Rate Determining Factors in Multi-Step Electrocatalytic Processes
Authors: Gottesfeld Shimshon 
Published: May 2020

This paper offers a mechanistic perspective applicable to a range of technically significant electrocatalytic processes , based on measured polarization curves and impedance spectra. The diagnostics offered is based on a comprehensive rate equation which includes a potential dependent pre-exponential factor.
A common pattern observed in mechanisms of electrocatalytic processes, involves a step preceding the RDS, that establishes the surface composition required for the onset of the RDS [1,2]. Such “pre-step” can involve activation of surface sites by removal of surface blocking species and/or formation of adsorbed intermediates which serve as reactants in the RDS. Electrically speaking, these “pre-steps” are overpotential-driven surface charging processes, i.e., the current associated with the pre-step is pseudocapacitive in nature. Consequently, the rate of the electrocatalytic process is determined by combined effects of the overpotential on: (i) the catalyst surface composition and, (ii) the activation energy of the RDS.
Recognizing that active intermediate formation and/or surface site activation involve switching of a surface redox system, the comprehensive expression for the rate of a cathodic electrocatalytic process, is expected to have the following general form [1,2] :
(1) J(Ecath) = Cr
g Fk0 A

∗

× f(Ecath−E0
redox)×10ˆ{[−
D
H#
act
/2.3RT]−[(Ecath−E◦
cell)/b]}

where, f
(Ecath−E0
surf. redox) represents the fraction of surface sites in active form at Ecath

For a 1e surface redox system obeying the Nernst equation, the fractional population of sites in active form is given by:
(2) f(Ecath−E0
redox) = 10ˆ [(F/2.3RT) (Ecath− E0
surf. redox )+1]−1

and the explicit , full expression for J(Ecath), becomes:
(3) J(Ecath) = Cr
g Fk0 A

∗

× 10ˆ[(F/2.3RT)(Ecath−E0
redox )+1]−1 ×10ˆ{[−
D
H#
act
/2.3RT]−[(Ecath−E◦
cell)/b]}

The last equation reveals that both types of over-potential driven surface transformation processes --site activation and active intermediate formation-- are expected to leave the same signature in the polarization curve. : a low Tafel slope of ~ 60 mV/decade at lower current densities, gradually transitioning to a slope of ~120mV/decade with increase of the current. We show in this contribution that these two different causes of a lower Tafel slope at low current density, can be distinguished from EIS measurements.
In the case of the HOR, a sequence of two steps, taking place ,for example, according to the Heyrovsky-Volmer mechanism, results in two capacitive arcs in the Nyquist plot. In contrast, the EIS reported in the literature in the low current range of the ORR , typically exhibits only one capacitive arc in the frequency range 5kHz- 0.1Hz [ 3 ]. The low Tafel slope observed near the onset potential of the ORR has been ascribed to overpotential-driven removal of a surface blocking oxide formed by water discharge [ 4 ] , however, no spectral feature corresponding to this process could be detected in the EIS spectrum in the frequency range 5kHz- 0.1Hz [3]. This “miss” is resolved when EIS spectra for the ORR are recorded down to significantly lower frequencies [5]. At frequencies under 0.1Hz, the EIS spectrum for the ORR , exhibits an additional, inductive loop .
The inductive loop in the EIS observed for the ORR, reflects the slow process of surface oxide reduction which enhances the rate of electron transfer to the dioxygen molecule by increasing the population of active, metal surface sites. Another example of an EIS exhibiting an inductive loop at low frequency , is that recorded for hydrogen oxidation at Pt in the presence of COads [6]. The similar patterns of the spectra for ORR and, for HOR in the presence of COads, provide further support for the assignment of the inductive loop in the EIS for the ORR to slow removal of a site blocking species.
These different types of EIS spectra will be further discussed in this talk, with reference to the comprehensive dependence of the rate of multi-step electrocatalytic processes on overpotential .
Acknowledgement:
This is a contribution to the Electrocatalysis Symposium at the ECS meeting in Montreal , memorizing Andrzej Wieckowski.
I remember vividly many technical discussions and very friendly interactions with Andrzej over many years of close acquaintance.

References:

1. S. Gottesfeld, in Fuel Cell Science, A. Wieckowski and J.K.Norskov, Eds., John Wiley, (2010), p. vii
2. S. Gottesfeld, J. Electrochem. Soc. 165, J3405-J3412 ( 2018)
3. T.E. Springer, T.A. Zawodzinski, M.S. Wilson and S. Gottesfeld, , J. Electrochem. Soc.,
143, 587-599 (1996)
4. F. Uribe , M.S. Wilson, T.E. Springer and S. Gottesfeld, Proceedings Volume 92-11, The ECS Proceedings Series, Pennington, NJ (1992).
5. R. Makharia, M. F. Mathias and D. R. Baker,
J. Electrochem. Soc.,
152 , A970-A977 (2005)
6. M. Ciureanu and H. WangJ. Electrochem. Soc. ,
146 , 4031-4040 (1999)