Electrochemical formation and growth of a new phase: what to do next?
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Electrochemical formation and growth of a new phase: what to do next? Alexander Milchev 1 Received: 17 June 2020 / Revised: 17 June 2020 / Accepted: 19 June 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
The electrochemical formation and growth of new-phase metal and alloy clusters are certainly important processes both from a scientific and from a purely practical point of view. This is the reason why they were studied by many authors all over the world, and the obtained theoretical and experimental results were published not only in separate scientific papers but also in high-level scientific books [1–3]. Valuable information on the same subjects can also be found in some more recent scientific books, which are certainly worth reading, too [4–10]. What to do next? This is apparently an important question, which is however not easy to answer. Still, in what follows, I will share my personal opinion on this subject. It is well known that very often, the electrochemical formation of new-phase metal clusters is a result of multi-step ion discharge consisting of zf fast steps preceding the slow, ratedetermining step repeated ν times and followed by z-zf-ν fast steps. In this case, the current Im [A] due to the multi-step ion discharge reaction is given as [4]: eη i eη io n h z h z−z f f þα −α I m ¼ Si0;m exp −exp − ð1Þ kT kT v v which differs significantly from the theoretical equation for the current Is [A] in case of a simple, single-step, z-electron reaction, Ox + ze ⇄ Red, h αzeη i ð1−αÞzeη I s ¼ Si0;s exp ð2Þ −exp − kT kT In Eqs. (1) and (2), S/cm2 is the working electrode surface area, where the new-phase clusters are formed and grow, i0,m * Alexander Milchev [email protected] 1
Rostislaw Kaischew Institute of Physical Chemistry, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 11, 1113 Sofia, Bulgaria
[A cm−2] and i0,s [A cm−2] are the corresponding exchange current densities, i0,m depends on the value of ν, α is the ions’ transfer coefficient, and e is the elementary electric charge defined as e = F/NA, F, and NA being the Faraday and the Avogadro numbers, respectively. Аs usual, the symbols k and T stand for the Boltzmann constant and for the absolute temperature, and η [V] is the electrochemical overpotential (or electrochemical overvoltage) expressed as1 η ¼ E∞ −E
ð3Þ
Here, E is the actual potential of the working electrode and E∞ is the equilibrium potential of the depositing bulk new phase at an ionic activity asol ∞ and a constant temperature T, given by the equation of Nernst E∞ ¼ E0 þ
kT ln asol ∞ ze
ð4Þ
E0 being the standard electrode potential at asol ∞ ¼ 1. Note that the product below defines the electrochemical supersaturation Δμ, which is another important theoretical quantity. Δμ ¼ zeη
ð5Þ
And here comes my first suggestion for new theoretical research. Its purpose must be to derive a theoretical expression for the current Im if the final step, Redz−1 + e− ⇄ Red, is a slow step, too. Say, as slow as the step Redz f þ e− →Redz f
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