Theoretical Hydrogen Electrode for ORR S. Sinthika

Standard Hydrogen Electrode A redox electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. pressure of hydrogen gas is 1 bar and the concentration of hydrogen ions is 1. consists of a platinum electrode immersed in acid of pH = 0 H + (aq) + e – ⇌ ½ H 2(g) ---- (1) E 0 = 0.0 V

Reversible Hydrogen Electrode The measured potential does not change with pH. The electrode is in the actual electrolyte solution and not separated by a salt bridge. The hydrogen ion concentration is not 1, but corresponds to that of the electrolyte solution. can achieve a stable potential with a changing pH value E 0 = 0.00 – 0.059*pH

Environments for ORR The equilibrium potential for ORR is 1.23 V in acidic (pH =0) environments and V in alkaline environments (pH=14) in the SHE scale. The potential window is hence 0 to 1.23 V in acidic medium and V to V in alkaline medium. However, when measured vs. the RHE the window is from 0 to 1.23 V irrespective of the medium.

Computational Standard Hydrogen Electrode H + (aq) + e – ⇌ H* ⇌ ½ H 2(g) H* is bound to the surface. Ignoring H*, H + (aq) + e – ⇌ ½ H 2(g) At T = 300K, p H2 = 1 bar, and pH = 0, ∆G, is zero. Hence, the free energies of ½ H 2(g) and H + (aq) + e – are equal. This defines U = 0 V. At another potential, the chemical potential of the electrons e – is changed by a factor of -eU with respect to H 2 in the gas phase.

Using the CSHE to find the Free Energies reference potential : SHE Equation (1) is in equilibrium free energy per H for the reaction H + + e – is equal to ½ H 2 Effect of a bias (states involving an electron) : shift the energy of this state by -eU, where U is the electrode potential ΔG U = -eU Effect of pH: ΔG pH = k B T ln 10 × pH free energy correction due to the electrochemical double layer, ΔG field is small ΔG= ΔE+ ΔZPE −TΔS+ ΔG U + ΔG pH + ΔG field

Reaction Steps 4H + + 4e - + O 2 +Pt_111 (0) 3H + + 3e - + OOH/Pt_111 (1) 2H + + 2e - + H 2 O + O/Pt_111 (2) H + + e - + H 2 O + OH/Pt_111 (3) 2H 2 O + Pt_111 (4)

E (H 2 ) = eV E (H 2 O) = eV Entropy (TS) values: O 2 = 0.64 eV H 2 = 0.41 eV H 2 O = 0.67 eV G(H 2 ) = E(H 2 ) – TS(H 2 ) = = eV G(H 2 O) = E(H 2 O) – TS(H 2 O) = = eV G(O 2 ) = 2G(H 2 O) – 2G(H 2 ) = eV G(H + ) = (1/2)G(H 2 ) = eV Free Energies of Intermediates U = 0, pH = 0 The calculated values are the same for SHE and RHE as pH = 0

G(0) = 4* (1/2) G(H 2 ) + G(O 2 ) + E(Pt_111) = eV G(1) = 3* (1/2) G(H 2 ) + E(OOH/Pt_111) = eV G(2) = 2* (1/2) G(H 2 ) + G(H 2 O) + E(O/Pt_111) = eV G(3) = (1/2) G(H 2 ) + G(H 2 O) + E(OH/Pt_111) = eV G(4) = 2G(H 2 O) + E(pt_111) = eV G(0) – G(4) = 4.92 eV (1/2) G(H 2 ) = G(H + +e - ) Free Energies of Reactions, U = 0, pH = 0 The calculated values are the same for SHE and RHE as pH = 0

E (H 2 ) = eV E (H 2 O) = eV Entropy (TS) values: O 2 = 0.64 eV H 2 = 0.41 eV H 2 O = 0.67 eV G(H 2 ) = E(H 2 ) – TS(H 2 ) = = eV G(H 2 O) = E(H 2 O) – TS(H 2 O) = = eV G(O 2 ) = 2G(H 2 O) – 2G(H 2 ) = eV G(H + ) = (1/2)G(H 2 ) – K B Tln10 * pH = (1/2)G(H 2 ) – eV = eV Free Energies of Intermediates U = 0, pH = 3 The calculations are for SHE as pH is changing; for RHE the potential window is same as pH= 0

G(0) = 4* G(H + ) + G(O 2 ) + E(Pt_111) = eV G(1) = 3* G(H + ) + E(OOH/Pt_111) = eV G(2) = 2* G(H + ) + G(H 2 O) + E(O/Pt_111) = eV G(3) = G(H + ) + G(H 2 O) + E(OH/Pt_111) = eV G(4) = 2G(H 2 O) + E(pt_111) = eV G(0) – G(4) = eV Free Energies of Reaction U = 0, pH = 3 U=0, pH = 3 same as U= , pH = 0 The calculations are for SHE as pH is changing, for RHE the potential window is same as pH= 0

Free Energies of Intermediates U = 0, pH = 14 E (H 2 ) = eV E (H 2 O) = eV Entropy (TS) values: O 2 = 0.64 eV H 2 = 0.41 eV H 2 O = 0.67 eV G(H 2 ) = E(H 2 ) – TS(H 2 ) = = eV G(H 2 O) = E(H 2 O) – TS(H 2 O) = = eV G(O 2 ) = 2G(H 2 O) – 2G(H 2 ) = eV G(H + ) = (1/2)G(H 2 ) – K B Tln10 * 14 = (1/2)G(H 2 ) – eV = eV U=0, pH = 14 same as U= +0.83, pH = 0 The calculations are for SHE as pH is changing, for RHE the potential window is same as pH= 0

G(0) = 4* G(H + ) + G(O 2 ) + E(Pt_111) = eV G(1) = 3* G(H + ) + E(OOH/Pt_111) = eV G(2) = 2* G(H + ) + G(H 2 O) + E(O/Pt_111) = eV G(3) = G(H + ) + G(H 2 O) + E(OH/Pt_111) = eV G(4) = 2G(H 2 O) + E(pt_111) = eV G(0) – G(4) = eV Free Energies of Reaction U = 0, pH = 14 U=0, pH = 14 is the same as U= +0.83, pH = 0 The calculations are for SHE as pH is changing, for RHE the potential window is same as pH= 0