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[J. Phys. Soc. Jpn. 77 (2008) 024802]
Simulations of Electrochemical Processes by First-Principles Molecular Dynamics [February 12, 2008]
(Japan Advanced Institute of Science and Technology)
Energy conservation and reduction of CO2 are critical and urgent problems for all creatures on earth. The use of hydrogen as a fuel is one of the promising solutions to these problems. Therefore, hydrogen-gas production, hydrogen-gas storage, and fuel cells are important technical targets in this context. Hydrogen gas may be produced by electrolysis using solar cells, for example, and the produced hydrogen gas can be used in a fuel cell. In order to make these technologies more efficient and economical, it is highly desirable to understand the microscopic mechanisms of the chemical reactions involved and therefore physicists and chemists must play important roles in the further development of these technologies.[3]
The reactions in electrolysis and in the fuel cell are mutually reverse chemical processes. The fundamental chemical reactions are described below:
At the O2 electrode, which is the anode (cathode) in electrolysis (fuel cell),
H2O ↔ (1/2)O2 + 2H+ + 2e−, (1)
and at the H2 electrode, which is the cathode (anode) in electrolysis (fuel cell),
2H+ + 2e− ↔ H2. (2)
The net reaction is simply expressed as:
H2O ↔ (1/2)O2 + H2. (3)
In electrolysis (fuel cell), the reactions from left (right) to right (left) in eqs.(1) - (3) dominate.
The chemical potential of the left-hand-side object (liquid water) of eq.(3) is lower than that of the right-hand-side object (half of an oxygen molecule and a hydrogen molecule in gas phase). Under the standard condition (25°C and 1.0 atm), we obtain
ΔG = μlH2O − (0.5μgO2 + μgH2) = − 237.2 kJ/mol.
Because two electrons are involved in this reaction, the electrostatic potential difference ΔE corresponding to ΔG is given by
ΔE = | ΔG | / 2F =1.23 V,
where F denotes the Faraday constant. This means that the production of O2 gas and H2 gas by water electrolysis occurs, in principle, by applying a voltage greater than 1.23 V and that the electromotive force of 1.23 V is produced by the H2-O2 fuel cell.
Fig. 1: A unit cell of the model system for studying the hydrogen evolution reaction (HER) on the Pt(111) surface. The model consists of three Pt layers, water, and vacuum. The yellow sphere in the water layer denotes an oxygen atom of the hydronium ion. (From Fig. 1 of Ref. 2)
Among the present industrial problems related to fuel cells, particularly the polymer electrolyte fuel cell (PEFC), the most important one is to devise a method for reducing the amount of Pt required at the O2 electrode to function as the catalyst for the O2 reduction. In order to accelerate the O2 reduction, a large amount of Pt is needed. Reaction (1) involves several elementary processes, whose details are yet to be elucidated. On the other hand, reaction (2) that occurs at the H2 electrode seems to be simple and relatively well understood. Nevertheless, the detailed microscopic reaction process has not yet been fully understood despite the considerable research done on this topic for more than 50 years.
The main aim of this short article is to introduce the work of Otani et al.[2] In their study, Otani et al. simulated the first step of the hydrogen evolution reaction (HER), i.e., the reaction from left to right in eq.(2), in an acidic solution with a Pt(111) plate as the electrode. It is generally believed that the HER consists of two successive steps:
H+ + e− → H(a) (Volumer step)
and then either
2H(a) → H2 (Tafel step)
or
H(a) + H+ + e− → H2 (Heyrovsky step).
In the above equations, H(a) denotes the hydrogen atom adsorbed on the Pt surface. Otani et al.’s work[2] contributed to the elucidation of the microscopic process of Volmer step and favored the possibility of the Tafel step being the second step of the HER.
The simulation uses the model system shown in Fig.1, which is a unit cell in the periodic boundary condition. In Fig.1, the bottom portion is a vacuum followed by a three-layered slab of Pt(111). The water layer contacts the Pt surface, and a semi-infinite conductor with an infinite dielectric constant is placed at the top of the unit cell. There are two features to be noticed in the method. First, in contrast to the existing quantum chemistry simulations that mostly adopt the isolated cluster model, the present method adopts a slab geometry, which may be more appropriate for simulating the metal electrode. Second, Otani et al.’s simulation uses the “effective screening medium (ESM)” developed by Otani and Sugino[4] in order to simulate the case with an applied electric field. This ESM method makes it possible to control the electric field more easily and precisely. In order to apply the electric field in a direction that is perpendicular to the Pt slab, a certain amount (possibly, a fractional amount) of electrons is added (or subtracted) to the Pt slab and then the same amount of electric charge of the opposite sign is induced in the conductor placed at the top of the unit cell.
Fig. 2: A series of snapshots of the proton transfer process from a hydronium ion to the Pt(111) surface. When a water molecule (right) approaches the hydronium ion in order to form a hydrogen bond between Oh and Hw and the distance Oh-Hw becomes smaller than 2 Å, the proton Hc+ jumps from the hydronium ion to the Pt surface. The proton becomes neutral and stays atop the Pt surface. (From Fig. 3(b) of Ref. 2)
In order to simulate the HER process in an acidic solution, one proton is added to the water. Further, the Pt slab is negatively charged in order to produce an electric field that is directed from the top to the bottom in Fig.1. This leads to the diffusion of the H+ ions toward the Pt surface. In water, the actual state of H+ is the hydronium ion state, H3O+. It was found that with an addition of 0.08 electrons per surface Pt atom, which corresponds to −19.1 μC / cm2, the H+ ion gets detached from the hydronium ion and stays as a nearly neutral hydrogen atom adsorbed atop the Pt(111) surface. Figure 2 shows the representative configurations in the process represented by the Volmer step, which is now expressed in a more suitable way as H3O+ + e− → H(a) + H2O. One should note the following interesting features in Fig.2:
1) orientation of H2O and H3O+
Due to the applied electric field, the orientation of the OH bond is such that the H atom is closer to the Pt surface. Such a configuration can be seen in the first interface layer of water, as also shown in Fig.1.
2) hydrogen bond associated with hydronium ion
A hydronium ion in vacuum has an umbrella shape with the H-O-H angle of about 112°. However, if it is in water, an Eigen complex (H9O4)+ is formed because of a hydrogen bond with the surrounding water molecules, and the hydronium ion becomes almost flat.[5] In the process of proton diffusion, a Zundel complex (H5O2)+ is also formed. These complexes are shown in Fig.3. In both cases, the hydronium ion acts as a proton donor to the neighboring solvation water molecules. The (H5O2)+ complex shown in Fig.2 is in strong contrast to these features. A neighboring water molecule acts as a proton donor to the hydronium ion, and its H-O-H angle seems to be much smaller than 112°.
The formation of the unique (H5O2)+ complex is important for a proton of the hydronium ion to jump to the surface. It was observed in the simulation that the proton jump occurs when the Hw-Oh distance in Fig.2 becomes less than 2 Å. Note that the O-H distance of the hydrogen bond in the water dimer is almost 2 Å.[6] Certainly, the hydrogen-bond formation seen in the complex assists the proton jump. Therefore, it can be said that Otani et al.’s simulation[2] has succeeded in elucidating the very details of the atomic process of the Volmer step in HER.
I would like to point out two more important results of their work. One is that the adsorbed hydrogen H(a) is located atop the Pt(111) surface, which is in clear contrast to the hollow site adsorption in the case of an UHV condition. The calculated stretching mode frequency for Pt-H(a) is 2286 cm−1, which is close to the experimental observation of 2090 cm−1.[7,8] The other is the observation that H(a) diffuses quickly between adjacent atop sites. This observation strongly suggests that the Tafel step is the second step in the HER and that the H(a) ions collide with each other in order to form H2 gas. There is also a strong experimental support for the Tafel step.[7,8]
As mentioned above, Otani et al.’s work analyzed the HER process. The reverse process, hydrogen oxidation reaction (HOR), dominates in a fuel cell. Depending on the sign of the applied electric field, either HER or HOR is promoted (see Fig.6 of Ref.9).
The importance of FPMD simulation will increase even more in future for the analysis of solution chemistry including biological systems. In such studies, there are two basic methodological aspects. One is the efficient and highly accurate electronic structure calculation, and the other is the efficient method of the phase space search.[10-12] There have been continuing efforts for developing and improving the methodology in both aspects.
I would like to express my sincere gratitude to Prof. Y. Morikawa and Prof. M. Osawa for their beneficial comments.
References
[1] R. Car and M. Parrinello: Phys. Rev. Lett. 55 (1985) 2471.
[2] M. Otani et al.: J. Phys. Soc. Jpn. 77 (2008) 024802.
[3] As a review, see for example, N. M. Markovic and P. N. Ross, Jr.: Surf. Sci. Rep. 45 (2002) 117.
[4] M. Otani and O. Sugino: Phys. Rev. B 73 (2006) 115407.
[5] M. Tuckerman et al.: J. Chem. Phys. 103 (1995) 150.
[6] X. Xu and W. A. Goddard, III: J. Phys. Chem. A 108 (2004) 2305.
[7] K. Kunimatsu et al.: Chem. Phys. Lett. 401 (2005) 451.
[8] K. Kunimatsu et al.: J. Electroanal. Chem. 587 (2006) 299.
[9] Y. Ishikawa et al.: J. Electroanal. Chem. 607 (2007) 37.
[10] M. Sprik and G. Ciccotti: J. Chem. Phys. 109 (1998) 7737.
[11] A. Laio and M. Parrinello: Proc. Natl. Acad. Sci. U.S.A. 99 (2002) 12562.
[12] M. Iannuzzi et al.: Phys. Rev. Lett. 90 (2003) 238302.
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