Research Article | Open Access
Takayoshi Ishimoto, Michihisa Koyama, "Theoretical Study on Solubility from Pt Electrocatalyst and Reactivity in Electrolyte Environment of Pt Complex in PEFC", International Journal of Electrochemistry, vol. 2012, Article ID 318461, 9 pages, 2012. https://doi.org/10.1155/2012/318461
Theoretical Study on Solubility from Pt Electrocatalyst and Reactivity in Electrolyte Environment of Pt Complex in PEFC
We theoretically analyzed the formation energy and solvation free energy of Pt(II) and Pt(IV) complexes with three types of ligands in electrolyte environment under the low- and high-humidity conditions to study the Pt electrocatalyst degradation and dissolution mechanisms for polymer electrolyte fuel cell. To represent the low- and high-humidity conditions in perfluorosulfonic acid (PFSA) polymer electrolyte membrane, we controlled the dielectric constant based on the experimental result. We observed general tendencies that the formation energy becomes larger while the solvation free energy becomes smaller under the low-humidity condition. The degradation of Pt complex from Pt surface is indicated to be accelerated by the adsorption of the end group of PFSA polymer side chain, on the Pt surface by comparing the desorption energies of [Pt(H2O)2(OH)3(CF3SO3)] and [Pt(H2O)2(OH)4]. The [Pt(H2O)4]2+ is not formed by the proton addition reaction between Pt complexes under the low-humidity condition of PFSA environment. From the analysis of possible reaction pathways of Pt complexes, we found the influence of humidity on the reactivity of Pt complex.
Polymer electrolyte fuel cell (PEFC) has attracted much interest as a promising power source for automobiles and cogeneration systems because of its high-energy conversion efficiency with environmental benefits. For the practical long-term operation of PEFC, the durability of the membrane electrode assemble (MEA) is one of the main issues. PEFC catalysts in MEA typically consist of Pt nanoparticles with 2-3 nm diameter, which are dispersed on the surface of primary carbon particles of 20–50 nm. The degradation of Pt electrocatalyst is particularly significant for the overall performance of MEA although the Pt-based alloys are usually utilized as electrocatalyst due to the electrochemical stability over a wide potential region in various fields. Iterative Pt dissolution and reprecipitation processes lead to the growth of Pt particles called Ostwald ripening, causing the degradation of the electrocatalytic activity.
Many studies have reported the loss of electrochemical surface area by the Pt dissolution and reprecipitation phenomena during the operation [1–15]. It is found that Pt dissolution depends on the voltage, acidity, and temperature. For example, Wang et al. reported the increasing of dissolved Pt concentration by the high electrostatic potential . For the detailed understandings, Mitsushima et al. analyzed the solubility and the dissolution mechanism of Pt in acidic media at different temperature and pH . They found high solubility of Pt at high temperature. In addition, Umeda et al. found the Pt(OH)4 formation for first step of Pt degradation in concentrated sulfuric acid by using rotating ring-disk electrode (RRDE) and electrochemical quartz crystal microbalance (EQCM) . Based on these experimental studies, we have already analyzed the dissolved species in concentrated sulfuric acid as a first step to tackle the Pt dissolution and precipitation phenomena by using the density functional theory (DFT) calculation from an atomistic point of view . We have found that the [Pt(H2O)2(OH)4] and [Pt(OH)4]2− are important complexes for desorption from the Pt surface based on the desorption energy analysis. This theoretical analysis explained well the experimental observations for concentrated sulfuric acid, however, the behavior of Pt complex in perfluorosulfonic acid (PFSA) polymer electrolyte membrane, such as Nafion, remains unclear. Recently, there are some experimental studies analyzing the Pt dissolution in the PFSA environment [17–23]. The adsorption of PFSA polymer on Pt surface was studied by using a voltammetric fingerprinting approach and infrared reflection absorption spectroscopy [20, 21]. They clearly found the direct adsorption of sulfonate anions, which is an end group of PFSA polymer side chain, onto the Pt surface. Yoshida et al. clarified that the side chain end group of Nafion is acting as a ligand of six-coordinate Pt(IV) complex by using extended X-ray absorption fine structure (EXAFS) [7, 13]. In addition, the dependence of the solubility of Pt complex in different PFSA polymer electrolyte was observed . In addition, higher degradation under low humidity condition was observed [24–26]. The experimental results suggest that the interaction between Pt and PFSA polymer humidity are playing key roles in the degradation of Pt catalyst because the solubility of Pt complex becomes large with the existence of PFSA polymer electrolyte membrane. Those findings indicate that the stability and reactivity of Pt complexes under PFSA environment is different from our preceding results for the concentrated sulfuric acid . One of the differences of concentrated sulfuric acid and PFSA environment is the dielectric property as well as the possible ligand, that is, sulfate anion.
In this study, we analyzed the Pt dissolution and precipitation phenomena under the low- and high-humidity PFSA conditions. We theoretically analyzed the solvation structures and thermodynamic stabilities of Pt complex in PFSA polymer assuming H2O, , and as ligands. We also analyzed the desorption energy of Pt complex from Pt surface. The reactivity of Pt complex is discussed by comparing the results obtained for the different dielectric constants.
2. Computational Details
All calculations were performed under the generalized gradient approximation with Becke-88 exchange and Lee-Yang-Parr correlation functionals (BLYP) as implemented in the DMol3 package [27, 28]. Double numerical atomic basis sets augmented with polarization function (DNP) were used to describe the valence electrons, and the core electrons were represented by effective core potentials (ECP). Solvent effects were estimated using the conductor-like screening model (COSMO). Table 1 shows the various dielectric constants to represent the surrounding condition of Pt complexes. Because the experimental result of dielectric constant in PFSA at working temperature is unavailable, we used the dielectric constants of 5 and 20 reported for low- and high-humidity condition of Nafion membrane at 303.15 K . Those values for bulk properties of Nafion membrane might be different from the local dielectric properties around Pt catalyst because of the water formation as results of cathodic reaction especially at high current density operation. We therefore set the dielectric constant of 61.0 for water at 353.15  as one extreme. Full geometry optimization was performed for each system by using these dielectric constants. All thermodynamic data have been evaluated for a typical working temperature of 353.15 K.
We used four- and six-coordinated Pt(II) and Pt(IV) complexes with three types of ligands (H2O, , and ) as models of dissolved Pt species in PFSA environment for analyzing the formation energy and Gibbs free energy. Note that we consider as a ligand even in the acidic PEFC condition assuming that formed on Pt surface could play an important role in the formation of intermediate species for dissolution [6, 31–33]. The is a model compound of end group of PFSA polymer side chain.
3. Results and Discussion
3.1. Analysis of Dissolved Pt Complexes in Various Dielectric Constants
We first analyzed the formation energy () and solvation free energy () of the four- and six-coordinate Pt(II) and Pt(IV) complexes as the dissolved species under various dielectric constant. The optimized structures of Pt(II) and Pt(IV) complexes (ε = 5.0) with three ligands (H2O, , and ) are shown in Figures 1 and 2, respectively. Two coordination configurations of is not considered in present calculation due to the low stability . Four- and six-coordinate Pt(II) and Pt(IV) complexes were square and octahedral structures, respectively. Oxygen atoms are coordinating to Pt in all optimized structures. The of Pt(II) and Pt(IV) complexes were evaluated by the following equations, Here L stands for or . To evaluate the stability of Pt complex in water solution or PFSA polymer electrolyte membrane, the Δ was calculated by following equation:
The G(COSMO) and G(Gas) indicate the free energy for the solvated and gas phases of the optimized geometry, respectively. The of Pt(II) complexes are summarized in Table 2. The and Δ of [Pt(H2O)4]2+ at ε = 5.0 are −628.6 and −670.9 kJ/mol, respectively. By the substitution of for H2O, the of [Pt(H2O)3(OH)]+ became stable largely by about 530 kJ/mol in comparison with [Pt(H2O)4]2+. On the contrary, modest stabilization was observed when the H2O was substituted with . When we compare the Δ, we found that the charged species shows large solvation energy. The Δ’s of Pt(II) complexes ((1) and (5)) show higher stability than that of singly charged complexes ((2), (4), and (6)). The neutral Pt(II) complexes ((3), (7), and (8)) had less gain in the solvation. We then analyzed the and Δ under high-humidity condition by comparing the results for the dielectric constants of 5.0 and 20.0. The and Δ of [Pt(H2O)4]2+ are −506.4 and −858.8 kJ/mol, respectively, at ε = 20.0. The becomes larger, that is, the complex becomes unstable, when the dielectric constant becomes large. On the other hand, the Δ becomes smaller indicating the larger solvation gain. This means that the humidity unstabilizes the complex while making its solvation favorable thermodynamically. We also analyzed the and Δ of Pt(II) and Pt(IV) complexes in water solution at 353.15 K setting ε = 61.0 to see the properties of extremely humidified electrocatalyst at local scale. The Δ’s of Pt complexes in water solution are larger than those in PFSA. On the contrary, the Δ’s of Pt complex in water solution are smaller as observed in the comparison of results obtained for ε = 5.0 and 20.0. Considering that the dielectric constants of water at 298.15 and 353.15 are 78.5 and 61.0, respectively, the actual properties in PFSA environment under low- and high-humidity at 353.15 K can be estimated by extrapolating and interpolating the results obtained for dielectric constant at 303.15 K, that is, ε = 5.0 and 20.0, respectively. This means that the lower temperature has thermodynamically the effect on the Pt degradation similar to the higher humidity.
In case of six-coordinate Pt(IV) complexes (Table 3), at ε = 5.0, the (−2571.7 kJ/mol) and Δ (−2407.6 kJ/mol) of [Pt(H2O)6]4+ are much more stable than those of [Pt(H2O)4]2+. We observed the dependencies of and Δ on dielectric constant similar to that observed for the Pt(II) complexes.
3.2. Desorption Energy of Pt Complex from Pt Surface
We next focused on the desorption energy (Δ) of Pt(II) and Pt(IV) complexes from the Pt surface to estimate the initial dissolved species. We used a simple Pt4 cluster as a Pt surface model to estimate the Δ of Pt(II) and Pt(IV) complexes from Pt surface. Although the Pt4 cluster is small to represent the Pt surface, the useful results for Pt surface stability and reactivity are already reported by using Pt4 cluster [35, 36]. We assumed the and adsorption on the Pt surface because these species are proposed as the adsorption molecules on the Pt surface. Here, L stands for or . Tables 4 and 5 summarize the Δ of Pt(II) and Pt(IV) complexes from the Pt surface model. The Δ of Pt(II) and Pt(IV) complexes were evaluated by the following equations The negative value of Δ indicates that the desorption of Pt complex to the solvent from the Pt surface is favorable. For Pt(II) complexes, the Δ becomes larger as the dielectric constant becomes larger. Although most of Pt(II) complexes have positive desorption energies, only [Pt(OH)4]2− is found as a candidate for initial dissolution species from the Pt surface. The desorption of [Pt(OH)4]2− at ε = 5.0 is small in comparison with high humidity (ε = 20.0) and water (ε = 61.0) environments. Also we note that higher temperature corresponds to lower dielectric constant. We thus conclude higher dissolution of Pt under low-humidity condition at high temperature.
On the other hand, we have found two possible Pt(IV) complexes, [Pt(H2O)2(OH)4] and [Pt(H2O)2(OH)3(CF3SO3)], for the desorption from Pt surface. The Δ of [Pt(H2O)2(OH)3(CF3SO3)] is about 3 kJ/mol smaller than that of [Pt(H2O)2(OH)4]. This result indicates that the desorption of Pt complex from Pt surface will be accelerated by the adsorption of end group of PFSA polymer side chain on the Pt surface, which is in agreement with the experimental observation . The Δ of [Pt(H2O)2(OH)4] and [Pt(H2O)2(OH)3(CF3SO3)] complexes become larger when the dielectric constant becomes larger. In addition, the Δ of [Pt(H2O)3(OH)3]+ becomes close to zero at ε = 5.0. This result indicates that the [Pt(H2O)3(OH)3]+ complex would dissolve from Pt surface in PFSA environment under low-humidity condition at high temperature during the PEFC operation.
3.3. Structural Changes in Various Dielectric Environments
We then analyzed the geometrical parameters of selected Pt(II) and Pt(IV) complexes to see more details of structural change by the dielectric constant. The Pt…O distance with three ligands (H2O, , and ) for Pt(II) and Pt(IV) complexes are shown in Tables 6 and 7, respectively. The Pt…O distance of [Pt(H2O)2]2+ and [Pt(H2O)6]4+ is almost the same regardless of dielectric constant. By the substitution of or for H2O, the Pt…O distance with and becomes longer when the dielectric constant becomes larger. Contrary, the Pt…O distance with H2O becomes shorter. This result indicates that the surrounding environment in electrolyte solution strongly influences the anionic species, and . These geometrical changes are one of the reasons for changing the stability and reactivity of Pt complexes.
3.4. Reactivity of Pt Complex
We discuss the reactivity of Pt complex, which is dissolved species from Pt surface, in PFSA environment. We focused on the reactivity based on the thermodynamical properties. The four reactions of Pt complexes are considered as shown by the following equations, taking [Pt(H2O)3(OH)]+ as an example.
Proton addition reaction H2O/ substitution reaction / substitution reaction Reduction reaction from Pt(IV) to Pt(II) complex The reaction energies for (5), (6), and (7) of Pt(II) and Pt(IV) complexes are listed in Tables 8 and 9, respectively. For Pt(II) complexes, many proton addition reactions are thermodynamically favorable. It is noticed that the proton addition reaction energy to [Pt(H2O)3(OH)]+ was only positive when . This result indicates that the [Pt(H2O)4]2+ is not formed in the low-humidity PFSA environment. The H2O/ substitution reaction also becomes thermodynamically favorable with decreasing the dielectric property of the environment. On the other hand, the / substitution reaction is difficult.
For Pt(IV) complexes, the proton addition reaction to [Pt(OH)2(OH)4] becomes thermodynamically favorable with decreasing the dielectric constant. While the [Pt(H2O)3(OH)3]+ will be possible complex by the proton addition reaction in water (), the [Pt(H2O4(OH)2)]2+ is not formed in PFSA environment ( and 20.0) by the positive proton addition reaction energy of [Pt(H2O)3(OH)3]+. The product of proton addition reaction is different depending on the surrounding environment. We also found some negative proton addition reaction energy of Pt(IV) complexes including , that is, [Pt(H2O)3(CF3SO3)3]+ and [Pt(H2O)3(OH)(CF3SO3)2]+. The H2O/ and / substitution reactions for Pt(IV) complexes show a tendency (negative and positive reaction energies) similar to that of Pt(II) complexes.
The result of reduction reaction (8) from Pt(IV) to Pt(II) complexes is listed in Table 10. The reduction energies of [Pt(H2O)6]4+, [Pt(H2O)5(OH)]3+, and [Pt(H2O)4(OH)2]2+ become smaller when the dielectric constant becomes larger. On the contrary, the reduction energy of [Pt(H2O)2(OH)4] becomes larger. The reduction energy of [Pt(H2O)3(OH)3]+ was less influenced by the dielectric constant. These species, [Pt(H2O)2(OH)4], [Pt(H2O)3(OH)3]+, and [Pt(H2O)4(OH)2]2+, which are stabilized by proton addition reaction after desorption from Pt surface, would be important concerning the reduction reaction from Pt(IV) to Pt(II). Especially, the reduction from [Pt(H2O)2(OH)4] or [Pt(H2O)3(OH)3]+ is favorable reaction during the PEFC operating condition. After reduction reaction from [Pt(H2O)2(OH)4] or [Pt(H2O)3(OH)3]+, the proton addition reaction for [Pt(OH)4]2− or [Pt(H2O)(OH)3]− proceeds proton addition reaction because the reaction energy of proton addition is more stable than the Δ. Then, the [Pt(H2O)4]2+, which is not stable under low-humidity condition, and [Pt(H2O)3(OH)]+ are one of the reprecipitation species because of large positive Δ between Pt(II) complex and Pt surface.
In this study, we calculated the and Δ of four- and six-coordinate Pt(II) and Pt(IV) complexes with three types of ligands (H2O, , and ). To represent the low- and high-humidity condition in PFSA environment, we changed the dielectric constant and analyzed the stability and reactivity of Pt complexes. The stability of Pt complexes is changed by dielectric constant because the and Δ, respectively, become larger and smaller when the dielectric constant becomes large. We also analyzed the Δ of Pt complex from Pt surface. We found three important complexes, [Pt(H2O)2(OH)4], [Pt(H2O)2(OH)3(CF3SO3)], and [Pt(OH)4]2−, for the initial Pt dissolution mechanism. The degradation of Pt complex from Pt surface is to be accelerated by the adsorption of on the Pt surface because the Δ of [Pt(H2O)2(OH)3(CF3SO3)] was smaller than that of [Pt(H2O)2(OH)4]. The possible pathways, proton addition, H2O/, /, and reduction reactions, are analyzed between the Pt complexes. The [Pt(H2O)2]2+ are not stabilized in PFSA environment under the low-humidity condition. The different stable species, [Pt(H2O)3(OH)3]+ and [Pt(H2O)4(OH)2]2+, are obtained by the proton addition reaction from [Pt(H2O)2(OH)4] in PFSA and water environment, respectively. The [Pt(H2O)4]2+ and [Pt(H2O)3(OH)]+ are possible reprecipitation species. This result suggests that the surrounding dielectric environment will change the reaction pathways of the dissolved Pt complexes. We theoretically estimated the effect of surrounding condition in PFSA environment for the Pt dissolution and reprecipitation mechanisms in comparison with water solution.
The authors are grateful for the financial support from KYOCERA corporation.
- Y. Shao-Horn, W. C. Sheng, S. Chen, P. J. Ferreira, E. F. Holby, and D. Morgan, “Instability of supported platinum nanoparticles in low-temperature fuel cells,” Topics in Catalysis, vol. 46, no. 3-4, pp. 285–305, 2007.
- R. Borup, J. Meyers, B. Pivovar et al., “Scientific aspects of polymer electrolyte fuel cell durability and degradation,” Chemical Reviews, vol. 107, no. 10, pp. 3904–3951, 2007.
- K. Yasuda, A. Taniguchi, T. Akita, T. Ioroi, and Z. Siroma, “Characteristics of a platinum black catalyst layer with regard to platinum dissolution phenomena in a membrane electrode assembly,” Journal of the Electrochemical Society, vol. 153, no. 8, pp. A1599–A1603, 2006.
- J. Xie, D. L. Wood III, D. M. Wayne, T. A. Zawodzinski, P. Atanassov, and R. L. Borup, “Durability of PEFCs at high humidity conditions,” Journal of the Electrochemical Society, vol. 152, no. 1, pp. A104–A113, 2005.
- E. Antolini, J. R. C. Salgado, R. M. da Silva, and E. R. Gonzalez, “Preparation of carbon supported binary Pt-M alloy catalysts (M first row transition metals) by low/medium temperature methods,” Materials Chemistry and Physics, vol. 101, no. 2-3, pp. 395–403, 2007.
- S. Takizawa, A. Nakazawa, M. Inoue, and M. Umeda, “Anodic Pt dissolution in concentrated trifluoromethanesulfonic acid,” Journal of Power Sources, vol. 195, no. 18, pp. 5966–5970, 2010.
- Project Annual Report for FYH20 (ID: 100014110), http://www.nedo.go.jp/.
- M. Umeda, Y. Kuwahara, A. Nakazawa, and M. Inoue, “Pt degradation mechanism in concentrated sulfuric acid studied using rotating ring-disk electrode and electrochemical quartz crystal microbalance,” Journal of Physical Chemistry C, vol. 113, no. 35, pp. 15707–15713, 2009.
- L. Kim, C. G. Chung, Y. W. Sung, and J. S. Chung, “Dissolution and migration of platinum after long-term operation of a polymer electrolyte fuel cell under various conditions,” Journal of Power Sources, vol. 183, no. 2, pp. 524–532, 2008.
- S. Mitsushima, Y. Koizumi, S. Uzuka, and K. I. Ota, “Dissolution of platinum in acidic media,” Electrochimica Acta, vol. 54, no. 2, pp. 455–460, 2008.
- X. Yu and S. Ye, “Recent advances in activity and durability enhancement of Pt/C catalytic cathode in PEMFC. Part II: degradation mechanism and durability enhancement of carbon supported platinum catalyst,” Journal of Power Sources, vol. 172, no. 1, pp. 145–154, 2007.
- W. Bi, G. E. Gray, and T. F. Fuller, “PEM fuel cell PtC dissolution and deposition in Nafion electrolyte,” Electrochemical and Solid-State Letters, vol. 10, no. 5, pp. B101–B104, 2007.
- H. Yoshida, T. Kinumoto, Y. Iriyama, Y. Uchimoto, and Z. Ogumi, “XAS study for degradation mechanism of Pt/C catalyst during potential cycling test,” ECS Transactions, vol. 11, no. 1, pp. 1321–1329, 2007.
- S. Mitsushima, S. Kawahara, K. Ota, and N. Kamiya, “Consumption rate of Pt under potential cycling,” Journal of the Electrochemical Society, vol. 154, no. 2, pp. B153–B158, 2007.
- X. Wang, R. Kumar, and D. J. Myers, “Effect of voltage on platinum dissolution,” Electrochemical and Solid-State Letters, vol. 9, no. 5, pp. A225–A227, 2006.
- T. Ishimoto, T. Ogura, M. Umeda, and M. Koyama, “Theoretical study on dissolution and reprecipitation mechanism of Pt complex in Pt electrocatalyst,” Journal of Physical Chemistry C, vol. 115, no. 7, pp. 3136–3142, 2011.
- H. Schulenburg, B. Schwanitz, J. Krbanjevic, N. Linse, G. G. Scherer, and A. Wokaun, “Quantification of platinum deposition in polymer electrolyte fuel cell membranes,” Electrochemistry Communications, vol. 13, no. 9, pp. 921–923, 2011.
- A. S. Danerol, C. Bas, L. Flandin, E. Claude, and N. D. Alberola, “Influence of ageing in fuel cell on membrane/electrodes interfaces,” Journal of Power Sources, vol. 196, no. 7, pp. 3479–3484, 2011.
- S. Mitsushima, K. Shinkoda, K. Matsuzawa, and K. Ota, “Solubility and permeability of Pt ion in polymer electrolyte,” in Proceedings of the 62nd Annual Meeting of the International Society of Electrochemistry Abstract, Niigata, Japan, September 2011.
- A. M. Gómez-Marín, A. Berná, and J. M. Feliu, “Spectroelectrochemical studies of the Pt(111)/Nafion interface cast electrode,” Journal of Physical Chemistry C, vol. 114, no. 47, pp. 20130–20140, 2010.
- R. Subbaraman, D. Strmcnik, V. Stamenkovic, and N. M. Markovic, “Three phase interfaces at electrified metal-solid electrolyte systems 1. Study of the pt(hkl)-Nafion interface,” Journal of Physical Chemistry C, vol. 114, no. 18, pp. 8414–8422, 2010.
- A. Ohma, K. Fushinobu, and K. Okazaki, “Influence of Nafion film on oxygen reduction reaction and hydrogen peroxide formation on Pt electrode for proton exchange membrane fuel cell,” Electrochimica Acta, vol. 55, no. 28, pp. 8829–8838, 2010.
- O. J. Curnick, P. M. Mendes, and B. G. Pollet, “Enhanced durability of a Pt/C electrocatalyst derived from Nafion-stabilised colloidal platinum nanoparticles,” Electrochemistry Communications, vol. 12, no. 8, pp. 1017–1020, 2010.
- J. Healy, C. Hayden, T. Xie et al., “Aspects of the chemical degradation of PFSA ionomers used in PEM fuel cellsx,” Fuel Cells, vol. 5, no. 2, pp. 302–308, 2005.
- S. D. Knights, K. M. Colbow, J. St-Pierre, and D. P. Wilkinson, “Aging mechanisms and lifetime of PEFC and DMFC,” Journal of Power Sources, vol. 127, no. 1-2, pp. 127–134, 2004.
- E. Endoh, S. Terazono, W. Hardiyanto, and T. Yasuyuki, “Degradation study of MEA for PEMFCs under low humidity conditions,” Electrochemical and Solid-State Letters, vol. 7, no. 7, pp. A209–A211, 2004.
- S. J. Paddison, D. W. Reagor, and T. A. Zawodzinski Jr., “High frequency dielectric studies of hydrated Nafion,” Journal of Electroanalytical Chemistry, vol. 459, no. 1, pp. 91–97, 1998.
- G. Oster and J. G. Kirkwood, “The influence of hindered molecular rotation on the dielectric constants of water, alcohols, and other polar liquids,” The Journal of Chemical Physics, vol. 11, no. 4, pp. 175–178, 1943.
- B. Delley, “From molecules to solids with the DMol3 approach,” Journal of Chemical Physics, vol. 113, no. 18, pp. 7756–7764, 2000.
- B. Delley, “An all-electron numerical method for solving the local density functional for polyatomic molecules,” The Journal of Chemical Physics, vol. 92, no. 1, pp. 508–517, 1990.
- F. Kodera, Y. Kuwahara, A. Nakazawa, and M. Umeda, “Electrochemical corrosion of platinum electrode in concentrated sulfuric acid,” Journal of Power Sources, vol. 172, no. 2, pp. 698–703, 2007.
- J. F. Llopis and F. Colom, Encyclopedia of Electrochemistry of The Elements, vol. 6, Edited by A. J. Bard, Marcel Decker, New York, NY, USA, 1976.
- K. Shimazu and H. Kita, “In situ measurements of water adsorption on a platinum electrode by an electrochemical quartz crystal microbalance,” Journal of Electroanalytical Chemistry, vol. 341, no. 1-2, pp. 361–367, 1992.
- T. Ishimoto, T. Ogura, R. Nagumo, and M. Koyama, “Theoretical study on dissolved structure of Pt complex in polymer electrolyte fuel cell,” ECS Transactions, vol. 25, no. 1, pp. 799–806, 2009.
- A. Roudgar, M. Eikerling, and R. van Santen, “Ab initio study of oxygen reduction mechanism at Pt4 cluster,” Physical Chemistry Chemical Physics, vol. 12, no. 3, pp. 614–620, 2010.
- R. L. Parreira, G. F. Caramori, S. E. Galembeck, and F. Huguenin, “The nature of the interactions between Pt4 cluster and the adsorbates H, OH, and H2O,” Journal of Physical Chemistry A, vol. 112, no. 46, pp. 11731–11743, 2008.
Copyright © 2012 Takayoshi Ishimoto and Michihisa Koyama. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.