Molecular origin of negative component of Helmholtz capacitance at electrified Pt(111)/water interface

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Science Advances  07 Oct 2020:
Vol. 6, no. 41, eabb1219
DOI: 10.1126/sciadv.abb1219


Electrified solid/liquid interfaces are the key to many physicochemical processes in a myriad of areas including electrochemistry and colloid science. With tremendous efforts devoted to this topic, it is unexpected that molecular-level understanding of electric double layers is still lacking. Particularly, it is perplexing why compact Helmholtz layers often show bell-shaped differential capacitances on metal electrodes, as this would suggest a negative capacitance in some layer of interface water. Here, we report state-of-the-art ab initio molecular dynamics simulations of electrified Pt(111)/water interfaces, aiming at unraveling the structure and capacitive behavior of interface water. Our calculation reproduces the bell-shaped differential Helmholtz capacitance and shows that the interface water follows the Frumkin adsorption isotherm when varying the electrode potential, leading to a peculiar negative capacitive response. Our work provides valuable insight into the structure and capacitance of interface water, which can help understand important processes in electrocatalysis and energy storage in supercapacitors.


An electric double layer (EDL) formed at an electrified interface can afford a potential change of a few volts within a very thin layer of 3 to 5 Å (13), amounting to an extremely large electric field of similar strength to that in a particle accelerator. Naturally, one would wonder how solvent molecules such as water or any other reactive species inside the EDL would behave in response to such a strong electric field. Answering this question is not only of fundamental interest but also of technological importance in a broad range of research areas in science and technology, to name a few, energy storage in supercapacitors (4, 5), electrocatalysis of relevance to energy and environmental applications (68), self-assembly of colloidal particles (9), ion transport across biological membranes (10), and mineralization processes in earth science (11). Despite its significance, molecular-level understanding of EDL is largely missing, owing to its complexity and difficulty to probe. Because of the advent of advanced experimental (e.g., synchrotron-based techniques and Raman spectroscopy) and computational methods [e.g., ab intio molecular dynamics (AIMD) (1214)], it is not until recently that the microscopic structures of EDL have started to be unveiled.

One of the key characteristics of EDL is its capacitance measuring the ratio of change in surface charge to potential change, which is accessible by conventional electrochemistry techniques such as voltammetry and impedance spectroscopy. The potential dependence of capacitance, i.e., differential capacitance, led to development of the well-known Gouy-Chapman-Stern (GCS) model of EDL, in which EDL consists of a Helmholtz (compact) layer and Gouy-Chapman (diffuse) layer, acting as two capacitors connected in series (see Fig. 1, A and B). The GCS theory, proposed about 100 years ago, successfully predicts the Gouy-Chapman minima in differential capacitance curves at the dilute limit (15) and remains as, yet, the main conceptual model for EDL. Among many others, one long standing puzzle is how to understand the bell-shaped differential capacitance curve of the Helmholtz layer (15, 16). If representing the Helmholtz layer as capacitors in series, then it is inevitable to introduce negative capacitances for some of the layers (17, 18). Although this is not excluded in principle, it is not satisfactory because of lack of physical underpinning. It was first noted in the 1970s by Trasatti that the Helmholtz capacitances of the simple sp metals correlate with their electronic densities (19). Since then, several theoretical models were proposed in attempts to relate this peculiar phenomenon with electronic effects of metal electrodes (20, 18). For example, applying the jellium model to the sp metals, Schmickler (18) derived negative capacitances from change in surface potentials due to the response of electronic spillover to surface charges. Halley, Price, and colleagues (17, 21) used first principles methods to calculate the capacitance curve of the Cu water interface.

Fig. 1 Structure of electrified Pt(111)/water interface.

(A) Schematic representation of the GCS model of the EDL. The EDL consists of a Helmholtz layer and Gouy-Chapman (diffuse) layer, and the interface potential distribution is shown by the red curve. (B) The EDL capacitance can be represented by the capacitors corresponding to the two layers (i.e., CH and CGC) connected in series. (C) Model of Pt(111)/water interface at PZC. There is significant interface electron redistribution along the surface normal z owing to water chemisorption, as indicated by the blue curve. (D) Profiles of water density (ρH2O) along the surface normal z at different potentials. The positions of water molecules are indicated by those of the oxygen atoms, and the zero in z coordinate indicates the position of the nuclei of the uppermost layer of Pt(111). All the potentials are referenced to the PZC of Pt(111). (E and F) Representative snapshots of the electrified Pt(111)/water interfaces at −0.93 and 0.84 V versus PZC. The Pt, Na, F, O, and H atoms are colored in gray, blue, violet, red, and white, respectively. The chemisorbed water is highlighted with the ball-and-stick model in comparison to other water with the stick model.

Although insightful, these early attempts either completely ignored the metal lattice structures (18) or unrealistically represented the metal electronic structures, e.g., Cu pseudo-potential only treating s valence electrons (21), and, thus, cannot correctly describe the electronic interaction between metals and electrolyte solution. Starting from about three decades ago, chemisorption of molecules has been studied in great depth using new surface science techniques such as scanning tunneling microscopy (STM) and modern density functional theory (DFT) under ultrahigh vacuum conditions. For example, Michaelides and colleagues (2224) studied the detailed microscopic structures of water monomers, clusters, and layers adsorbed on metal surfaces (e.g., Pt) by combining STM and DFT calculation. Very recently, state-of-the-art AIMD simulations have been applied to metal/water interfaces to calculate the interface structures and potentials (2533). Notably, Cheng and colleagues (25) accurately computed the potentials of zero charge (PZC) of several transition metals and found that charge redistribution due to water chemisorption (see Fig. 1C) can induce substantial interface dipole potentials at PZC conditions, e.g., on the order of ∼1 V on Pt (34). The question then arises: Will the water chemisorbed on metal surfaces contribute to the capacitative response of EDL when a bias is applied?

Aiming at unraveling the molecular origin of the Helmholtz capacitance, in this work, we perform extensive AIMD simulations of electrified Pt(111)/water interfaces and calculate the electrode potentials using the recently developed computational standard hydrogen electrode (cSHE) method as a function of surface charge densities. We reproduce the bell-shaped differential capacitance curve, and detailed analyses show that the surface coverage of chemisorbed water can vary with the applied potential. Our calculation demonstrates that the adsorption/desorption processes of surface water with varying potentials give rise to the negative component of the Helmholtz capacitance. We further propose a theoretical model based on the Frumkin adsorption isotherm that can well describe our calculated results. Our work highlights the importance of the molecular-level picture and electronic structure of EDL for understanding the capacitive behavior of the interface water.


Structure of interface water

As illustrated in fig. S1, a series of electrified Pt(111)/water interface models have been built at different surface charge densities (σ), in which the surface charges are compensated by counter ions, i.e., Na+ or F, located at the outer Helmholtz planes. Note that our EDL models do not account for the Gouy-Chapman layer and, therefore, correspond to high concentration conditions.

The simulation cells are kept charge neutral, and the surface charge densities are controlled by the number of counter ions added in the cells. Detailed descriptions on the models are given in Materials and Methods section, and charge distribution plots in fig. S2 show where the charges are located at the electrified interfaces. These models are simulated using AIMD for first equilibration and then production of data, and the corresponding electrode potentials versus SHE can be obtained from these AIMD trajectories using the cSHE method [see the Supplementary Materials and (25, 35, 36) for detailed explanation on the methodology]. We have successfully applied the same method to the Au(111)/water interface for elucidating the molecular structure of water inside the Helmholtz layer at negative bias (12).

These models cover a potential window ranging from −0.93 to 0.84 V with respect to the PZC of Pt(111) [i.e., 0.2 to 0.3 V versus SHE (25, 3740)], which enables us to investigate the water structure and capacitance of the Helmholtz layer on Pt(111). It is worth mentioning that, in this work, we ignore the specific adsorption of H and OH, which amounts to the pH conditions when specific adsorption is insignificant, and the experimental capacitances we compare against are removed with pseudo-capacitances due to specific adsorption (4143).

Detailed analyses of the AIMD trajectories show that the density and orientation of the interface water are strongly dependent on the applied potential and the profiles of water density (ρH2O) and orientation distribution, indicated by the angle φ between the bisector of water and the surface normal and the angle θ between the O─H bond of water and the surface normal, are illustrated in Fig. 1 and Fig. 2 (A and B), respectively. Note from the density profiles that there are two distinct peaks of interface water in the Helmholtz layer (z < ∼4 Å, where z is the distance from the surface); one peak at z = 2.3 Å corresponds to the water directly chemisorbed on the surface, and the other at z = 3.3 Å represents the nonchemisorbed water in the Helmholtz layer. This finding of two layers of interface water is also in line with the understanding from the work of Feliu and co-workers (44) on Pt(111). At the very negative potential of −0.93 V, there is no water chemisorbed on the surface due to Coulombic repulsion, and thereby, the first peak at z = 2.3 Å disappears. All the water molecules in the Helmholtz layer take a “one-H-down” configuration with one hydrogen atom pointing to the metal surface (see Fig. 1E), and the hydrogen bond analysis shown in Fig. 2C indicates that the other hydrogen of the one-H-down water forms a hydrogen bond with the neighboring water, similar to those observed on Au(111) at negative bias (12). This type of water features φ peaked at ~135° and θ at ~90° and ~165° in the orientation distribution profile of Fig. 2 (A and B). As the potential increases, the interface water starts to adsorb on the surface, leading to gradual increase in the intensity of the first peak and decrease in the second peak at z = 3.3 Å in the water density profile of Fig. 1D. At the very positive potential of 0.84 V, almost all the water molecules in the Helmholtz layer are chemisorbed on the surface, approaching to the saturated coverage of ∼0.5 monolayer (ML). As shown in Fig. 1F and Fig. 2 (A and B), the chemisorbed water sits on the top site of Pt(111), with its molecular plane nearly paralleled to the surface and two hydrogen atoms slightly tilting up, and the orientation takes φ peaked at ~60° and both θ at ~75°. Moreover, it is revealed from Fig. 2C that at very positive potentials, each chemisorbed water accepts approximately one hydrogen bond from the neighboring chemisorbed water, indicating the formation of a two-dimensional (2D) hydrogen bond network on Pt(111). The 2D hydrogen bond network benefits from the matching of the hydrogen bonds between chemisorbed water and the underlying Pt lattice (both being ∼2.8 Å) and helps stabilize the structure of chemisorbed water at positive potentials.

Fig. 2 Orientation and hydrogen bonding of interface water.

Probability distribution profiles of angle φ (A) between the bisector of water and the surface normal and angle θ (B) between the O─H bond of water and the surface normal of the interface water at different applied potentials. Both angles are shown in the insets, and the interface water is taken as being within 4 Å̊ from the metal surface. The potentials are referenced to the PZC of Pt(111). (C) Number of hydrogen bond donors (pink circle) and acceptors (green diamond) of interface water molecules as a function of potential. A hydrogen bond is defined when the O─O distance is shorter than 3.5 Å and the O─O─H angle is less than 35°. The insets show the structural models of interface water at very negative and positive potentials. a.u., arbitrary units.

Capacitance of interface water

As mentioned above, a small fraction of ML of chemisorbed water at PZC can induce a significant interface potential (∼1 V) on Pt (25, 45, 46). It can, thus, be conceived that the observed potential dependence of surface coverage of chemisorbed water may have direct impact on the capacitive response of interface water. A simple model in Fig. 3 can be proposed to demonstrate this effect. The interface potential change (Δψ) across the Helmholtz layer can be decomposed into two parts, namely, the usual potential change induced by the surface charge (Δψsol) and the potential due to water chemisorption (ΔψA). At PZC, the surface charge is zero, and thus, Δψsol = 0. Whereas, there is a remaining contribution from ΔψA due to water chemisorption (see Fig. 3B) (25). Since the electron density transfers from water to Pt, ΔψA will lead to a negative shift of the electrode potential. At a potential much more negative than PZC (Fig. 3A), all chemisorbed water desorbs from the surface, indicating that ΔψA = 0 and only Δψsol contributes to the overall Δψ. At a potential more positive than PZC (Fig. 3C), both Δψsol and ΔψA are finite but with opposite signs and, thus, compensate each other to give a smaller overall Δψ. This qualitative analysis shows that involving the ΔψA term due to chemisorbed water can give a smaller potential change and, thus, an increased capacitance. When the surface charge changes from negative to positive, more water is adsorb on the surface, and ΔψA shifts to more negative (opposite to Δψsol), thereby implying a negative capacitance.

Fig. 3 Proposed model of Helmholtz layer.

Potential profiles at the Pt(111)/water interface at different applied potentials (A) <PZC without water chemisorption, (B) PZC, and (C) >PZC. The Pt electrode and water solution are the regions colored by gray and light blue, respectively. The balls in red, white, blue, and violet stand for oxygen atoms, hydrogen atoms, cations, and anions, respectively. The interface potential change ∆ψ (blue) consists of the usual potential change Δψsol induced by the surface charge (green) and the potential ∆ψA caused by water chemisorption (red). The potential in bulk solution is set to zero. lA and lH denote the distance separation of the dipole induced by chemisorbed water and Helmholtz layer, respectively.

To further show a quantitative picture, we plot the surface charge density σ and the coverage of chemisorbed water θA as a function of the electrode potential U, as illustrated in Fig. 4. It is clear that the σ − U plot is nonlinear and shows an S-shaped relation, which implies a bell-shaped differential capacitance CH of the Helmholtz layer. The θA − U plot is also S-shaped, which is familiar from adsorption isotherms. Since chemisorbed water can induce interface dipole and, thus, must repel with each other, the water adsorption/desorption process upon charging would follow the Frumkin adsorption isotherm (47). We thus adopt this isotherm to formulate the capacitative behavior of the Helmholtz layer on Pt, and detailed derivation of the relations of σ, U, and θA is given in the Supplementary Materials. In our formalism, we assume that the electronic dipole of chemisorbed water is independent of the electrode potential, but note that the chemisorption-induced dipole should be generally polarizable in the presence of an electric field (48). The polarizable effect, however, is small in our case, and moreover, the electric field due to surface charge is compensated by the lateral dipole-dipole interaction between chemisorbed water (see section S4).

Fig. 4 AIMD data and model fitting.

Plots of surface charge density σ (A) and surface coverage of chemisorbed water θA (B) as a function of the electrode potential U. The solid dots with error bars represent the computed data from AIMD simulations, and the black curves are the corresponding fits using the proposed theoretical model. The convergence of the computed U and the corresponding θA can found in figs. S3 and S7. The insets in (A) show the representative configurations of the chemisorbed water on Pt(111) at −0.93 V, PZC, and 0.84 V, respectively. The dashed lines in (B) indicate the respective θA at PZC and ∼0.1 V. The potentials are referenced to the PZC (UPZC).

As can be seen in Fig. 4 and fig. S8, the fitted curves (black) can very well describe the computed data. On the basis of the fitted curves, we find that CH shows a maximum of ∼100 μF/cm2 at a potential slightly more positive (∼0.1 V) than the PZC, and it decays to ∼20 μF/cm2 when the electrode potential moves away from the PZC. Most of the features of the CH (blue curve in Fig. 5) are very similar to the experimental differential capacitance curves (4143). It is worth mentioning that the comparison is more informative near the double layer region as, for example, significant specific adsorption of H outside this region could result in narrowing of the CH peak (42).

Fig. 5 Capacitance of the Helmholtz layer.

Decomposition of differential Helmholtz capacitance CH (blue) as a function of electrode potential U into two constituent components, the solvent capacitance Csol (green) and the capacitance CA (red) due to water chemisorption. The inset indicates that Csol and CA are connected in series. The potential window (∼0.2 V) of the double layer region of the Pt(111)/water interface at pH 4 is highlighted by light blue (38).

We also derive a theoretical model consisting of two capacitors in series for representing the Helmholtz capacitance (CH). In this model, one component, denoted by Csol, corresponds to the usual dielectric response of solvent in the Helmholtz layer, and the fitted value is ∼20 μF/cm2, closely resembling the Helmholtz capacitance on inert metals such as Hg. The other component CA accounts for the effect of water chemisorption. The obtained value of CA is negative, with the maximum around the PZC, as shown in Fig. 5. Connecting the two capacitors (Csol and CA) can give rise to the bell-shaped profile of CH. From the formula of CA (i.e., eq. S16), we note that CA reaches maximum when the θA is equal to the half of the maximum coverage of the chemisorbed water on Pt(111), i.e., ∼0.25 ML. As shown in Fig. 4B, the corresponding potential is ∼0.1 V versus PZC, and the θA at PZC is ∼0.16 ML. This explains why the potential corresponding to the CH maximum is slightly more positive than the PZC on Pt (41, 42).


Our calculation and proposed model clearly show that the peak of differential capacitance CH is caused by water chemisorption, leading to a negative capacitance CA. The magnitude of the latter depends strongly on the dipole of chemisorbed water on the metal surface (see eq. S10) and, thus, the binding strength of water. This may help rationalize the trend of the Helmholtz capacitance on other transition metals [e.g., Au and Ag (49, 50)] and sd metals [e.g., Hg (15)]; for example, the maximum of CH on Pt is more pronounced than those on Au and Hg. Moreover, our results suggest that incorporation of solvent chemisorption on electrodes could offer a new strategy for enhancing the double layer capacitance for energy storage in supercapacitors. Our new model also reveals detailed changes in solvation environment at interfaces under different potentials, which would be of close relevance to electrocatalytic reactions (e.g., hydrogen evolution, oxygen reduction, and CO2 reduction) occurring inside the Helmholtz layers.

To summarize, we investigate the Helmholtz layer at the Pt(111)/water interfaces at different potential conditions using AIMD calculation. The focus is to reveal the molecular structure of interface water and the response to the electric field in the Helmholtz layer. We find that the surface coverage of chemisorbed water increases when shifting the potential from negative to positive. As chemisorbed water can induce a significant interface dipole potential, change in its coverage will lead to a potential change and, hence, a negative capacitive response. Combining with the normal dielectric response of the solvent, we can obtain the experimentally observed bell-shaped differential capacitance of the Helmholtz layer. Our work demonstrates the importance of water chemisorption on metal electrodes to the EDL capacitance and, thus, sheds new light on the relationship between the molecular structure and capacitative behavior of interface water. Furthermore, our finding lays the foundation for future exploration of tuning electronic interactions between electrodes and electrolyte solutions for optimizing the performances of energy materials in electrocatalysis and supercapacitors.


Models of electrified Pt(111)/water interfaces

The Pt(111) surface was modeled with a p(4 × 4) periodic slab of four atomic layers. The vacuum space between the slab and its periodic images is 21 Å and fully filled with water molecules. The cell contains 64 Pt atoms and 68 water molecules with the size of 11.246 Å × 11.246 Å × 27.887 Å. The metal work function and the PZC of this model, as reported in (25), are close to the experimental values (3840, 51). The electrified Pt(111)/H2O interfaces were modeled by inserting Na+ or F ions near the Pt(111) surface. Note that Na+ and F ions do not specifically adsorb on Pt(111), thus forming the outer Helmholtz plane, and at the time scale of AIMD, these ions do not diffuse away into the bulk water. All the models are charge neutral, and the electronic structures of the interfaces are optimized to generate double layers with ions and charged surfaces with opposite signs. The charges of ions in the models are evidenced by the calculated projected density of states, as shown in fig. S5. Varying the number of Na+ or F in the model amounts to controlling the surface charge density and, hence, the electrode potential. Using this approach, six electrified Pt(111)/water interfaces were constructed with the surface charge density of −43.8, −29.2, 14.6, 29.2, 43.8, and 58.4 μC/cm2. The densities of the bulk water in these models were kept close to 1 g/cm3. These models contain two symmetrical interfaces, and therefore, the net dipoles of these models are canceled, as illustrated in the averaged electrostatic potential profiles in fig. S4. The electrode potentials of the electrified interface models were calculated with the cSHE method (25). Note that Gouy-Chapman layers are not included in the interface models, and thus, our EDL models correspond to the high concentration limit where the surface charges are effectively screened within the Helmholtz layer. Co-ions are also omitted in our models, which may not affect our study on the water structure and capacitance of the Helmholtz layer since our EDL models have the correct charge excess. It is worth mentioning that the same model setup was successfully used in elucidating the structure of the Helmholtz layer on Au (12).

Computational setup

The AIMD simulations were performed using the freely available CP2K/Quickstep package (52). The DFT implemented in CP2K is based on a hybrid Gaussian plane wave scheme. The orbitals are described by an atom-centered Gaussian-type basis set, and an auxiliary plane wave basis set is used to reexpand the electron density in the reciprocal space. The 2s and 2p electrons of O; 2s, 2p, and 3s electrons of Na; 2s and 2p electrons of F; and 5d and 6s electrons of Pt are treated as valence, and the rest core electrons were represented by Goedecker-Teter-Hutter pseudo-potentials (53, 54). The Gaussian basis sets were double ζ with one set of polarization functions (55), and the energy cutoff was set to 400 rydbergs. We used the Perdew-Burke-Ernzerhof functional (56) to describe exchange-correlation effects, and the dispersion correction was applied in all calculations with the Grimme D3 method (57). Because of the large size of the cells, only the Γ point in the reciprocal space was used in our calculations. The second-generation Car-Parrinello molecular dynamics (SGCPMD) (58, 59) was used for sampling structures of the interface models, and the target temperature was set to 330 K. The correction step was obtained by five iterations of the orbital transformation optimization (60), and the integration time for each step was 0.5 fs. The Langevin friction coefficient (γL) was set to 0.001 fs−1, and the intrinsic friction coefficient (γD) was varied, i.e., 5 × 105 fs−1 for Pt and 2.2 × 104 fs−1 for H2O and ions. More details on the SGCPMD setup can be found in (59). For each AIMD simulation, an initial ∼5 ps (∼10,000 steps) of molecular dynamics trajectory was used to equilibrate the system and then followed by a production period of more than 15 ps.


Supplementary material for this article is available at

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Acknowledgments: We thank J. Lan and M. Iannuzzi for technical support on CP2K and setup of the SGCPMD, and J. Feliu, M. T. M. Koper, J. Lipkowski, and C. Amatore for helpful discussion. Funding: J.C. is grateful for funding support by the National Natural Science Foundation of China (grant nos. 21991151, 21861132015, and 21621091) and the Principal’s Fund of Xiamen University (20720190047). J.-B.L. thanks for the funding from the National Natural Science Foundation of China (grant no. 21902136) and the China Postdoctoral Science Foundation (2018M642563). Author contributions: J.C. and J.-B.L. conceived and designed the project and wrote the manuscript. J.-B.L. performed the calculation, and J.-B.L., J.C., Q.-Y.F., and J.-Q.L. analyzed the results. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

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