文摘
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.