Thermodynamic Limiting Potential Analysis of the AEM Reaction Scheme

The AEM reaction scheme comprises four elementary steps, as outlined below:

Step 1: H2O + * → *OH + H+ + e- (1) Step 2: *OH → *O + H+ + e- (2) Step 3: *O + H2O → *OOH + H+ + e- (3) Step 4: *OOH → O2 + * + H+ + e- (4)

To determine the reaction free energy change under electrode potential, the CHE model can be used. The free energy of a proton-electron pair is equal to 1/2 H2 in the gas phase at standard conditions plus -eU, where U is the electrode potential with respect to the reversible hydrogen electrode (RHE). Using this framework, the Gibbs free energy change of each step at standard conditions (pH = 0, T =298.15 K) can be expressed by defining the adsorption free energy of intermediates (e.g., *OH) with respect to H2O and H2. The adsorption free energies on metal oxides are inter-connected by a scaling relationship, which allows us to substitute the expression of Gibbs free energy changes with the scaling relationship equations.

By doing so, we obtain the following expressions for the Gibbs free energy changes:

∆G_1 (U) ≈ 0.61∆G_(O*)-0.58 eV-eU (11) ∆G_2 (U) ≈ 0.39∆G_(*O)+0.58 eV-eU (12) ∆G_3 (U) ≈ -0.36∆G_(*O)+2.40 eV-eU (13) ∆G_4 (U) ≈ -0.64∆G_(*O)+2.52 eV-eU (14)

We can define a thermodynamic limiting potential (UL) in each step as the least potential applied to make the reaction free energy change negative by setting Eqs. 11-14 to zero:

UL1 = (0.61∆G_(O*)-0.58 eV)/e (15) UL2 = (0.39∆G_(*O)+0.58 eV)/e (16) UL3 = (-0.36∆G_(*O)+2.40 eV)/e (17) UL4 = (-0.64∆G_(*O)+2.52 eV)/e (18)

Overall, this approach allows us to determine the thermodynamic limiting potential for each step in the AEM reaction scheme, providing important insights into the underlying processes and enabling the design of more efficient and effective catalysts.