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

In many fields, including electrochemistry and colloidal science, the electrified solid/liquid interface is the key to many physical and chemical processes. With great efforts dedicated to this topic, unexpectedly, there is still a lack of understanding of the molecular level of the electric double layer. It is particularly confusing why the dense Helmholtz layer often shows a bell-shaped differential capacitance on the metal electrode, because this would imply that the capacitance in some layers of the interface water is negative. Here, we report a state-of-the-art ab initio molecular dynamics simulation of a charged Pt(111)/water interface, aiming to reveal the structure and capacitive behavior of the interface water. Our calculations reproduce the bell-shaped Helmholtz differential capacitance and show that when the electrode potential is changed, the interface water follows the Frumkin adsorption isotherm, resulting in a special negative capacitance response. Our work provides valuable insights into the structure and capacitance of interface water, which can help you understand the important processes of electrocatalysis and energy storage in supercapacitors.

The electric double layer (EDL) formed on the charged interface can provide a potential change of several volts in a very thin layer of 3 to 5 Å (

-

), which is equivalent to a very large electric field, and its intensity is similar to that in a particle accelerator. Naturally, people will want to know how solvent molecules such as water or any other reactive molecules inside the EDL will behave in response to such a strong electric field. Answering this question is not only of fundamental significance, but also of technical importance in a wide range of scientific and technological research fields, to name a few, namely, energy storage in supercapacitors (

,

), electrocatalysis related to energy and environmental applications (

), self-assembly of colloidal particles (

), the transport of ions across biological membranes (

), and the mineralization process in earth science (

). Despite its important significance, due to its complexity and difficulty in exploring EDL, the understanding of EDL at the molecular level has been greatly lacked. Due to advanced experimental methods (such as synchrotron-based technology and Raman spectroscopy) and computational methods (such as ab initio molecular dynamics (AIMD),

)], only recently began to reveal the microstructure of EDL.

One of the key characteristics of EDL is that its capacitance can measure the ratio of surface charge change to potential change, which can be obtained by conventional electrochemical techniques (such as voltammetry and impedance spectroscopy). The potential dependence of the capacitance, the differential capacitance, led to the development of the well-known EDL Gouy-Chapman-Stern (GCS) model, where the EDL is composed of a Helmholtz (compact) layer and a Gouy-Chapman (diffusion) layer, used as two series connected Capacitor (see

). The GCS theory proposed about 100 years ago successfully predicted the Gouy-Chapman minimum value in the differential capacitance curve at the limit of dilution (

), and is still the main conceptual model of EDL. Among other things, a long-standing problem is how to understand the bell-shaped differential capacitance curve of the Helmholtz layer (

). If the Helmholtz layer is expressed as a series capacitor, then negative capacitance will inevitably be introduced to some layers (

). Although this is not ruled out in principle, it is not satisfactory due to the lack of physical foundation. Trasatti first noticed in the 1970s that simple Helmholtz capacitors

Metal is related to its electron density (

). Since then, several theoretical models have been proposed to try to link this special phenomenon with the electronic effects of metal electrodes (

). For example, applying the jellium model to

Metal, Schmickler (

) Is the negative capacitance caused by the surface potential change caused by the overflow of electrons in response to the surface charge. Halle, Price and colleagues (

) Use the first principles method to calculate the capacitance curve of the copper-water interface.

(

) Schematic diagram of EDL's GCS model. EDL is composed of Helmholtz layer and Gouy-Chapman (diffusion) layer, and the interface potential distribution is represented by the red curve. (

) EDL capacitance can be represented by capacitors corresponding to two layers (ie,

with

) Concatenation. (

) Pt(111)/water interface model of PZC. There is a significant redistribution of interface electrons along the surface normal

Due to the chemical adsorption of water, as shown by the blue curve. (

) Water density distribution (ρ

) Along the surface normal

In different potentials. The position of the water molecule is indicated by the position of the oxygen atom, where zero means

The coordinates indicate the position of the top nucleus of Pt(111). All potentials refer to PZC of Pt (111). (

) Typical snapshots of the charged Pt(111)/water interface relative to PZC at −0.93 and 0.84 V. Pt, Na, F, O and H atoms are colored in gray, blue, purple, red, and white, respectively. Compared with the bat model, the bat model highlights the chemically adsorbed water.

Although very insightful, these early attempts either completely ignored the metal lattice structure (

) Or impractically represent the electronic structure of the metal, such as using only copper pseudo-potential treatment

Valence electron (

), so the electronic interaction between the metal and the electrolyte solution cannot be described correctly. Since about thirty years ago, new surface science technologies, such as scanning tunneling microscope (STM) and modern density functional theory (DFT), have been used in ultra-high vacuum conditions to conduct in-depth research on molecular chemical adsorption. For example, Michaelides and colleagues (

) The detailed microstructures of water monomers, clusters and layers adsorbed on metal surfaces (such as Pt) have been studied by combining STM and DFT calculations. Recently, the most advanced AIMD simulation has been applied to the metal/water interface to calculate the interface structure and potential (

). It is worth noting that colleague Zheng He (

) Accurately calculated the zero charge (PZC) potential of several transition metals, and found that the charge redistribution caused by the chemical adsorption of water (see

) A large number of interface dipole potentials can be induced under PZC conditions, for example, about ~1 V on Pt (

). Then a question arises: When a bias voltage is applied, will water chemically adsorbed on the metal surface contribute to the capacitive response of the EDL?

In order to reveal the molecular origin of Helmholtz capacitance, in this work, we performed extensive AIMD simulations on the charged Pt(111)/water interface and calculated electrodes using the recently developed calculation standard hydrogen electrode (cSHE) method Potential, calculate the surface charge density. We reproduced the bell-shaped differential capacitance curve and performed a detailed analysis. The results showed that the surface coverage of chemisorbed water may vary with the applied potential. Our calculations show that the adsorption/desorption process of surface water with different potentials will cause the negative component of Helmholtz capacitance. We further proposed a theoretical model based on Frumkin adsorption isotherm, which can describe our calculation results well. Our work emphasizes the importance of EDL molecular-level pictures and electronic structure for understanding the capacitive behavior of interface water.

as the picture shows. S1, a series of charged Pt(111)/water interface models are established under different surface charge densities (σ), in which the surface charge is compensated by the counter ion, namely Na

Or F

, Located on the outer Helmholtz plane. Please note that our EDL model does not consider the Gouy-Chapman layer and therefore corresponds to high concentration conditions.

The analog cell maintains charge neutrality, and the surface charge density is controlled by the number of counterions added to the cell. For a detailed description of these models, see the "Materials and Methods" section, as well as the charge distribution diagram in Figure 6. S2 shows the location of the charge at the electrical interface. Use AIMD to simulate these models first, then perform data balancing, and then use the cSHE method to obtain the corresponding electrode potential and SHE relationship from these AIMD trajectories [see Supplementary Materials and (

) For a detailed description of the method]. We have successfully applied the same method to the Au(111)/water interface to clarify the molecular structure of water in the Helmholtz layer under negative bias (

).

The PZC of these models relative to Pt(111) covers a potential window range of -0.93 to 0.84 V [ie, 0.2 to 0.3 V relative to SHE (

)], which allows us to study the water structure and capacitance of the Helmholtz layer on Pt(111). It is worth mentioning that in this work, we ignored the specific adsorption of H and OH. When the specific adsorption is insignificant, this is equivalent to pH conditions. The experimental capacitance we compared was removed by the pseudo capacitance due to specific adsorption (

A detailed analysis of the AIMD trajectory shows that the density and direction of the interfacial water largely depend on the applied potential and the distribution of water density (ρ

) And direction distribution, represented 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

, Respectively. Note from the density distribution map that there are two different interface water peaks in the Helmholtz layer (

<~4Å, where

Is the distance to the surface); at a peak

= 2.3Å corresponds to water chemically adsorbed directly on the surface, the other corresponds to

= 3.3Å represents the unchemically adsorbed water in the Helmholtz layer. The discovery of water at the two-layer interface is also in line with the understanding of Fei Liu and his colleagues (

) On Pt(111). At a very negative potential of -0.93 V, there is no water chemically adsorbed on the surface due to Coulomb repulsion, so the first peak is

= 2.3Å disappears. All water molecules in the Helmholtz layer are in a "one hydrogen down" configuration, with one hydrogen atom pointing towards the metal surface (see

), the hydrogen bond analysis is shown in the figure

It means that one hydrogen forms a hydrogen bond with another hydrogen in the water and nearby water, which is similar to the hydrogen bond observed on Au (111) under negative bias (

). This type of water is characterized by the φ peak in the orientation distribution curve of φ at ~135° and the θ peak at ~90° and ~165°.

. As the potential increases, the interface water begins to adsorb on the surface, causing the intensity of the first peak to gradually increase, while the intensity of the second peak

= 3.3Å in the water density curve

. Under a positive potential of 0.84 V, almost all water molecules in the Helmholtz layer are chemically adsorbed on the surface, reaching a saturation coverage of about 0.5 monolayer (ML). as the picture shows

, The chemically adsorbed water is located on the top of Pt(111), its molecular plane is almost parallel to the surface, and the two hydrogen atoms are slightly inclined upward, the φ peak of orientation is at ~60°, and the two θ are both at ~75°. And, from

Under a very positive potential, each chemically adsorbed water accepts about one hydrogen bond from the adjacent chemically adsorbed water, indicating that a two-dimensional (2D) hydrogen bond network is formed on Pt(111). The 2D hydrogen bond network benefits from the hydrogen bond matching between the chemisorbed water and the underlying Pt lattice (both 2.8 A), which helps stabilize the structure of the chemisorbed water at a positive potential.

Angle φ (

Between the bisector of water and the surface normal and the angle θ)

) The distance between the OH bond of water and the surface normal of the interface water under different applied potentials). The illustration shows two angles, the interface water is within 4 angstroms of the metal surface. The potential refers to PZC of Pt (111). (

) The relationship between the number of hydrogen bond donors (pink circles) and acceptors (green diamonds) of the interface water molecules and the potential. When the OO distance is less than 3.5Å and the OOH angle is less than 35°, it is defined as a hydrogen bond. The illustration shows the structural model of interface water at very negative and positive potentials. au, arbitrary unit.

As mentioned above, a small part of the chemically adsorbed water of PZC can generate a significant interface potential (~1 V) on Pt (

). Therefore, it can be considered that the observed potential dependence of the surface coverage of chemisorbed water may directly affect the capacitance response of the interface water. A simple model

Can be proposed to prove this effect. The interface potential change (Δψ) of the entire Helmholtz layer can be decomposed into two parts, that is, the usual potential change (Δψ) caused by surface charges

) And water chemical adsorption (Δψ

). At PZC, the surface charge is zero, so Δψ

=0. And Δψ still has a remaining contribution

Due to the chemical adsorption of water (see

) (

). Since the electron density is transferred from water to Pt, Δψ

Will cause a negative shift in electrode potential. Potential is much worse than PZC (

), all chemically adsorbed water will desorb from the surface, indicating that Δψ

= 0 and only Δψ

Contribute to the total Δψ. Has a more positive potential than PZC (

), both Δψ

And Δψ

Is limited, but the signs are opposite, so they can compensate each other to get a smaller overall Δψ. Qualitative analysis shows that Δψ is involved

The "long-term" term due to chemically adsorbed water may produce smaller changes in potential, thereby increasing capacitance. When the surface charge changes from negative to positive, more water is adsorbed on the surface, and Δψ

Move to a larger negative number (as opposed to Δψ)

), thereby implying negative capacitance.

The potential distribution at the Pt(111)/water interface under different applied potentials (

)

) PZC and (

)> PZC. The Pt electrode and the aqueous solution are the areas colored by gray and light blue, respectively. The red, white, blue and purple balls represent oxygen atoms, hydrogen atoms, cations and anions respectively. The interface potential change ∆ψ (blue) is composed of the usual potential change ∆ψ

Induced by surface charge (green) and electric potential Δψ

Caused by water chemisorption (red). The potential in the bulk solution is set to zero.

Respectively indicate the distance separation of the dipole caused by the chemically adsorbed water and the Helmholtz layer.

In order to further show the quantitative image, we plot the surface charge density σ and the coverage θ of chemisorbed water

Function of electrode potential

,as the picture shows

. Obviously, σ-

The graph is non-linear and shows an S-shaped relationship, which means that the bell-shaped differential capacitor

Helmholtz layer. θ

The curve is also S-shaped, which is familiar to adsorption isotherms. Since chemically adsorbed water will cause interface dipoles, they must repel each other, so the water adsorption/desorption process after charging will follow the Frumkin adsorption isotherm (

). Therefore, we use isotherms to formulate the capacitance behavior of the Helmholtz layer on Pt, and derive the relationship of σ in detail,

And θ

Given in the supplementary material. In formalism, we assume that the electronic dipole of chemically adsorbed water has nothing to do with the electrode potential, but please note that the chemically induced dipole should usually be polarized in the presence of an electric field (

). However, in our case, the effect of the polarizability is very small, and due to the lateral dipole-dipole interaction between the chemically adsorbed water, the electric field caused by the surface charge is compensated (see section S4) .

Surface charge density σ(

) And the surface coverage of chemically adsorbed water θ

(

) As a function of electrode potential

. The solid points with error bars represent the calculated data of AIMD simulation, and the black curve is the corresponding fit using the proposed theoretical model. Computational convergence

Corresponding θ

Can be found in figs. S3 and S7. The illustrations in (A) show the representative configurations of chemically adsorbed water on Pt(111) at -0.93 V, PZC and 0.84 V, respectively. The dotted lines in (B) indicate their respective θ

At PZC and ~0.1 V. The potential is PZC (

As can be seen

And figure. S8, the fitted curve (black) can describe the calculated data well. According to the fitted curve, we find

Maximum display is ~100μF/cm

The potential is slightly higher than PZC (~0.1 V), then attenuates to ~20μF/cm

When the electrode potential is removed from PZC. Most features

(Blue curve

) Very similar to the experimental differential capacitance curve (

). It is worth mentioning that the comparison is more useful in the vicinity of the double-layer region, for example, outside this region, the significant ratio of H adsorption may cause the narrowing of H.

peak(

Decomposition of differential Helmholtz capacitance

(Blue) as a function of electrode potential

Divided into two components, solvent capacitor

(Green) and capacitance

(Red) Due to chemical adsorption of water. The illustration shows

Connected in series. The potential window (~0.2 V) of the double-layer region of the Pt(111)/water interface at pH 4 is light blue (

We also derived a theoretical model consisting of two capacitors connected in series to represent Helmholtz capacitance (

). In this model, use

, Corresponding to the usual dielectric response of the solvent in the Helmholtz layer, the fitted value is ~20μF/cm

, Very similar to Helmholtz capacitors on inert metals such as mercury. Other ingredients

Explain the role of water chemical adsorption. Obtained value

Is negative, the maximum value is near PZC, as shown in the figure

. Connect two capacitors (

) Can produce bell-shaped contours

. From the formula

(Ie equation S16), we notice

When θ reaches its maximum

It is equal to half of the maximum coverage of chemically adsorbed water on Pt(111), which is 0.25 ML. as the picture shows

, Relative to PZC, the corresponding potential is ~0.1 V, θ

Approximately 0.16 ML in PZC. This explains why the potential corresponds to

The maximum value is slightly positive than PZC on Pt (

Our calculations and the proposed model clearly show that the peak value of the differential capacitance

Caused by the chemical adsorption of water, leading to negative capacitance

. The size of the latter depends to a large extent on the dipole that chemically adsorbs water on the metal surface (see equation S10) and therefore also depends on the binding strength of water. This may help rationalize other transition metals such as Au and Ag(

) And sd metal [for example, mercury (

)]; For example, max

The content of platinum is higher than that of gold and mercury. In addition, our results indicate that the incorporation of solvent chemical adsorption on the electrodes can provide a new strategy for enhancing the energy storage double-layer capacitance in supercapacitors. Our new model also reveals detailed changes in the solvation environment at the interface at different potentials, which are closely related to electrocatalytic reactions such as hydrogen release, oxygen reduction and carbon monoxide.

Reduction) occurs inside the Helmholtz layer.

In summary, we used AIMD calculations to study the Helmholtz layer at the Pt(111)/water interface under different potential conditions. The focus is to reveal the molecular structure of the interface water and the response to the electric field in the Helmholtz layer. We found that when the potential is shifted from negative to positive, the surface coverage of chemisorbed water increases. Since the chemically adsorbed water can induce a significant interface dipole potential, the change in its coverage will result in a change in the potential, leading to a negative capacitance response. Combined with the normal dielectric response of the solvent, we can obtain the experimentally observed Helmholtz layer's bell-shaped differential capacitance. Our work proves the importance of the chemical adsorption of water on the metal electrode to the capacitance of the EDL, thus providing a new idea for the relationship between the molecular structure of the interface water and the capacitance behavior. In addition, our findings lay the foundation for future exploration of adjusting the electronic interaction between electrodes and electrolyte solutions to optimize the performance of energy materials in electrocatalysis and supercapacitors.

Pt (111) surface

(4×4) Periodic slab of four atomic layers. The vacuum space between the plate and its periodic image is 21 Å and is filled with water molecules. The battery contains 64 Pt atoms and 68 water molecules, with a size of 11.246Å×11.246Å×27.887Å. The metal work function and PZC of the model, such as (

), close to the experimental value (

). Charged Pt(111)/H

The O interface is modeled by inserting Na

Ions near the surface of Pt(111). Pay attention to that

And F

Ions are not specifically adsorbed on Pt(111), so the outer Helmholtz plane is formed, and on the AIMD time scale, these ions will not diffuse into a large amount of water. All models are charge-neutral, and the electronic structure of the interface is optimized to generate double layers with ions and charged surfaces with opposite signs. The charge of the ions in the model is proved by the calculated expected state density, as shown in Figure 2. S5. The amount of Na changes

The "α" in this model is equal to controlling the surface charge density, thereby controlling the electrode potential. Using this method, six charged Pt(111)/water interfaces were constructed with surface charge densities of -43.8, -29.2, 14.6, 29.2, 43.8 and 58.4μC/cm

. The bulk water density in these models remains close to 1 g/cm

. These models contain two symmetrical interfaces, so the net dipoles of these models are cancelled out, as shown in the average electrostatic potential curve in Figure 2. S4. Use the cSHE method to calculate the electrode potential of the charged interface model (

). Please note that the Gouy-Chapman layer is not included in the interface model. Therefore, our EDL model corresponds to the high concentration limit under which the surface charge in the Helmholtz layer is effectively shielded. In our model, Co ions are also omitted, which may not affect our research on the water structure and capacitance of the Helmholtz layer, because our EDL model has the correct charge excess. It is worth mentioning that the same model setup has been successfully used to clarify Au (

AIMD simulation uses the freely available CP2K/Quickstep software package (

). The DFT implemented in CP2K is based on a mixed Gaussian plane wave scheme. The orbit is described by the Gaussian basis set with the atom as the center, and the auxiliary plane wave basis set is used to expand the electron density in the reciprocal space. The 2s and 2p electrons of O; the 2s, 2p and 3s electrons of Na; the 2s and 2p electrons of F; the 5d and 6s electrons of Pt are regarded as valences, and the remaining core electrons are determined by the Goedecker-Teter-Hutter pseudopotential (

). The Gaussian set is double ζ, with a set of polarization functions (

), the energy cut-off value is set to 400 Redberg. We used the Perdew-Burke-Ernzerhof function (

) To describe exchange-related effects, and the Grimme D3 method is used in all calculations for dispersion correction (

). Because the size of the pixel is very large, only the Γ point in the reciprocal space is used in our calculation. The second generation of Car-Parrinello Molecular Dynamics (SGCPMD) (

) Is used as the structural sample of the interface model, and the target temperature is set to 330 K. The correction step is obtained by five iterations of optimization of the orbit transformation (

), the integration time of each step is 0.5 fs. Langevin friction coefficient (γ

) Is set to 0.001 fs

, And the inherent friction coefficient (γ

) Is different, ie 5×10

fs

For Pt and 2.2×10

For H

O and ions. For more detailed information about SGCPMD settings, see (

). For each AIMD simulation, the initial molecular dynamics trajectory of about 5 ps (about 10,000 steps) is used to balance the system, and then a production cycle of 15 ps or more is generated.

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For commercial interest, and provide the original works appropriately cited.

Volume 6, Number 41

October 7, 2020

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Water chemisorption in response to changes in electrode potential results in negative capacitance of the electric double layer.

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