Atomic-Scale Simulation of Electrochemical Processes at Electrode

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Atomic-Scale Simulation of Electrochemical Processes at Electrode/Water Interfaces under Referenced Bias Potential Assil Bouzid, and Alfredo Pasquarello J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00573 • Publication Date (Web): 28 Mar 2018 Downloaded from http://pubs.acs.org on March 28, 2018

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The Journal of Physical Chemistry Letters

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 E-mail: [email protected]

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 µFcm−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 modelling scheme allows one not only to access atomic-scale processes at metal/water interfaces, but also to quantitatively estimate macroscopic electrochemical properties.

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Electrochemical 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, modelling the metal/water electrochemical interface at constant electrode potential is of paramount importance towards 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 modelling 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. 2


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Previous modelling schemes studied the metal/water interface through either an implicit 1–4 or an explicit but static 5,6 solvent. In the latter case, only 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 in modelling the metal/water interface under variable bias potential. In a pioneering work, Lozovoi et al. 9 modelled electrified interfaces 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 non-repeated cell. In this modeling scheme, an effective screening medium 11 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 different pHs and electrode potentials and uses the experimental SHE to determine the calculated work function of each configuration on an absolute energy scale.

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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 properties 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 H3 O+ ion. The details of the model and the computational setup are given in the Supplementary 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 Supplementary 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 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

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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 our work.

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 Supplementary Information. Next, we focus on the alignment of the electrode potential to the standard hydrogen

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electrode. The SHE reaction is given by:

− 1 H+ aq + e → 2 H2 (g).

(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, we here consider the Had adsorbed at the Pt electrode (Had ) as an intermediate step, as illustrated in Fig. 2, and write the SHE as follows: − H+ aq + e → Had

(2)

Had → 12 H2 (g) + Pt

(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 Supplementary Information. We now focus on two electrochemical properties of the Pt(111)/water interface system, the double layer capacitance and the potential of zero charge. We define the excess charge at Pt surface Qdl as Qdl = 21 (ηQtot − 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 Supplementary 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 Fig. 1 before the Volmer step takes place. 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. SHE 19–21 ). Another accessible macroscopic electrochemical quantity 6


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200

20

150 2

2

theory theory fit expt.

Cdl (µF/cm )

40 Qdl (µC/cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

100

-20

50 2

C= 19 µF/cm

-40

-0.9 -0.6 -0.3 0 0.3 0.6 U (eV)

-0.9 -0.6 -0.3 0 0.3 0.6 U (eV)

0

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.

is the double layer capacitance Cdl = dQdl /dU , and is compared to respective measured data in Fig. 3. The dependence of the calculated capacitance on U reproduces well the shape of the experimental data, and yields Cdl ≃ 19 µFcm−2 , in excellent agreement with the commonly accepted experimental value of ∼ 20 µFcm−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 modelling 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 7



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 downwards. In this work, we take advantage of our theoretical scheme to study the structural reorganization of the water double layer at the Pt(111)/H2 O 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 Fig. 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 principal peak centered at 2.6 Å. The orientation of the water molecules can be inferred from the dipole orientation, as presented in Figs. 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 towards the liquid [see Fig. 5(a)]. Specifically, we find two main dipole orientations at 55◦ and 86◦ for U = 0.44 eV (see Fig. S6). The dipole orientation of the water molecules in the second layer shows a very broad peak around 90◦ (see Fig. S6). As the potential decreases, the intensity of the first O peak diminishes, while that of the second peak increases (Fig. 4). This trend is accompanied by a reduction in the intensity of the first peak of the H distribution and the appearance of a second broad peak centered at 3.8 Å (Fig. 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 Hdown configurations [see Figs. S6

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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.

and 5(b)]. Under negative bias, all the water molecules are found in Hdown configurations leading to the disappearance of the first O peak in Fig. 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

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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.

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 [Fig. 5(d)]. Accordingly, two main dipole orientations are found at 96◦ and 134◦ at U = −0.92 eV (see Fig. 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 hydronium ion H+ aq and the gas phase H2 (g). Through the 10


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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 µFcm−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 potentials above the pzc the water structure is dominated by Odown configurations, in which the dipole of the water molecules is on average pointing towards 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 their H atoms toward the electrode. Our modeling scheme gives simultaneously 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 modelling of electrode/electrolyte interfaces under bias potential.

Acknowledgement 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, CSEAEPFL, and SCITAS. The Supplementary Information contains computational details on molecular dynamics, SHE determination and alignment scheme, effect of background charge, mechanistic aspects of the Volmer reaction and angular distributions at various electrode potentials. It also

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contains supplementary references [ 34–49].

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Atomic-Scale Simulation of Electrochemical Processes at Electrode

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