Why conclusions from platinum model surfaces do not necessarily lead to enhanced nanoparticle catalysts for the oxygen reduction reaction

Platinum model-surface and nanoparticle catalysts for the oxygen reduction reaction are enhanced by the presence of concave sites.

We approximate the free energies of the adsorbates as: E DFT is the DFT-calculated total energy. ZPE is the zero-point energy estimated through vibrational-frequency analysis within the harmonic-oscillator approximation. E solvation is the solvation energy granted by the liquid, which is -0.575 for *OH, in line with previously reported values [5,6,12]. Entropy corrections for adsorbed species were taken to be zero, so that our results can be directly compared to other studies in the literature [5,7]. Reaction energies (ΔG MERGEFORMAT (S8). In order to represent liquid-phase water, TS is that of the gas phase and E solvation is the difference between the formation energies of gas-phase and liquid-phase water, namely -0.087 eV at 298 K [4,8]. For H 2 , E solvation is zero, and TS is taken from thermodynamic tables. All corrections used in this study appear in Table S2.  Figure   1 in the main text), it is important to elucidate the qualitative and quantitative aspects of its adsorption on Pt surfaces. At the reference electrode potential of 0.9 V RHE , ideally flat Pt (111) surfaces adsorb ~1/3 monolayer (ML) of *OH in cyclic voltammetry [9]. Besides, recent findings (see [10,11,12,13]) strongly suggest that *OH is an atop adsorbate on Pt(111) embedded in a half-dissociated water layer. Those two conditions can be modelled through a surface lattice of the type (see Figure S1), in which every *OH adsorbate is 3 3 30 R  o surrounded by water only and its coverage is 1/3 ML. Importantly, we do not include *H 2 O species in the calculation of in view of their weak adsorption energies on Pt extended ____ CN surfaces and nanoparticles [14]. At 0.9 V RHE , defective Pt surfaces such as stepped single crystals adsorb not only *OH but also *O. The latter adsorbate is supposed to be located at the step edges, while the (111) terraces will tend to form a half-dissociated water layer, the extension of which depends on the terrace width. Figure 2 in the main text gives an overview of the most probable *O adsorption sites on various stepped Pt surfaces. At these electrode potentials, *O blocks step edges. Its low mobility is due to its substantial adsorption energies and relatively high diffusion barriers [15]. Besides, *O is not part of the (half-dissociated) water layer due to its poor solvation and adsorption configuration (threefold hollow sites on terraces, and bridge sites at step edges, while adsorbates at water layers are atop) [12,13]. In view of these features, *O is included in the calculation of S5 for the neighboring sites. However, as can be seen in Table S3,    provided. In all cases, *OH is located at step edges and *O is adsorbed at the same sites as in Figure 2 in the main text, though its coverage is lower due to the site competition with *OH.
The common feature of the sites in panels A-G in Figure S2 is that , due to the low  The data used to build Figure 3 in the main text are provided in Table S3. It contains the site descriptions of Figures 2, 4, S3 and S8 and the potentials for *OH transformation into H 2 O, which is the potential-limiting step for the ORR on the Pt catalysts under study.

S3. Experimental assessment of *OH adsorption energies
Experimentally, the apparent difference in the adsorption energies of certain adsorbates can be assessed using data obtained using voltammetry experiments [16,17]. This is possible when the interpretation of a peak is clear, which is the case for *OH on Pt at potentials in the range 0.6-0.8 V RHE . First of all, adsorption isotherms are constructed by integrating the relevant part of the voltammogram, giving rise to a plot correlating *OH coverage and electrode potential (black curves in Figure S4). The differences in *OH adsorption energies, which are identical to the differences in *OH adsorption potentials, are determined at a coverage of 0.5 ML (blue lines in Figure S4). Figure S4. Schematics of the procedure used to estimate the relative change in *OH energy based on experimental voltammograms (in this case using integrated anodic parts of them). The difference between the potentials where half of the maximal fractional coverage is reached at different surfaces are considered to be a good approximation of the ΔU OH between them.

S4. Electrochemical measurements
All original electrochemical experiments in this work were performed in a three-electrode electrochemical cell under so-called hanging meniscus configuration, as schematically shown in Figure S5.  Figure S6 shows the schematics of the initial stages of the coalescence of two Pt nanoparticles, in which sites with are present near the junction. ____ 7.5 CN  S10 Figure S6. Schematic representation of the initial stage of coalescence of two convex nanoparticles. This situation is probable at high nanoparticle loading [18] and when nanoparticles form super-ordered arrays [19]. The arrow schematically shows an OH-adsorption site with the generalized coordination number greater than 7.5. Figure S7 contains schematics of the mesoporous Pt ORR catalysts reported in [20]. reported in [20]. Figure S8 shows a comparison between pristine and missing-row-reconstructed Pt(110). Purple arrows indicate the location of the missing rows. Finally, Figure S9 shows all of the inequivalent sites on Pt 201 , and 3 sites on Pt 368 the activities of which appear in Figure 3 in the main text and in Table S3 in this Supporting Information.

S6. Concave region of the coordination-activity plot
In Figure S10 we present a zoom in the concave region of Figure 3 in the main text to facilitate its detailed visualization. Figure S10. Concave region of the coordination-activity plot for the electrocatalysis of the oxygen reduction reaction on pure Pt sites.