Slow scan rate

At slow scan rates there should be no separation between the oxidative and reductive peaks.

• A one-electron site (e.g. a heme or FeS cluster) gives a broad peak (fig 1A). The equation that gives the shape and intensity of the peak is:

${\displaystyle {\frac {i}{F^{2}\nu A\Gamma /RT}}=\pm {\frac {\exp \left({\frac {F}{RT}}(E-E^{0})\right)}{(1+\exp \left({\frac {F}{RT}}(E-E^{0})\right)^{2}}}}$

Ideally, the peak position is ${\displaystyle E_{p}=E^{0}}$ in both directions. The peak current is ${\displaystyle i_{p}=F^{2}\nu A\Gamma /4RT}$ (it is proportional to scan rate, ${\displaystyle \nu }$, and to the amount of redox sites on the electrode, ${\displaystyle A\Gamma }$). The ideal half width at half height (HWHH) equates ${\displaystyle RT/F\times \ln(3+2{\sqrt {2}})=89}$ mV at 20 °C. Non-ideal behaviour may result in the peak being broader than the ideal limit.

• The peak shape for a two-electron redox site (e.g. a flavin) depends on the stability of the half-reduced state (fig 1B). If the half-reduced state is stable over a large range of electrode potential, the signal is the sum of two one-electron peaks (purple line in fig 1B). If the half reduced state is unstable, the signal is a single peak (red line in fig 1B), which may have up to four times the height and half the width of a one-electron peak.^[6],[8]
• A protein that contains multiple redox centers should give multiple peaks which all have the same area (scaled by ${\displaystyle n}$).

Fast scan rates

If the reaction is a simple electron transfer reaction, the peaks should remain symmetrical at fast scan rates. A peak separation is observed when the scan rate ${\displaystyle \nu \gg RTk^{0}/F}$, where ${\displaystyle k_{0}}$ is the exchange electron transfer rate constant in Butler Volmer theory. Laviron equation^[4],[8],[9] predicts that at fast scan rates, the peaks separate in proportion to ${\displaystyle \log(\nu /k^{0})}$. The larger ${\displaystyle \nu }$ or the smaller ${\displaystyle k^{0}}$, the larger the peak separation. The peak potentials are ${\displaystyle E_{p}=E^{0}\pm {\frac {RT}{\alpha F}}\ln {\frac {\alpha F\nu }{k^{0}RT}}}$,^[4] as shown by lines in fig 2B (${\displaystyle \alpha }$ is the charge transfer coefficient). Examining the experimental change in peak position against scan rate therefore informs on the rate of interfacial electron transfer ${\displaystyle k^{0}}$.

Effect of coupled chemical reactions

Coupled reactions are reactions whose rate or equilibrium constant is not the same for the oxidized and reduced forms of the species that is being investigated. For example, reduction should favour protonation (${\displaystyle pK_{a}^{\rm {ox}}<pK_{a}^{\rm {red}}}$): the protonation reaction is coupled to the reduction at ${\displaystyle pK_{a}^{\rm {ox}}<pH<pK_{a}^{\rm {red}}}$. The binding of a small molecule (other than the proton) may also be coupled to a redox reaction.

Two cases must be considered depending on whether the coupled reaction is slow or fast (meaning that the time scale of the coupled reaction is larger or smaller than the voltammetric time scale^[10] ${\displaystyle \tau =RT/F\nu }$).

• Fast chemical reactions that are coupled to electron transfer (such as protonation) only affect the apparent values of ${\displaystyle E^{0}}$ and ${\displaystyle k^{0}}$,^[7] but the peaks remain symmetrical. The dependence of ${\displaystyle E^{0}}$ on ligand concentration (e.g. the dependence of ${\displaystyle E^{0}}$ on pH plotted in a Pourbaix diagram) can be interpreted to obtain the dissociation constants (e.g. acidity constants) from the oxidized or reduced forms of the redox species.
• Asymmetry may result from slow chemical reactions that are coupled to (and gate) the electron transfer. From fast scan voltammetry, information can be gained about the rates of the reactions that are coupled to electron transfer. The case of ${\displaystyle n=1}$ and ${\displaystyle n=2}$ reversible surface electrochemical reactions followed by irreversible chemical reactions was addressed by Laviron in refs^[6],[11] but the data are usually interpreted using the numerical solution of the appropriate differential equations.^[9]