Electric double layer structure in aqueous electrolyte and its electrocatalytic importance


 To design electrochemical interfaces for efficient electric-chemical energy interconversion, it is critical to reveal the electric double layer (EDL) structure and relate it with electrochemical activity; nonetheless, this has been a long-standing challenge. Of particular, no molecular-level theories have fully explained the characteristic two peaks arising in the potential-dependence of the EDL capacitance, which is sensitively dependent on the EDL structure. We herein demonstrate that our first-principles-based molecular simulation reproduces the experimental capacitance peaks. The origin of two peaks emerging at anodic and cathodic potentials is unveiled to be an electrosorption of ions and an EDL structural phase transition, respectively. We further find a cation complexation gradually modifies the EDL structure and the field strength, which linearly scales the carbon dioxide reduction activity. This study deciphers the complex structural response of the EDL and highlights its catalytic importance, which bridges the mechanistic gap between the EDL structure and electrocatalysis.

the complex structural response of the EDL and highlights its catalytic importance, which bridges the mechanistic gap between the EDL structure and electrocatalysis.

INTRODUCTION
Electrocatalysis lies at the core of most modern technologies, such as, fuel cells, electrolyzers, and carbon dioxide recycling, for sustainable energy conversion. All such processes separate into half-cells in which electrochemistry happens under an electrochemical potential difference between the cathode and anode. The application of a potential difference leads to the formation 5 of an electric double layer (EDL) at the interface of an electrode and liquid electrolyte. The EDL is one of the oldest and most fundamental concepts in electrochemistry 1,2 . As a recent example, the electrochemical carbon dioxide reduction reaction (CO2RR) has been suggested to be controlled by the EDL structure [3][4][5][6][7][8][9][10] .
Nonetheless, to date, the microscopic structure of the EDL has not been fully resolved not 10 only because the EDL is spatially concealed between the two bulk phases of solid and liquid 11 , but also because the electrochemical signals are highly convoluted by the complex, coupled EDL responses of the multiple components in the electrified interface 12 . Despite the recent successes based on X-ray absorption spectroscopy 13 and shell-isolated nanoparticle-enhanced Raman spectroscopy (SHINERS) 14 , these spectroscopy-based investigations have been focused only to 15 the explanation of the water orientations, and their quantitative association with electrocatalysis is yet to be established. However, a notable point of these studies is that the computational simulation has inevitably been employed; the simulated and experimental spectra have been matched with each other, based on which the structural details about the EDL have been obtained from the molecular simulations. 20 Instead of explaining the peaks from photon-based spectroscopy, we herein demonstrate that our molecular simulation accurately reproduces the characteristic peaks from an electrochemical impedance spectroscopy -the famous camel-shaped curve [15][16][17][18][19] of the capacitance in dilute aqueous electrolyte -without the requirement of empirical adjustment in the simulation. To reliably compute the differential capacitance, , using its definition of = ⁄ (where is a surface charge density, and is an electrode potential), the sensitive changes in the potential must be captured that require an extremely fine sampling of the data points, which is practically impossible using a full ab initio approach 20 . Therefore, we utilize a multiscale approach, density 5 functional theory in classical explicit solvents (DFT-CES), that combines a density functional description of the metal electrode with a classical molecular dynamic description of the electrolyte 21 . Most notably, the interfacial interaction of the DFT-CES is developed as based on the quantum-mechanical energetics, i.e., so-called first-principles based multiscale approach, that enables us to directly validate our simulation results through comparison with experimental 10 results (for the simulation details and backgrounds, the reader may refer to our previous publications 21-23 , and a summary is also presented in the Supplementary Notes 1-5).

RESULTS
With varying the by changing number of excess electrons in the Ag(111) electrode and excess 15 ions (Na + or F − ) in the electrolyte, DFT-CES simulation of the interfacial system ( Fig. 1a) predicts the change of the , which is calculated using Trasatti's absolute electrode potential 24 (Supplementary Fig. 1 and Supplementary Fig. 2), yielding a -curve (Fig. 1b). Prior to evaluating the , which is derivative of , we observe a most unprecedented feature in thecurve: an S-shaped region in the negative region. Thermodynamically, the S-shaped profile is a 20 consequence of a bistable free energy landscape (its microscopic origin will be discussed in the following section) by considering the thermodynamic relation of = − d + d (where and are the interfacial Helmholtz free energy and entropy, respectively, and is the temperature). Thus, a Maxwell tie-line can be constructed along which two bistable states coexist in equilibrium (Supplementary Fig. 3). Such a phase coexistence line in the free energy curve yields a horizontal (or vertical) line in the -(or -) curve that eventually causes thecurve, a derivative of the -curve, to exhibit a capacitance peak. 5 Our theoretically predicted EDL capacitance curve is well matched with the curve corresponding to the experimental staircase potentiostatic electrochemical impedance spectroscopy (SPEIS) data measured for Ag(111) in a dilute 3 mM NaF electrolyte (Fig. 1c). In particular, the double-hump camel-shape of the capacitance curve is successfully reproduced at the peak potentials, comparable to that observed in the experiment within approximately 0.1 V. 10 Both theoretical and experimental -curves exhibit a minimum capacitance at the same , that exactly corresponds to the point of zero charge (PZC) potential (EPZC). In addition, the capacitance values are predicted to be approximately 20 μF cm −2 near EPZC and in the highly polarized regions beyond the two humps on the curve; this is also consistent with the experimental results 17 . Theoretical peak behaviors are more exaggerated than those observed in 15 the experiments and this can be attributed to the adiabatic potential change in theory. Indeed, the sharpness of the peaks increases as the potential sweep rate decreases in the experiments 15 .
Therefore, we are now ready to elucidate the microscopic structural details of the EDL, which have been questioned but not fully resolved since the development of the early EDL theories in the 1900s 2 . In particular, we focus on what type of molecular structural response in the EDL is 20 responsible for the two humps in the camel-shaped capacitance curves that have been measured from simple systems, such as the interfaces between planar metal electrodes and dilute aqueous electrolytes 25-34 .

Molecular origin of the camel-shape
The key components of the EDL are water molecules, excess charges stored in the metal electrode, and ions in the electrolyte; all the local profiles of these along the -direction are summarized to illustrate the complete structural details of the EDL in Figure 1d. Hereafter, the 5 -directional distances are referenced relative to the center of the top-surface atoms of the metal electrode.
The local water density profile, wat , shows that two water layers are formed near the electrode at around = 3 Å and 6 Å at all applied potentials, wherein the first layer is significantly adsorbed by the metal electrode (Supplementary Fig. 4). Therefore, it is 10 reasonable to define the location of the inner Helmholtz layer (IHL) with respect to the location of this water adlayer 33 . Further, the ion charge density profile, ion , exhibits a peak at around = 5 Å that is attributed to the solvated ions near the electrode, and it is used to define the location of the outer Helmholtz layer (OHL) 33 . In addition, a region beyond the OHL is a diffuse layer  As widely presumed 37 , when the electrode is negatively charged ( < PZC ), the Na + ions are primarily accumulated at the OHL (Fig. 1d), keeping their first hydration shell intact ( Supplementary Fig. 5) because of their low dispersive attraction toward the electrode 36 , which 5 is shown regardless of choice different water models (Supplementary Fig. 6). The absence of specific adsorption causes almost no change in (Fig. 2a), and therefore, the capacitance hump corresponding to the cathodic potential is primarily attributed to the change in eff .
Upon the negative charging of the electrode, eff increases from 30 to 50, and subsequently decreases to 10, resulting in a peak at around = −10 μC cm −2 (Fig. 2a). For the electrode less 10 negatively charged than −10 μC cm −2 (−10 < < 0 μC cm −2 ), the water molecules at the interface rotate in a collective manner because of the hydrogen bond (HB) interaction via the following mechanism. As the electrode is negatively charged, the water@IHL favors an H-down orientation (see lower left panels of Fig. 2b), in agreement with the findings of the previous in situ sum frequency generation 38 and SHINERS 14 studies. Such a molecular orientation offers an 15 HB accepting O to the water@OHL, leading the water@OHL to favor an H-down orientation and further promoting an H-down orientation of the water@DifL in a similar manner. Because of the cooperative behavior of water dipoles, a surface-normal macroscopic dipole of water layers, ⊥ , concurrently increases in all parts of the EDL (including IHL, OHL, and DifL) for −10 < < 0 μC cm −2 (Fig. 2c), increasing the magnitude of eff . However, the negative charging of the 20 electrode causes an accumulation of cations at the OHL that collapses the HB network formed across the IHL and OHL and therefore, impedes the cooperative rotation of the water dipoles ( Supplementary Fig. 7). Furthermore, the cations accumulated at the OHL cause the nearby water at the OHL and DifL to have an O-down orientation that populates more anti-screening dipoles and thereby, decreases ⊥ at the OHL and DifL (Fig. 2c), decreasing the magnitude of εeff when < −10 μC cm −2 . Notably, this dielectric saturation mechanism is different from the previously suggested and broadly accepted speculations. Unlike the previous assumption that the water at the IHL cannot rotate further and therefore shows no further orientation polarization 5 beyond a critical field strength 30,31 , the water at the IHL can indeed rotate its dipole further to screen the field (see lower right panel of Fig. 2b and Fig. 2c) because such a molecular orientation is accommodated by the cation at the OHL (see lower middle panel of Fig. 2b); nonetheless, the suppressed field-screening ability at the OHL and DifL leads to dielectric saturation. 10

EDL structural phase transition
We now demonstrate how the peak behavior of eff can result in the cathodic hump. For a twoplate capacitor model, the interfacial potential drop is proportional to / eff . Consequently, when 15 eff monotonically increases as | | increases for −10 < < 0 μC cm −2 , as shown in Figure 2a, , can have the same interfacial potential drop. In other words, at the same cathodic potential of , two states with different EDL structures characterized by h and l are bistable (Fig. 3a). Then, the Landau-type free energy density per interfacial area, F, is given as where < 0 for the bistable region, > 0, and the two states have the same when = � , at which � = ( h + l )/2. Using the Landau-Khalatnikov equation 39 , we define the time variation of EDL charging as, where s is the solution phase resistance. Using the equilibrium condition of / = 0, we 5 finally obtain the equilibrium as a cubic equation of , that yields an S-shape in the -plane (black solid line in Fig. 3b). Therefore, the origin of the S-shaped region in Figure 1b is attributed to the bistability of two different surface charge states in the cathodic potential range. Upon decreasing the potential from PZC (by following the red 10 dashed line in Fig. 3b), Landau-type theory predicts that an EDL structural phase transition will occur from the lowly charged phase ( > � ) to the highly charged phase ( < � ) at the mesocopically large electrode-electrolyte interface; furthermore, phase coexistence occurs at = � (Fig. 3c), where the cathodic peak emerges.
Notably, some theoretical models have predicted the emergence of a camel shape in the 15 capacitance 34,40-42 ; thus, it is useful to compare our approach to the previous model. One of the most recent and elaborate EDL models predicting the camel shape is the Kornyshev model 34, [43][44][45][46][47] , which is a lattice-gas model incorporating ion saturation behavior into the Gouy 25 -Chapman 26 theory, where water is coarse-grained as a dielectric. Although our mechanism for the cathodic hump indicates that the key to bistability is orientation polarization of the water molecular 20 dipoles in the EDL, the Kornyshev model ascribes the emergence of the capacitance hump to ion saturation 34 . Thus, a concentrated electrolyte is essential to manifest a camel shape in the Kornyshev model, and in the dilute limit, the results of this model approach those of Gouy 25 -Chapman 26 model. Therefore, the Kornyshev model is suitable for explaining the camel-shaped capacitance measured in a dense Coulomb system such as an ionic-liquid electrolyte 34,43-48 , whereas our mechanism explains the camel-shaped capacitance measured in a dilute aqueous 5 electrolyte [15][16][17][18][19] .

EDL structure and electrocatalysis
To modify the EDL structure near the cathodically polarized electrode, we utilize the strategy of the complexation of Na + with 15-Crown-5 (15C5). Through the DFT-CES simulation, we first 10 identify that the 15C5 complexation prohibits the cation from being stably hydrated by the water at the IHL (Supplementary Fig. 8) that hinders the formation of a compact EDL structure and therefore increases approximately 1.5 times (Fig. 4a and Supplementary Fig. 9). This also increases the interfacial potential drop at the same that shifts the S-shaped region to a more negative potential in the -plane (Supplementary Fig. 10). Consequently, our simulation 15 predicts the negative potential shift of the cathodic hump in the -curve that is also confirmed by our experiments (Fig. 4b).
The increase of leads to a weakened interfacial field when the same potential is applied at the interface (Fig. 4c). Therefore, the EDL structural modification through cation complexation provides an appropriate experimental platform for selectively controlling the field strength with 20 maintaining the same electrode potential 49,50 .
Recently, the mechanistic role of the local electric field in electrocatalytic reactions has been extensively discussed 5,7-9,49-52 . It is suggested that the rate of the electrochemical CO2RR to carbon monoxide (CO), is limited by the CO2 adsorption on the electrode surface, driven by the adsorbate dipole-field interaction 8 . From our CO2RR experiments on Ag(111) with varying 15C5 concentration in the 100 mM NaHCO3 electrolyte, we observe that the CO partial current 5 density, CO , logarithmically decreases with an increasing 15C5 concentration ( Fig. 4d and   Supplementary Fig. 11). We conceive that the macroscopically large EDL has a locally inhomogeneous structure comprising a compact part consisting of uncomplexed cations (with small ) and an uncondensed part consisting of 15C5-complexed cations (with large ); our experimental results indicate that the CO2RR of the compact part of the structure, where the 10 interfacial electric field is more intense, dominates the total activity, and therefore, a linear dependence of the log CO on the ratio of the compact part that is considered to be proportional to the bulk 15C5 concentration, is exhibited. Not only the long-range dipole-field interaction, but also the short-range direct interaction of the cation with the adsorbate CO2 has been highlighted recently 10,53 . Our DFT-CES simulation further revealed that the coordination number of Na + to 15 the adsorbed CO2 decreases from 1.0 to 0.3 when the cation is complexed with 15C5 ( Supplementary Fig. 12). Thus, the decrease in the CO2RR activity can also be explained in terms of the decrease in the coordinating ability of a cation to the adsorbed CO2. In both mechanistic possibilities, our work demonstrates the importance of identifying the EDL structure for controlling the electrocatalytic activity. 20 In summary, we have elucidated the complete structural details of the EDL based on a direct theory-experiment comparison of the EDL capacitance that is an electrochemical signal known to be sensitive to the EDL structure. This study demonstrates the ability to explore the detailed 13 EDL structures based on a combination of the first-principles-based simulation and SPEIS experiments and to further manipulate the electrocatalytic activity by tuning the EDL structure; this lays a foundation for establishing a link between the EDL structure and the electrocatalytic activity at a molecular level, that is a long-standing challenge in the electrochemistry.

DFT-CES simulations
Our mean-field quantum mechanics/molecular mechanics (QM/MM) multiscale simulation, namely, DFT-CES 21 , is implemented in our in-house code that combines the Quantum ESPRESSO 54 density functional theory simulation engine and LAMMPS 55 molecular dynamics 5 simulation engine. Computational details can be found in the Supplementary Note 1.

Electrochemical measurements
Electrochemical measurements were conducted using an SP-150 potentiostat (Bio-Logic). An H- Alfa Aesar) with a volume ratio of 1.5/1 for 3 s, during which vigorous gas evolution occurred 5 and thereafter, it was exposed to air for another 3 s. The Ag electrode was subsequently soaked in a 0.55 M KCN solution until gas evolution ceased, and it was thoroughly washed with ultrapure water. A highly reflective and homogenous surface was obtained after repeating the chemical polishing procedure 10 times. The Ag electrode surface was protected by a droplet of ultrapure water before it was transferred to the electrochemical cell. The differential capacitance 10 was measured through SPEIS. The measurement was performed in a potential range from −1.3 to The electrochemical CO2RR on the Ag(111) electrode was conducted in an H-type customized 15 reactor consisting of separated compartments for the counter/reference and working electrodes, with a Nafion 115 membrane (DuPont). A 100 mM NaHCO3 solution (≥99.7%, Sigma-Aldrich) with and without 15C5 was used as the electrolyte, in which CO2 gas (5N) was continually bubbled at a flow rate of 20 sccm during the CO2RR. A sequential chronoamperometry was conducted for 1 h at each potential in a range from −1.4 to −0.8 V (vs SHE). The reaction 20 products, H2 and CO, were monitored using an online gas chromatograph (GC; YL6500, YL Instrument) equipped with a thermal conductivity detector (TCD) and flame ionization detector (FID). A Carboxen-1000 column (12390-U, Supelco) was used for both TCD and FID, and Ar was used as the reference gas. All the potentials were compensated for IR loss.

DATA AVAILABILITY
All data is available in the main text or the supplementary information.

CODE AVAILABILITY
The DFT-CES code as well as input and output files are available from the corresponding authors upon reasonable request.   The regions shaded pale-yellow correspond to the -range responsible for the humps in the differential capacitance curve. b, Schematics illustrating the structural changes of water molecules and ions upon EDL charging (left panels). Distinct orientational responses of the water dipoles are resolved depending on the layer at which water is located and also depending on whether the ion is coordinated (coord.) or not (uncoord.) (right panels), based on the average cos ( is the angle between the water dipole and the surface 5 normal) that is a function of . Depending on whether the water dipole screens or anti-screens the field, the increasing or decreasing trend of cos is labeled using the arrows with different colors. c, Surface-normal macroscopic dipole moment, ⊥ , of different water layers is shown as a function of , where ⊥ = ∑ cos ∈{IHL,OHL,DifL} ( is the water molecule dipole). with more-aligned water dipoles (that is, large | | and large eff ; h state) and lower charged state with less-aligned water dipoles (that is, small | | and small eff ; l state) are bistable at the same cathodic potential, . b, Phase transition between bistable states, which is modeled using 5 Landau-type theory, yields the S-shaped region, at which the Maxwell tie-line is constructed. c, At the mesoscopically large interface, l state is more populated when > � , forming a lowly charged phase (right panels), and h state is more populated when < � , forming a highly charged phase (left panels). Negative-potential sweep induces a phase transition from the lowly charged phase to the highly charged phase via a phase coexistence at = � . snapshots showing that uncomplexed Na + develops a more direct interaction with the adsorbed CO2 than 15C5-complexed Na + , forming a compact EDL structure with a stronger field. Also, 10 the uncomplexed Na + can easily make a direct coordination to the adsorbed CO2 (*CO2). d, A