# Theory

### What  is  an  “ec”  mechanism?

Cyclic voltammetry (CV) works well to determine the mechanism and rate of a chemical reaction (c) that may follow an electron transfer (e) step. The ec mechanism is illustrated below for the oxidation of species R to form species Ox, with Ox undergoing a chemical reaction to form product P:

\begin{align} &e\: \textrm{step} &&\mathrm{R \leftrightarrow Ox + ne^- \:\:\:E^\circ = +0.25\: V} \tag{1}\\ &c\: \textrm{step} &&\mathrm{Ox \overset{k_f}{\underset{k_b}{\longleftrightarrow}}} P \tag{2} \end{align}

If R/Ox electrode reaction is reversible, that is the heterogeneous electron transfer step is fast, and kf = 0 so that the follow-up chemical reaction does not occur, the cyclic voltammogram shown in Figure 1, trace A, is observed.

Figure 1. Computer simulated CV waves for an ec mechanism.
A) Reaction 1 is reversible, kf = 0;
B) kf = 0.30 and kf >>kb;
C) kf = 1.0 and kf >>kb.
Simulated for 1 mM of R species, electrode area = 0.010 cm2, scan rate 100 mV/s.

As discussed earlier, the anodic peak current, Ipa, and cathodic peak current, Ipc, are equal in magnitude when the transport of species R and Ox in the solution to and from the electrode is controlled only by diffusion. We are assuming that the CV is run at a planar (flat) electrode immersed in a quiet, unstirred solution. The reversible potential, E0, is equal to the electrode potential, E0.85, (the potential found 85% up the CV wave to Ipa (or Epa)). In this example, the E0 = +0.25 V so that the oxidative wave is seen in the potential range of the forward scan, going from 0.0 V to 0.5 V. The Ox species is reduced back to R during the reverse scan from 0.5 V back to the initial potential of 0.0 V.

When there is a follow-up chemical reaction, as in the case of a ec mechanism, and the kf of reaction (2) is finite, Ox will be converted to P. This results in less Ox so that the magnitude of Ipc diminishes during the reverse can (see CV wave B in Figure 1 ). The time window to capture Ox is determined by the scan rate. The consequence of an ec mechanism, where kf >> kb is illustrated in curve C of Figure 1. The parameters used in computer simulations of the theoretical CV waves, shown in curves A, B and C in Figure 1, are listed under the captions.

If Ox is long-lived, Ipc appears even at slow scan rates. If Ox is very short-lived, it may not be seen even at very fast scan rates. CV is uniquely able to adjust the time window of observations by the scan rate. Several potentiostats are commercially available that are capable of scanning at very high rates so that kf values as high as 105 - 106 l/m/s can be determined.

The ratio of the currents, Irev/Ifwd, can be conveniently measured by the empirical method of Nicholson [ref. 6,7], that requires the evaluation of Ipa, Ipc, and Iλ, where Iλ is the value of the current at the switching potential, Eλ (where the direction of the CV scan is reversed). These quantities are then used to obtain the current ratio, Irev/Ifwd in equation 3.

$\mathrm{I_{rev}/I_{fwd} = I_{pc}/I_{pa} + 0.48\: I_λ /I_{pa} +0.086} \tag{3}$

This current ratio is used to calculate the apparent rate constant, kf, for the follow-up chemical reaction, Ox $$\rightarrow$$ P from the theoretical working curve.

### Mechanism study on Dopamine and Norepinephrine Neurotransmitters

We can apply CV to determine the ec oxidative characteristics of the catecholamines, dopamine and norepinephrine, whose structures are shown below. The catecholamines are oxidized to the corresponding quinone, as illustrated for dopamine. Following the initial oxidation, a pH dependent, 1,4-addition reaction can occur, forming a cyclized product called a leucochrome. At low pH values, the open-chain quinones are protonated to a great extent, and the cyclization reaction is unfavorable. At higher pH values, a sufficient amount of unprotonated quinone is available so that cyclization is observed.

The leucochrome formed in the vicinity of the electrode following the 2-electron oxidation can be observed as a reductive wave at potentials negative of that for the reduction of the non-cyclized quinone. The extent of leucochrome formed is indicated by the ratio of the forward, Ipa, to reverse-scan, Ipc, peak currents for the catecholamine and its corresponding quinone. Further, it is possible to calculate the relative rates at which each cyclization takes place by evaluating the peak currents at different scan rates.