental spectra are referenced to the spectrum at −0.6 V\u003csub\u003eSHE\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7166816/v1/3ca6df46a29fdca33929e8bd.png"},{"id":107398143,"identity":"34b8edae-8acb-4da5-a4af-168446b035af","added_by":"auto","created_at":"2026-04-21 07:06:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3194549,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7166816/v1/83c4810f-0214-44f5-9622-3e7c2063f142.pdf"},{"id":88299885,"identity":"1f97bed5-f7ef-49bb-a39c-4867ea5e31be","added_by":"auto","created_at":"2025-08-05 04:15:25","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":6908266,"visible":true,"origin":"","legend":"Supplementary notes, figures and tables","description":"","filename":"EDLstructureSIfinal.docx","url":"https://assets-eu.researchsquare.com/files/rs-7166816/v1/66f3b975595948f2a13b46a4.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Electric double layer structure in concentrated aqueous solution","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eThe electric double layer (EDL), which is formed at electrochemical interfaces when the electrolyte region screens a charged electrode, is one of the most fundamental concepts in electrochemistry\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Because electrochemical reactions occur within the EDL, understanding its structure and behaviour is directly relevant to the electrocatalytic performance. In particular, optimisation of the EDL structure for tuning of the local microenvironment has gained significant attention as a strategy for the development of high-performance electrocatalysts, especially for key reactions related to sustainable technologies, such as electrochemical CO\u003csub\u003e2\u003c/sub\u003e reduction and hydrogen evolution\u003csup\u003e\u003cspan additionalcitationids=\"CR4 CR5 CR6 CR7 CR8 CR9 CR10 CR11 CR12 CR13 CR14 CR15 CR16 CR17 CR18 CR19 CR20 CR21 CR22 CR23 CR24\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eNevertheless, the atomic-scale structure of the EDL remains largely elusive, particularly under a finite bulk concentration (e.g., 0.1\u0026minus;1 M), which is the condition most representative of practical electrochemical operations. The EDL structure is primarily defined by water orientation and local ion concentration (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea), both of which contribute to charge storage at the interface in response to an applied potential difference across the EDL, \u003cem\u003eE\u003c/em\u003e. Consequently, the change in the stored interfacial charge density, \u003cem\u003eσ\u003c/em\u003e, with respect to the changes in \u003cem\u003eE\u003c/em\u003e reflects the underlying structural details of the EDL, while the differential capacitance, defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C=\\partial\\:\\sigma\\:/\\partial\\:E\\)\u003c/span\u003e\u003c/span\u003e, serves as a sensitive fingerprint of EDL structure.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe \u003cem\u003ecamel-to-bell\u003c/em\u003e shape transition is a characteristic feature observed in the EDL capacitance curve when the bulk electrolyte concentration is increased from the very dilute to finite regime\u003csup\u003e\u003cspan additionalcitationids=\"CR27 CR28 CR29\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. When measuring the capacitance of an interface composed of a single-crystal electrode (e.g. silver) and an aqueous electrolyte containing non-specifically adsorbing ions (e.g. NaF electrolyte), a two-peak (\u003cem\u003ecamel-shaped\u003c/em\u003e) curve shifts to a single-peak (\u003cem\u003ebell-shaped\u003c/em\u003e) curve with increasing concentration. Starting with the traditional Gouy-Chapman-Stern (GCS) theory\u003csup\u003e\u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e, various theories have been proposed to explain this transition. However, these theories have failed to explain the peak behaviour (Supplementary Fig.\u0026nbsp;1), and have been mostly based on mesoscopic to macroscopic models\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan additionalcitationids=\"CR35\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. For example, Kornyshev introduced a lattice gas model that accounts for the steric effects among ions\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. This model predicts the merging of the two peaks when the capacitance decreases owing to ion saturation at high bias potentials; however, it is mainly applicable to highly concentrated electrolytes with large ion sizes, such as ionic liquids, rather than to aqueous electrolytes.\u003c/p\u003e\u003cp\u003eModern atomic-level simulations serve as computational microscopes for EDL structure exploration. Using \u003cem\u003eab initio\u003c/em\u003e molecular dynamics (AIMD) simulations of the Pt(111)-water interface, Cheng \u003cem\u003eet al.\u003c/em\u003e proposed that the \u003cem\u003ebell-shaped\u003c/em\u003e Helmholtz capacitance curve originated from water adsorption\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. Later, the Koper group combined their simulation results with the Gouy-Chapman (GC) model to reproduce the \u003cem\u003ecamel-to-bell\u003c/em\u003e shaped transition at the Pt(111)-electrolyte interface\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. However, this combined model does not include atomic-level details beyond the Helmholtz layer region (mostly due to the size limitations of the computationally expensive AIMD simulations); thus, the full atomic-scale origins of the \u003cem\u003ecamel-to-bell\u003c/em\u003e shape transition remain elusive.\u003c/p\u003e\u003cp\u003eUsing mean-field quantum mechanics/molecular mechanics (QM/MM) simulation framework, known as density functional theory in classical explicit solvents (DFT-CES)\u003csup\u003e\u003cspan additionalcitationids=\"CR39\" citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e, we recently reproduced a characteristic \u003cem\u003ecamel-shaped\u003c/em\u003e curve of an aqueous EDL in the dilute limit\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. However, this study was limited to the dilute regime in which only a minimal number of counterions were included to screen the electrode charge. Thus, this approach cannot capture the full complexity of the EDL structural responses under practical, non-dilute conditions, thereby limiting the comprehensive understanding of its potentiodynamic behaviour.\u003c/p\u003e\u003cp\u003eIn this study, we investigate the EDL atomic structure as a function of the bulk electrolyte concentration by developing a constant-concentration simulation method, termed \u003cem\u003eChemostat\u003c/em\u003e, which is essential for capturing realistic interfacial behaviours where ion and bulk concentrations can differ by up to 80-fold\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. Our simulations revealed that the capacitance peaks arise from EDL phase transitions, with a concentration-independent cathodic peak linked to water reorientation at the inner Helmholtz layer (IHL) and a concentration-dependent anodic peak due to anion condensation. A full EDL phase diagram was constructed, connecting these transitions to the \u003cem\u003ecamel-to-bell\u003c/em\u003e shape transition of the capacitance curves, and the predicted water structures were confirmed by \u003cem\u003ein situ\u003c/em\u003e attenuated total reflectance-surface-enhanced infrared absorption spectroscopy (ATR-SEIRAS). We expect that our work will provide a comprehensive picture of the interfacial microenvironment at potentials relevant to practical electrocatalytic applications.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eDFT-CES simulations on the interfaces of Ag(100) and Ag(111) electrodes with the NaF electrolyte are performed by varying \u003cem\u003eσ\u003c/em\u003e to evaluate \u003cem\u003eE\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea and Supplementary Note 1). Here, the results for the Ag(100) electrode are presented unless stated otherwise. During the simulation, the bulk concentration of the electrolyte was controlled using the \u003cem\u003eChemostat\u003c/em\u003e method (Supplementary Note 2 and Supplementary Fig.\u0026nbsp;2), producing smoothly varying ion concentration profiles at various electrode potentials (Supplementary Figs.\u0026nbsp;3\u0026ndash;5). Furthermore, the simulation results for finite concentrations are quantitatively consistent with the available experimental data on the potential of zero charge (PZC; \u0026minus;0.63 V\u003csub\u003eSHE\u003c/sub\u003e for both simulation and experiment) and the interfacial water profile (Supplementary Fig.\u0026nbsp;6) \u003csup\u003e\u003cspan additionalcitationids=\"CR44\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eEDL charging curves (\u003cem\u003eσ\u003c/em\u003e-\u003cem\u003eE\u003c/em\u003e curves) are calculated for bulk concentrations in the dilute limit (only counter-ions included to neutralise \u003cem\u003eσ\u003c/em\u003e), and in the finite value of 0.1 and 0.2 M (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). These curves reveal two noticeable features: a concentration-independent \u003cem\u003eS\u003c/em\u003e-shaped region in the negative \u003cem\u003eσ\u003c/em\u003e (cathodic) region and a concentration-dependent \u003cem\u003eS\u003c/em\u003e-shaped region in the positive \u003cem\u003eσ\u003c/em\u003e (anodic) region. In the \u003cem\u003eS\u003c/em\u003e-shaped region, a thermodynamic instability exists (refer to Supplementary Note 3), causing \u003cem\u003eσ\u003c/em\u003e to change along the Maxwell construction line at equilibrium (dashed red line in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec), where two phases coexist. This implies the presence of a first-order phase transition, described using the order parameter \u003cem\u003eσ\u003c/em\u003e, which results in capacitance divergence as the potential remains fixed, yielding a capacitance peak (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed). Considering EDL charging as a thermodynamic process in which entropy decreases due to electric work (defined by \u003cem\u003ew\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eσE\u003c/em\u003e), the peak in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C=\\partial\\:\\sigma\\:/\\partial\\:E\\)\u003c/span\u003e\u003c/span\u003e is analogous to the divergence of the isothermal compressibility \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\kappa\\:\\sim\\:\\partial\\:V/\\partial\\:p\\)\u003c/span\u003e\u003c/span\u003e during a liquid-gas phase transition, which is another entropy-decreasing thermodynamic process that is driven by pressure-volume (\u003cem\u003ew\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003epV\u003c/em\u003e) work.\u003c/p\u003e\u003cp\u003eThus, our simulation results indicate the emergence of two capacitance peaks, each associated with a distinct phase transition in the cathodic and anodic regions, respectively. Similarly, the Rotenberg group reported an anomalous capacitance peak driven by structural changes in ionic-liquid-based EDLs\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eUsing the potential corresponding to the Maxwell construction line (i.e., the phase transition potential), we predict the theoretical peak positions at different concentrations and find that they are consistent with experimental values (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee), with an error of less than ~\u0026thinsp;0.1 V (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In the cathodic region, the peak position remains relatively unchanged, whereas in the anodic region, it shifts to lower \u003cem\u003eE\u003c/em\u003e values as the bulk concentration increases. Notably, the anodic peak shift is attributed to the development of a more pronounced \u003cem\u003eS\u003c/em\u003e-shape in the \u003cem\u003eσ\u003c/em\u003e-\u003cem\u003eE\u003c/em\u003e curve (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb), suggesting that stronger thermodynamic instability is induced at higher concentrations (its microscopic origin will be discussed below). Finally, the two peaks merge at high concentrations, resulting in the \u003cem\u003ecamel-to-bell\u003c/em\u003e shape transition. Same trends were observed for the Ag(111) electrode (Supplementary Fig.\u0026nbsp;7 and Supplementary Table\u0026nbsp;1). To the best of our knowledge, this is the first study that reproduces the \u003cem\u003ecamel-to-bell\u003c/em\u003e shape transition in aqueous EDLs using all-atom simulations.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003e\u003cb\u003eComparison of phase transition potentials predicted from all-atom simulations with experimental capacitance peak positions.\u003c/b\u003e Theoretical phase-transition potentials are determined using Maxwell construction lines on the \u003cem\u003eS\u003c/em\u003e-shaped curves in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, while experimental peak positions are extracted from the capacitance curves in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eV\u003csub\u003eSHE\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003eCathodic peak\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eAnodic peak\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSimulation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eExperiment\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSimulation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eExperiment\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5 mM\u003c/p\u003e\u003cp\u003e(Dilute in simulation)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;0.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.34\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e100 mM\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.49\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e200 mM\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;0.77\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.59\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eWater structure reorientation at the cathodic interface\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe local charge profiles of cations\u0026mdash;the dominant ionic species near the electrode under cathodic potential\u0026mdash;reveal the formation of two compact cation layers located at the distances of 5.1 and 7.4 \u0026Aring; from the electrode (Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea,b and Supplementary Figs.\u0026nbsp;3\u0026ndash;5). These layers are referred to as OHL\u003csub\u003e1\u003c/sub\u003e (the outer Helmholtz layer 1) and OHL\u003csub\u003e2\u003c/sub\u003e (outer Helmholtz layer 2), respectively. The formation of the two OHLs is attributed to the short-range correlation between the solvated cations. Beyond these OHLs, the local cation concentration decays exponentially, which is a typical characteristic of diffuse layers. Thus, our findings suggest the formation of two OHLs and a diffuse layer\u0026mdash;distinct from the conventional view based on the GCS model which simplifies the EDL structure by ignoring atomic-level details and ion-ion correlations.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSurprisingly, the net charge profile (including both cationic and anionic contributions) was found to be almost independent of bulk concentration. The net ionic charges that accumulated in OHL\u003csub\u003e1\u003c/sub\u003e and OHL\u003csub\u003e2\u003c/sub\u003e remained nearly the same across different bulk concentrations (Supplementary Note 4). Furthermore, the fitted exponent of the net charge profile in the diffuse layer, that is the Debye length, was consistently 5.6 \u0026Aring; under all concentration conditions (Supplementary Fig.\u0026nbsp;8). The small Debye length suggests substantial electric field screening between the electrode and OHL\u003csub\u003e1\u003c/sub\u003e where a water adlayer exists. This is correlated with the conclusions reached by the Willard group who suggested that water molecules can mute the dependence on ionic strength\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. The water adlayer effectively screens the field of \u003cem\u003eσ\u003c/em\u003e, leading to a similar \u003cem\u003eE\u003c/em\u003e. Thus, the capacitance becomes concentration-independent at the cathodic potential.\u003c/p\u003e\u003cp\u003eTo quantify the water-screening effect, we develop a multi-layer capacitor model consisting of three dielectric layers\u0026mdash;\u003cem\u003eε\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, and \u003cem\u003eε\u003c/em\u003e\u003csub\u003eDifL\u003c/sub\u003e\u0026mdash;corresponding to the OHL\u003csub\u003e1\u003c/sub\u003e, OHL\u003csub\u003e2\u003c/sub\u003e, and diffuse layers, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). This model can be considered an extended GCS model with additional OHLs. Using the amounts of ions stored in each region obtained from our all-atom simulation, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003eε\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e are adjusted to reproduce the \u003cem\u003eE\u003c/em\u003e values obtained by the simulations (Supplementary Note 4). This yields a positive \u003cem\u003eε\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and a negative \u003cem\u003eε\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec), consistent with previous work\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e. Moreover, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e exhibits \u003cem\u003eσ\u003c/em\u003e-dependent behaviour, reaching a maximum at \u0026minus;\u0026thinsp;13 \u003cem\u003e\u0026micro;\u003c/em\u003eC cm\u003csup\u003e\u0026minus;2\u003c/sup\u003e within the \u003cem\u003eS\u003c/em\u003e-shape region, indicating the crucial role of water adlayer screening in shaping the cathodic capacitance peak.\u003c/p\u003e\u003cp\u003eAs orientational polarisation is the major field-screening mechanism for water, we analysed the orientation of water in the adlayer region at different electrode potentials (Supplementary Fig.\u0026nbsp;9). At PZC, two distinct peaks are observed in the probability distribution of \u003cem\u003eφ\u003c/em\u003e (the angle between the water bisector and the surface normal). The distribution of \u003cem\u003eθ\u003c/em\u003e (the angle between the O\u0026thinsp;\u0026minus;\u0026thinsp;H bond and the surface normal) further shows that two water orientations are possible at PZC: (1) both O\u0026thinsp;\u0026minus;\u0026thinsp;H bonds are parallel to the surface, \u0026ldquo;\u003cem\u003eparallel\u003c/em\u003e state\u0026rdquo;, and (2) one parallel O\u0026thinsp;\u0026minus;\u0026thinsp;H bond with the other bond pointing toward the bulk region, \u0026ldquo;\u003cem\u003eH-up\u003c/em\u003e state\u0026rdquo;. Under a more negative potential, the water orientations converge into a single state, characterised by \u003cem\u003eφ\u003c/em\u003e = ~140\u0026deg;, corresponding to a configuration where one O\u0026thinsp;\u0026minus;\u0026thinsp;H bond is parallel and the other points toward the electrode, \u0026ldquo;\u003cem\u003eH-down\u003c/em\u003e state\u0026rdquo;.\u003c/p\u003e\u003cp\u003eBased on this three-state classification of the water orientation, which is also consistent with previous studies (see the water configurations in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed)\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e,\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e, we observed the coexistence of \u003cem\u003eparallel\u003c/em\u003e and \u003cem\u003eH-up\u003c/em\u003e states at the PZC, stabilised by favourable metal-O(water) interactions and the maximum number of hydrogen bonds. As the electrode potential decreased, a transition to the \u003cem\u003eH-down\u003c/em\u003e state was induced (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed), driven by the strong interaction between the OH bond dipole and the electric field from the electrode. As this interaction must overcome the energetic penalty of forming a dangling hydrogen bond by restructuring the hydrogen-bond network (Supplementary Fig.\u0026nbsp;10), the phase transition occurs collectively in a first-order manner (similar to the 2D spin-1 Ising model; Supplementary Note 5). This leads to the non-monotonic behaviour of \u003cem\u003eE\u003c/em\u003e as a function of \u003cem\u003eσ\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee), giving rise to the capacitance peak\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eConcentration-dependent anion condensation at the anodic interface\u003c/b\u003e\u003c/p\u003e\u003cp\u003eNotably different from the cathodic interface, many anions are adsorbed on the electrode under anodic bias (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea)\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e while no dramatic change in the water structure with \u003cem\u003eparallel\u003c/em\u003e or \u003cem\u003eH-up\u003c/em\u003e state in the IHL is observed (Supplementary Fig.\u0026nbsp;9). The anion adsorption process is accompanied by the partial desolvation of anions to develop a direct electrostatic interaction with the positively charged electrode, which is facilitated by the dispersion interaction (Supplementary Fig.\u0026nbsp;11).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe total charge of the adsorbed anions in the IHL (\u003cem\u003eσ\u003c/em\u003e\u003csub\u003eIHL\u003c/sub\u003e) screens \u003cem\u003eσ\u003c/em\u003e. Surprisingly, we observe a transition from underscreening (|\u003cem\u003eσ\u003c/em\u003e\u003csub\u003eIHL\u003c/sub\u003e| \u0026lt; \u003cem\u003eσ\u003c/em\u003e) to either complete screening or overscreening (|\u003cem\u003eσ\u003c/em\u003e\u003csub\u003eIHL\u003c/sub\u003e| \u0026ge; \u003cem\u003eσ\u003c/em\u003e) as \u003cem\u003eσ\u003c/em\u003e increases (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec), with the tendency for overscreening becoming more pronounced at higher bulk concentrations. Consequently, the net charge of the anion-adsorbed electrode (\u003cem\u003eσ\u0026thinsp;+\u0026thinsp;σ\u003c/em\u003e\u003csub\u003eIHL\u003c/sub\u003e) decreases with increasing \u003cem\u003eσ\u003c/em\u003e, yielding the \u003cem\u003eS\u003c/em\u003e-shaped curve and thereby producing a concentration-dependent peak at the anodic potential. In addition, overscreening causes the net electrode charge to become negative, leading to the formation of two cationic OHLs and a diffuse layer, similar to the structure in the cathodic region (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). This behaviour was also modelled using a multilayer capacitor model consisting of the IHL, OHL\u003csub\u003e1\u003c/sub\u003e, OHL\u003csub\u003e2\u003c/sub\u003e, and diffuse layers, as described in Supplementary Note 4.\u003c/p\u003e\u003cp\u003eAlthough previous studies ascribed the origin of the capacitance peak to ion saturation at the interface (i.e., as a result of repulsion)\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e, our all-atom simulations showed no evidence of such ion saturation behaviour (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). Rather, the adsorbed anions are closely and quasi-regularly spaced on the electrode surface (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed). This unexpected two-dimensional (2D) dense ionic structure was observed even at dilute concentrations, implying the presence of an effective attraction that overcomes the strong Coulomb repulsion among the anions. Further analysis reveals that water monomers or dimers bridge adjacent anions in the IHL, maintaining their separation at 3.9 or 6.4 \u0026Aring;, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea).\u003c/p\u003e\u003cp\u003eSince the formation of a 2D dense ionic structure is enabled by effective attraction mediated by water molecules, the anion adsorption process involves anionic condensation, similar to the \u0026ldquo;surface condensation\u0026rdquo; of gas. From this perspective, increasing the bulk concentration lowers the entropy of the gas-like free anions; thus, their condensation into a liquid-like 2D anion layer incurs a lower entropic cost, reducing the work required for the phase transition (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee). Consequently, the phase transition potential decreases with increasing concentration.\u003c/p\u003e\u003cp\u003e\u003cb\u003ePhase diagram of EDL structure\u003c/b\u003e\u003c/p\u003e\u003cp\u003eUsing the aforementioned multi-layer capacitor models fine-tuned to reproduce our all-atom simulation results, we inter- and extrapolate the simulated \u003cem\u003eE-σ\u003c/em\u003e curves originally obtained at 0, 0.1, and 0.2 M to cover the \u003cem\u003ec\u003c/em\u003e range from 0 to 0.3 M (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). This enabled us to construct a full \u003cem\u003eE-c\u003c/em\u003e phase diagram of the EDL structure (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe phase diagram of the EDL structure consists of three major phases: the \u003cem\u003eH-down water\u003c/em\u003e phase, \u003cem\u003eparallel\u0026thinsp;+\u0026thinsp;H-up water\u003c/em\u003e phase, and \u003cem\u003econdensed anion\u003c/em\u003e phase (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). At low concentrations (0\u0026ndash;0.24 M), increasing the potential from \u0026minus;\u0026thinsp;0.5 to +\u0026thinsp;0.5 V\u003csub\u003ePZC\u003c/sub\u003e induces two phase transitions: first from the \u003cem\u003eH-down water\u003c/em\u003e to the \u003cem\u003eparallel\u0026thinsp;+\u0026thinsp;H-up water\u003c/em\u003e phase, and then from the \u003cem\u003eparallel\u0026thinsp;+\u0026thinsp;H-up water\u003c/em\u003e phase to the \u003cem\u003econdensed anion\u003c/em\u003e phase. These transitions give rise to cathodic and anodic peaks, defining the \u003cem\u003ecamel-shaped\u003c/em\u003e capacitance curve, and the phase boundary between the \u003cem\u003eparallel\u0026thinsp;+\u0026thinsp;H-up water\u003c/em\u003e and \u003cem\u003econdensed anion\u003c/em\u003e phases is concentration-dependent, accounting for the anodic peak shift with increasing concentration \u003cem\u003ec\u003c/em\u003e. For \u003cem\u003ec\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.24 M (triple point), the phase transition occurred directly from the \u003cem\u003eH-down water\u003c/em\u003e phase to the \u003cem\u003eanion-condensation\u003c/em\u003e phase, resulting in a single peak in the capacitance curve, corresponding to the transition from the camel shape to the bell shape.\u003c/p\u003e\u003cp\u003e\u003cb\u003eSpectroscopic features supporting the EDL phase transition\u003c/b\u003e\u003c/p\u003e\u003cp\u003eTo identify the spectroscopic features supporting the proposed EDL structural phase transitions, we simulated the infrared (IR) spectra of the interfacial water molecules in the first two layers using DFT calculations (Supplementary Note 6). At PZC (approximately \u0026minus;\u0026thinsp;0.6 V\u003csub\u003eSHE\u003c/sub\u003e), the IR spectra for both the dilute and 0.2 M concentrations are dominated by the contributions from the 2nd layer water (~\u0026thinsp;3390 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and the \u003cem\u003eparallel\u0026thinsp;+\u0026thinsp;H-up water\u003c/em\u003e phase in the adlayer (~\u0026thinsp;3380 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; Supplementary Fig.\u0026nbsp;12 and Supplementary Tables\u0026nbsp;2,3). Using these as references, we observed a reduction in the intensity of the O\u0026ndash;H vibrational mode under a cathodic bias (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea,b), which is attributed to a decreased population of the \u003cem\u003eparallel\u0026thinsp;+\u0026thinsp;H-up water\u003c/em\u003e phase (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec), whereas the signals from the 2nd water layer remained largely unchanged. Notably, although the formation of \u003cem\u003eH-down water\u003c/em\u003e phase under cathodic bias contributes a signal near ~\u0026thinsp;3340 cm⁻\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;13), its intensity is weaker due to both a smaller population and the lower transition dipoles (Supplementary Fig.\u0026nbsp;14). Consequently, this signal is obscured by a more pronounced intensity reduction in the same frequency range.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eUnder anodic bias, we observe increases in the intensities of two characteristic IR bands at ~\u0026thinsp;3400 and ~\u0026thinsp;3300 cm⁻\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea,b). These features are attributed to the asymmetric and symmetric stretching modes of water molecules coordinated with F⁻ anions at the IHL, indicating the formation of the \u003cem\u003eanion-condensed\u003c/em\u003e phase. Notably, these spectral increases are more pronounced and emerge at lower bias potentials for the 0.2 M case compared to the dilute regime, reflecting a lower phase transition potential at higher electrolyte concentrations.\u003c/p\u003e\u003cp\u003eThese simulated spectral features are supported by the experimental results. \u003cem\u003eIn situ\u003c/em\u003e ATR-SEIRAS measurements, conducted using an Ag-coated Ge ATR electrode and referenced to the spectrum obtained at \u0026minus;\u0026thinsp;0.6 V\u003csub\u003eSHE\u003c/sub\u003e, show a decrease in the spectral intensity at approximately 3400 cm⁻\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e under cathodic bias in both dilute (5 mM) and concentrated (200 mM) NaF electrolytes (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed). Conversely, two IR band intensities increased with anodic bias. Despite broader spectral features\u0026mdash;likely resulting from the multi-faceted surface\u0026mdash;and the associated uncertainty in spectral deconvolution, the experimentally observed trends are in good agreement with our simulated results within a reasonable error margin (~\u0026thinsp;100 cm⁻\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e). More importantly, the experiments also reproduced the trend of stronger anodic spectral features at higher electrolyte concentrations, validating the EDL phase transitions predicted by DFT-CES calculations.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eIn summary, our study reveals the molecular origins of the capacitance behaviour at electrode-electrolyte interfaces under practical, non-dilute ion concentrations. Using predictive all-atom simulations, we identify two distinct phase transitions: concentration-independent water reorientation in the cathodic region and concentration-sensitive anion condensation in the anodic region. These transitions, whose spectroscopic signatures were also captured in our \u003cem\u003ein situ\u003c/em\u003e experiments, give rise to the characteristic \u003cem\u003ecamel-to-bell\u003c/em\u003e shape evolution of the capacitance curve with increasing ion concentration, a long-standing unresolved phenomenon in the study of EDL. By constructing the EDL phase diagram, we provide a unified framework that relates the interfacial structure, potential, and concentration. These insights deepen our understanding of the EDL microenvironment and offer guiding principles for the rational design of next-generation electrocatalysts and energy-conversion systems.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003e\u003cb\u003eDFT-CES simulations\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe mean-field QM/MM simulations were performed using the DFT-CES approach developed by our group, with the incorporation of the \u003cem\u003eChemostat\u003c/em\u003e method. DFT-CES enables accurate sampling of all-atomic information of the EDL. The \u003cem\u003eChemostat\u003c/em\u003e method was developed in this study to maintain the bulk concentration of the non-dilute EDL. The method is described in detail in Supplementary Notes 1\u0026ndash;2.\u003c/p\u003e\u003cp\u003e\u003cb\u003eElectrochemical measurements\u003c/b\u003e\u003c/p\u003e\u003cp\u003eElectrochemical measurements were performed using an SP-150 potentiostat (BioLogic) in a custom-made (polyetheretherketone) H-type electrochemical cell. Prior to each measurement, the cell was cleaned by sequential boiling in 0.5 M H\u003csub\u003e2\u003c/sub\u003eSO\u003csub\u003e4\u003c/sub\u003e (98%, Daejung) and deionised (DI) water (\u0026gt;\u0026thinsp;18.2 MΩ\u0026middot;cm, Arium\u0026reg; Pro, Sartorius) over 3 h. Single-crystalline Ag foils with (111) and (100) orientations (1 \u0026times; 1 cm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, 99.999%, MTI) were used as working electrodes. The Ag electrodes were chemically polished using a previously reported procedure\u003csup\u003e\u003cspan additionalcitationids=\"CR51\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. Briefly, each electrode was immersed in a mixed solution of 0.3 M KCN (\u0026ge;\u0026thinsp;96%, Sigma-Aldrich) and H\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e (29\u0026ndash;32%, Alfa Aesar) at a volume ratio of 1.5:1 for 3 s, during which vigorous gas evolution occurred. The electrode was then exposed to air for an additional 3 s, followed by immersion in a 0.55 M KCN solution until gas evolution ceased. The electrode was then thoroughly rinsed with DI water. This polishing cycle was repeated 8\u0026ndash;12 times to obtain a highly reflective surface. Prior to use, the polished Ag surface was protected using a water droplet.\u003c/p\u003e\u003cp\u003eThe differential capacitance was measured using staircase potentiostatic electrochemical impedance spectroscopy (SPEIS). A graphite rod and saturated Ag/AgCl electrode (RE-1A, EC-Frontier) served as the counter and reference electrodes, respectively. The geometric area of the working electrode exposed to the electrolyte was limited to 0.16 cm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Electrolytes were prepared by dissolving NaF (~\u0026thinsp;99%, Sigma-Aldrich) in deionised (DI) water. To prevent unexpected contamination, the working electrode was spatially separated from the counter and reference compartments using a Nafion 115 membrane (DuPont). Measurements were conducted over a potential range from \u0026minus;\u0026thinsp;1.1 to 0 V\u003csub\u003eSHE\u003c/sub\u003e at a frequency of 20 Hz with a potential amplitude of 10 mV. All measurements were carried out in a deaerated electrolyte under continuous Ar (99.999%, Donghae Gas Ind.) flow. The ohmic drop was manually compensated by 85% during the SPEIS experiments.\u003c/p\u003e\u003cp\u003e\u003cb\u003eIn situ\u003c/b\u003e \u003cb\u003eATR-SEIRAS measurements\u003c/b\u003e\u003c/p\u003e\u003cp\u003eChemically deposited Ag films were prepared by immersing a Ge substrate (60\u0026deg; angle, 20 mm radius; PIKE Technologies) into a mixed solution consisting of a hydrazine solution (50 \u0026micro;L, 0.02 M) and a silver nitrate solution (10 mL, 0.01 M) containing ammonium hydroxide (0.46 M) and EDTA (0.14 M).\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e The deposition was conducted for 150 s. Following the deposition, the substrate was thoroughly rinsed with DI water and dried under Ar atmosphere. \u003cem\u003eIn situ\u003c/em\u003e ATR-SEIRAS measurements were performed using a Nicolet iS50 FTIR spectrometer (Thermo Fisher Scientific) equipped with a liquid-nitrogen-cooled mercury cadmium telluride (MCT) detector. To eliminate interference from ambient water vapour and CO\u003csub\u003e2\u003c/sub\u003e, the entire optical path was purged with high-purity N\u003csub\u003e2\u003c/sub\u003e (99.999% purity, Donghae Gas Ind.). Spectra were collected using a specular reflection unit (VeeMax III, PIKE Technologies) equipped with a Ge attenuated total reflection (ATR) prism and a light polariser, with the incident angle fixed at 60\u0026deg;. The measurements were performed at a spectral resolution of 8 cm⁻\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e by averaging 128 scans per spectrum. A spectrochemical flow-type cell was mounted on the Ge prism, with the Ag-coated Ge surface serving as the working electrode (exposed geometric area of 0.5 cm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e). A silver wire and saturated Ag/AgCl electrode were used as the counter and reference electrodes, respectively. Electrolytes were 5 and 200 mM NaF. All spectra are presented relative to a reference spectrum recorded at \u0026minus;\u0026thinsp;0.6 V\u003csub\u003eSHE\u003c/sub\u003e, a potential close to the PZC.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eCOMPETING INTERESTS\u003c/h2\u003e\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\u003ch2\u003eAUTHOR CONTRIBUTIONS\u003c/h2\u003e\u003cp\u003eH.K. and S.-J.S. conceived the initial idea and H.K., C.H.C., and S.-J.S. supervised the project. M.M.K. performed the DFT-CES simulations and analysed the data. D.H.K. and J.C. performed the SPEIS and ATR-SEIRAS experiments, respectively. M.M.K., D.H.K., and J.C. contributed equally. All authors have written and revised the manuscript.\u003c/p\u003e\u003ch2\u003eACKNOWLEDGEMENTS\u003c/h2\u003e\u003cp\u003eThis research was supported by the Samsung Science and Technology Foundation (Grant No. SSTF-BA2101-08 (H.K. and C.H.C.), and National Research Foundation of Korea funded by the Korean government (Grant Nos. RS-2024-00450102 and 2021R1A5A1030054).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHelmholtz H (1853) Ueber einige Gesetze der Vertheilung elektrischer Str\u0026ouml;me in k\u0026ouml;rperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche. Ann Phys 165:211\u0026ndash;233\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSchmickler W (2020) Double layer theory. 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Langmuir 21:8809\u0026ndash;8816\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7166816/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7166816/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eToward tailored electrocatalysis, significant attention has been directed to the electrode-electrolyte interface. The electric double layer (EDL) provides a crucial microenvironment for electrochemical reactions. However, its atomic-scale structure remains unresolved, particularly for non-dilute electrolyte concentrations relevant to practical systems. A notable example is the \u003cem\u003ecamel-to-bell\u003c/em\u003e shape transition in the capacitance curve, where two peaks merge as the concentration increases, which is still poorly understood at the molecular level. Herein, using all-atom simulations, we elucidate the EDL structures and their phase transitions which give rise to capacitance peaks. The predicted transition potentials match the experimental peak positions. We observe collective water reorientation in the cathodic region and anion surface condensation in the anodic region, which are further validated by \u003cem\u003ein situ\u003c/em\u003e spectroscopy. Finally, we construct an EDL structural phase diagram to provide detailed insight into the EDL microenvironment. This work presents a valuable framework for design of improved interfaces.\u003c/p\u003e","manuscriptTitle":"Electric double layer structure in concentrated aqueous solution","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-05 04:15:20","doi":"10.21203/rs.3.rs-7166816/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"6bfd81b5-7bf7-4165-b833-be0070582dda","owner":[],"postedDate":"August 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":51928261,"name":"Physical sciences/Chemistry/Electrochemistry/Electrocatalysis"},{"id":51928262,"name":"Physical sciences/Chemistry/Theoretical chemistry/Computational chemistry"},{"id":51928263,"name":"Physical sciences/Chemistry/Surface chemistry/Surface spectroscopy"}],"tags":[],"updatedAt":"2026-04-21T07:05:54+00:00","versionOfRecord":{"articleIdentity":"rs-7166816","link":"https://doi.org/10.1038/s41467-026-70322-5","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2026-03-07 05:00:00","publishedOnDateReadable":"March 7th, 2026"},"versionCreatedAt":"2025-08-05 04:15:20","video":"","vorDoi":"10.1038/s41467-026-70322-5","vorDoiUrl":"https://doi.org/10.1038/s41467-026-70322-5","workflowStages":[]},"version":"v1","identity":"rs-7166816","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7166816","identity":"rs-7166816","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}