*2.2. Activation Overvoltage*

Based on the Butler–Volmer equation, the activation overpotential *E*act,*<sup>i</sup>* can be estimated as a function of current density *i*, exchange current density *i*<sup>0</sup> as well as temperature *T* and charge transfer coefficient α*<sup>i</sup>* [12,13]:

$$E\_{\text{act},i} = \frac{RT\_i}{\alpha\_i F} \text{arcsinh}\left(\frac{i}{2i\_{0,i}}\right) \tag{5}$$

where *R* denotes the universal gas constant and *F* the Faraday constant.

The exchange current density *i*<sup>0</sup> of a platinum electrode as a function of partial pressure *pi*, temperature *T*, catalyst loading *Li* and specific area *ai* can be calculated on the basis of a reference value *i*0,ref [11]:

$$i\_{0,i} = \ i\_{0, \text{ref},i} a\_i! L\_i \left(\frac{p\_i}{p\_{\text{ref}}}\right)^\prime \exp\left[-\frac{\Lambda G\_i}{RT\_i} \left(1 - \frac{T\_i}{T\_{\text{ref}}}\right)\right] \tag{6}$$

$$T\_{\text{ref}} = 298.15 \text{ K}; \ p\_{\text{ref}} = 1.0125 \text{ bar}.$$

For simplicity, a constant value was used for the activation energy Δ*Gi*, even though it can vary under real operating conditions [14].
