Atomic-Scale Simulation of Electrochemical Processes at Electrode

Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 1880−1884

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Atomic-Scale Simulation of Electrochemical Processes at Electrode/ Water Interfaces under Referenced Bias Potential Assil Bouzid* and Alfredo Pasquarello Chaire de Simulation à l’Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

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S Supporting Information *

ABSTRACT: Based on constant Fermi-level molecular dynamics and a proper alignment scheme, we perform simulations of the Pt(111)/water interface under variable bias potential referenced to the standard hydrogen electrode (SHE). Our scheme yields a potential of zero charge μpzc of ∼0.22 eV relative to the SHE and a double layer capacitance Cdl of ≃19 μF cm−2, in excellent agreement with experimental measurements. In addition, we study the structural reorganization of the electrical double layer for bias potentials ranging from −0.92 eV to +0.44 eV and find that Odown configurations, which are dominant at potentials above the pzc, reorient to favor Hdown configurations as the measured potential becomes negative. Our modeling scheme allows one to not only access atomic-scale processes at metal/water interfaces, but also to quantitatively estimate macroscopic electrochemical quantities.

E

by allowing the slab to exchange electrons with a reference electrode under constant preset chemical potential. While this approach made possible the simulation of charged slabs like in electrochemical set-ups, it suffered from strong fluctuations of the electron density, and electronic structure calculations were difficult to converge.9,10 Subsequently, Otani et al.11 and Jinnouchi et al.1 introduced alternative schemes to study the dynamics at the solvent/electrode interface at fixed excess charge.12,13 More recently, Bonnet et al. performed molecular dynamics simulations at constant electrode potential,10 in which the metal/electrolyte interface was simulated in a nonrepeated cell. In this modeling scheme, an effective screening medium11 was adopted to ensure the charge neutrality of the simulation cell. This technique revealed mechanistic aspects of electrochemical processes at metal/water interfaces,12,14 but the energetics were affected, and the band alignment was thus difficult to access. As far as the band alignment is considered, the standard hydrogen electrode (SHE) as set by Cheng and Sprik enables a direct comparison of the computed electrochemical energy levels to experiments either in bulk liquid water or at electrode/ water interfaces.8,15 This technique is based on a Born−Haber cycle linking the aqueous H+aq to H+(g) in gas phase and the associated energy level is evaluated through the Gibbs free energies of the reaction. Rossmeisl et al. introduced a generalized scheme, in which not only the potential, but also the pH could be varied.16,17 This method constructs the grand canonical potential by performing several simulations at

lectrochemical reactions involving electron/proton transfer at metal/water interfaces occur in several technologically relevant environments, such as solar cells, energy conversion, and storage devices. In these systems, the electron/proton transfer is governed by the applied bias potential, which defines the amount of excess charge at the interface. Hence, modeling the electrochemical metal/water interface at constant electrode potential is of paramount importance toward controlling and understanding the electrochemical properties of the interface. In practice, this task is not trivial and several challenges are faced when density functional theory (DFT) based methods are used within periodically repeated cells. First, the control of the electrode potential is still at a pioneering stage and a universal grand canonical method is still not available. Second, the lack of an alignment scheme to simulate systems at well-defined electrode potential represents a major issue toward the advancement of this field. In this context, an ideal modeling scheme should, on the one hand, allow one to reference the electrode potential to the standard hydrogen electrode (SHE), and, on the other hand, give access to the reaction mechanisms and the structural properties of the electrical double layer at the interface with the electrode. Previous modeling schemes studied the metal/water interface through either an implicit1−4 or an explicit but static5,6 solvent. In the latter case, only a few layers were considered. These models were used to access the hydrogen and oxygen evolution reactions. Recently, interface models from first-principles molecular dynamics (MD) with explicit water have given access to the potential of zero charge (pzc) at the Pt(111)/ water interface.7,8 A further step consists of modeling the metal/water interface under variable bias potential. In a pioneering work, Lozovoi et al.9 modeled electrified interfaces © 2018 American Chemical Society

Received: February 22, 2018 Accepted: March 28, 2018 Published: March 28, 2018 1880

DOI: 10.1021/acs.jpclett.8b00573 J. Phys. Chem. Lett. 2018, 9, 1880−1884

Letter

The Journal of Physical Chemistry Letters

evolution of the total electronic charge Qtot of the system. For each fixed Fermi level, the corresponding total electronic charge fluctuates around a constant value, except at U = −0.88 and −0.92 eV, for which Qtot exhibits a jump at 6.2 and 4.3 ps, respectively. This change in the electronic charge corresponds to the adsorption of the H+aq ion at the Pt surface and signals electron transfer from the electron reservoir to the electrode according to the Volmer reaction: H+aq + e− → Had. This reaction is expected to occur stochastically for electrode potentials lower than the SHE level provided that the simulation time is long enough. The observed mechanism of the reaction is in accord with a previous investigation,13 thereby validating the present setup. A comprehensive description is provided in the Supporting Information. Next, we focus on the alignment of the electrode potential to the standard hydrogen electrode. The SHE reaction is given by

different pHs and electrode potentials and uses the experimental SHE to determine the calculated work function of each configuration on an absolute energy scale. While these methods advanced the field and improved our understanding of electrochemical interfaces, none of them provides at the same time a simulation at constant bias potential referenced to the SHE and a description of the mechanistic aspects of electrochemical reactions at the atomic scale. Here we introduce a new simulation scheme by combining constant Fermi-level molecular dynamics and an alignment procedure to model the Pt(111)/water interface at varying electrode potential properly referenced to the SHE. To demonstrate the potential of this method, we obtain macroscopic electrochemical quantities in good agreement with experiment. Moreover, we achieve an atomic-scale description of the structural reorganization of the water bilayer as a function of applied voltage. We model the metal/water interface through a Pt(111) slab, 31 water molecules, and one hydronium H3O+ ion. The details of the model and the computational setup are given in the Supporting Information. In order to control the bias potential, we resort to constant Fermi-level molecular dynamics.10,18 Within this technique, the system is allowed to exchange electrons with an external reservoir while keeping the Fermi level constant. Hence, the system is driven by the grand canonical potential Ω (see Supporting Information). The electronic charge is now a dynamical variable evolving according to fictitious Newton-like equations of motion. Further details about the implementation of this technique can be found in refs 18 and 10. We applied constant Fermi level MD to the Pt(111)/water interface by setting the Fermi level at various positions within the band gap of liquid water. Figure 1 represents the time

H+aq + e− →

1 H 2(g) 2

(1)

Conventional methods for the determination of the SHE use the gaseous proton H+(g) as an intermediate step in a Born− Haber cycle.8,15 Instead, here we consider the Had adsorbed at the Pt electrode (Had) as an intermediate step, as illustrated in Figure 2, and write the SHE as follows: H+aq + e− → Had

Had →

1 H 2(g) + Pt 2

(2)

(3)

In this formulation, reaction 2 deals with the proton transfer from the liquid to the metal surface, and its corresponding free energy of reaction is obtained by combining the Blue Moon method with constant Fermi energy MD. In reaction 3, all the species are neutral and the free energy is trivially evaluated through the thermodynamic integration method. A full description of this alignment scheme is given in the Supporting Information. We now focus on two electrochemical quantities of the Pt(111)/water interface system: the double layer capacitance and the potential of zero charge. We define the excess charge at 1 Pt surface Qdl as Q dl = 2 (ηQ tot − 1), where η is the fractional volume corresponding to water in the supercell and accounts for the passivation of the background charge in the metal slab (see Supporting Information). In this definition, it is assumed that the aqueous hydronium ion H+aq always carries a positive charge and that the electronic charge is shared between the two Pt interfaces in the cell. The electronic charge is obtained as a statistical average from Figure 1 before the Volmer step takes place.

Figure 1. Time evolution of the total electronic charge Qtot in constant Fermi-level molecular dynamics of the Pt(111)/water interface at various electrode potentials (in eV). Qtot is defined as the total electronic charge and is here given per number of Pt surface atoms. The energies (in eV) are referred to the SHE.

Figure 2. Schematic representation of the three steps of the standard hydrogen reaction considered in this work. 1881


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Figure 3. (left panel) Double layer charge Qdl as a function of the applied electrode potential U. The red line represents a linear fit, from which the double layer capacitance Cdl is derived. (right panel) Double layer capacitance (blue dots) as a function of the applied electrode potential U. The simulation data are fitted through a polynomial function (blue dashed line) and are compared to experimental results (green line) from ref 19. The energies are referred to the SHE.

Figure 3 presents the evolution of the double layer charge as a function of the electrode potential. The pzc corresponds to the Fermi level of the neutral system with respect to the SHE level and is found at 0.22 eV in our simulation, in agreement with reported experimental values (0.28−0.37 eV vs SHE19−21). Another accessible macroscopic electrochemical quantity is the double layer capacitance Cdl = dQdl/dU, and is compared to respective measured data in Figure 3. The dependence of the calculated capacitance on U reproduces well the shape of the experimental data, and yields Cdl ≃ 19 μF cm−2, in excellent agreement with the commonly accepted experimental value of ∼20 μF cm−2 (refs 22, 23, and 19). We remark that the main peak in the Cdl at U ≃ 0.33 eV is associated with a rapid change in the double layer capacitance, which in turn is linked to the atomic-scale structural reorganization of the electrical double layer, as will be discussed in the analysis below. These results demonstrate the predictive power of our modeling scheme in accessing macroscopic electrochemical properties. The atomic-scale structure of the electrical double layer is an important aspect in defining the metal/water interface and the electrochemical activity of the electrode.24 Several experimental studies investigated the structure at interfacial water systems, either in neutral conditions or under bias potential. Water molecules have been observed to undergo reorientation depending on the applied potential in a variety of systems, including Pt(111),25,26 polycrystalline Pt,27 Au(111),28 air/ water, and lipid/water charged interfaces.29−33 In particular, at metal surfaces, the interfacial water molecules are strongly hydrogen bonded with the O atoms pointing toward the metal surface for potentials above the pzc. At variance, for potentials below the pzc, the water molecules are weakly bonded and point their H atoms downward. In this work, we take advantage of our theoretical scheme to study the structural reorganization of the water double layer at the Pt(111)/H2O interface as a function of the bias electrode potential referenced to the SHE. Figure 4 shows the distribution of O and H atoms, and the water dipole orientation as a function of a coordinate along the surface normal direction as the electrode potential U is varied. We also provide in Figure 5 representative snapshots of the Pt(111)/water interface at various values of U. For electrode potentials above the pzc (U > 0.22 eV), the O distribution features a first sharp peak at 2.3 Å and a second broad peak around 3.35 Å, while the H distribution exhibits a single

Figure 4. Distribution of O (top panel) atoms, H (middle panel) atoms, and dipole orientation (bottom panel) as a function of the coordinate Z oriented along the surface normal direction, at various electrode potentials (in eV). The Z coordinate is referenced with respect to the Pt surface. The distributions are obtained from an average over the two interfaces in our model and have been smoothed with a Gaussian function having a width of 0.05 Å.

principal peak centered at 2.6 Å. The orientation of the water molecules can be inferred from the dipole orientation, as presented in Figures 4 and S6. The positive peak of the dipole distribution indicates that the water molecules in the first contact layer are in Odown configurations with the H atoms pointing toward the liquid (see Figure 5a). Specifically, we find two main dipole orientations at 55° and 86° for U = 0.44 eV (see Figure S6). The dipole orientation of the water molecules in the second layer shows a very broad peak around 90° (see Figure S6). As the potential decreases, the intensity of the first O peak diminishes, while that of the second peak increases (Figure 4). This trend is accompanied by a reduction in the 1882


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potentials above the pzc, the water structure is dominated by Odown configurations, in which the dipole of the water molecules is on average pointing toward the bulk water layer. At the pzc, Hdown configurations coexist with Odown structures, but the latter disappear completely at negative bias potential, for which all the water dipoles are fully oriented toward the Pt surface. At the lowest potential considered, the water molecules orient both of their H atoms toward the electrode. Our modeling scheme simultaneously gives access to the macroscopic properties of the metal/water interface and to the atomic-scale description of the electrical double layer at the interface. This technique will considerably contribute to advancing the predictive power of the DFT modeling of electrode/electrolyte interfaces under bias potential.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b00573. Computational details on molecular dynamics, SHE determination and alignment scheme, effect of background charge, mechanistic aspects of the Volmer reaction, angular distributions at various electrode potentials, and supplementary references (PDF)

Figure 5. Representative snapshots illustrating the structure of the water double layer when the electrode potential U is set at (a) 0.44 eV, (b) 0.22 eV (pzc), (c) −0.61 eV, and (d) −0.92 eV.

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intensity of the first peak of the H distribution and the appearance of a second broad peak centered at 3.8 Å (Figure 4). Focusing on the dipole orientation, we infer that some of the water molecules in the first contact layer reorient from Odown to Hdown configurations, as the electrode potential drops. At the pzc (0.22 eV), we observe coexistence of the two configurations with a slight prevalence of the H down configurations [see Figures S6 and 5b]. Under negative bias, all the water molecules are found in Hdown configurations leading to the disappearance of the first O peak in Figure 4. In addition, the first peak in the H distribution shifts toward 2.35 Å and a second H peak appears around 3.43 Å. The dipole orientation features a negative peak signifying that the water orientation is predominantly Hdown. A further broad negative region appearing under strong negative bias indicates that also the molecules in the second water layer (4 < Z < 6 Å) orient their H atoms toward the interface (Figure 5d). Accordingly, two main dipole orientations are found at 96° and 134° at U = −0.92 eV (see Figure S6). However, deep in the water layer (Z > 6.5 Å), the dipole is found to be randomly oriented, and the water structure can be taken as representative of the bulk phase. The atomistic description emerging from our work is fully consistent with the picture of water reorientation under bias potential inferred from experimental data.25−31 We used constant Fermi-level molecular dynamics to study the Pt(111)/water interface under variable bias potential. First, we established an alignment scheme to determine the SHE reference level by considering the hydrogen adsorbed at the Pt surface as an intermediate step between the aqueous hydro+ nium ion Haq and the gas phase H2(g). Through the determination of the SHE level, our scheme allows one to reference the electrode potentials on an absolute scale. Second, we studied the double layer capacitance and the pzc, and found μpzc = 0.22 eV and Cdl ≃ 19 μF cm−2, in very good agreement with experiment. Finally, we investigated the atomic-scale structural reorganization of the electrical double layer as a function of the bias potential. Our results reveal that at

AUTHOR INFORMATION

Corresponding Author

*E-mail: assil.bouzid@epfl.ch. ORCID

Assil Bouzid: 0000-0002-9363-7240 Alfredo Pasquarello: 0000-0002-9142-2799 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Francesco Ambrosio for fruitful discussions. This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under Grant Agreement No. 291771 (call 2014). This work has been performed in the context of the National Center of Competence in Research (NCCR) “Materials’ Revolution: Computational Design and Discovery of Novel Materials (MARVEL)” of the Swiss National Science Foundation. We used computational resources of CSCS, CSEA-EPFL, and SCITAS.

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REFERENCES

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Atomic-Scale Simulation of Electrochemical Processes at Electrode

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