Atomic-scale understanding of particle size effects for
the oxygen reduction reaction on Pt

G. A. Tritsarisa,b, J. Greeleyc, J. Rossmeisla, J. K. Nørskovb,d

Center for Atomic-scale Materials Design, Department of Physics, Technical University of Denmark, DK 2800, Denmarka

Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, United Statesb

Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL 60439, United Statesc

Department of Chemical Engineering, Stanford University, Stanford, CA 94305, United Statesd

Supplementary material includes additional computational details, calculated adsorption energies and additional references.

Computational details

Extended slabs were constructed for modeling the fcc(544) surface (Figure S1). The slabs comprisethree atomic layers in the direction perpendicular to the (100) plane, surrounded with 13Å of vacuum in a (1x2) simulation cell. Total energy calculations are done with the GPAW program package, a DFT implementation based on the projector-augmented wave (all electron, frozen core approximation) method[1], which uses real-space uniform grids and multigrid methods[2,3]. For the description of exchange and correlation, the RPBE functional[4] is chosen and a Monkhorst-Pack mesh is used for k-space integration resulting in a set of 4 special points for the sampling of the irreducible Brillouin zone. The grid spacing is set to h = 0.18Å as a tradeoff between computational efficiency and accuracy and a stencil of O(h8) accuracy is used to discretize the kinetic energy Laplacian. The energies are converged to 10-4 eV per valence electron. For structure optimization, the top slab layer was relaxed by the minimization of all inter-atomic forces to the upper limit of 0.045 eV/Å.


Fig. S1Slab model of an fcc(544) surface.

Calculated adsorption energies are given with reference to gas-phase H2O and H2 energies,ΔEH2O(g)= -14.02eV and ΔEH2(g) = -6.72eV,corrected with zero-point energy and entropy contributions (see also the work of Nørskov et al.[5]). Thermal corrections to enthalpy are assumed negligible. The corrections are taken from the work of Ferrin et al.[6].

Adsorption free energies of oxygen reduction intermediates

The adsorption free energies ΔG of the O and OH intermediates used for making the plots shown in Figure5are summarized in Table S1.

Step coverage / Step / 1st row / 2nd row / 3rd row
ΔGO / non-occupied / 1.10 / 1.53 / 1.50 / 1.43
half-occupied / 2.02 / 1.62 / 1.51 / 1.44
ΔΔGO / 0.92 / 0.09 / 0.01 / 0.01
ΔGOH / non-occupied / 0.46 / 1.31 / 1.33 / 1.29
half-occupied / 1.32 / 1.20 / 1.34 / 1.30
ΔΔGO / 0.86 / -0.11 / 0.01 / 0.01

Table S1. Adsorption free energies of O and OH on Pt(544).

References

[1]P. E. Blöchl, Phys Rev B 50, 17953 (1994).

[2]J. J. Mortensen, L. B. Hansen, and K. W. Jacobsen, Phys Rev B 71, 035109 (2005).

[3]J. Enkovaara, C. Rostgaard, J. Mortensen, J. Chen, M. Dułak, L. Ferrighi, J. Gavnholt, C. Glinsvad, V. Haikola, H. Hansen, H. Kristoffersen, M. Kuisma, A. Larsen, L. Lehtovaara, M. Ljungberg, O. Lopez-Acevedo, P. Moses, J. Ojanen, T. Olsen, V. Petzold, N. Romero, J. Stausholm-Møller, M. Strange, G. Tritsaris, M. Vanin, M. Walter, B. Hammer, H. Häkkinen, G. Madsen, R. Nieminen, J. Nørskov, M. Puska, T. Rantala, J. Schiøtz, K. Thygesen, and K. Jacobsen, J Phys Condens Matter 22, 253202 (2010).

[4]B. Hammer, L. B. Hansen, and J. K. Nørskov, Phys Rev B 59, 7413 (1999).

[5]J. K. Nørskov, J. Rossmeisl, A. Logadottir, L. Lindqvist, J. R. Kitchin, T. Bligaard, and H. Jónsson, J Phys Chem B 108, 17886-17892 (2004).

[6]P. Ferrin, A. U. Nilekar, J. Greeley, M. Mavrikakis, and J. Rossmeisl, Surf Sci 602, 3424-3431 (2008).

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