Full derivations of Heyrovsky–Volmer
(HV), Tafel–Volmer
(TV), Heyrovsky–Tafel (HT), and Heyrovsky–Tafel–Volmer
(HTV) mechanisms under steady state conditions are provided utilizing
a new theoretical framework which allows better understanding of each
of the mechanistic currents and part currents. Simple and easily implemented
equations are presented, which provide both the hydrogen coverage
and electrochemical current as a function of overpotential and relevant
kinetic parameters. It is shown how these responses are governed by
a set of dimensionless parameters associated with the ratio of electrokinetic
parameters. For each of the different mechanisms, an “atlas”
of Hads coverage with overpotential and corresponding current
density is provided, allowing an understanding of all possible responses
depending on the dimensionless parameters. Analysis of these mechanisms
provides the limiting reaction orders of the exchange current density
for protons and bimolecular hydrogen for each of the different mechanisms,
as well as the possible Tafel slopes as a function of the molecular
symmetry factor, β. Only the HV mechanism is influenced by pH,
whereas the TV, HT, and HTV mechanisms are not. The cases where the
equations simplify to limiting forms are discussed. Analysis of the
exchange current density from experimental data is discussed, and
it is shown that fitting the linear region around the equilibrium
potential underestimates the true exchange current density for all
of the mechanisms studied. Furthermore, estimates of exchange current
density via back-extrapolation from large overpotentials are also
shown to be highly inaccurate. Analysis of Tafel slopes is discussed
along with the mechanistic information which can and cannot be determined.
The new models are used to simultaneously fit 16 experimental responses
of Pt/C electrodes in acid toward the hydrogen evolution reaction
(her)/hydrogen oxidation reaction (hor) as a function of η,
pH, p(H2), and temperature, using a consistent
set of electrokinetic parameters. Examples of implementation of the
equations as both computable document format and Excel spreadsheets
are provided.