SUPPORTING INFORMATION

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1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2018 SUPPOING INFORMATION Unifying theoretical framework for deciphering the oxygen reduction reaction on platinum Jun Huang, 1,2,z Jianbo Zhang, 2,3 Michael Eikerling 4 1 College of Chemistry and Chemical Engineering, Central South University, Changsha , PR China 2 Department of Automotive Engineering, State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing , China 3 Beijing Co-innovation Center for Electric Vehicles, Beijing Institute of Technology, Beijing , China 4 Department of Chemistry, Simon Fraser University, Burnaby, BC V5A 1S6, Canada Corresponding authors: jhuangelectrochem@qq.com

2 Lateral interaction effect Figure S 1. Effect of ξ OH on the coverage of adsorbed oxygen intermediates (left) with ξ O = 10 kj mol 1. Effect of ξ O on the coverage of adsorbed oxygen intermediates (right) with ξ OH = 10 kj mol 1. Other parameters are given in Figure 2 of the main-text.

3 Interfacial parameters Table S1. Parameters of the electrified interface in calculation of σ M. Category Item Value Note General Gas constant, R J K 1 mol 1 Constant Faraday constant, F C mol 1 Constant Temperature, T K Typical value Elementary charge, e C Constant Avogadro's number, N A mol 1 Constant Water dipole moment, 3.1 D Typical value Dielectric and structural μ w Pt atom density, N tot m 2 Calculated using 2 4/ 3a Pt with a Pt = 3.92Å Vacuum permittivity, ε F m 1 Constant Permittivity of oxide layer, ε PtO Permittivity of the IHP, 1.0 ε 0 Nothing but 06.0 ε 0 1 vacuum inside the oxide layer ε IHP Permittivity of the OHP, ε OHP Permittivity of bulk solution, ε s Thickness of the oxide layer, δ PtO Net charge number per oxide site, ς OH Thickness of the IHP, δ IHP Thickness of the OHP, δ OHP Potential difference between bulk and 30.0 ε ε 0 Constant (bulk water) 0.18 nm DFT calculation DFT calculation nm Constant (the diameter of water dipole) nm V 1 interfacial metal, Δφ M

4 A collection of ORR Tafel slopes of Pt electrocatalysts. Table S2. A collection of ORR Tafel slopes of Pt electrocatalysts. Sample Pt/Vulcan Pt(111) 50% wt Pt/Vulcan Pt(111) Pt-poly, Pt 3 Ni, Pt 3 Co Pt disk electrode Method & condition RDE, O 2 -saturated 0.1M HClO 4, mass-transfer corrected RDE, O 2 -saturated 0.1M HClO 4 IR-free voltage of a catalyst layer in H 2 /O 2 gas condition at 100% RH and 80 RDE, O 2 -saturated 0.1M HClO 4 at 296 K, intrinsic kinetic current RDE, O 2 -saturated 0.1M HClO 4 at 293 K, mass-transfer corrected RDE, HClO 4 and H 2 SO 4 Tafel Potential Potential slope / dependence mv dec 1 range / V Reference 60~ Decreasing Not shown Decreasing 5 ~ Decreasing Decreasing Decreasing 8

5 Effect of ionic strength Figure S 2. Effect of ionic strength on the ORR for the case of ph=1.2 in Figure 3.

6 Rate constants Figure S 3. Variations in the rate constants as a function of electrode potential for ph=1.2 in Figure 3.

7 Oxide coverage as a function of the chemisorption energy Figure S 4. Normalized total oxide coverage, θ OX = (θ OH + θ O )/θ max, as a function of hydroxyl binding energy. The data are calculated at E = 0.9 V (RHE) using the same parameter set as in Figure 7.

8 0 Relation between ORR activity and G OH According to the definition we obtain, K 3 = k 3 = [H + ] exp ( E a, 3 E a,3 ) = [H + ] exp ( ΔG 3 k 3 ) (S1) = [H + ] exp ( F(E E eq 3 ) + δg OH δg O ). Based on the scaling relation, E 3 eq 0 of a catalyst having a different ΔG OH relative to ΔG Pt,0 OH is expressed as, Pt,0 ) E eq 3 = E Pt,eq 3 + (ζ O 1)(ΔG 0 OH ΔG OH F. (S2) where E 3 Pt,eq = 0.95 V as in Table 1. Substituting Eq.(S2) into Eq.(S1) leads to, K 3 = [H + ] exp ( F(E E 3 4 Pt,eq ) ) exp ( δg O δg OH ) exp ( F e (ζ O (S3) 1)(ΔG 0 OH ΔG Pt,0 OH )) = K Pt, 3 exp ( 1 (ζ O 1)(ΔG 0 OH ΔG Pt,0 OH )), with K Pt, 3 = [H + ] exp ( F(E E Pt,eq 3 ) ) exp ( δg O δg OH ). Similarly, we have, Pt,0 ) K 4 = K Pt, 4 exp ( (ΔG OH 0 ΔG OH ), (S4) with K Pt, 4 = [H + ] exp ( F(E E Pt,eq 4 ) ) exp ( δg OH ). For step (1),

9 Pt,0 ) k 1 = k Pt, 1 exp ( β 1ζ OOH (ΔG 0 OH ΔG OH ), (S5) with k Pt, 1 = k 0 1 exp ( E 0 Pt,eq a,i β1 F(E E 1 ) ) [O 2 ][H + ]. For step (3), Pt,0 ) k 3 = k Pt, 3 exp ( β 3(ζ O 1)(ΔG 0 OH ΔG OH ), (S6) with k Pt, 3 = k 0 3 exp ( E a,3 0 Pt,eq β 3 F(E E 3 ) ) θ O [H + ]. For step (4), Pt,0 ) k 4 = k Pt, 4 exp ( β 4(ΔG 0 OH ΔG OH ), (S7) with k Pt, 4 = k 0 4 exp ( E a,4 0 Pt,eq β 4 F(E E 4 ) ) θ OH [H + ]. Combining Eqs. (S3)-(S7) into the relation v ORR = (K 3 ) ν (K 4 ) μ k i gives, 0 v ORR = v ORR exp ( (ν(ζ O 1) + μ ζ i ) (ΔG 0 OH ΔG Pt,0 OH )), (S8) 0 with v ORR = (K 3 Pt, ) ν (K 4 Pt, ) μ k i Pt, and β 1 ζ OOH, i = 1 ζ i = { β 3 (ζ O 1), i = 3, β 4, i = 4 (S9)

10 Rate determining term Figure S 5. Rate-determining term of the ORR rate expression for (ΔG 0 OH ΔG Pt,0 OH ) = 0 and 0.2 ev. Labels for the curves are the same as in Figure 5. References 1. J. Huang, A. Malek, J. Zhang and M. H. Eikerling, The Journal of Physical Chemistry C, 2016, 120, A. Malek and M. H. Eikerling, Electrocatalysis, 2017, DOI: /s E. J. Coleman and A. C. Co, ACS Catalysis, 2015, 5, A. M. Gomez-Marin, R. Rizo and J. M. Feliu, Catalysis Science & Technology, 2014, 4, N. P. Subramanian, T. Greszler, J. Zhang, W. Gu and R. R. Makharia, ECS Transactions, 2011, 41,

11 J. X. Wang, J. Zhang and R. R. Adzic, The Journal of Physical Chemistry A, 2007, 111, N. Markovic, T. Schmidt, V. Stamenkovic and P. Ross, FUEL CELLS-WEINHEIM-, 2001, 1, D. B. Sepa, M. V. Vojnovic and A. Damjanovic, Electrochimica Acta, 1981, 26,