A redox couple at an electrode: cyclic voltammetry

Cyclic voltammetry of Fe³⁺ + e⁻ ⇌ Fe²⁺ at platinum, in 0.5 M KCl: the voltammogram as it's swept, and the electrode's Fermi level, the couple's redox level and each ion's level across the layer of solution by the electrode. Vary the scan rate, the stirring (as the thickness of a stagnant layer) and the rate constant k⁰. (More about the model below.)

scan rate stagnant layer k⁰ playback

About this simulation

The electrode faces a stagnant layer, then a stirred bulk. Only the solution within a few √(Dt) of the electrode is ever converted; the bulk is a fixed reservoir. A thin layer stands for vigorous stirring (a rotating disk): once the depleted zone fills it, the wave is steady and sigmoidal. A thick one is a still solution, where the depleted zone keeps growing through the sweep and the current peaks then sags: the classic "duck". With fast kinetics (k⁰ ≳ 1) its peaks sit 59 mV apart, plus a few mV of ohmic drop through the solution; a smaller rate constant pulls them further apart (quasi-reversible, then irreversible). Faster scans outrun diffusion.

The first level diagram is electronic: the platinum's Fermi level, and the couple's redox level, the electronic level at which the local Fe³⁺/Fe²⁺ mixture is in equilibrium. The gap between them at the surface is the overpotential, which drives Butler–Volmer kinetics; the redox level's slope across the layer is concentration polarisation. It sits V_T ln(c₃/c₂) from the couple's standard level, which in turn rides a fixed distance above the SHE's standard level, φ itself with table μ°. That one is nearly level thanks to the supporting electrolyte, and "vs SHE" means against it in the stirred bulk, at the right.

The last diagram is the same story ion by ion, using the species voltage V_i = μ̄_i/(z_iF): an ion's electrochemical potential per unit charge, in volts, so it can be drawn on the same axis as the electrons' Fermi level. Each ion moves down its own μ̄_i, so its current flows down slopes in its own V_i (thick; cations move downhill, anions uphill); the thin line under each, the standard level V°_i, is where V_i would sit at the reference concentration. K⁺, about 3 V lower, is left out.