cyclic voltammetry experimental conditions

What is CV? A comprehensive guide to Cyclic Voltammetry

Cyclic voltammetry: a key electrochemistry technique.

Cyclic Voltammetry is, along with EIS (Electrochemical Impedance Spectroscopy), one of the key techniques used to study the kinetics of electrochemical reactions.

Cyclic Voltammetry extends from the more basic step methods such as chronoamperometry and potentiometry. Voltammetry is, in fact, a contraction of voltamperometry, meaning that the current is measured as a function of the voltage (or potential).

With the step methods, one needs to measure the long-time or (steady-state) response of a system to a series of potential or current steps in order to access its complete electrochemical behavior, namely its $I\,vs.E$ characteristic. In terms of execution, this can be quite time-consuming, and the resulting $I\,vs.E$ curve could itself be difficult to analyze.

These two pitfalls can be overcome by recording the current response to a potential sweep $\text{d}E/\text{d}t$ or $v_{\text{b}}$, directly producing the $I\,vs.E$ characteristic.

This potential sweep, most commonly a linear ramp (but it could be a sine wave…), is generally performed at rates ranging from 10 mV/s to 1 V/s for conventional, millimetric electrodes. With smaller micrometric or submicrometric electrodes, sweep rates can reach up to 1 MV/s.

The current is recorded as a function of the potential, which is equivalent to recording versus time. One needs to define two limits between which the potential is scanned. In this case, the technique is simply called Linear Scan Voltammetry (LSV) (Figure 1a). If between these two potentials, we want the voltage to be repeatedly swept between two vertex potentials, the technique is then called Cyclic Voltammetry (CV) (Figure 1b).

Figure 1: Schematic description from EC-Lab of a) Linear Scan Voltammetry and b) Cyclic Voltammetry. In both cases, the current is recorded, and the main output is an $I\,vs.E$ curve.

In this topic, we will try to cover a broad range of technical aspects concerning Cyclic Voltammetry. First of all, we will introduce the notions of reversibility, and then describe how Cyclic Voltammetry can be used and which useful information can be obtained, introducing two important tools in EC-Lab®: CV Sim and CV Fit.

We will then discuss the specific subject of steady-state voltammetry, and more precisely, which factors allow it to be carried out.

Thirdly and finally, we will move on to experimental and instrumental considerations and provide guidelines to optimize the setup as well as the experimental settings of voltammetric measurements.

What information can I obtain with Cyclic Voltammetry?

In this section, we will present how Cyclic Voltammetry can be used to determine whether the behavior of the reaction is reversible or irreversible, or neither reversible nor irreversible, and which relationships can be used to determine kinetic parameters such as the standard reaction rate constant or the diffusion constant of the electroactive species.

We will focus on the simplest example, the E reaction:

$$\text{A} + n\text{e}^-\overset{K_\text r}{\underset{K_\text o}{\Leftrightarrow}}\text{B}\tag{1}$$

Where $\text{A}$ and $\text{B}$ are the reducing (oxidized) and oxidizing (reduced) species, respectively, $n$ the number of electrons involved in the reaction, $K_\text r$ and $K_{\text{o}}$ the electronic transfer rate constants of the reduction and the oxidation reaction respectively.

CV Sim and CV Fit allow users to study more complex reactions: EE, EC, CE, EEE and so on…

When the steady-state potential of the electrode $E$ is equal to the standard equilibrium potential of the redox couple $E^{\circ}_\text{A/B}$, then $K_\text r = K_\text o =k^{\circ}$ with $k^{\circ}$ the standard reaction rate constant.

CV Sim  and CV Fit

CV Sim (Cyclic Voltammetry simulation) and CV Fit (Cyclic Voltammetry Fitting) are tools dedicated to the Cyclic Voltammetry technique, in the same way, that Z Sim and Z Fit are dedicated to Electrochemical Impedance Spectroscopy. These tools are available in EC-Lab®, BioLogic’s control, and analysis software. These tools, which are excellent for teaching, are available in a demo version of EC-Lab® .

CV Sim and CV Fit can be accessed using the following path in EC-Lab®: Analysis>General Electrochemistry (Figure 2). CV Fit will appear greyed-in because no data are currently opened. Once any $I\,vs.E$ curve is opened or created using CV Sim, the CV Fit tool will become active.

Figure 2: How to access CV Sim and CV Fit in EC-Lab®

The CV Sim window shows two tabs, one is the type of reaction that is being simulated, along with the initial parameters (Figure 3), and the second shows other simulation parameters such as the type of electrode, the voltage limits, the scan rate, other experimental artefacts such as the ohmic drop, measurement noise, double layer capacitance (Figure 4).

Figure 3: CV Sim tab from EC-Lab with the type of reaction, direction, kinetic parameters and experimental conditions

Figure 4: CV Sim setup tab with electrode shape and radius, voltage limits, scan rate, and additional artefacts.

Rapid, sluggish, reversible, or irreversible reaction?

When studying the kinetics of an electrochemical (or chemical) process, one important piece of information the user should know is whether the behavior of the electrochemical reaction of interest is reversible, irreversible, or neither reversible nor irreversible (also referred to by Faulkner and Bard as quasi-reversible [1, p. 104]). The reversible behavior of a reaction will lead to different solutions and expressions when trying to analytically solve the kinetic equations.

The value of the reaction rate constant $k^{\circ}$ defines whether the heterogeneous electronic transfer reaction is rapid or sluggish [1, p. 96]. A rule of thumb is that $k^{\circ}\,\geq\,1\,\text{cm s}^{-1}$ is considered large, and the corresponding reaction fast or rapid. If $k^{\circ}\,\leq \,10^{-5}\,\text{cm s}^{-1}$, it is considered small and the reaction slow or sluggish.

Reversibility is somewhat more complex as it depends on various parameters, and one of them only is the value of $k^{\circ}$. The behavior of a reaction is said to be kinetically reversible when the full reaction rate $v(t)$ is small with respect to the partial oxidation or reduction rates, $v_{\text{o}}(t)$ and $v_{\text{r}}(t)$, respectively [2, p. 135]:

$$v_\text o (t)\gg v(t) \, \text{and}\, v_{\text{r}}(t) \gg v(t)\Leftrightarrow v_\text o(t)\approx v_{\text{r}}(t) \tag{2}$$

The corresponding redox system is called Nernstian.

The reaction is said to be irreversible when one of the partial reaction rates is much larger than the other one and, consequently, the full reaction rate is almost equal to the larger partial reaction rate.

In other terms, in the oxidation direction:

$$ v_{\text{r}}(t)<< v_{\text{o}}(t) \iff v(t)\approx v_{\text{o}}(t) \iff v_{\text{r}}(t)<< v(t) \tag{3}$$

and in the reduction direction:

$$v_{\text{o}}(t)<< v_{\text{r}}(t) \iff v(t)\approx v_{\text{r}}(t) \iff v_{\text{o}}(t)<< v(t) \tag{4}$$

It is a mistake to consider that a large $k^{\circ}$ only, corresponds to a reversible behavior as the reaction rate $v(t)$ depends both on the electronic transfer and the interfacial concentrations of the electroactive species, themselves governed by mass transport laws and the potential scan rate.

The determination of  kinetic factors

Using CV Sim, we can demonstrate that by performing Cyclic Voltammetries at various scan rates and recording the peak and the current potentials, one can determine whether the behavior of the considered reaction is reversible, irreversible, or neither reversible nor irreversible. Other kinetic factors can also be accessed, once the reversible behavior of the reaction is determined.

Reversible reaction

Let’s open CV Sim, and simulate a few $I\,vs.E$ curves.

Let us consider an E reaction in the reduction direction with $z=1$, $E^{\circ}=0.2\, V$, $\alpha_{\text{f}}=0.5$, $k^{\circ}=10\,\text{cm s}^{-1}$, $C_{\text{A}}=10^{-5}\,\text{mol cm}^{-3}= 10^{-2}\,\text{mol L}^{-1}$, $C_{\text{B}}=0$, $D_{\text{A}}=D_{\text{B}}=10^{-6}\,\text{cm}^{-2}\,\text{s}^{-1}$.

$k^{\circ}$ was chosen so that the reaction can be considered rapid, favoring a priori, a reversible behavior.

In the Setup tab, let us enter the following parameters: Geometry = Linear semi-infinite, Radius $=1$ mm, 800 points per scan, no ohmic drop or double layer capacitance, $E_{\text{init}}=E_1=0.5\,\text{V},\,E_2=-0.3\,\text{V}$.

The scan rates $v_{\text{b}}$ will be chosen according to the following relationship:

$$v_{\text{b}_{n+1}}=4 v_{\text{b}_n}\tag{5}$$

with $n$ an integer and $v_{\text{b}_0}\,=\,10\,\text{V s}^{\text{-1}}$.

The results are shown in Figure 5 for $n+1\,=\,5$. Both the peak potential and current, $E_{\text{p}}$ and $I_{\text{p}}$, are noted.

We can see that $E_{\text{p}}$ is constant while $I_{\text{p}}$ increases (in absolute value), which demonstrates that the redox system is a Nernstian system or the reaction has a reversible behavior.

The expression of the peak current $I_{\text{p}}$ is then given by:

$$ I_{\text{p}}\,=\,-0.446AzF C_{\text{A}}\sqrt{zf_\text N v_{\text{b}}D_{\text{A}}}\;;f_\text N\,=\,F/RT\tag{6}$$

where $A$ is the surface of the disk electrode, $R$ is the perfect gas constant, $F$ is the Faraday constant and $T$ is the temperature.

Figure 5: $I\,vs.E$ curves with increasing scan rates and $k^{\circ}\,=\,10\,\text{cm s}^{-1}$.

Equation 6 can be used to calculate the diffusion coefficient of the electroactive species A.

It should be noted that the 0.446 coefficient in Eq. 6 only holds for a reversible reaction or (Nernstian system), in our case the lower scan rates of Fig. 5. For example, at 2560 V/S, this coefficient is not 0.446, but 0.444. 0.446 is the theoretical value given by Faulkner and Bard [1, p. 231]. This means that if we scan the potential fast enough, we can slightly shift from a reversible to an irreversible reaction.

Furthermore, Eq. 6 and the factor 0.446 only hold if species B is initially absent from the solution. If this is not the case in your experiment, you can use CV Sim to calculate the right value of the factor and then use this value to recalculate the diffusion coefficient. This is better explained in the corresponding Learning Center article – Using CVSim as a Learning tool  with more detailed information in Application Note 41-1 .

For YouTube video tutorials on how to obtain  and interpret these curves please see the CVSIM videos part 1 and Part 2.1 below

Irreversible reaction

Let’s go back to CV Sim and set $k^{\circ}\,=\,0.001\,\text{cm s}^{-1}$, all the other parameters being the same. With such a small $k^{\circ}$ we can infer that the reaction is sluggish, and its behavior a priori , irreversible.

The different $I\,vs.E$ curves are given in Figure 6. Both $E_{\text{p}}$ and $I_{\text{p}}$ change with the scanning rate, which demonstrates that the reaction is irreversible.

Figure 6: $I\,vs.E$ curves with increasing scan rates and $k^{\circ}\,=\,0.001\,\text{cm s}^{-1}$.

The equation 6 now becomes:

$$ I_{\text{p}}\,=\,-0.496AzF C_{\text{A}}\sqrt{\alpha_{\text{r}}f_\text N v_\text b D_{\text{A}}}\;;f_\text N \,=\,F/RT\tag{7}$$

With $\alpha_{\text{r}}$ being the symmetry factor of the reaction in the reduction direction. $\alpha_{\text{r}}$ + $\alpha_{\text{o}}$ = 1, with $\alpha_{\text{o}}$ being the symmetry factor of the reaction in the oxidation direction.

Equation 7 can be used to determine $D_{\text{A}}$ or $\alpha_{\text{r}}$ and is given by Bard and Faulkner [1, p. 236].

The peak potential $E_{\text{p}}$ is proportional to $\ln v_\text b$ following this relationship [1, p. 236]:

$$E_{\text{p}}\,=\,E^{\circ}+\frac{1}{\alpha_{\text{r}}nf_\text N}\left(0.78+\ln\frac{k^{\circ}}{\sqrt{\alpha_{\text{r}}nf_\text N v_\text b D_{\text{A}}}}\right)\tag{8}$$

In this case, the standard reaction constant $k^{\circ}$ can be determined as well as the symmetry factor $\alpha_{\text{r}}$.

Again, more detailed information can be found in Application Note 41-1 .

For a YouTube video tutorial on how to obtain  and interpret these curves please watch CVSIM video part 1 (above)  and Part 2.2 (below)

Steady-state voltammetry

Why work in a steady-state.

In this part of this Cyclic Voltammetry article, we will discuss the notion of steady-state. As mentioned earlier, when it was not possible to program a voltage ramp, the only way to plot the $I\,vs.E$ characteristic of a system was to apply a potential or current step and then record the response at long times when it was constant. This way the steady-state $I\,vs.E$ characteristic could be constructed, but with this approach, it would be time-consuming. The electrochemical response of a redox system in steady-state is easier to analytically describe, as any time-dependent term is equal to 0.

This is for example the case for a Rotating Disk Electrode (RDE): the measurement of the steady-state mass-transport-controlled current allows users to easily reach important kinetic parameters such as the diffusion coefficient, symmetry parameter $\alpha$ and the already mentioned standard reaction constant $k^{\circ}$ using Levich and Koutecký-Levich equations. More information can be found in the corresponding article: rotating disk electrode, how does the Koutecký-Levich analysis work? . Furthermore, steady-state is also a requirement in Electrochemical Impedance Spectroscopy (EIS).

How do I know the voltammetric curve was performed in steady-state conditions?

The simplest way to recognize a steady-state voltammetric curve is to see if the forward and backward potential scans give the same current response. In other words, the two parts of the curves are superimposed, as is illustrated in Figs. 7a and c.

Figure 7: Cyclic Voltammetry curves obtained on a) a 15 µm diameter Au disk b) a 5 mm diameter Au disk, and c) a Rotating 2 mm Pt Disk Electrode (RDE). (Conditions: 5 mM FeII/FeIII, 0.1 M KCl, potential ranges: 0 V/OCP, 0.650 and  -0.250 V/Ag/AgCl a) and b) 10 mV/s, c) 25 mV/s, 5000 rpm).

Figure 7a is the $I\,vs. E$ response obtained on a 15 µm diameter disk electrode (also called an UltraMicroElectrode, UME). When the potential is scanned backward or forward, it produces the same curve (although we can see a slight shift) with a typical S-shape. In this case, what we see is a steady-state curve. If the potential scan is stopped and the potential held at a certain value, the current value remains constant.

Figure 7b shows the same experiment but performed on a 5 mm Au disk electrode. The shape is totally different as the forward and backward scans are not superimposed. In this case, the steady-state conditions are not reached. If the potential scan is stopped and the potential held at a certain value, the current decreases and reaches 0.

Finally, in Figure 7c, the Cyclic Voltammetry measurement was performed on a Rotating Disk Electrode (RDE). In this case, also, it can be seen from the shape of the curve that we are in steady-state conditions. The same S-shaped curve as in Fig. 2a can be seen. Again, as for the UME curve, if the potential scan is stopped and the potential held at a certain value, the current value remains constant.

Also, it can be seen in Figs. 7a and 7c, on steady-state curves that for a given potential range, the current does not change with potential anymore. At these potential ranges, the current depends on mass transport conditions, interfacial concentrations, and diffusion coefficients.

In electrochemistry, steady-state conditions mean that at any point of the curve the species concentrations do not vary over time, only with the distance from the electrode. The overall reaction rate and consequently the current are constant with time.

The influence of the electrode geometry and the mass transport conditions

Now we will explain why steady-state conditions can only be reached with a UME or an RDE but not with large planar electrodes.

We will take a step back here and describe what happens at each electrode interface when we apply a potential step in Cottrell conditions, again examining the E reaction. In Cottrell conditions, a large amplitude potential step is applied to the mass-transport region. The concentration of the electroactive species is zero at the electrode/electrolyte interface and the Faradaic current is controlled by mass transport. Electroactive species are being produced/consumed and their concentrations, in the vicinity of the electrode, change with time, creating concentration gradients.

Figures 8, 9 and 10 show for a given time $t_0$, is concentration lines and diffusion/current fluxes for three types of electrode geometries: a large conventional planar electrode (Fig. 8), a hemispherical electrode (Fig. 9), and a disk Ultra MicroElectrode (UME) (Fig. 10), which we can simply define as a disk electrode with a radius of around 25 µm or lower.

In the case of the large planar and the hemispherical electrodes, the isoconcentration lines are parallel to the electrode surface (blue lines in Figs. 8 and 9). The electroactive species’ mass transport occurs by diffusion, perpendicularly to the isoconcentration lines as indicated by the arrows (yellow arrows in Figs. 8 and 9). For a conventional planar electrode, the diffusion is linear semi-infinite and hemispherical semi-infinite for a hemispherical electrode.

Figure 8: Isoconcentration lines and geometry of diffusion at a conventional planar electrode at a given time. The blue lines are isoconcentration lines. The concentration outside of the furthest line from the electrode is the bulk concentration. The orange arrows show diffusion fluxes of electroactive species and current lines.

Figure 9: Isoconcentration lines and geometry of diffusion at a hemispherical electrode at a given time. The blue lines are isoconcentration lines. The concentration outside of the furthest line from the electrode is the bulk concentration. The orange arrows show diffusion fluxes of charged species and current lines.

In the case of a disk UME, it is a bit more complicated as diffusion at a UME is linear semi-infinite, and augmented by a radial component at the edges of the electrode (Fig. 10).

In the case of a Rotating Disk Electrode (RDE), the augmentation of mass-transport is performed by convection, which allows it to behave in a manner similar to a UME and a hemispherical electrode.

Figure 10: Isoconcentration lines and geometry of diffusion at an Ultra Micro Electrode at intermediate times. The blue lines are isoconcentration lines. The arrows show diffusion fluxes of charged species and current lines. The edge effects can be seen: the current and diffusion lines are not always perpendicular to the surface.

Different mass transport conditions mean different boundary conditions and lead to different solutions of the mass transport equations, and eventually current-potential equations. This is described in great detail in the books by Faulkner and Bard [1, Chapter 5] and Diard, Le Gorrec, and Montella (in French) [2, Chapter II].

Let us now examine how the concentrations at the interface and the concentration profile away from the electrode change with time for each geometry.

In the case of a large planar electrode (linear diffusion) (Fig. 11), in Cottrell conditions, the depletion region, ie the region where concentration gradients exist, will grow indefinitely with time and, in the case of voltammetry, with the potential.  Eventually, the concentration gradient at the electrode surface and the current will reach zero as can be seen in Fig. 11.

Figure 11: left) $I vs. t$ at the electrode/electrolyte interface, right) $ C\,vs.x$ at times shown in the left figure, in the case of a large planar electrode where semi-infinite linear diffusion occurs in Cottrell conditions, for the reversible redox reaction E, $\text{A}\,+\,n\text{e}\,\rightarrow\, \text{B}$. $C$ is the concentration of species $\text{A}$ and $x$ the distance normal to the planar electrode.

In the case of a hemispherical electrode, a disk UME, or an RDE, depletion will only occur in a definite and constant length, because the diffusion field is able to draw material from a continually larger area at its outer limit. After a certain time, the concentration gradient at the interface and the current are constant with time and with potential, in the case of voltammetry, as can be seen in Fig. 3.

Figure 12: left) $I\,vs. t$ at the electrode | electrolyte interface, right) $ C\,vs.x$ at times shown in the left figure, in the case of an hemispherical electrode, or a disk UME, or an RDE where semi-infinite linear diffusion, radial diffusion or diffusion-convection, respectively, occurs in Cottrell conditions, for the reversible redox reaction E, $\text{A}\,+\,n\text{e}\,\rightarrow\, \text{B}$. $C$ is the concentration of species $\text{A}$ and $x$ the distance normal to the center of the electrode.

To summarize, steady-state conditions can be reached when the electroactive species depletion/enrichment region which results from the redox reaction has a finite dimension, that does not change with time, and the concentration gradient, at the interface is constant. This is possible only when sufficient electroactive species are available thanks to additional mass transport by convection (RDE), radial (UME), or hemispherical diffusion (hemispheric electrode) compared to linear diffusion at a large planar electrode.

Let us now return to voltammetry and see what happens when we change the potential of the electrode linearly with time.

The influence of the scan rate

The effect of scan rate can be inferred by considering that the larger the scan rate, the smaller the duration of the potential scan and the less likely the steady-state regime will be reached, considering steady-state corresponds to the state of the system at infinite time. This means that even though diffusion conditions are such that steady-state conditions could be reached, if the scan rate is too fast, the $I\,vs.E$ characteristic of the system will not be steady-state.

This is illustrated in Fig. 13, which shows the evolution of $I\,vs.E$ on the left and the interfacial concentrations of electroactive species on the right with the scan rate in the case of a hemispherical electrode of 10 µm radius. These curves were obtained using CV Sim.

At lower scan rates (1 and 10 mV/s), we can see on the left, that the diffusion current plateaus, and both backward and forward scans are superimposed. On the right, we can see that the interfacial concentration of the produced species is maximal. From 100 mV/s to 10 V/s, we can see on the left the curves are not steady-state anymore: the current plateau disappears, the forward and backward scans are not superimposed, and on the right, the interfacial concentration of the produced species is not maximal anymore.

These results could also apply to a UME and an RDE.

Figure 13 : Evolution of left) $I vs. E$ curve and right) interfacial concentrations with scan rate for the redox E reaction $\text{A}\,+\,n\text{e}\,\rightarrow\, \text{B}.\; \text{Parameters}:n=1,\, E^{\circ} = 0.2\,\text{V},\, k^{\circ} = 0.01\,\text{cm}\,\text{s}^{-1},\, \alpha_\text f = 0.5,\, C^*_\text{A} = 0.01\,\text{mol}\,\text{L}^{-1},\, C^*_\text{B} = 0,\, D_\text{A} = 10^{-5}\,\text{cm}^2\,\text{s}^{-1},\, D_\text{B} = 5\times10^{-6} \,\text{cm}^2\,\text{s}^{-1},\, r_0 = 10\,$µ$\text{m}$.

Let us now compare the $I\,vs.E$ obtained on a large planar electrode and at a hemispherical electrode of the same size at different scan rates. Figure 14 shows the $I\,vs. E$ curves for linear (in blue) and spherical (in red) diffusion at different scan rates. We can see that the faster the scan rate, the more similar both curves are. As the scan rate gets lower, the red curve corresponding to a hemispherical electrode tends to be a typical steady-state curve, with superimposed backward and forward scan and current plateaus. As the scan rate increases, the behavior of a hemispherical electrode and a planar electrode of the same size are the same.

The same behavior as the hemispherical electrode could be seen for a UME or an RDE. The curves in Fig. 14 were obtained with CV Sim.

Figure 14: Comparison of the $I\,vs.E$ curve for a linear semi-infinite diffusion (blue curve)and spherical semi-infinite diffusion (red curve) for various scan rates. $\text{A}\,+\,n\text{e}\,\rightarrow\, \text{B}.\; \text{Parameters}: n=1,\,E^{\circ} = 0.2\,\text{V},\, k^{\circ} = 0.01\,\text{cm}\,\text{s}^{-1},\, \alpha_f = 0.5,\, C^*_\text{A} = 0.01\,\text{mol}\,\text{L}^{-1},\, C^*_\text{B} = 0,\, D_\text{A} = 10^{-5}\,\text{cm}^2\,\text{s}^{-1},\, D_\text{B} = 5\times10^{-6} \,\text{cm}^2\,\text{s}^{-1},\, r_0 = 1\,\text{mm (linear diffusion)},\, r_0 = 0.707\,\text{mm (spherical diffusion)}$

To summarize, we can say that:

• It is not possible to perform steady-state voltammetry on a large (millimetric) quiescent planar electrode.
• In systems where steady-state voltammetry is possible, according to diffusion conditions (hemispherical electrode, UME, RDE), there always exists a scan rate value high enough so that diffusion conditions become linear, and conditions are not steady-state anymore, as is the case on a large planar electrode.

These two experimental sets of conditions, the diffusion mode and the scan rate, can be contained within one single parameter that is called the sphericity parameter, which we describe in the next part of this topic.

The sphericity parameter

The sphericity  parameter $L$ is a dimensionless parameter defined as follows for a redox reaction $\text{A}\,+\,n\text{e}\,\rightarrow\, \text{B}$ occurring on an electrode with a radius $ r_{\text{hemi}}$.

$$L= r_{\text{hemi}}\sqrt{\frac{|n|f_\text{N}v_{\text{b}}}{D_\text{O}}}\tag{9}$$

With $n$ the number of exchanged electrons, $f_\text{N}=F/(RT)$, $v_{\text{b}}$ the scan rate and $ D_\text{O}$ the diffusion coefficient of the electroactive species $\text{O}$.

In case you are using a planar electrode, you can also use the equation above by assuming that $r_{\text{hemi}}=0.07 r_{\text{disk}}$ where $r_{\text{disk}}$ is the radius of a disk electrode [3]. It shows that there is an equivalence between hemispherical and linear+radial diffusion.

When $L \rightarrow +\infty$ then we are in the case of a linear semi-infinite diffusion and hence no steady-state voltammetry is possible. It is easy to see that the condition $L \rightarrow +\infty$ corresponds to a large $r$ so a large electrode, or large $v_\text b$ ie fast scan rates.

On the opposite, when $L \rightarrow 0$, we are in the conditions of a hemispherical diffusion, which means that steady-state or quasi steady-state voltammetry can be performed. The curve then shows a plateau at the limiting current $i_\text{lim} = 2\pi FD_\text{O}C_\text{O}^*r$. The condition $L \rightarrow0$ corresponds to either a small $r$ so a small electrode, or small $v_\text b$ ie slow scan rates.

One could add that the sphericity parameter could be better-named as a “linearity parameter”, as the magnitude of $L$ quantifies the degree of linearity of diffusion in the case of a hemispherical (or a UME) electrode.

Figure 15 shows the evolution of $I\,vs. E$ curves in the case of a hemispherical diffusion. We can see that we move from a steady-state curve to a quasi-steady-state curve to a non-steady-state curve, like the linear diffusion case. The only parameter that changes is the radius of the electrode that is changing from 0.01 mm in the case of the steady-state curve to 0.1, 1, and finally 10 mm. The evolution of the corresponding $L$ parameter is shown in the graph.

Figure 15: $I\,vs. E$ curves for a spherical semi-infinite diffusion for $r$ varying from 0.01 to 10 mm by decades. $E^\circ$ = 0.2 V; $k^\circ$ = 0.01 cm s -1 ; $\alpha_f$ = 0.5 ; $C^*_\text{A}$ = 0.01 mol L -1 ; $C^*_\text{B}$ = 0 ; $D_\text{A} = 10^{-5}$ cm² s -1 ; $D_\text{B} = 5\,\times\,10^{-6}$ cm² s -1 . The evolution of the $L$ parameter in these conditions is shown.

The same type of graphs can be obtained for a fixed radius by increasing the scan rate. This is shown in Fig. 16, which we plot again here below but instead of the scan rate, we plot the $L$ parameter, which characterizes only the “spherical” diffusion ie the red curve below.

Figure 16: Comparison of the $I\,vs. E$ curve for a linear semi-infinite diffusion (blue curve) and spherical semi-infinite diffusion (red curve) for various scan rates from 0.01 to 100 mV/s per decade. $E^\circ$ = 0.2 V; $k^\circ $ = 0.01 cm s -1 ; $\alpha_f$ = 0.5 ; $C^*_\text{A}$ = 0.01 mol L -1 ; $C^*_\text{B}$ = 0 ; $D_\text{A} = 10^{-5}$ cm² s -1 ; $D_\text{B} = 5\,\times\,10^{-6}$ cm² s -1 ; $r_0$ = 1 mm (linear diffusion) ; $r_0$ = 0.707 mm (spherical diffusion). The $L$ parameter is shown for the spherical diffusion (red curve).

It can be seen in Fig. 16, that the discrepancy between the linear and spherical behavior occurs below a value of L = 62.4 and above a value of 19.7, for the set of parameters described in Figure 16 caption.

We can more precisely evaluate when this discrepancy occurs by plotting the ratio $I_{\text{p, lin}}/ I_{\text{p, sph}} \,vs. \,L$ where $I_{\text{p, lin}}$ and $I_{\text{p, sph}}$ are the forward peak currents for the linear and the spherical diffusion, respectively. This is shown in Fig. 17. The plotted point corresponds to a ratio of 95% and an $L$ value of ≈ 32. This number only holds for the set of parameters shown in Fig. 16. Above this value, diffusion occurs linearly (even if the electrode is hemispherical). Below this value, edge effects (radial diffusion) start to appear.

Figure 18 shows the combination of $r$ and $v_{\text{b}}$ for which $L\,=\,32$, that defines the boundary between linear diffusion and linear diffusion with radial components, for a hemispherical electrode in the conditions given in the Fig. 16 caption.

Figure 17: Evolution of the ratio $I_{\text{p, lin}}/ I_{\text{p, sph}} \,vs. \,L$ $(10^{1.5}=32)$.

Figure 18: $v_{\text{b}}\,vs.r$ with $L\,=\,32$, where $r$ is the radius of the hemispherical electrode. Any $v_{\text{b}}$ and $r$ combination which falls in the light blue area corresponds to conditions where spherical diffusion starts to occur, for parameters described in the Fig. 16 caption.

To summarize, we can say that the sphericity (or linearity) factor defines, in the case of a simple E reaction with only reacting species A in the solution, the scan rate and the electrode size combinations for which linear diffusion can occur, preventing steady-state conditions from being reached, even in the case of a UME or a hemispherical electrode. CV Sim can be used to perform the same study on a different set of parameters.

Instrumental and experimental considerations

In the last part of this topic, we will discuss various instrumental and experimental factors to account for when performing Cyclic Voltammetry measurements:

• What to do when the ohmic drop and double-layer capacitance are non-negligible?
• How do I set up the parameters of the CV technique?
• What is an Analog Ramp Generator and when do I need it?

The effect of the ohmic drop and the double layer capacitance

Double-layer capacitance.

The electrode | electrolyte interface, which is a metal-solution junction, behaves, as a first approximation, like a capacitor. When polarizing an electrode in an electrolyte where electroactive species can be reduced or oxidized at the interface, the current is the sum of a Faradaic current $I_{\text{f}}$, related to the redox reaction, and a capacitive current $I_{\text{c}}$ related to the electrical charge transfer due to the double layer capacitance.

$$I=I_{\text{c}} + I_{\text{f}}\tag{10}$$

The capacitive current depends on time-derivative of the potential $E(t)$ and the double layer capacitance $C_{\text{dl}}$:

$$ I_{\text{c}}=C_{\text{dl}}\left(\frac{\text{d}E}{\text{d}t}\right) \tag{11}$$

In the specific case of a voltage sweep at a scan rate $v_{\text{b}}$, $\text{d}E/\text{d}t=v_{\text{b}}$ and

$$ I_{\text{c}}=C_{\text{dl}} v_{\text{b}}\tag{12}$$

The ohmic drop

In a three-electrode cell configuration, the ohmic drop is the resistance between the working electrode and the reference electrode. This resistance $R_\Omega$, modifies the potential « seen » by the electrode $V(t)$ compared to the potential value applied by the potentiostat $E(t)$ by a value $R_\Omega I(t)$ with $I\lt0$ for a reduction current and $I\gt0$ for an oxidation current (Figure 19):

$$V(t)=E(t)+R_\Omega I(t) \tag{12}$$

If we move on to the special case of Cyclic Voltammetry, with $v_{\text{b}}$ the scan rate and $E_{\text{init}}$ the initial potential, we have:

$$E(t)= E_{\text{init}}+ v_{\text{b}}(t)- R_\Omega I(t) \tag{13}$$

Figure 19: A three-electrode setup with the illustration of the ohmic drop and the double-layer capacitance.

How does this affect measurements?

Using CV Sim the effects of both non-negligible ohmic drop and double layer capacitance can be simulated.

Let’s use the same parameters as in Fig. 3 and 4, except for $C_{\text{dl}}$ that we set at 100 µF and we use an electrode radius of 1 mm. We performed one half-cycle for the sake of simplicity. The results are shown in Figure 20a. The capacitive current in red leads to a negative shift of the total current in blue compared to the Faradaic current in green. In Figure 20a, the capacitive current could be considered negligible because we are scanning relatively slowly. It can be a problem at higher scan rates for example at 1 V/s where the capacitive current is around one-half of the Faradaic current (Fig. 20b). One can see that the capacitive current can be determined when the voltage scan starts and the total current is equal to the capacitive current.

By way of a reminder, it is important to note that the capacitive current is proportional to $v_\text b$, whereas the Faradaic current is proportional to $\sqrt{ v_\text b}$ (Eqs. 6 and 7). It must be noted that for very high scan rates, the capacitive current might overshadow the Faradaic current.

Figure 20: Total, Faradaic and capacitive currents in blue, green and red, respectively, $vs.E$ simulated using CV Sim and the conditions shown in Fig. 3 and 4 with a radius of 1 mm and a $C_{\text{dl}}$ value of 100 µF. a) $v_{\text{b}}=10\,\text{mV}\text{s}^{\text{-1}}$, b) $v_{\text{b}}=1\,\text{V}\text{s}^{\text{-1}}$

Let us now set $C_{\text{dl}}=0$ and $ R_\Omega=20\,\Omega$, the results are given in Figure 21 for the same scan rates as in Fig. 20. It can be seen that at low scan rates, in our case 10 mV/s, the ohmic drop has little influence on the Faradaic current (Fig. 21a). Its influence can be seen at higher scan rates, which means larger currents (Fig. 21b). Unlike capacitance, both the peak current and potential are shifted: the peak current is larger in absolute value and the peak potential is shifted to more negative values for a reduction reaction (more positive values for an oxidation reaction).

Figure 21: Total current with different ohmic drop values, simulated using CV Sim and the conditions shown in Fig. 3 and 4 with a radius of 1 mm. a) $v_{\text{b}}=10\,\text{mV}\,\text{s}^{\text{-1}}$, b) $v_{\text{b}}=1\,\text{V}\,\text{s}^{\text{-1}}$

For more detailed information and a description of the combined effects of both non-negligible ohmic drop and double layer capacitance, please read the Application Note 41-2 CV Sim: Simulation of the simple redox reaction (E) Part II: The effect of ohmic drop and double layer capacitance .

For the various methods available to compensate for ohmic drop please take a look at the following Learning Center article (ohmic drop correction, a means of improving measurement accuracy with potentiostats and the corresponding application notes .

The numeric ramp

When we add a Cyclic Voltammetry technique, there are quite a number of settings as shown in Fig. 22. The parameters “Ei”, “E1”, “E2” have already been explained at the beginning of the article. The scan rate $v_{\text{b}}=\text{d}E/\text{d}t$ was also explained before, but because we are using an instrument that is numerically controlled, the voltage ramp is not exactly linear but rather a succession of small voltage steps (Fig. 23). $\text{d}E$ is defined by the potential range $\text{E}_{\text{range}}$ and the resolution of the Digital-To-Analog (DAC) converter. In the case of BioLogic systems, it is 16 bytes. We then have, assuming a constant $\text{d}E$:

$$\text{d}E=\frac{\text{E}_{\text{range}}}{2^{16}}\tag{14}$$

Then the scan rate $\text{d}E/\text{d}t$ sets the value of $\text{d}t$ and $N$ the number of potential steps over which the average current is recorded, represented by the black dots in Fig. 23. There is one point for each $\text{d}E_{\text{N}} = \text{d}E\,N$. For each step, the current is measured over a certain duration defined as a remaining percentage of $\text{d}t$.

Figure 22: Cyclic Voltammetry settings window.

Figure 23: How a voltage sweep is actually performed with the EC-Lab® CV technique, here in the scan of a positive potential ramp.

The number of data points $N_{\text{data}}$ per cycle is then defined as:

$$N_{\text{data}}=2\frac{\left\lvert E_2-E_1\right\rvert}{\text{d}E_{\text{N}}}\tag{14}$$

With $E_2$ and $E_1$ the vertices potentials. The factor 2 is due to the fact that one cycle is defined as the return to an initial condition: $E_1 \to E_2 \to E_1$.

The benefit of being able to choose the duration the current is recorded at, is that the capacitive contribution of the current can be removed, as it occurs mostly at the beginning of the step. Nonetheless, it is always better to record all contributions and hence set 100%.

The main limitation of the numeric ramp is actually related to the minimum available acquisition time, namely 200 µs, which does not allow the sweeping of potentials at very high rates, because the number of data points is then too low. The following formula can be used to calculate the number of data points for a given scan rate $ v_{\text{b}}$ and time step $\text{d}t$.

$$ N_{\text{data}}=2\frac{\left\lvert E_2-E_1\right\rvert}{v_{\text{b}}\,\text{d}t\,{N}}\tag{15}$$

Scanning from -1 to 1 V, at 100 V/s and averaging over 5 voltage steps gives a number of 40 points per cycle which is rather small. Also, the software ohmic drop compensation requires 400 µs, and it can also be a problem at very high scan rates. In such cases, the Analog Ramp Generator (ARG) option is required.

The Analog Ramp Generator (ARG)

The ARG is an optional board, that can be extremely easily mounted on the channel board, which allows the acquisition time to go down to 1 µs, and hence allows very high scan rates to be used. Furthermore, the capacitive current is also reduced because the shape of the potential ramp is an actual linear ramp and not a succession of steps. At the beginning of each step the potential variation $\text{d}E/\text{d}t$ is very large (almost infinite…) and so the capacitive current is also very large (Eq. 12). This is avoided when using a linear ramp and the capacitive current is constant with time, similarly to the simulation results shown in Fig. 20.

Figure 24 illustrates the effect of using a numerical ramp on the total measured current and how it compares with an analog linear ramp. When the scan rate is very large or for highly capacitive systems, at each potential step there is a huge decrease (or increase for an increasing potential sweep) of the capacitive current, which can lead to a change in the current range, hence decreasing the quality of the current measurement.

Figure 24: Illustration of the effect of highly capacitive systems or very fast scan rates on the total current when using a numerical ramp or an analog ramp.

Another advantage of the ARG is that it allows the ohmic drop compensation to be performed analogically and not by software, as is generally the case. The software ohmic drop compensation requires a minimum time of 400 µs to be performed, so when using very fast scan rates it cannot be used. With the ARG, the ohmic drop compensation is performed analogically with no specific speed limitation.

Cyclic Voltammetry: A glossary of terms

[1] A. J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, Wiley, Hoboken, (2001).

[2] J.-P. Diard, B. Le Gorrec, C. Montella, Cinétique Electrochimique, Hermann Editeurs, Paris (1996).

[3] K. B. Oldham, C. G. Zoski, Comparison of voltammetric steady states at hemispherical and disk microelectrodes. J. Electroanal. Chem. 256 (1988), 11–19.

The following articles may also be of interest with regards to Cyclic Voltammetry

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CVSim as a learning tool. I. Diffusion coefficient

Cvsim as a learning tool. ii interfacial concentrations, cvsim as a learning tool iii: linearity in eis, how to measure reaction kinetics parameters using cycling voltammetry (cv), related products, sp-200 potentiostat, sp-300 potentiostat, sp-150e potentiostat, sp-50 potentiostat.

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11.4: Voltammetric Methods

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In voltammetry we apply a time-dependent potential to an electrochemical cell and measure the resulting current as a function of that potential. We call the resulting plot of current versus applied potential a voltammogram , and it is the electrochemical equivalent of a spectrum in spectroscopy, providing quantitative and qualitative information about the species involved in the oxidation or reduction reaction. 13 The earliest voltammetric technique is polarography, developed by Jaroslav Heyrovsky in the early 1920s—an achievement for which he was awarded the Nobel Prize in Chemistry in 1959. Since then, many different forms of voltammetry have been developed, a few of which are highlighted in Figure 11.6 . Before examining these techniques and their applications in more detail, we must first consider the basic experimental design for voltammetry and the factors influencing the shape of the resulting voltammogram.

11.4.1 Voltammetric Measurements

Although early voltammetric methods used only two electrodes, a modern voltammeter makes use of a three-electrode potentiostat, such as that shown in Figure 11.5 . In voltammetry we apply a time-dependent potential excitation signal to the working electrode—changing its potential relative to the fixed potential of the reference electrode—and measure the current that flows between the working and auxiliary electrodes. The auxiliary electrode is generally a platinum wire, and the reference electrode is usually a SCE or a Ag/AgCl electrode.

Figure 11.5 shows an example of a manual three-electrode potentiostat. Although a modern potentiostat uses very different circuitry, you can use Figure 11.5 and the accompanying discussion to understand how we can control the potential of working electrode and measure the resulting current.

Later in the chapter we will examine several different potential excitation signals, but if you want to sneak a peak, see Figure 11.44 , Figure 11.45 , Figure 11.46 , and Figure 11.47 .

For the working electrode we can choose among several different materials, including mercury, platinum, gold, silver, and carbon. The earliest voltammetric techniques, including polarography, used a mercury working electrode. Because mercury is a liquid, the working electrode is often a drop suspended from the end of a capillary tube. In the hanging mercury drop electrode , or HMDE, we extrude the drop of Hg by rotating a micrometer screw that pushes the mercury from a reservoir through a narrow capillary tube (Figure 11.34a).

In the dropping mercury electrode , or DME, mercury drops form at the end of the capillary tube as a result of gravity (Figure 11.34b). Unlike the HMDE, the mercury drop of a DME grows continuously—as mercury flows from the reservoir under the influence of gravity—and has a finite lifetime of several seconds. At the end of its lifetime the mercury drop is dislodged, either manually or on its own, and replaced by a new drop.

The static mercury drop electrode , or SMDE, uses a solenoid driven plunger to control the flow of mercury (Figure 11.34c). Activation of the solenoid momentarily lifts the plunger, allowing mercury to flow through the capillary and forming a single, hanging Hg drop. Repeatedly activating the solenoid produces a series of Hg drops. In this way the SMDE may be used as either a HMDE or a DME.

Figure 11.34 Three examples of mercury electrodes: (a) hanging mercury drop electrode, or HMDE; (b) dropping mercury electrode, or DME; and (c) static mercury drop electrode, or SMDE.

There is one additional type of mercury electrode: the mercury film electrode . A solid electrode—typically carbon, platinum, or gold—is placed in a solution of Hg 2+ and held at a potential where the reduction of Hg 2 + to Hg is favorable, forming a thin mercury film on the solid electrode’s surface.

Figure 11.36 shows a typical solid electrode.

Mercury has several advantages as a working electrode. Perhaps the most important advantage is its high overpotential for the reduction of H 3 O + to H 2 , which makes accessible potentials as negative as –1 V versus the SCE in acidic solutions and –2 V versus the SCE in basic solutions (Figure 11.35). A species such as Zn 2+ , which is difficult to reduce at other electrodes without simultaneously reducing H 3 O + , is easily reduced at a mercury working electrode. Other advantages include the ability of metals to dissolve in mercury—resulting in the formation of an amalgam —and the ability to easily renew the surface of the electrode by extruding a new drop. One limitation to using mercury as a working electrode is the ease with which it is oxidized. Depending on the solvent, a mercury electrode can not be used at potentials more positive than approximately –0.3 V to +0.4 V versus the SCE.

Figure 11.35 Approximate potential windows for mercury, platinum, and carbon (graphite) electrodes in acidic, neutral, and basic aqueous solvents. The useful potential windows are shown in green ; potentials in red result in the oxidation or reduction of the solvent or the electrode. Complied from Adams, R. N. Electrochemistry at Solid Electrodes , Marcel Dekker, Inc.: New York, 1969 and Bard, A. J.; Faulkner, L. R. Electrochemical Methods , John Wiley & Sons: New York, 1980.

Solid electrodes constructed using platinum, gold, silver, or carbon may be used over a range of potentials, including potentials that are negative and positive with respect to the SCE (Figure 11.35). For example, the potential window for a Pt electrode extends from approximately +1.2 V to –0.2 V versus the SCE in acidic solutions, and from +0.7 V to –1 V versus the SCE in basic solutions. A solid electrode can replace a mercury electrode for many voltammetric analyses that require negative potentials, and is the electrode of choice at more positive potentials. Except for the carbon paste electrode, a solid electrode is fashioned into a disk and sealed into the end of an inert support with an electrical lead (Figure 11.36). The carbon paste electrode is made by filling the cavity at the end of the inert support with a paste consisting of carbon particles and a viscous oil. Solid electrodes are not without problems, the most important of which is the ease with which the electrode’s surface is altered by the adsorption of a solution species or by the formation of an oxide layer. For this reason a solid electrode needs frequent reconditioning, either by applying an appropriate potential or by polishing.

Figure 11.36 Schematic showing a solid electrode. The electrode is fashioned into a disk and sealed in the end of an inert polymer support along with an electrical lead.

A typical arrangement for a voltammetric electrochemical cell is shown in Figure 11.37. In addition to the working electrode, the reference electrode, and the auxiliary electrode, the cell also includes a N 2 -purge line for removing dissolved O 2 , and an optional stir bar. Electrochemical cells are available in a variety of sizes, allowing the analysis of solution volumes ranging from more than 100 mL to as small as 50 μL.

Figure 11.37 Typical electrochemical cell for voltammetry.

11.4.2 Current in Voltammetry

When we oxidize an analyte at the working electrode, the resulting electrons pass through the potentiostat to the auxiliary electrode, reducing the solvent or some other component of the solution matrix. If we reduce the analyte at the working electrode, the current flows from the auxiliary electrode to the cathode. In either case, the current from redox reactions at the working electrode and the auxiliary electrodes is called a faradaic current . In this section we consider the factors affecting the magnitude of the faradaic current, as well as the sources of any non-faradaic currents.

Sign Conventions

Because the reaction of interest occurs at the working electrode, we describe the faradaic current using this reaction. A faradaic current due to the analyte’s reduction is a cathodic current , and its sign is positive. An anodic current is due to an oxidation reaction at the working electrode, and its sign is negative.

Influence of Applied Potential on the Faradaic Current

As an example, let’s consider the faradaic current when we reduce Fe(CN) 6 3– to Fe(CN) 6 4– at the working electrode. The relationship between the concentrations of Fe(CN) 6 3– , the concentration of Fe(CN) 6 4– , and the potential is given by the Nernst equation

\[E = +0.356\: \ce V - 0.05916\log\dfrac{[\ce{Fe(CN)6^4-}]_{x=0}}{[\ce{Fe(CN)6^3-}]_{x=0}}\]

where +0.356 V is the standard-state potential for the Fe(CN) 6 3– /Fe(CN) 6 4– redox couple, and x = 0 indicates that the concentrations of Fe(CN) 6 3– and Fe(CN) 6 4– are those at the surface of the working electrode. We use surface concentrations instead of bulk concentrations because the equilibrium position for the redox reaction

\[\ce{Fe(CN)6^3-}(aq) + e^– ⇋ \ce{Fe(CN)6^4-}(aq)\]

is established at the electrode’s surface.

Let’s assume we have a solution for which the initial concentration of Fe(CN) 6 3– is 1.0 mM, and in which Fe(CN) 6 4– is absent. Figure 11.38 shows the ladder diagram for this solution. If we apply a potential of +0.530 V to the working electrode, the concentrations of Fe(CN) 6 3– and Fe(CN) 6 4– at the surface of the electrode are unaffected, and no faradaic current is observed (see Figure 11.38). If we switch the potential to +0.356 V some of the Fe(CN) 6 3– at the electrode’s surface reduces to Fe(CN) 6 4– until we reach a condition where

\[[\ce{Fe(CN)6^3-}]_{x=0} = [\ce{Fe(CN)6^4-}]_{x=0} = \mathrm{0.50\: mM}\]

This is the first of the five important principles of electrochemistry outlined in Section 11.1 : the electrode’s potential determines the analyte’s form at the electrode’s surface.

Figure 11.38 Ladder diagram for the Fe(CN) 6 3– /Fe(CN) 6 4– redox half-reaction.

If this is all that happens after we apply the potential, then there would be a brief surge of faradaic current that quickly returns to zero—not the most interesting of results. Although the concentrations of Fe(CN) 6 3– and Fe(CN) 6 4– at the electrode surface are 0.50 mM, their concentrations in bulk solution remains unchanged. Because of this difference in concentration, there is a concentration gradient between the solution at the electrode’s surface and the bulk solution. This concentration gradient creates a driving force that transports Fe(CN) 6 4– away from the electrode and that transports Fe(CN) 6 3– to the electrode (Figure 11.39). As the Fe(CN) 6 3– arrives at the electrode it, too, is reduced to Fe(CN) 6 4– . A faradaic current continues to flow until there is no difference between the concentrations of Fe(CN) 6 3– and Fe(CN) 6 4– at the electrode and their concentrations in bulk solution.

This is the second of the five important principles of electrochemistry outlined in Section 11.1 : the analyte’s concentration at the electrode may not be the same as its concentration in bulk solution.

Figure 11.39 Schematic showing the transport of Fe(CN) 6 4– away from the electrode’s surface and the transport of Fe(CN) 6 3– toward the electrode’s surface following the reduction of Fe(CN) 6 3– to Fe(CN) 6 4– .

Although the potential at the working electrode determines if a faradaic current flows, the magnitude of the current is determined by the rate of the resulting oxidation or reduction reaction. Two factors contribute to the rate of the electrochemical reaction: the rate at which the reactants and products are transported to and from the electrode—what we call mass transport —and the rate at which electrons pass between the electrode and the reactants and products in solution.

This is the fourth of the five important principles of electrochemistry outlined in Section 11.1 : current is a measure of rate.

Influence of Mass Transport on the Faradaic Current

There are three modes of mass transport that affect the rate at which reactants and products move toward or away from the electrode surface: diffusion, migration, and convection. Diffusion occurs whenever the concentration of an ion or molecule at the surface of the electrode is different from that in bulk solution. If we apply a potential sufficient to completely reduce Fe(CN) 6 3– at the electrode surface, the result is a concentration gradient similar to that shown in Figure 11.40. The region of solution over which diffusion occurs is the diffusion layer . In the absence of other modes of mass transport, the width of the diffusion layer, δ , increases with time as the Fe(CN) 6 3– must diffuse from increasingly greater distances.

Figure 11.40 Concentration gradients (in red ) for Fe(CN) 6 3– following the application of a potential that completely reduces it to Fe(CN) 6 4– . Before applying the potential ( t = 0) the concentration of Fe(CN) 6 3– is the same at all distances from the electrode’s surface. After applying the potential, its concentration at the electrode’s surface decreases to zero and Fe(CN) 6 3– diffuses to the electrode from bulk solution. The longer we apply the potential, the greater the distance over which diffusion occurs. The dashed red line shows the extent of the diffusion layer at time t 3 . These profiles assume that convection and migration do not significantly contribute to the mass transport of Fe(CN) 6 3– .

Convection occurs when we mechanically mix the solution, carrying reactants toward the electrode and removing products from the electrode. The most common form of convection is stirring the solution with a stir bar. Other methods that have been used include rotating the electrode and incorporating the electrode into a flow-cell.

The final mode of mass transport is migration , which occurs when a charged particle in solution is attracted to or repelled from an electrode that carries a surface charge. If the electrode carries a positive charge, for example, an anion will move toward the electrode and a cation will move toward the bulk solution. Unlike diffusion and convection, migration only affects the mass transport of charged particles.

The movement of material to and from the electrode surface is a complex function of all three modes of mass transport. In the limit where diffusion is the only significant form of mass transport, the current in a voltammetric cell is equal to

\[i = \dfrac{nFAD(C_\ce{bulk} − C_{x=0})}{δ}\tag{11.36}\]

where n the number of electrons in the redox reaction, F is Faraday’s constant, A is the area of the electrode, D is the diffusion coefficient for the species reacting at the electrode, C bulk and C x =0 are its concentrations in bulk solution and at the electrode surface, and δ is the thickness of the diffusion layer.

For equation 11.36 to be valid, convection and migration must not interfere with the formation of a diffusion layer. We can eliminate migration by adding a high concentration of an inert supporting electrolyte. Because ions of similar charge are equally attracted to or repelled from the surface of the electrode, each has an equal probability of undergoing migration. A large excess of an inert electrolyte ensures that few reactants or products experience migration. Although it is easy to eliminate convection by not stirring the solution, there are experimental designs where we cannot avoid convection, either because we must stir the solution or because we are using electrochemical flow cell. Fortunately, as shown in Figure 11.41, the dynamics of a fluid moving past an electrode results in a small diffusion layer—typically 1–10 μm in thickness—in which the rate of mass transport by convection drops to zero.

Figure 11.41 Concentration gradient for Fe(CN) 6 3– when stirring the solution. Diffusion is the only significant form of mass transport close to the electrode’s surface. At distances greater than δ , convection is the only significant form of mass transport, maintaining a homogeneous solution in which the concentration of Fe(CN) 6 3– at d is the same as its concentration in bulk solution.

Effect of Electron Transfer Kinetics on the Faradaic Current

The rate of mass transport is one factor influencing the current in voltammetry. The ease with which electrons move between the electrode and the species reacting at the electrode also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium. Under these conditions the redox reaction is electrochemically reversible and the Nernst equation applies. If the electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface—and thus the magnitude of the faradaic current—are not what is predicted by the Nernst equation. In this case the system is electrochemically irreversible .

Charing Currents

In addition to current resulting from redox reactions—what we call faradaic current—the current in an electrochemical cell includes other, nonfaradaic sources. Suppose the charge on an electrode is zero and that we suddenly change its potential so that the electrode’s surface acquires a positive charge. Cations near the electrode’s surface respond to this positive charge by migrating away from the electrode; anions, on the other hand, migrate toward the electrode. This migration of ions occurs until the electrode’s positive surface charge and the negative charge of the solution near the electrode are equal. Because the movement of ions and the movement of electrons are indistinguishable, the result is a small, short-lived nonfaradaic current that we call the charging current . Every time we change the electrode’s potential, a transient charging current flows.

The migration of ions in response to the electrode’s surface charge leads to the formation of a structured electrode-solution interface that we call the electrical double layer , or EDL. When we change an electrode’s potential, the charging current is the result of a restructuring of the EDL. The exact structure of the electrical double layer is not important in the context of this text, but you can consult this chapter’s additional resources for additional information.

Residual Current

Even in the absence of analyte, a small, measurable current flows through an electrochemical cell. This residual current has two components: a faradaic current due to the oxidation or reduction of trace impurities and the charging current. Methods for discriminating between the analyte’s faradaic current and the residual current are discussed later in this chapter.

11.4.3 Shape of Voltammograms

The shape of a voltammogram is determined by several experimental factors, the most important of which are how we measure the current and whether convection is included as a means of mass transport. As shown in Figure 11.42, despite an abundance of different voltammetric techniques, several of which are discussed in this chapter, there are only three common shapes for voltammograms.

For the voltammogram in Figure 11.42a, the current increases from a background residual current to a limiting current , i l . Because the faradaic current is inversely proportional to δ (equation 11.36), a limiting current can only occur if the thickness of the diffusion layer remains constant because we are stirring the solution (see Figure 11.41). In the absence of convection the diffusion layer increases with time (see Figure 11.40). As shown in Figure 11.42b, the resulting voltammogram has a peak current instead of a limiting current.

For the voltammograms in Figures 11.42a and 11.42b, we measure the current as a function of the applied potential. We also can monitor the change in current, ∆ i , following a change in potential. The resulting voltammogram, shown in Figure 11.42c, also has a peak current.

Figure 11.42 The three common shapes for voltammograms. The dashed red line shows the residual current.

11.4.4 Quantitative and Qualitative Aspects of Voltammetry

Earlier we described a voltammogram as the electrochemical equivalent of a spectrum in spectroscopy. In this section we consider how we can extract quantitative and qualitative information from a voltammogram. For simplicity we will limit our treatment to voltammograms similar to Figure 11.42a.

Determining Concentration

Let’s assume that the redox reaction at the working electrode is

\[\ce O + ne^− ⇋ \ce R\tag{11.37}\]

where O is the analyte’s oxidized form and R is its reduced form. Let’s also assume that only O is present in bulk solution and that we are stirring the solution. When we apply a potential causing the reduction of O to R, the current depends on the rate at which O diffuses through the fixed diffusion layer shown in Figure 11.41. Using equation 11.36, the current, i , is

\[i = K_\ce{O}(\mathrm{[O]_{bulk} − [O]}_{x=0})\tag{11.38}\]

where K O is a constant equal to nFAD O / δ . When we reach the limiting current, i l , the concentration of O at the electrode surface is zero and equation 11.38 simplifies to

\[\mathrm{\mathit{i}_l = \mathit{K}_O[O]_{bulk}}\tag{11.39}\]

Equation 11.39 shows us that the limiting current is a linear function of the concentration of O in bulk solution. To determine the value of K O we can use any of the standardization methods covered in Chapter 5. Equations similar to equation 11.39 can be developed for the voltammograms shown in Figure 11.42b and Figure 11.42c.

Determining the Standard-state Potential

To extract the standard-state potential from a voltammogram, we need to rewrite the Nernst equation for reaction 11.37

\[E = E^\circ_\textrm{O/R} − \dfrac{0.05916}{n}\log\dfrac{[\ce R]_{x=0}}{[\ce O]_{x=0}}\tag{11.40}\]

in terms of current instead of the concentrations of O and R. We will do this in several steps. First, we substitute equation 11.39 into equation 11.38 and rearrange to give

\[[\ce O]_{x=0} = \dfrac{i_\ce{l} − i}{K_\ce{O}}\tag{11.41}\]

Next, we derive a similar equation for [R] x=0 , by noting that

\[i = K_\ce{R}([\ce R]_{x=0} − \mathrm{[R]_{bulk}})\]

Because the concentration of [R] bulk is zero—remember our assumption that the initial solution contains only O—we can simplify this equation

\[i = K_\ce{R}[\ce R]_{x=0}\]

and solve for [R] x=0 .

\[[\ce R]_{x=0} = \dfrac{i}{K_\ce{R}}\tag{11.42}\]

Now we are ready to finish our derivation. Substituting equation 11.42 and equation 11.41 into equation 11.40 and rearranging leaves us with

\[E = E^\circ_\textrm{O/R} - \dfrac{0.05916}{n}\log\dfrac{K_\ce{O}}{K_\ce{R}} - \dfrac{0.05916}{n}\log\dfrac{i}{i_\ce{l} - i}\tag{11.43}\]

When the current, i , is half of the limiting current, i l ,

\[i = 0.5 × i_\ce{l}\]

we can simplify equation 11.43 to

\[E_{1/2} = E^\circ_\textrm{O/R} - \dfrac{0.05916}{n}\log\dfrac{K_\ce{O}}{K_\ce{R}}\tag{11.44}\]

where E 1 /2 is the half-wave potential (Figure 11.43). If K O is approximately equal to K R , which is often the case, then the half-wave potential is equal to the standard-state potential. Note that equation 11.44 is valid only if the redox reaction is electrochemically reversible. We also can use a voltammogram with a peak potential to determine a redox reaction’s standard-state potential.

\[\log\dfrac{i}{i_\ce{l} − i} = \log\dfrac{0.5 × i_\ce{l}}{i_\ce{l} − 0.5 × i_\ce{l}} = \log\dfrac{0.5 × i_\ce{l}}{0.5 × i_\ce{l}} = \log(1) = 0\]

Figure 11.43 Determination of the limiting current , i l , and the half-wave potential , E 1 /2 , for the voltammogram in Figure 11.42a.

11.4.5 Voltammetric Techniques

In voltammetry there are three important experimental parameters under our control: how we change the potential we apply to the working electrode, when we choose to measure the current, and whether we choose to stir the solution. Not surprisingly, there are many different voltammetric techniques. In this section we consider several important examples.

Polarography

The first important voltammetric technique to be developed— polarography —uses the dropping mercury electrode shown in Figure 11.34b as the working electrode. As shown in Figure 11.44, the current flowing through the electrochemical cell is measured while applying a linear potential ramp.

Figure 11.44 Details of normal polarography: (a) the linear potential-excitation signal, and (b) the resulting voltammogram.

Although polarography takes place in an unstirred solution, we obtain a limiting current instead of a peak current. When a Hg drop separates from the glass capillary and falls to the bottom of the electrochemical cell, it mixes the solution. Each new Hg drop, therefore, grows into a solution whose composition is identical to the bulk solution. The oscillations in the current are a result of the Hg drop’s growth, which leads to a time-dependent change in the area of the working electrode. The limiting current—which is also called the diffusion current—is measured using either the maximum current, i max , or from the average current, i avg . The relationship between the analyte’s concentration, C A , and the limiting current is given by the Ilkovic equation

\[(i_\ce{l})_\ce{max} = 706nD^{1/2}m^{2/3}t^{1/6}C_\ce{A}= K_\ce{max}C_\ce{A}\]

\[(i_\ce{l})_\ce{avg} = 607nD^{1/2}m^{2/3}t^{1/6}C_\ce{A}=K_\ce{avg}C_\ce{A}\]

where n is the number of electrons in the redox reaction, D is the analyte’s diffusion coefficient, m is the flow rate of the Hg, t is the drop’s lifetime and K max and K avg are constants. The half-wave potential, E 1 /2 , provides qualitative information about the redox reaction.

See Appendix 15 for a list of selected polarographic half-wave potentials.

Normal polarography has been replaced by various forms of pulse polarography , several examples of which are shown in Figure 11.45. 14 Normal pulse polarography (Figure 11.45a), for example, uses a series of potential pulses characterized by a cycle of time of τ , a pulse-time of t p , a pulse potential of ∆ E p , and a change in potential per cycle of ∆ E s . Typical experimental conditions for normal pulse polarography are τ ≈ 1 s, t p ≈ 50 ms, and ∆ E s ≈ 2 mV. The initial value of ∆ E p is ≈ 2 mV, and it increases by ≈ 2 mV with each pulse. The current is sampled at the end of each potential pulse for approximately 17 ms before returning the potential to its initial value. The shape of the resulting voltammogram is similar to Figure 11.44, but without the current oscillations. Because we apply the potential for only a small portion of the drop’s lifetime, there is less time for the analyte to undergo oxidation or reduction and a smaller diffusion layer. As a result, the faradaic current in normal pulse polarography is greater than in the polarography, resulting in better sensitivity and smaller detection limits.

In differential pulse polarography (Figure 11.45b) the current is measured twice per cycle: for approximately 17 ms before applying the pulse and for approximately 17 ms at the end of the cycle. The difference in the two currents gives rise to the peak-shaped voltammogram. Typical experimental conditions for differential pulse polarography are τ ≈ 1 s, t p ≈ 50 ms, ∆ E p ≈ 50 mV, and ∆ E s ≈ 2 mV.

The voltammogram for differential pulse polarography is approximately the first derivative of the voltammogram for normal pulse polarography. To see why this is the case, note that the change in current over a fixed change in potential, ∆ i /∆ E , approximates the slope of the voltammogram for normal pulse polarography. You may recall that the first derivative of a function returns the slope of the function at each point. The first derivative of a sigmoidal function is a peak-shaped function.

Other forms of pulse polarography include staircase polarography (Figure 11.45c) and square-wave polarography (Figure 11.45d). One advantage of square-wave polarography is that we can make τ very small—perhaps as small as 5 ms, compared to 1 s for other pulse polarographies—which can significantly decrease analysis time. For example, suppose we need to scan a potential range of 400 mV. If we use normal pulse polarography with a ∆ E s of 2 mV/cycle and a τ of 1 s/cycle, then we need 200 s to complete the scan. If we use square-wave polarography with a ∆ E s of 2 mV/cycle and a τ of 5 ms/cycle, we can complete the scan in 1 s. At this rate, we can acquire a complete voltammogram using a single drop of Hg!

Polarography is used extensively for the analysis of metal ions and inorganic anions, such as IO 3 – and NO 3 – . We also can use polarography to study organic compounds with easily reducible or oxidizable functional groups, such as carbonyls, carboxylic acids, and carbon-carbon double bonds.

Figure 11.45 Potential-excitation signals and voltammograms for (a) normal pulse polarography, (b) differential pulse polarography, (c) staircase polarography, and (d) square-wave polarography. The current is sampled at the time intervals shown by the black rectangles. When measuring a change in current, ∆ i , the current at point 1 is subtracted from the current at point 2. The symbols in the diagrams are as follows: τ is the cycle time; ∆ E p is a fixed or variable pulse potential; ∆ E s is the fixed change in potential per cycle, and t p is the pulse time.

Hydrodynamic Voltammetry

In polarography we obtain a limiting current because as each drop of mercury mixes the solution as it falls to the bottom of the electrochemical cell. If we replace the DME with a solid electrode (see Figure 11.36) we can still obtain a limiting current if we mechanically stir the solution during the analysis, either using a stir bar or by rotating the electrode. We call this approach hydrodynamic voltammetry .

Hydrodynamic voltammetry uses the same potential profiles as in polarography, such as a linear scan (Figure 11.44) or a differential pulse (Figure 11.45b). The resulting voltammograms are identical to those for polarography, except for the lack of current oscillations from the growth of the mercury drops. Because hydrodynamic voltammetry is not limited to Hg electrodes, it is useful for analytes that undergo oxidation or reduction at more positive potentials.

Stripping Voltammetry

Another important voltammetric technique is stripping voltammetry , which consists of three related techniques: anodic stripping voltammetry, cathodic stripping voltammetry, and adsorptive stripping voltammetry. Because anodic stripping voltammetry is the more widely used of these techniques, we will consider it in greatest detail.

Anodic stripping voltammetry consists of two steps (Figure 11.46). The first step is a controlled potential electrolysis in which we hold the working electrode—usually a hanging mercury drop or a mercury film electrode—at a cathodic potential sufficient to deposit the metal ion on the electrode. For example, when analyzing Cu 2 + the deposition reaction is

\[\ce{Cu^2+}(aq) + 2e^− ⇋ \ce{Cu(Hg)}\]

where Cu(Hg) indicates that the copper is amalgamated with the mercury. This step essentially serves as a means of concentrating the analyte by transferring it from the larger volume of the solution to the smaller volume of the electrode. During most of the electrolysis we stir the solution to increase the rate of deposition. Near the end of the deposition time we stop the stirring—eliminating convection as a mode of mass transport—and allow the solution to become quiescent. Typical deposition times are 1–30 min are common, with analytes at lower concentrations requiring longer times.

Figure 11.46 Potential-excitation signal and voltammogram for anodic stripping voltammetry at a hanging mercury drop electrode or a mercury film electrode.

In the second step, we scan the potential anodically—that is, toward a more positive potential. When the working electrode’s potential is sufficiently positive, the analyte is stripped from the electrode, returning to solution in its oxidized form.

\[\ce{Cu(Hg)} \rightleftharpoons \ce{Cu^2+}_{(aq)} + 2e^−\]

Monitoring the current during the stripping step gives the peak-shaped voltammogram, as shown in Figure 11.46. The peak current is proportional to the analyte’s concentration in the solution. Because we are concentrating the analyte in the electrode, detection limits are much smaller than other electrochemical techniques. An improvement of three orders of magnitude—the equivalent of parts per billion instead of parts per million—is fairly routine.

Anodic stripping voltammetry is very sensitive to experimental conditions, which we must carefully control if our results are to be accurate and precise. Key variables include the area of the mercury film or the size of the hanging Hg drop, the deposition time, the rest time, the rate of stirring, and the scan rate during the stripping step. Anodic stripping voltammetry is particularly useful for metals that form amalgams with mercury, several examples of which are listed in Table 11.11.

Source: Compiled from Peterson, W. M.; Wong, R. V. Am. Lab. November 1981, 116–128; Wang, J. Am. Lab. May 1985, 41–50.

The experimental design for cathodic stripping voltammetry is similar to anodic stripping voltammetry with two exceptions. First, the deposition step involves the oxidation of the Hg electrode to Hg 2 2+ , which then reacts with the analyte to form an insoluble film at the surface of the electrode. For example, when Cl – is the analyte the deposition step is

\[\ce{2Hg}(l) + \ce{2Cl-}(aq) ⇋ \ce{Hg2Cl2}(s) + 2e^−\]

Second, stripping is accomplished by scanning cathodically toward a more negative potential, reducing Hg 2 2+ back to Hg and returning the analyte to solution.

\[\ce{Hg2Cl2}(s) + 2e^− ⇋ \ce{2Hg}(l) + \ce{2Cl-}(aq)\]

Table 11.11 lists several analytes that have been analyzed successfully by cathodic stripping voltammetry.

In adsorptive stripping voltammetry the deposition step occurs without electrolysis. Instead, the analyte adsorbs to the electrode’s surface. During deposition we maintain the electrode at a potential that enhances adsorption. For example, we can adsorb a neutral molecule on a Hg drop if we apply a potential of –0.4 V versus the SCE, a potential where the surface charge of mercury is approximately zero. When deposition is complete, we scan the potential in an anodic or a cathodic direction depending on whether we are oxidizing or reducing the analyte. Examples of compounds that have been analyzed by absorptive stripping voltammetry also are listed in Table 11.11.

Cyclic Voltammetry

In the voltammetric techniques we have consider to this point, we scan the potential in one direction, either to more positive potentials or to more negative potentials. In cyclic voltammetry we complete a scan in both directions. Figure 11.47a shows a typical potential-excitation signal. In this example, we first scan the potential to more positive values, resulting in the following oxidation reaction for the species R.

\[\mathrm{R ⇋ O} + ne^−\]

When the potential reaches a predetermined switching potential, we reverse the direction of the scan toward more negative potentials. Because we generated the species O on the forward scan, during the reverse scan it is reduced back to R.

\[\ce O + ne^− ⇋ \ce R\]

Because we carry out cyclic voltammetry in an unstirred solution, the resulting cyclic voltammogram, as shown in Figure 11.47b, has peak currents instead of limiting currents. The voltammogram has separate peaks for the oxidation reaction and the reduction reaction, each characterized by a peak potential and a peak current.

Figure 11.47 Details for cyclic voltammetry. (a) One cycle of the triangular potential-excitation signal showing the initial potential and the switching potential. A cyclic voltammetry experiment can consist of one cycle or many cycles. Although the initial potential in this example is the negative switching potential, the cycle can begin with an intermediate initial potential and cycle between two limits. (b) The resulting cyclic voltammogram showing the measurement of the peak currents and peak potentials.

The peak current in cyclic voltammetry is given by the Randles-Sevcik equation

\[i_\ce{p} = (2.69×10^5)n^{3/2}AD^{1/2}ν^{1/2}C = KC\]

where n is the number of electrons in the redox reaction, A is the area of the working electrode, D is the diffusion coefficient for the electroactive species, ν is the scan rate, and C is the concentration of the electroactive species at the electrode. For a well-behaved system, the anodic and cathodic peak currents are equal, and the ratio i p ,a / i p ,c is 1.00. The half-wave potential, E 1 /2 , is midway between the anodic and cathodic peak potentials.

\[E_{1/2} =\dfrac{E_\textrm{p,a} + E_\textrm{p,c}}{2}\]

Scanning the potential in both directions provides us with the opportunity to explore the electrochemical behavior of species generated at the electrode. This is a distinct advantage of cyclic voltammetry over other voltammetric techniques. Figure 11.48 shows the cyclic voltammogram for the same redox couple at both a faster and a slower scan rate. At the faster scan rate we see two peaks. At the slower scan rate in Figure 11.48b, however, the peak on the reverse scan disappears. One explanation for this is that the products from the reduction of R on the forward scan have sufficient time to participate in a chemical reaction whose products are not electroactive.

Figure 11.48 Cyclic voltammograms for R obtained at (a) a faster scan rate and (b) a slower scan rate. One of the principal uses of cyclic voltammetry is to study the chemical and electrochemical behavior of compounds. See this chapter’s additional resources for further information.

Amperometry

The final voltammetric technique we will consider is amperometry , in which we apply a constant potential to the working electrode and measure current as a function of time. Because we do not vary the potential, amperometry does not result in a voltammogram.

One important application of amperometry is in the construction of chemical sensors. One of the first amperometric sensors was developed in 1956 by L. C. Clark to measure dissolved O 2 in blood. Figure 11.49 shows the sensor’s design, which is similar to potentiometric membrane electrodes. A thin, gas-permeable membrane is stretched across the end of the sensor and is separated from the working electrode and the counter electrode by a thin solution of KCl. The working electrode is a Pt disk cathode, and a Ag ring anode serves as the counter electrode. Although several gases can diffuse across the membrane, including O 2 , N 2 , and CO 2 , only oxygen undergoes reduction at the cathode

\[\ce{O2}(aq) + \ce{4H3O+}(aq) + 4e^− ⇋ \ce{6H2O}(l)\]

with its concentration at the electrode’s surface quickly reaching zero. The concentration of O 2 at the membrane’s inner surface is fixed by its diffusion through the membrane, creating a diffusion profile similar to that in Figure 11.41. The result is a steady-state current proportional to the concentration of dissolved oxygen. Because the electrode consumes oxygen, the sample must be stirred to prevent the depletion of O 2 at the membrane’s outer surface.

The oxidation of the Ag anode

\[\ce{Ag}(s) + \ce{Cl-}(aq) ⇋ \ce{AgCl}(s) + e^−\]

is the other half-reaction.

Figure 11.49 Clark amperometric sensor for determining dissolved O 2 . The diagram on the right is a cross-section through the electrode, showing the Ag ring electrode and the Pt disk electrode.

Another example of an amperometric sensor is the glucose sensor. In this sensor the single membrane in Figure 11.49 is replaced with three membranes. The outermost membrane is of polycarbonate, which is permeable to glucose and O 2 . The second membrane contains an immobilized preparation of glucose oxidase that catalyzes the oxidation of glucose to gluconolactone and hydrogen peroxide.

\[\textrm{β-D-glucose}(aq) + \ce{O2}(aq) + \ce{H2O}(l) ⇋ \ce{gluconolactone}(aq) + \ce{H2O2}(aq)\]

The hydrogen peroxide diffuses through the innermost membrane of cellulose acetate where it undergoes oxidation at a Pt anode.

\[\ce{H2O2}(aq) + \ce{2OH-}(aq) ⇋ \ce{O2}(aq) + \ce{2H2O}(l) + 2e^−\]

Figure 11.50 summarizes the reactions taking place in this amperometric sensor. FAD is the oxidized form of flavin adenine nucleotide—the active site of the enzyme glucose oxidase—and FADH 2 is the active site’s reduced form. Note that O 2 serves a mediator, carrying electrons to the electrode.

Figure 11.50 Schematic showing the reactions by which an amperometric biosensor responds to glucose.

By changing the enzyme and mediator, it is easy to extend to the amperometric sensor in Figure 11.50 to the analysis of other analytes. For example, a CO 2 sensor has been developed using an amperometric O 2 sensor with a two-layer membrane, one of which contains an immobilized preparation of autotrophic bacteria. 15 As CO 2 diffuses through the membranes it is converted to O 2 by the bacteria, increasing the concentration of O 2 at the Pt cathode.

11.4.6 Quantitative Applications

Voltammetry has been used for the quantitative analysis of a wide variety of samples, including environmental samples, clinical samples, pharmaceutical formulations, steels, gasoline, and oil.

Selecting the Voltammetric Technique

The choice of which voltammetric technique to use depends on the sample’s characteristics, including the analyte’s expected concentration and the sample’s location. For example, amperometry is ideally suited for detecting analytes in flow systems, including the in vivo analysis of a patient’s blood, or as a selective sensor for the rapid analysis of a single analyte. The portability of amperometric sensors, which are similar to potentiometric sensors, also make them ideal for field studies. Although cyclic voltammetry can be used to determine an analyte’s concentration, other methods described in this chapter are better suited for quantitative work.

Pulse polarography and stripping voltammetry frequently are interchangeable. The choice of which technique to use often depends on the analyte’s concentration, and the desired accuracy and precision. Detection limits for normal pulse polarography generally are on the order of 10 –6 M to 10 –7 M, and those for differential pulse polarography, staircase, and square wave polarography are between 10 –7 M and 10 –9 M. Because we concentrate the analyte in stripping voltammetry, the detection limit for many analytes is as little as 10 –10 M to 10 –12 M. On the other hand, the current in stripping voltammetry is much more sensitive than pulse polarography to changes in experimental conditions, which may lead to poorer precision and accuracy. We also can use pulse polarography to analyze a wider range of inorganic and organic analytes because there is no need to first deposit the analyte at the electrode surface.

Stripping voltammetry also suffers from occasional interferences when two metals, such as Cu and Zn, combine to form an intermetallic compound in the mercury amalgam. The deposition potential for Zn 2 + is sufficiently negative that any Cu 2 + in the sample also deposits into the mercury drop or film, leading to the formation of intermetallic compounds such as CuZn and CuZn 2 . During the stripping step, zinc in the intermetallic compounds strips at potentials near that of copper, decreasing the current for zinc and increasing the apparent current for copper. It is often possible to overcome this problem by adding an element that forms a stronger intermetallic compound with the interfering metal. Thus, adding Ga 3+ minimizes the interference of Cu when analyzing for Zn by forming an intermetallic compound of Cu and Ga.

Correcting for Residual Current

In any quantitative analysis we must correct the analyte’s signal for signals arising from other sources. The total current, i tot , in voltammetry consists of two parts: the current from the analyte’s oxidation or reduction, i a , and a background or residual current, i r .

\[i_\ce{tot} = i_\ce{a} + i_\ce{r}\]

The residual current, in turn, has two sources. One source is a faradaic current from the oxidation or reduction of trace impurities in the sample, i int .The other source is the charging current, i ch , that accompanies a change in the working electrode’s potential.

\[i_\ce{r} = i_\ce{int} + i_\ce{ch}\]

We can minimize the faradaic current due to impurities by carefully preparing the sample. For example, one important impurity is dissolved O 2 , which undergoes a two-step reduction: first to H 2 O 2 at a potential of –0.1 V versus the SCE, and then to H 2 O at a potential of –0.9 V versus the SCE. Removing dissolved O 2 by bubbling an inert gas such as N 2 through the sample eliminates this interference. After removing the dissolved O 2 , passing a blanket of N 2 over the top of the solution prevents O 2 from reentering the solution.

The cell in Figure 11.37 shows a typical N 2 purge line.

There are two methods for compensating for the residual current. One method is to measure the total current at potentials where the analyte’s faradaic current is zero and extrapolate it to other potentials. This is the method shown in Figure 11.42. One advantage of extrapolating is that we do not need to acquire additional data. An important disadvantage is that an extrapolation assumes that the change in the residual current with potential is predictable, which may not be the case. A second, and more rigorous approach, is to obtain a voltammogram for an appropriate blank. The blank’s residual current is then subtracted from the sample’s total current.

Analysis for Single Components

The analysis of a sample with a single analyte is straightforward. Any of the standardization methods discussed in Chapter 5 can be used to determine the relationship between the current and the analyte’s concentration.

Example 11.12

The concentration of As(III) in water can be determined by differential pulse polarography in 1 M HCl. The initial potential is set to –0.1 V versus the SCE and is scanned toward more negative potentials at a rate of 5 mV/s. Reduction of As(III) to As(0) occurs at a potential of approximately –0.44 V versus the SCE. The peak currents for a set of standard solutions, which are corrected for the residual current, are shown in the following table.

What is the concentration of As(III) in a sample of water if its peak current is 1.37 μA?

Linear regression gives the calibration curve shown in Figure 11.51, with an equation of

\[\mathrm{\mathit{i}_p(\mu A) = 0.0176 + 3.01 × [As(III)] (\mu M)}\]

Substituting the sample’s peak current into the regression equation gives the concentration of As(III) as 4.49 × 10 –6 M.

Figure 11.51 Calibration curve for the data in Example 11.12.

Exercise 11.8

The concentration of copper in a sample of sea water is determined by anodic stripping voltammetry using the method of standard additions. The analysis of a 50.0-mL sample gives a peak current of 0.886 μA. After adding a 5.00-μL spike of 10.0 mg/L Cu 2 + , the peak current increases to 2.52 μA. Calculate the μg/L copper in the sample of sea water.

Click here to review your answer to this exercise.

Multicomponent Analysis

Voltammetry is a particularly attractive technique for the analysis of samples containing two or more analytes. Provided that the analytes behave independently, the voltammogram of a multicomponent mixture is a summation of each analyte’s individual voltammograms. As shown in Figure 11.52, if the separation between the half-wave potentials or between the peak potentials is sufficient, we can independently determine each analyte as if it is the only analyte in the sample. The minimum separation between the half-wave potentials or peak potentials for two analytes depends on several factors, including the type of electrode and the potential-excitation signal. For normal polarography the separation must be at least ±0.2–0.3 V, and differential pulse voltammetry requires a minimum separation of ±0.04–0.05 V.

Figure 11.52 Voltammograms for a sample containing two analytes showing the measurement of (a) limiting currents, and (b) peak currents.

If the voltammograms for two analytes are not sufficiently separated, a simultaneous analysis may be possible. An example of this approach is outlined in Example 11.13.

Example 11.13

The differential pulse polarographic analysis of a mixture of indium and cadmium in 0.1 M HCl is complicated by the overlap of their respective voltammograms. 16 The peak potential for indium is at –0.557 V and that for cadmium is at –0.597 V. When a 0.800 ppm indium standard is analyzed, ∆ i p (in arbitrary units) is 200.5 at –0.557 V and 87.5 at –0.597 V. A standard solution of 0.793 ppm cadmium has a ∆ i p of 58.5 at –0.557 V and 128.5 at –0.597 V. What is the concentration of indium and cadmium in a sample if ∆ i p is 167.0 at a potential of –0.557 V and 99.5 at a potential of –0.597V. Note: All potentials are relative to a saturated Ag/AgCl reference electrode.

The change in current, ∆ i p , in differential pulse polarography is a linear function of the analyte’s concentration

\[i_\ce{p} = k_\ce{A}C_\ce{A}\]

where k A is a constant that depends on the analyte and the applied potential, and C A is the analyte’s concentration. To determine the concentrations of indium and cadmium in the sample we must first find the value of k A for each analyte at each potential. For simplicity we will identify the potential of –0.557 V as E 1 , and that for –0.597 V as E 2 . The values of k A are

\[\mathrm{\mathit{k}_{In,\mathit{E}_1} = \dfrac{200.5}{0.800\: ppm} = 250.6\: ppm^{-1}\: \mathit{k}_{In,\mathit{E}_2} = \dfrac{87.5}{0.800\: ppm} = 109.4\: ppm^{-1}}\]

\[\mathrm{\mathit{k}_{Cd,\mathit{E}_1} = \dfrac{58.5}{0.793\: ppm} = 73.8\: ppm^{-1}\:\mathit{k}_{Cd,\mathit{E}_2} = \dfrac{128.5}{0.793\: ppm} = 162.0\: ppm^{-1}}\]

Next, we write simultaneous equations for the current at the two potentials.

\[i_{E_1}= \mathrm{250.6\: ppm^{−1} × \mathit{C}_{In} + 73.8\: ppm^{−1} × \mathit{C}_{Cd} = 167.0}\]

\[i_{E_2}= \mathrm{109.4\: ppm^{-1} × \mathit{C}_{In} + 162.0\: ppm^{-1} × \mathit{C}_{Cd} = 99.5}\]

Solving the simultaneous equations, which is left as an exercise, gives the concentration of indium as 0.606 ppm and the concentration of cadmium as 0.206 ppm.

Environmental Samples

Voltammetry is one of several important analytical techniques for the analysis of trace metals in environmental samples, including groundwater, lakes, rivers and streams, seawater, rain, and snow. Detection limits at the parts-per-billion level are routine for many trace metals using differential pulse polarography, with anodic stripping voltammetry providing parts-per-trillion detection limits for some trace metals.

Other important techniques are atomic absorption spectroscopy ( Chapter 10.4 ), atomic emission spectroscopy ( Chapter 10.7 ), and ion-exchange chromatography ( Chapter 12.6 ).

One interesting environmental application of anodic stripping voltammetry is the determination of a trace metal’s chemical form within a water sample. Speciation is important because a trace metal’s bioavailability, toxicity, and ease of transport through the environment often depend on its chemical form. For example, a trace metal strongly bound to colloidal particles generally is not toxic because it is not available to aquatic life-forms. Unfortunately, anodic stripping voltammetry can not distinguish a trace metal’s exact chemical form because closely related species, such as Pb 2 + and PbCl + , produce a single stripping peak. Instead, trace metals are divided into “operationally defined” categories that have environmental significance.

Operationally defined means that an analyte is divided into categories by the specific methods used to isolate it from the sample. There are many examples of operational definitions in the environmental literature. The distribution of trace metals in soils and sediments, for example, is often defined in terms of the reagents used to extract them; thus, you might find an operational definition for Zn 2 + in a lake sediment as that extracted using 1.0 M sodium acetate, or that extracted using 1.0 M HCl.

Although there are many speciation schemes in the environmental literature, we will consider a speciation scheme proposed by Batley and Florence. 17 This scheme, which is outlined in Table 11.12, combines anodic stripping voltammetry with ion-exchange and UV irradiation, dividing soluble trace metals into seven groups. In the first step, anodic stripping voltammetry in a pH 4.8 acetic acid buffer differentiates between labile metals and nonlabile metals. Only labile metals—those present as hydrated ions, weakly bound complexes, or weakly adsorbed on colloidal surfaces—deposit at the electrode and give rise to a signal. Total metal concentration are determined by ASV after digesting the sample in 2 M HNO 3 for 5 min, which converts all metals into an ASV-labile form.

a As defined by (a) Batley, G. E.; Florence, T. M. Anal. Lett. 1976 , 9 , 379–388; (b) Batley, G. E.; Florence, T. M. Talanta 1977 , 24 , 151–158; (c) Batley, G. E.; Florence, T. M. Anal. Chem. 1980 , 52 , 1962–1963; (d) Florence, T. M., Batley, G. E.; CRC Crit. Rev. Anal. Chem. 1980 , 9 , 219–296.

A Chelex-100 ion-exchange resin further differentiates between strongly bound metals—usually those metals bound to inorganic and organic solids, but also those tightly bound to chelating ligands—and more loosely bound metals. Finally, UV radiation differentiates between metals bound to organic phases and inorganic phases. The analysis of seawater samples, for example, suggests that cadmium, copper, and lead are primarily present as labile organic complexes or as labile adsorbates on organic colloids (group II in Table 11.12).

Problem 11.31 asks you to determine the speciation of trace metals in a sample of sea water.

Differential pulse polarography and stripping voltammetry also have been used to determine trace metals in airborne particulates, incinerator fly ash, rocks, minerals, and sediments. The trace metals, of course, are first brought into solution using a digestion or an extraction.

See Chapter 7 for a discussion of digestions and extraction.

Amperometric sensors also are used to analyze environmental samples. For example, the dissolved O 2 sensor described earlier is used to determine the level of dissolved oxygen and the biochemical oxygen demand, or BOD, of waters and wastewaters. The latter test—which is a measure of the amount of oxygen required by aquatic bacteria when decomposing organic matter—is important when evaluating the efficiency of a wastewater treatment plant and for monitoring organic pollution in natural waters. A high BOD suggests that the water has a high concentration of organic matter. Decomposition of this organic matter may seriously deplete the level of dissolved oxygen in the water, adversely affecting aquatic life. Other amperometric sensors have been developed to monitor anionic surfactants in water, and CO 2 , H 2 SO 4 , and NH 3 in atmospheric gases.

Clinical Samples

Differential pulse polarography and stripping voltammetry may be used to determine the concentration of trace metals in a variety of clinical samples, including blood, urine, and tissue. The determination of lead in blood is of considerable interest due to concerns about lead poisoning. Because the concentration of lead in blood is so small, anodic stripping voltammetry frequently is the more appropriate technique. The analysis is complicated, however, by the presence of proteins that may adsorb to the mercury electrode, inhibiting either the deposition or stripping of lead. In addition, proteins may prevent the electrodeposition of lead through the formation of stable, nonlabile complexes. Digesting and ashing the blood sample minimizes this problem. Differential pulse polarography is useful for the routine quantitative analysis of drugs in biological fluids, at concentrations of less than 10 –6 M. 18 Amperometric sensors using enzyme catalysts also have many clinical uses, several examples of which are shown in Table 11.13.

Source: Cammann, K.; Lemke, U.; Rohen, A.; Sander, J.; Wilken, H.; Winter, B. Angew. Chem. Int. Ed. Engl. 1991 , 30 , 516–539.

Miscellaneous Samples

In addition to environmental samples and clinical samples, differential pulse polarography and stripping voltammetry have been used for the analysis of trace metals in other sample, including food, steels and other alloys, gasoline, gunpowder residues, and pharmaceuticals. Voltammetry is an important technique for the quantitative analysis of organics, particularly in the pharmaceutical industry where it is used to determine the concentration of drugs and vitamins in formulations. For example, voltammetric methods have been developed for the quantitative analysis of vitamin A, niacinamide, and riboflavin. When the compound of interest is not electroactive, it often can be derivatized to an electroactive form. One example is the differential pulse polarographic determination of sulfanilamide, which is converted into an electroactive azo dye by coupling with sulfamic acid and 1-napthol.

The best way to appreciate the theoretical and practical details discussed in this section is to carefully examine a typical analytical method. Although each method is unique, the following description of the determination of chloropromazine in a pharmaceutical product provides an instructive example of a typical procedure. The description here is based on a method from Pungor, E. A Practical Guide to Instrumental Analysis , CRC Press: Boca Raton, FL, 1995, pp. 34–37.

Representative Method 11.3

Determination of Chlorpromazine in a Pharmaceutical Product

Description of Method

Chlorpromazine, which also is known by the trade name Thorazine, is an antipsychotic drug used in the treatment of schizophrenia. The amount of chlorpromazine in a pharmaceutical product is determined voltammetrically at a graphite working electrode in a unstirred solution, with calibration by the method of standard additions.

Add 10.00 mL of an electrolyte solution consisting of 0.01 M HCl and 0.1 M KCl to the electrochemical cell. Place a graphite working electrode, a Pt auxiliary electrode, and a SCE reference electrode in the cell, and record the voltammogram from 0.2 V to 2.0 V at a scan rate of 50 mV/s. Weigh out an appropriate amount of the pharmaceutical product and dissolve it in a small amount of the electrolyte. Transfer the solution to a 100-mL volumetric flask and dilute to volume with the electrolyte. Filter a small amount of the diluted solution and transfer 1.00 mL of the filtrate to the voltammetric cell. Mix the contents of the voltammetric cell and allow the solution to sit for 10 s before recording the voltammogram. Return the potential to 0.2 V, add 1.00 mL of a chlorpromazine standard and record the voltammogram. Report the %w/w chlorpromazine in the formulation.

1. Is chlorpromazine undergoing oxidation or reduction at the graphite working electrode?

Because we are scanning toward more positive potentials, we are oxidizing chlorpromazine.

2. Why does this procedure use a graphite electrode instead of a Hg electrode?

As shown in Figure 11.35, the potential window for a Hg electrode extends from approximately –0.3 V to between –1V and –2 V, depending upon the pH. Because we are scanning the potential from 0.2 V to 2.0 V, we cannot use a Hg electrode.

3. Many voltammetric procedures require that we first remove dissolved O 2 by bubbling N 2 through the solution. Why is this not necessary for this analysis?

Dissolved O 2 is a problem when we scan toward more negative potentials, because its reduction may produce a significant cathodic current. In this procedure we are scanning toward more positive potentials and generating anodic currents; thus, dissolved O 2 is not an interferent and does not need to be removed.

4. What is the purpose of recording a voltammogram in the absence of chlorpromazine?

This voltammogram serves as a blank, providing a measure of residual current due to the electrolyte. Because the potential window for a graphite working electrode (see Figure 11.35) does not extend to 2.0 V, there will be a measurable anodic residual current due to the solvent’s oxidation. Having measured this residual current, we can subtract it from the total current in the presence of chlorpromazine.

5. Based on the description of this procedure, what is the shape of the resulting voltammogram. You may wish to review the three common shapes shown in Figure 11.42.

Because the solution is unstirred, the voltammogram will have a peak current similar to that shown in Figure 11.42b.

11.4.7 Characterization Applications

In the previous section we learned how to use voltammetry to determine an analyte’s concentration in a variety of different samples. We also can use voltammetry to characterize an analyte’s properties, including verifying its electrochemical reversibility, determining the number of electrons transferred during its oxidation or reduction, and determining its equilibrium constant in a coupled chemical reaction.

Electrochemical Reversibility and Determination of n

Earlier in this chapter we derived a relationship between E 1/2 and the standard-state potential for a redox couple (equation 11.44) noting that the redox reaction must be electrochemically reversible. How can we tell if a redox reaction is reversible by looking at its voltammogram? For a reversible redox reaction equation 11.43, which we repeat here, describes the relationship between potential and current for a voltammetric experiment with a limiting current.

\[E = E^\circ_\textrm{O/R} - \dfrac{0.05916}{n}\log\dfrac{K_\ce{O}}{K_\ce{R}} - \dfrac{0.05916}{n}\log\dfrac{i}{i_\ce{l}- i}\]

If a reaction is electrochemically reversible, a plot of E versus log( i / i l – i ) is a straight line with a slope of –0.05916/ n . In addition, the slope should yield an integer value for n .

Example 11.14

The following data were obtained from a linear scan hydrodynamic voltammogram of a reversible reduction reaction.

Figure 11.53 shows a plot of E cell versus log( i / i l – i ). Because the result is a straight line, we know that the reaction is electrochemically reversible under the conditions of the experiment. A linear regression analysis gives the equation for the straight line as

\[E = -0.391\: \textrm{V} - 0.0300\log\dfrac{i}{i_\textrm{l} - i}\]

From equation 11.43, the slope is equivalent to –0.05916/ n ; solving for n gives a value of 1.97, or 2 electrons. From equation 11.43 and equation 11.44, we know that E 1 /2 is the y -intercept for a plot of E cell versus log( i / i l – i ); thus, E 1 /2 for the data in this example is –0.391 V versus the SCE.

Figure 11.53 Determination of electrochemical reversibility for the data in Example 11.14.

We also can use cyclic voltammetry to evaluate electrochemical reversibility by looking at the difference between the peak potentials for the anodic and the cathodic scans. For an electrochemically reversible reaction, the following equation holds true.

\[E_\textrm{p}= E_\textrm{p,a}- E_\textrm{p,c} = \dfrac{0.05916\: \textrm{V}}{n}\]

For example, for a two-electron reduction, we expect a ∆ E p of approximately 29.6 mV. For an electrochemically irreversible reaction the value of ∆ E p will be larger than expected.

Determining Equilibrium Constants for Coupled Chemical Reactions

Another important application of voltammetry is determining the equilibrium constant for a solution reaction that is coupled to a redox reaction. The presence of the solution reaction affects the ease of electron transfer in the redox reaction, shifting E 1/2 to more negative or to more positive potentials. Consider, for example, the reduction of O to R

\[\textrm{O} + ne^- ⇋ \textrm{R}\]

the voltammogram for which is shown in Figure 11.54. If we introduce a ligand, L, that forms a strong complex with O, then we also must consider the reaction

\[\mathrm{O + \mathit{p}L ⇋ OL_\mathit{p}}\]

In the presence of the ligand, the overall redox reaction is

\[\mathrm{OL}_p + ne^- ⇋ \mathrm{R} + p\mathrm{L}\]

Because of its stability, the reduction of the OL p complex is less favorable than the reduction of O. As shown in Figure 11.54, the resulting voltammogram shifts to a potential that is more negative than that for O. Furthermore, the shift in the voltammogram increases as we increase the ligand’s concentration.

Figure 11.54 Effect of a metal-ligand complexation reaction on a voltammogram. The voltammogram in blue is for the reduction of O in the absence of ligand. Adding the ligand shifts the potentials to more negative potentials, as shown by the voltammograms in red .

We can use this shift in the value of E 1 /2 to determine both the stoichiometry and the formation constant for a metal-ligand complex. To derive a relationship between the relevant variables we begin with two equations: the Nernst equation for the reduction of O

\[E = E^\circ_\textrm{O/R} - \dfrac{0.05916}{n}\log\dfrac{[\textrm{R}]_{x=0}}{[\textrm{O}]_{x=0}}\tag{11.45}\]

and the stability constant, β p for the metal-ligand complex at the electrode surface.

\[β_p= \dfrac{[\mathrm{OL}_p]_{x=0}}{[\mathrm{O}]_{x=0}[\mathrm{L}]^p_{x=0}}\tag{11.46}\]

See Figure 3.5 to review the meaning of major, minor, and trace analytes.

In the absence of ligand the half-wave potential occurs when [R] x = 0 and [O] x = 0 are equal; thus, from the Nernst equation we have

\[(E_{1/2})_\textrm{nc} = E^\circ_\textrm{O/R}\tag{11.47}\]

where the subscript “nc” signifies that the complex is not present.

When ligand is present we must account for its effect on the concentration of O. Solving equation 11.46 for [O] x = 0 and substituting into the equation 11.45 gives

\[E = E^\circ_\textrm{O/R} - \dfrac{0.05916}{n}\log\dfrac{[\mathrm{R}]_{x=0}[\mathrm{L}]^p_{x=0}β_p}{[\mathrm{OL}_p]_{x=0}}\tag{11.48}\]

If the formation constant is sufficiently large, such that essentially all of O is present as the complex, then [R] x = 0 and [OL p ] x = 0 are equal at the half-wave potential, and equation 11.48 simplifies to

\[(E_{1/2})_\textrm{c} = E^\circ_\textrm{O/R} − \dfrac{0.05916}{n}\log[\mathrm{L}]^p_{x=0}β_p\tag{11.49}\]

where the subscript “c” indicates that the complex is present. Defining ∆ E 1/2 as

\[\Delta E_{1/2} = (E_{1/2})_\textrm{c} - (E_{1/2})_\textrm{nc}\tag{11.50}\]

and substituting equation 11.47 and equation 11.49 and expanding the log term leaves us with the following equation.

\[\Delta E_{1/2} = -\dfrac{0.05916}{n}\log β_p - \dfrac{0.05916p}{n}\log[\mathrm{L}]\tag{11.51}\]

A plot of ∆ E 1 /2 versus log[L] is a straight line, with a slope of that is a function of the metal-ligand complex’s stoichiometric coefficient, p , and a y -intercept that is a function of its formation constant β p .

Example 11.15

A voltammogram for the two-electron reduction ( n = 2) of a metal, M, has a half-wave potential of –0.226 V versus the SCE. In the presence of an excess of ligand, L, the following half-wave potentials are recorded.

Determine the stoichiometry of the metal-ligand complex and its formation constant.

We begin by calculating values of ∆E 1 /2 using equation 11.50, obtaining the values in the following table.

Figure 11.55 shows the resulting plot of ∆E 1 /2 as a function of log[L]. A linear regression analysis gives the equation for the straight line as

\[E_{1/2} = \mathrm{-0.370\: V - 0.0601\log[L]}\]

From equation 11.51 we know that the slope is equal to .0.05916 p / n . Using the slope and n = 2, we solve for p obtaining a value of 2.03 ≈ 2. The complex's stoichiometry, therefore, is ML 2 . We also know, from equation 11.51, that the y -intercept is equivalent to .(0.05916 p / n )logβ p . Solving for β 2 gives a formation constant of 3.5 × 10 12 .

Figure 11.55 Determination of the stoichiometry and formation constant for a metal-ligand complex using the data in Example 11.15.

Practice Exercise 11.9

The voltammogram for 0.50 mM Cd 2 + has an E 1 /2 of –0.565 V versus an SCE. After making the solution 0.115 M in ethylenediamine, E 1 /2 is –0.845 V, and E 1 /2 is –0.873 V when the solution is 0.231 M in ethylenediamine. Determine the stoichiometry of the Cd 2 + –ethylenediamine complex and its formation constant.

(The data in Practice Exercise 11.9 comes from Morinaga, K. “Polarographic Studies of Metal Complexes. V. Ethylenediamine Complexes of Cadmium, Nickel, and Zinc,” Bull. Chem. Soc. Japan 1956 , 29 , 793–799.)

As suggested by Figure 11.48, cyclic voltammetry is one of the most powerful electrochemical techniques for exploring the mechanism of coupled electrochemical and chemical reactions. The treatment of this aspect of cyclic voltammetry is beyond the level of this text, although you can consult this chapter’s additional resources for additional information.

11.4.8 Evaluation

Scale of operation.

Detection levels at the parts-per-million level are routine. For some analytes and for some voltammetric techniques, lower detection limits are possible. Detection limits at the parts-per-billion and the part-per-trillion level are possible with stripping voltammetry. Although most analyses are carried out in conventional electrochemical cells using macro samples, the availability of microelectrodes, with diameters as small as 2 μm, allows for the analysis of samples with volumes under 50 μL. For example, the concentration of glucose in 200-μm pond snail neurons has been successfully monitored using an amperometric glucose electrode with a 2 μm tip. 19

See Figure 3.5 to review the meaning of major, minor, and and trace analytes.

The accuracy of a voltammetric analysis usually is limited by our ability to correct for residual currents, particularly those due to charging. For an analyte at the parts-per-million level, an accuracy of ±1–3% is routine. Accuracy decreases when analyzing samples with significantly smaller concentrations of analyte.

Precision is generally limited by the uncertainty in measuring the limiting current or the peak current. Under most conditions, a precision of ±1–3% is reasonable. One exception is the analysis of ultratrace analytes in complex matrices by stripping voltammetry, in which the precision may be as poor as ±25%.

Sensitivity

In many voltammetric experiments, we can improve the sensitivity by adjusting the experimental conditions. For example, in stripping voltammetry we can improve sensitivity by increasing the deposition time, by increasing the rate of the linear potential scan, or by using a differential-pulse technique. One reason that potential pulse techniques are popular is that they provide an improvement in current relative to a linear potential scan.

Selectivity

Selectivity in voltammetry is determined by the difference between half-wave potentials or peak potentials, with a minimum difference of ±0.2–0.3 V for a linear potential scan and ±0.04–0.05 V for differential pulse voltammetry. We often can improve selectivity by adjusting solution conditions. The addition of a complexing ligand, for example, can substantially shift the potential where a species is oxidized or reduced to a potential where it no longer interferes with the determination of an analyte. Other solution parameters, such as pH, also can be used to improve selectivity.

Time, Cost, and Equipment

Commercial instrumentation for voltammetry ranges from <$1000 for simple instruments, to >$20,000 for a more sophisticated instrument. In general, less expensive instrumentation is limited to linear potential scans. More expensive instruments provide for more complex potential-excitation signals using potential pulses. Except for stripping voltammetry, which needs a long deposition time, voltammetric analyses are relatively rapid.

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Cyclic Voltammetry

Cyclic voltammogram, key parameters from voltammogram, applications.

Cyclic voltammetry is a powerful electrochemical technique used to study the redox reactions of compounds in solution. Researchers can obtain valuable information about the electron transfer processes at the electrode surface by applying a potential sweep to an electrochemical cell and measuring the resulting current. [1-4]

Cyclic voltammetry involves cycling the potential of an electrode between two limits at a specific scan rate while recording the current response. It allows researchers to investigate the oxidation and reduction behavior of analytes, determine their redox potentials, and study reaction kinetics.

Cyclic voltammetry (CV) analysis relies on fundamental equations to interpret electrochemical data accurately. Central to understanding redox processes in CV is the Nernst equation, a fundamental relation that elucidates the relationship between the redox potential, the concentration of species, and temperature, thereby facilitating the interpretation of experimental data in cyclic voltammetry. [3]

E = E 0 – (RT/zF) ln Q

E is the reduction potential

• E 0 is the standard potential
• R is the universal gas constant
• T is the temperature in kelvin
• z is the ion charge (moles of electrons)
• F is the Faraday constant
• Q is the reaction quotient

When scientists and engineers use cyclic voltammetry along with the Nernst equation, they can better understand electrochemical systems. It helps them study basic rules and create new technologies related to electrochemistry. It is especially important for figuring out energy storage and medical sensors.

While cyclic voltammetry is the experimental technique used to collect data, cyclic voltammogram is the visual representation of that data. Together, they provide insights into a system’s electrochemical behavior.

The cyclic voltammogram illustrates potential along the x-axis and current along the y-axis. However, there are two conventions for plotting the data: the American and IUPAC conventions. In the American convention, positive potential is depicted from right to left, with reduction currents represented as positive (while oxidation currents are negative). Conversely, the IUPAC convention displays positive potentials from left to right, with oxidation currents as positive. The IUPAC convention is predominantly used because of the prevalence of digital data collection and computer preferences for positive numbers. [3]

The figure above, depicting a representative cyclic voltammogram, shows the current-potential profile of a cyclic voltammetry experiment. As the potential is scanned towards more positive values, a point is reached where the electroactive species in the solution begin to undergo reduction. It increases current until a peak is reached, indicating that the current is then limited by the diffusion of additional reactant to the surface. Subsequently, as the potential becomes more positive, the diffusion layer near the electrode expands, resulting in a slower diffusion of additional reactant and a subsequent decrease in current. Upon reaching the potential limit, the current decreases until the potential reaches a point where oxidation of the reduced species near the surface occurs. This reversal leads to an increase in current in the opposite direction, culminating in a peak before decreasing until the initial potential is reached.

The voltammogram yields information crucial for comprehending electrochemical (redox) reactions. [3]

1. Redox Potential (E°): Cyclic voltammetry facilitates the assessment of the redox potential of an electroactive species. In reversible systems, the halfway potential between the peaks signifies equilibrium between oxidized and reduced species, offering a straightforward estimate of E 0 , the standard potential.

2. Electrochemical Reversibility: The cyclic voltammogram’s shape indicates the reversibility of the redox process—symmetrical peaks denote a reversible reaction, while asymmetrical peaks signify irreversibility.

3. Diffusion Coefficient (D): Through cyclic voltammetry, the diffusion coefficient of electroactive species can be inferred by conducting experiments at various scan rates. The Randles-Sevcik equation elucidates the relationship between peak current and scan rate, providing insights into species behavior—freely diffusing or adsorbed onto electrode surfaces.

4. Electroactive Species Concentration: The current peaks’ magnitude in cyclic voltammetry correlates directly with the concentration of participating electroactive species, facilitating concentration estimation.

5. Kinetic Parameters and Reaction Mechanism: Analysis of peak size, shape, and position enables the deduction of electron transfer rates, reaction kinetics, and the number of electrons involved in the redox process, shedding light on the reaction pathway.

6. Electrode Surface Area: Cyclic voltammetry may estimate electrode surface area, particularly for redox-active species with known diffusion coefficients.

7. Electrochemical Reaction Mechanisms: The cyclic voltammogram unveils electron transfer numbers and reaction pathways, offering crucial insights into reaction mechanisms.

This versatile technique finds applications across diverse fields owing to its simplicity and affordability. [3]

1. Electrochemical Sensors: Cyclic voltammetry detects analytes based on their redox activity, supporting glucose monitoring and pollutant detection applications.

2. Battery Research: Researchers utilize cyclic voltammetry to study battery materials, optimize performance, and understand degradation mechanisms.

3. Electroplating and Electrodeposition: For thin film deposition control, cyclic voltammetry optimizes parameters in electroplating and electrodeposition processes.

4. Medicine and Pharmaceuticals: In pharmaceutical research, cyclic voltammetry analyzes drug redox properties, aiding stability and interaction studies.

5. Fuel Cells: Cyclic voltammetry aids fuel cell development by evaluating catalysts and understanding electrochemical processes.

6. Electrochemical Capacitors (Supercapacitors): Cyclic voltammetry characterizes material behavior during charging and discharging for supercapacitor optimization.

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Cyclic Voltammetry Basic Principles and Theory

Cyclic voltammetry is an electrochemical technique used to measure the current response of a redox active solution to a linearly cycled potential sweep using a potentiostat . It is a useful method if you need to quickly find information about the thermodynamics of redox processes, the energy levels of the analyte and the kinetics of electronic-transfer reactions. This is important in the characterization of conductive polymers,  battery materials, supercapacitors, and fuel cell components.

Like other types of voltammetry, cyclic voltammetry uses a three-electrode system consisting of a working electrode, a reference electrode, and a counter electrode.

To perform cyclic voltammetry, you need to start by adding your electrolyte solution to an electrochemical cell, along with a reference solution and the three electrodes. After this, use a potentiostat to linearly sweep the potential between the working and reference electrodes. When the potentiostat reaches the pre-set limit, it will sweep back in the opposite direction.

The potentiostat will repeat this process multiple times during a scan. While doing so, it will record the changing current between the working and counter probes. The result is a characteristic duck-shaped plot known as a cyclic voltammogram.

• Basic theory and principles
• The potentiometry principle
• Introduction to voltammetry
• The three electrode system
• Cyclic voltammograms explained
• Cyclic voltammetry of ferrocene

Basic Theory and Principles

Cyclic voltammetry is a sophisticated potentiometric and voltammetric method. During a scan, the chemical either loses an electron (oxidation) or gains an electron (reduction). This will depend on the direction of the ramping potential.

The Potentiometry Principle

Potentiometry is a way of measuring the electrical potential of an electrochemical cell under static conditions (i.e. no current flow).

For a general reduction or oxidation (redox) reaction, the standard potential is related to the concentration of the reactants (A) and the products (B). This occurs at the electrode/solution interface and can be recognised according to the Nernst equation:

Here,  E is the electrode potential, E 0′ is the formal potential, R is the gas constant (8.3145 J·K -1 ·mol -1 ), T is temperature, n is the number of moles of electrons involved and F is the Faraday constant (96,485 C·mol -1 ).

The term [B] b /[A] a is the ratio of products to reactants, raised to their respective stoichiometric powers. You can use this in place of an activity term when the concentration is sufficiently low (< 0.1 mol·dm ˗3 ).

Under standard conditions of temperature and pressure, the Nernst equation can be written as:

Introduction to Voltammetry

Voltammetry is any technique that involves measuring the current while varying the potential between two electrodes. Voltammetric methods include cyclic voltammetry and linear sweep voltammetry, as well as similar electrochemical techniques such as staircase voltammetry, squarewave voltammetry, and fast-scan cyclic voltammetry.

In voltammetry, the current is generated by electron transfer between the redox species and the two electrodes. The diffusion and migration of ions carries this current through the solution.

The Three Electrode System

In principle, cyclic voltammetry (and other types of voltammetry) only requires two electrodes. However, in practice it is difficult to keep a constant potential while measuring the resistance between the working electrode and the solution. This is made more difficult as you try to pass the necessary current while also passing current to counteract the redox events at the working electrode.

It is the three-electrode system that separates the role of referencing the potential applied from the role of balancing the current produced.

To measure and control the potential difference applied, the potentiostat varies the potential of the working electrode while the potential of reference electrode remains fixed by an electrochemical redox reaction with a well-defined value.

To keep the potential fixed, the reference electrode must contain constant concentrations of each component of the reaction, such as a silver wire, and a saturated solution of silver ions.

It is important to note that minimal current passes between the reference and the working electrodes. The current observed at the working electrode is completely balanced by the current passing at the counter electrode, which has a much larger surface area.

The electron transfer between the redox species at the working electrode and counter electrode generates current that is carried through the solution by the diffusion of ions. This forms a capacitive electrical double layer at the surface of the electrode called the diffuse double layer (DDL). The DDL is composed of ions and orientated electric dipoles that serve to counteract the charge on the electrode.

The current response that you measure will be dependent on the concentration of the redox species (the analyte) at the working electrode surface. You can explain this by using a combination of Faraday’s law and Fick’s first law of diffusion:

Where i d is the diffusion-limited current, A is the electrode area, D 0 is the diffusion coefficient of the analyte and (∂C 0 /∂x 0 ) is concentration gradient at the electrode surface.

The product of the diffusion coefficient and concentration gradient can be thought of as the molar flux (mol·cm -2 ·s -1 ) of analyte to the electrode surface.

Cyclic Voltammograms Explained

A cyclic voltammogram is the ‘duck-shaped’ plot generated by cyclic voltammetry.

In the example cyclic voltammogram above, the scan starts at -0.4V and sweeps forward to more positive, oxidative potentials. Initially the potential is not sufficient to oxidise the analyte (a).

As the potential approaches several kT of the standard potential, the onset (E onset ) of oxidation is reached. Following this, the current exponentially increases (b) as the analyte begins its oxidation at the working electrode surface. For a reversible process, here the current rises initially as if there is no change in the concentration of oxidant. The current is dictated by the rate of diffusion of the oxidant to the electrode, as well as the proportion converted to the reduced form. This can be understood according to the Nernst equation. Gradually, as the scan continues, more oxidant is depleted. The concentration gradient adjusts to this. It is this change which causes a peak in the voltammogram. You can see how the decrease in current from depletion of the oxidant outweighs the increase from changing the proportion of oxidant oxidised at the electrode.

The current reaches peak maximum at point c (anodic peak current (i pa ) for oxidation at the anodic peak potential (E pa ). Here, more positive potentials cause an increase in current that is offset by a decreasing flux of analyte from further and further distance from the electrode surface.

From this point the current is limited by the mass transport of analyte from the bulk to the DDL interface, which is slow on the electrochemical timescale. This results in a decrease in current (d), as the potentials are scanned more positive. This occurs until a steady-state is reached where further increases in potential no longer has an effect.

Scan reversal to negative potentials (reductive scan) continues to oxidise the analyte. This continues until the applied potential reaches the value where the oxidised analyte (which has accumulated at the electrode surface) can be re-reduced (e).

The process for reduction mirrors that for the oxidation. The only difference is that it occurs with an opposite scan direction and a cathodic peak (i pc ) at the cathodic peak potential (E pc ) (f). The anodic and cathodic peak currents should be of equal magnitude but with opposite sign. This is only provided that the process is reversible (and if the cathodic peak is measured relative to the base line after the anodic peak).

The Randles-Sevcik equation

The peak current, i p , of the reversible redox process is described by the Randles-Sevcik equation.[1]

At 298 K, the  Randles-Sevcik equation is:

Where n is the number of electrons, A the electrode area (cm 2 ), C the concentration (mol·cm -3 ), D the diffusion coefficient (cm 2 ·s -1 ), and v the potential scan rate (V·s -1 ).

Cyclic Voltammetry of Ferrocene

Ferrocene (Fc) is a common internal standard for cyclic voltammetry. Its cyclic voltammogram can therefore be considered "typical". Like the general case which was described above, at the start of a cyclic voltammetry scan a positively ramping potential (the forward sweep) is applied between the working and reference electrodes. As the potential increases, ferrocene (Fc) physically close to the working electrode is oxidised (i.e. loses an electron). This converts it to Fc + , and the movement of the electrons creates a measurable electrical current.

As un-reacted Fc diffuses to the electrode and continues the oxidation process, the electrical current is increased and there is a build up of Fc +  at the electrode. This build up of Fc+ and depletion of Fc is called the the diffusion layer, and effects the rate at which un-reacted material can reach to the electrode. Once the diffusion layers reaches a certain size, the diffusion of Fc to the electrode slows down, resulting in a decrease in the oxidation rate and thus a decrease in electrical current.

When the potential ramp switches direction, the process reverses and the reverse sweep begins. Fc + close to the working electrode reduces (i.e., gains an electron), converting it back to Fc. The electrical current flows in the opposite direction, creating a negative current. The Fc + diffuses to the electrode, reducing to Fc and resulting in a increase in the negative current.

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Cyclic voltammetry is a versatile electrochemical method with a range of different applications.

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• Sevćik, A. Collection of Czechoslovak Chemical Communications 1958, 13 , 349
• A. L. Bard and L. Faulkner Electrochemical methods: Fundamentals and Applications, 2nd ed. John Wiley & Sons 2001
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• L. J, L. B, and P. G Advanced Practical Organic Chemistry, 3rd edition. Manipal: Routledge 2013
• J. L. Brédas, R. Silbey, D. S. Boudreaux, and R. R. Chance Chain-Length Dependence of Electronic and Electrochemical Properties of Conjugated Systems: Polyacetylene, Polyphenylene, Polythiophene, and Polypyrrole J. Am. Chem. Soc., vol. 105, no. 22, pp. 6555–6559, 1983
• N. Elgrishi, K. J. Rountree, B. D. McCarthy, E. S. Rountree, T. T. Eisenhart, and J. L. Dempsey A Practical Beginner’s Guide to Cyclic Voltammetry J. Chem. Educ., vol. 95, no. 2, pp. 197–206, 2018
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2022 Volume 90 Issue 10 Pages 102005

• Published: October 31, 2022 Received: July 13, 2022 Released on J-STAGE: October 31, 2022 Accepted: September 14, 2022 Advance online publication: - Revised: -

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“Cyclic voltammetry” is one of the most common electrochemical techniques, not only for electrochemists but also for researchers in other fields. However, the principles of cyclic voltammetry are very complex; beginners and even experts may struggle with their application. Therefore, we explain the fundamental principles in Part 1 and introduce the practical issues associated with recent trends such as fuel cells, capacitors, and sensors in Part 2. In this comprehensive paper, we focus on the electrochemical reversibility in cyclic voltammograms classified as reversible, quasi-reversible, and irreversible processes, which are useful for obtaining information on the reaction rates of electrodes. We also explain the relevant basic principles, experimental setup, and ideas of background current.

1)  A. J. Bard, L. R. Faulkner, and H. S. White, Electrochemical Methods: Fundamentals and Applications (3rd ed.), John Wiley & Sons (2022).

3)  T. Osakai, K. Kano, and S. Kuwabata, Basic Electrochemistry , Kagakudojin, Kyoto (2000).

9)  S. Izumi, S. Ishikawa, K. Katakura, Y. Aoi, and K. Nagao, Kiso Kara Wakaru Denkikagaku (2nd ed.), Morikita Publishing Co., Ltd., Tokyo (2019).

10)  P. T. Kissinger and W. R. Heineman, J. Chem. Educ. , 60 , 702 (1983).

14)  C. Sandford, M. A. Edwards, K. J. Klunder, D. P. Hickey, M. Li, K. Barman, M. S. Sigman, H. S. White, and S. D. Minteer, Chem. Sci. , 10 , 6404 (2019).

Cyclic voltammetry is a potential sweep method. Generally, the (open circuit/resting/equilibrium) potential at which no apparent external current flows is set as the initial potential ( E i /V), and the potential is scanned at a constant rate (represented by v and in units of V s −1 ) at the beginning time {measurement time ( t ) = 0}, followed by the reverse of the sweep direction at a reversal potential ( E λ /V).

The electrode potential is given by,   

Schematic of electron transfer during potential sweep on an electrode.

Using cyclic voltammetry, information such as the electron transfer rate, diffusion coefficient, redox potential, and amount of adsorbate (in the adsorption system) can be obtained. The electrochemical reversibility in CVs is classified as reversible, quasi-reversible, and irreversible, which is an important concept and can be evaluated from the shapes of the CVs. CVs strongly depend on the magnitude of correlation between the electron transfer rate and mass transfer rate of diffusion, as given below:

• •    Reversible process: electron transfer rate ≫ mass transfer rate of diffusion
• •    Quasi–reversible process: change from reversible to irreversible
• •    Irreversible process: electron transfer rate ≪ mass transfer rate of diffusion
• 　  　

In this chapter, we focus on reversibility and related principles to understand the theoretical treatment of cyclic voltammetry for a simple one-step, one-electron reaction. In addition, we drew a simple formula for CV simulation using Excel application to improve our understanding of cyclic voltammetry; for further details, refer to the supporting information (SI).

In the reversible electrode process, when the electron transfer rate is sufficiently higher than the mass transfer rate of diffusion, the potential is expressed by the following Nernst equation:   

Calculated concentration of oxidant (O) and reductant (R) profiles at electrode surface by Nernst equation (solid line: O, broken line: R). T = 298.15 K.

(a) Theoretical cyclic voltammogram (CV) at v = 0.01 V s −1 in a non-diffusion system, and (b) CVs at different scan rates. $VC_{\text{O}}{}^{\ast}$ = 1.0 × 10 −9 mol, n = 1, and T = 298.15 K.

In the previous section, we introduced a simple reversible system in which the active species were attached to the electrode surface. In contrast, we lack a thorough understanding of CV waves, including the diffusion effect, when active species of O and R are dissolved in the electrolyte solution, whereas it is useful to evaluate the reaction rate in experimental systems.

In electrochemical reactions, the charge transfer reaction occurs initially, such that a difference in concentration occurs near the electrode, and the reactive species diffuses to the electrode surface when electrochemically active species are present in the electrolyte. The mass transport caused by the difference in concentration, corresponding to that of the chemical potential and its range, is called diffusion and diffusion layers, respectively. It is important to understand these processes for evaluating electrochemical measurements.

In the charge transfer process, the current I depends on the electrode potential E as per the Butler–Volmer equation when the one-step, one-electron reaction occurs:   

In a static solution system, a mass transfer can be regarded as diffusion, whereas the effects of convection and electrophoresis are small compared with those of diffusion. When only O is dissolved in the electrolyte, reduction occurs; as shown in Eq. 4, O diffuses from the bulk solution to the electrode surface according to Fick’s first and second laws.   

(a) Theoretical CV in a reversible system. v = 0.05 V s −1 , k ° = 1 cm s −1 , D = 1.0 × 10 −5 cm 2 s −1 , $C_{\text{O}}{}^{\ast}$ = 1.0 × 10 −7 mol cm −3 , α = 0.5, and T = 298.15 K. (b) Schematic approximate surface concentration profiles of O during cathodic scan.

15)  T. Okajima, Electrochemistry , 81 , 655 (2013).

I p,c varies linearly with v 1/2 ( $I_{\text{p,c}} \propto v^{\frac{1}{2}}$ ), and must pass through the origin. The slope of the Randles–Sevcik type plot provides the diffusion coefficient. According to the Butler–Volmer equation expressed in Eqs. 15–17, the cathodic rate constant k c increased with a more negative potential sweep, whereas the current decreased. This was because of the mass transfer of diffusion. This situation resembled that of potential step chronoamperometry. The concentration gradient $(\frac{\partial C}{\partial x})_{x = 0}$ can be expressed using Eqs. 18 and 20 as follows:   

Theoretical CVs at different scan rates in the reversible process. k ° = 1 cm s −1 , D = 1.0 × 10 −5 cm 2 s −1 , $C_{\text{O}}{}^{\ast}$ = 1.0 × 10 −7 mol cm −3 , α = 0.5, and T = 298.15 K.

The term E 1/2 can be easily estimated from the cathodic and anodic peak potentials (points C and F, respectively) using Eq. 26; hence, these relationships are generally used to evaluate E °′. In addition, the two peak potentials are conventionally used to evaluate the reversibility of the electrode reactions using Eq. 27 as follows:   

Effect of standard electrode reaction rate constant of k ° for CVs from reversible to irreversible process. v = 0.05 V s −1 , D = 1.0 × 10 −5 cm 2 s −1 , $C_{\text{O}}{}^{\ast}$ = 1.0 × 10 −7 mol cm −3 , α = 0.5, and T = 298.15 K. (The black line of k ° at 1 cm s −1 overlaps the red line of k ° at 0.1 cm s −1 .)

Schematic of the reversibility in Randles–Sevcik plot I p vs. v 1/2 .

Correlation between Nicholson parameter Λ and k ° to determine the electron transfer mechanism, and the linearity between I p and v .

12)  N. Aristov and A. Habekost, World J. Chem. Educ. , 3 , 115 (2015).

16)  R. S. Nicholson and I. Shain, Anal. Chem. , 36 , 706 (1964).

20)  J. H. Brown, J. Chem. Educ. , 92 , 1490 (2015).

• •    Reversible process: $k^{\circ} > 0.35\sqrt{v} $
• •    Quasi-reversible process: $0.35\sqrt{v} > k^{\circ} > 3.5 \times 10^{ - 4}\sqrt{v} $

A three-electrode system is typically used for cyclic voltammetry measurements, namely the working electrode (WE), reference electrode (RE), and counter electrode (CE). These were immersed in an electrolyte and connected to a potentiostat. The WE and CE are generally placed on opposite sides of the cell, and the RE should be as close as possible to the WE to minimize the ohmic drop. The following explanation focuses on aqueous solution systems. To remove dissolved oxygen, an inert gas such as nitrogen or argon can be bubbled into the electrolyte prior to measurement. However, when gas bubbles are directly from the gas cylinder, the concentration of the electrolyte may change due to vaporization. Therefore, it is better to bubble gas into the electrolyte through the electrolyte without reactive species.

WE was used to perform the electrochemical events of interest, for example, an electrochemically inert electrode is preferable when evaluating the redox potential of a chemical species in an electrolyte. Pt, Au, and carbons, such as glassy carbon and pyrolytic graphite, whose surface areas are well-defined, are preferred as the WE. Additionally, a flat electrode that is significantly larger than the thickness of the diffusion layer should be used for analysis under the assumption of one-dimensional diffusion; a wire-shaped electrode is inappropriate. The capacitance and charging current of the electrical double layer and the adsorption behavior of gases on the electrode will vary with the type of electrode material; however, they do not interfere with the investigation of other electrode reactions as the electricity is constant (Notably, this does not apply when the measurement target is the adsorption behavior of the gas on the electrode). For measurements with high reproducibility, the WE surface should be extremely clean. A common cleaning method involves polishing the electrode surface mechanically with an abrasive such as alumina, followed by ultrasonic cleaning in ultrapure water. The polishing procedure depends on the electrode materials and may vary between different laboratories. Therefore, a thorough preliminary study is necessary before the measurement.

The RE controlled the potential of the WE, and the current did not flow at the RE during the measurement. To understand the electrode reaction thermodynamically, we must use an RE whose potential is highly reproducible and stable for a certain time. For measurements in aqueous electrolytes, Ag|AgCl| x mol dm −3 KCl and Hg|HgCl 2 |saturated KCl (saturated calomel electrode) are widely used. For these REs, porous glass or ceramic filters are used for liquid entanglement to avoid contamination by electrolytes. These electrodes can be fabricated in the laboratory; however, they are commercially available in recent years. Reservoir-type reversible hydrogen electrodes (RHE) are also available for purchase. Using the hydrogen formed in the RE through electrolysis, the potential of the WE can be controlled using the potential determined by the partial pressure of hydrogen and the activity of protons as a standard. When the potential of an RE needs to be stabilized for a long time, a salt bridge and a double-junction type RE are used.

CE is also known as an auxiliary electrode and undergoes a redox reaction that is complementary to that at WE. Reduction proceeds at WE when oxidation proceeds at CE, and vice versa. Although the reaction at the CE cannot be unambiguously attributed to electrolyte decomposition or the redox reaction of the active species, the CE must be capable of accepting a current greater than that observed at the WE. Generally, a mesh or coiled Pt or Au electrode, whose area is several dozen times larger than that of WE, is used to reduce the current density at the CE and to ensure that the polarization is associated with the electrode reaction at the WE.

Before performing cyclic voltammetry on the reactive species to determine the optimal value, we recommend measuring the background current (capacitive current) using an electrolyte that dissolves only the supporting electrolyte salt. Factors such as the decomposition of the solvent or supporting electrolyte salt, and the presence of impurities and dissolved oxygen hinder the measurement in the desired potential range. Therefore, their absence must be ensured before measurements.

(a) RC circuit, (b) triangular wave of potential sweep, (c) current–time, and (d) current–potential plots of background current.

21)  H. Yamada, K. Matsumoto, K. Kuratani, K. Ariyoshi, M. Matsui, and M. Mizuhata, Electrochemistry , 90 , 102000 (2022).

Hirohisa Yamada: Writing – original draft (Lead), Writing – review & editing (Lead)

Kazuki Yoshii: Writing – original draft (Lead), Writing – review & editing (Lead)

Masafumi Asahi: Writing – review & editing (Equal)

Masanobu Chiku: Writing – review & editing (Equal)

Yuki Kitazumi: Writing – review & editing (Equal)

The authors declare no conflict of interest in the manuscript.

This paper constitutes a collection of papers edited as the proceedings of the 51st Electrochemistry Workshop organized by the Kansai Branch of the Electrochemical Society of Japan.

H. Yamada and K. Yoshii: These authors contributed equally to this work.

H. Yamada, K. Yoshii, M. Asahi, M. Chiku, and Y. Kitazumi: ECSJ Active Members

• 1)   A. J. Bard, L. R. Faulkner, and H. S. White, Electrochemical Methods: Fundamentals and Applications (3rd ed.), John Wiley & Sons (2022).
• 2)   P. T. Kissinger and W. R. Heineman, Laboratory Techniques in Electroanalytical Chemistry (2nd ed.), Marcel Dekker, New York (1996).
• 3)   T. Osakai, K. Kano, and S. Kuwabata, Basic Electrochemistry , Kagakudojin, Kyoto (2000).
• 4)   J. O. M. Bockris and A. K. Reddy, Modern Electrochemistry 1: Ionics (2nd ed.), Kluwer Academic/Plenum Publishers, New York (1998).
• 5)   J. O. M. Bockris, A. K. Reddy, and M. E. Gamboa-Aldeco, Modern Electrochemistry 2A: Fundamentals of Electrodics (2nd ed.), Kluwer Academic/Plenum Publishers, New York (2000).
• 6)   J. O. M. Bockris, A. K. Reddy, and M. E. Gamboa-Aldeco, Modern Electrochemistry 2B: Electrodics in Chemistry, Engineering, Biology, and Environmental Science (2nd ed.), Kluwer Academic/Plenum Publishers, New York (2000).
• 7)   K. B. Oldham, J. C. Myland, and A. M. Bond, Electrochemical Science and Technology Fundamentals and Applications , John Wiley & Sons (2012).
• 8)   N. Eliaz and E. Gileadi, Physical Electrochemistry: Fundamentals, Techniques, and Applications (2nd ed.), John Wiley & Sons (2018).
• 9)   S. Izumi, S. Ishikawa, K. Katakura, Y. Aoi, and K. Nagao, Kiso Kara Wakaru Denkikagaku (2nd ed.), Morikita Publishing Co., Ltd., Tokyo (2019).
• 10)   P. T. Kissinger and W. R. Heineman, J. Chem. Educ. , 60 , 702 (1983).
• 11)   J. F. Rusling and S. L. Suib, Adv. Mater. , 6 , 922 (1994).
• 12)   N. Aristov and A. Habekost, World J. Chem. Educ. , 3 , 115 (2015).
• 13)   N. Elgrishi, K. J. Rountree, B. D. McCarthy, E. S. Rountree, T. T. Eisenhart, and J. L. Dempsey, J. Chem. Educ. , 95 , 197 (2018).
• 14)   C. Sandford, M. A. Edwards, K. J. Klunder, D. P. Hickey, M. Li, K. Barman, M. S. Sigman, H. S. White, and S. D. Minteer, Chem. Sci. , 10 , 6404 (2019).
• 15)   T. Okajima, Electrochemistry , 81 , 655 (2013).
• 16)   R. S. Nicholson and I. Shain, Anal. Chem. , 36 , 706 (1964).
• 17)   R. S. Nicholson, Anal. Chem. , 37 , 1351 (1965).
• 18)   A. Habekost, World J. Chem. Educ. , 7 , 53 (2019).
• 19)   I. Lavagnini, R. Antiochia, and F. Magno, Electroanalysis , 16 , 505 (2004).
• 20)   J. H. Brown, J. Chem. Educ. , 92 , 1490 (2015).
• 21)   H. Yamada, K. Matsumoto, K. Kuratani, K. Ariyoshi, M. Matsui, and M. Mizuhata, Electrochemistry , 90 , 102000 (2022).

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A synthetic chemist's guide to electroanalytical tools for studying reaction mechanisms

First published on 23rd May 2019

Monitoring reactive intermediates can provide vital information in the study of synthetic reaction mechanisms, enabling the design of new catalysts and methods. Many synthetic transformations are centred on the alteration of oxidation states, but these redox processes frequently pass through intermediates with short life-times, making their study challenging. A variety of electroanalytical tools can be utilised to investigate these redox-active intermediates: from voltammetry to in situ spectroelectrochemistry and scanning electrochemical microscopy. This perspective provides an overview of these tools, with examples of both electrochemically-initiated processes and monitoring redox-active intermediates formed chemically in solution. The article is designed to introduce synthetic organic and organometallic chemists to electroanalytical techniques and their use in probing key mechanistic questions.

1. Introduction

In recent years, the expansion of photoredox 2 and electrochemical 3 organic reaction methodologies has led to an impressive growth in synthetic processes involving electron transfer. This proliferation is in part due to the ability to tune the thermodynamics and/or kinetics of the electron transfer – chemoselectively forming reactive intermediates via careful manipulation of oxidation states of specific functional groups at rates commensurate with keeping radicals at low concentrations. The ability to understand how to fine-tune the reactivity and concentration is clearly related to knowledge of the feasibility and kinetics of the electron-transfer event. The development and application of techniques to interrogate such phenomena is at the heart of achieving high yields and selectivities in redox driven transformations.

As such, electroanalytical methods provide wide-ranging opportunities to gain knowledge of fundamental interactions, lifetimes, and reactivities underpinning redox processes. 4 However, these tools have not been widely adopted by the organic synthetic community, generally remaining as methods in the domain of physical and analytical chemists. This perspective aims to summarise the key techniques for an audience of synthetic chemists, suggesting methods to obtain valuable answers to mechanistic questions. Information summarised herein will exemplify electrochemistry as a tool to identify speciation, equilibria and binding, oxidation states of metals, catalytic turnover, and kinetics. Knowledge of how these factors affect a mechanism will allow greater understanding of organic and organometallic processes, and aid in the development of new synthetic methodologies.

The case studies selected throughout this review are aimed at highlighting singular modern mechanistic studies for each technique. We would encourage the interested reader to access more detailed reviews on each method referenced throughout and summarised in the conclusion for a thorough theoretical and mathematical background to the experiment. Additionally, the reader should note that this review is not designed as a hands-on guide to the techniques and will not discuss experimental details set-up, rather concentrating on the mechanistic information garnered by various methods.

2. Cyclic voltammetry

2.1 introduction, reduction potentials and diagnostic analysis.

For an electrochemically reversible process, E 1/2 is measured as halfway between the anodic and cathodic peak potentials, and is approximately equal to E 0′ . Additionally, the separation of the two peak potentials for a reversible redox event with fast electron-transfer kinetics is equal to ∼60/ n mV at room temperature, where n is the number of electrons transferred in the redox event. 4a A peak separation significantly greater than this value is an indication that the electron-transfer kinetics are slow on the time scale of the potential sweep, which is favored at fast CV scan rates. Accordingly, the variation in peak separation upon changing the CV scan rate can be used to quantify the heterogeneous electron transfer rate constant between the electrode and redox-active species. 5a

Cyclic voltammetry can be used as a rapid way to assess the ability of a molecule to undergo electron transfer. The thermodynamic driving force needed to generate different redox species can be compared, enabling selection of a suitable catalyst, 6 mediator, 7 sensitizer, 8 or terminal reductant/oxidant. 9 However, when comparing E 1/2 values, care should be taken if the measurements were conducted under different conditions – measured against a different reference electrode, or in a different solvent or electrolyte, the E 1/2 observed will vary.

Many organic compounds undergo chemically irreversible electron transfer, forming a highly reactive charged or radical species with a short half-life. These compounds may be unstable on the CV timescale, reacting in a homogenous chemical reaction with other substrates, intermediates, solvent, oxygen or water. The subsequent chemical step (denoted C in an EC mechanism) results in the loss of product electrogenerated on the forward scan, resulting in a decrease in the magnitude of the peak current on the reverse sweep. The shape of the voltammogram for an EC reaction with two different rates of the chemical step is shown in Fig. 1c . Importantly, the shape of the CV response can provide information on the stability and lifetime of the intermediate – if a CV response appears irreversible with no peak observed on the reverse scan in the absence of substrate, then the species will likely not be a good catalyst or mediator since it may decompose before the desired transformation can occur.

Quantitative data on the kinetics of the chemical step can also be obtained by measuring the voltammetric shape as a function of the scan rate, with the voltammogram appearing more reversible at higher scan rates (see Section 2.5). The characteristic half-peak potential ( E p/2 ) for an EC reaction is a function of the rate constant of the chemical reaction following the initial electron-transfer step, and thus generally cannot be employed to approximate E 0′ , as in the case of using E 1/2 values for chemically reversible electron-transfer reactions. Nevertheless, E p/2 can be used as a predictive tool for comparing relative thermodynamic redox potentials, with reference to the data tabulated by Nicewicz and co-workers. 10

2.2 Speciation and consecutive redox events

Case study 2: ECE mechanisms. Further to the identification of multiple species, CV can also be used to identify consecutive redox features of the same substrate. In work by Waldvogel and co-workers, 13 the oxidation of anilides was determined to occur through two consecutive electron-transfer processes separated by a chemical deprotonation (denoted as an ECE mechanism), first oxidation and deprotonation to the amidyl radical and then further oxidation to the corresponding cation ( Fig. 3 ). For the para -methylphenyl substrate 4 , the CV response displays two distinct irreversible oxidation peaks separated by 240 mV (the irreversibility of the CV response is consistent with a chemical deprotonation following the electron transfer).

In contrast, only one irreversible oxidation is observed for the para -methoxyphenyl substrate 5 . In this case, the redox potential is less positive than for substrate 4 since the mesomerically electron-donating methoxy group increases the electron density located on the aromatic ring and nitrogen lone pair. Furthermore, since the amino cation obtained from substrate 5 is stabilised by conjugation, and the second oxidation occurs at a potential either equal to or less positive than the first oxidation. Consequently, only one 2e anodic peak is observed in the CV of compound 5 . Knowledge of how to access the radical and/or cationic intermediates could then be utilised by the authors for differentiated reactivity.

2.3 Equilibria and binding

Case study 3: identifying the effect of additives on the thermodynamics of electron transfer. In extreme cases, binding can be used to change the thermodynamics of a reaction from endergonic to exergonic – for example, the coordination of Nd(OTf) 3 to a ketone was found by Zeitler and co-workers to shift the reduction potential of the ketone by over 250 mV ( Fig. 4 ). 14 This shift is consistent with the Lewis acidic neodymium binding to the ketone, which lowers the LUMO and facilitates reduction to the ketyl radical anion. Furthermore, the authors observed that the addition of water to the solvent mixture also lowers the redox potential of the ketone. In combination, using water and Nd(OTf) 3 shifted the potential by 450 mV, making reduction by the photoexcited state of Ir(ppy) 3 ( E 1/2 = −1.73 V) significantly more exergonic to enhance subsequent reactivity.

Case study 5: the manipulation of redox potentials by following chemical steps. Xu and Moeller have demonstrated that a chemical step following electron transfer can shift the reduction to a more negative potential to make the entire reaction feasible. 16 The intramolecular anodic coupling of an amine with a dithioketene acetal at first appears challenging, since the amine functional group in the product ( E p/2 = +0.89 V) has a lower redox potential than the isolated dithioketene motif that needs to be oxidised ( E p/2 = +1.06 V), suggesting that overoxidation would occur ( Scheme 1 ). However, rapid cyclisation of the nucleophilic amine depletes the equilibrium of the oxidised species through chemical step C. Shifting the equilibrium in this manner changes the redox potential. Indeed, when the redox potential of the substrate was measured by CV, the E p/2 was found to be only +0.60 V, 460 mV lower than the redox potential of the isolated dithioketene ( E p/2 = +1.06 V, measured in the absence of the amine, such that the cyclisation does not occur and the equilibrium is not perturbed). Since the potential of the substrate ( E p/2 = +0.60 V) is below that of the product ( E p/2 = +0.89 V), the authors determined that the process occurs without overoxidation, and the product was obtained in 84% yield.

2.4 Catalytic currents

Case study 6: how a catalytic waveform can inform mechanism. Example CV responses of an EC′ mechanism 19 are shown in Fig. 7a , reported by the groups of Minteer and Sigman. 20 It was found that the ligated Co( II )/Co( I ) displays a chemically reversible CV response (E mechanism) in the absence of substrate at a scan rate of 100 mV s −1 (dashed line). However, sequential additions of benzyl bromide lead increasing catalytic currents as a function of [BnBr]. This is consistent with oxidative addition of Co( I ) to BnBr forming a benzyl radical, simultaneously regenerating Co( II ) that is reduced at the cathode.

Case study 7: identifying active catalysts. The observation of a catalytic current can allow key mechanistic details to be analysed. For example, the groups of Du Bois, Waymouth, Sigman and Zare used CV studies to elucidate which ruthenium oxidation states can catalyse C–H oxidation of aliphatic substrates. 21 Multiple reversible oxidation couples were observed for the different catalyst oxidation states ( Fig. 7b ). When the substrate was added to the mixture, a current increase was observed for the peaks at 1.20 and 1.35 V, corresponding to the Ru( IV )/Ru( V ) and Ru( V )/Ru( VI ) couples, respectively. This increase in current is indicative of the oxidised ruthenium complex being catalytically active in the oxidation of the substrate. Since the increase in current is most pronounced for the Ru( V )/Ru( VI ) redox couple, this suggests that Ru( VI ) is the most catalytically active oxidation state. However, the increase in current for the Ru( IV )/Ru( V ) couple is comparatively small and could be the result of the start of the increase in current from the following Ru( V )/Ru( VI ) couple, and so further experiments were required to verify the catalytic activity of Ru( V ).

The use of CV to measure coupled chemical reactions allows determination of potential catalysts, as well as rapid screening for substrates with which they can react. 22 Whilst this technique is used in the screening of homogeneous electrocatalysts, its modern incorporation into other synthetic fields remains limited. For example, in the field of photoredox catalysis, Knowles and co-workers identified that a perester substrate can be reduced by an Ir( II ) photocatalytic intermediate. 23 Given the ease of this technique, we envision its wider incorporation in these areas in the near future.

2.5 Kinetic measurements

In contrast, for a cathodic EC mechanism, the chemical transformation depletes the concentration of the reduced species, and therefore results in a decrease in the peak anodic current ( i pa ) when compared to an E mechanism, resulting in a concomitant reduction in the i pa / i pc ratio. 25 Changing the scan rate of the CV alters the time taken between the peak cathodic and peak anodic potentials: decreasing the scan rate allows more time for the chemical reaction, resulting in a decreased concentration of Co( I ) for the return sweep. This results in greater irreversibility in the CV response and a decrease in the i pa / i pc ratio ( Fig. 8b ). Plotting the concentration of reduced cobalt remaining after a given time according to second order kinetics thereby allows determination of the rate constant of the disproportionation ( Fig. 8c ). The authors were able to use this method to calculate the disproportionation rate constants for a range of Co( I ) complexes ligated by N , N -bidentate ligands, and used these data to identify possible mechanisms of disproportionation. 26

In the domain of catalysis ( cf. , Fig. 6 ), the order of each reaction component and rate constants can also be obtained by comparison of the catalytic current ( i cat ) with the peak current in the absence of substrate ( i p ). 4d Kinetic studies of catalysis through electroanalytical techniques have become standard practice in the inorganic community. 27

Since the determination of the order of a reaction with respect to a given substrate in this manner allows identification of the rate-limiting step in catalysis, 31 these techniques enable the postulation of reaction mechanisms. Recently, Costentin and Savéant developed a rigorous technique to study the benchmarking and optimisation of molecular catalysts by examining thermodynamic and/or kinetic correlations between properties such as turnover frequency and overpotential. 32 The authors illustrated their analysis with an oxygen reduction reaction (ORR, see also Section 5.2), 33 but the same techniques can be readily applied for organic transformations.

In addition to quantitative kinetic measurements determined using currents from CV experiments, shifts in potential of a CV response at differing scan rates also allow determination of the relative concentrations of redox-active species, which thereby facilitates calculation of rate constants, as well as mechanistic paths for reactions involving multiple electron transfer and chemical steps. 34 The case study below exemplifies this in the scenario of an EC mechanism, but the same process can be applied to determine kinetic measurements of catalytic (EC′) reactions under specific experimental conditions (the ‘total’ catalysis regime). 5a,27c

Case study 10: determining rate constants of following chemical steps with peak potentials (EC mechanisms). In a study of proton-coupled electron transfer, Costentin et al. measured the rate constant for oxidative addition of chloroacetonitrile to cobalt( I ) tetraphenylporphyrin. 35 Given that cobalt is first reduced from the Co( II ) state, oxidative addition depletes the concentration of Co( I ) and shifts the equilibrium of the reversible reduction (an EC mechanism). In a similar manner to that discussed in Section 2.3, the peak potential has a dependence on the shift of the equilibrium of the two redox-active species. By increasing the concentration of the chloroacetonitrile 6 , an anodic (to a less negative potential) shift is observed ( Fig. 10 ). Plotting the peak potential against the base-10 logarithm of the concentration, the slope is consistent with a pseudo-first order reaction, and the intercept allows determination of the corresponding rate constant. 36

3. Pulsed voltammetric techniques

3.1 introduction to pulsed voltammetry.

In any electrochemical measurement, the current observed upon polarisation of an electrode ( e.g. , as a potential is applied during CV) is a composite of two factors: (a) the faradaic current, which reports the rate of consumption of an electroactive species at the electrode, and (b) capacitive (non-faradaic) current, which is caused by reorganisation of supporting electrolyte at the electrode–solvent interface and charging of the electric double layer. While faradaic current typically persists on the order of seconds, capacitive current decays completely within a few milliseconds (it should be noted that this time can increase with high-surface area electrodes). Pulse voltammetry methods employ a staircase-shaped waveform ( Fig. 11a ), in which an initial base applied potential (the reverse pulse) is alternated with pulses of higher applied potential (the forward pulse), and the net current is the difference between currents sampled during the forward and reverse pulse. In this way, the capacitive current can be removed to allow measurement of the desired faradaic current, which results from electron transfer at the electrodes. This net current results in a single uniform peak centred around the midpoint potential of the electroactive species ( Fig. 11b ), which allows direct measurement of the reduction potential ( E 1/2 ) of the species.

The two most commonly applied pulse voltammetry techniques, differential pulse voltammetry (DPV) and SWV, differ primarily in the duration of the forward pulse relative to the reverse pulse. While SWV is a specialised form of DPV, standard DPV experiments employ a short forward pulse relative to the backward pulse (typically, the forward pulse is ∼1% of the duration of the reverse pulse) to exhaust capacitive current and undesired redox processes. In contrast, SWV employs forward and reverse pulses of equal duration so that the overall time per waveform is dramatically decreased. The cumulative result is that DPV is limited to substantially slower sweep rates (∼10 mV s −1 ) than SWV (upper limit ∼1 V s −1 ). Consequently, SWV is highly preferable when studying short-lived electrochemically generated species.

It should be noted that whilst SWV can be a valuable tool for studying mechanistic aspects of electrochemically-coupled chemical reactions, it often requires the ability to simulate voltammograms to quantify more nuanced kinetic parameters (see Section 9). Nevertheless, some general trends have been ascertained – specifically, the width of a SWV peak at half-height ( W 1/2 ) for a reversible redox couple should be 100 mV for a reversible one-electron-transfer process. 40 This can be particularly useful in identifying the number of electrons transferred in overlapping SWV peaks.

3.2 Examples of square wave voltammetry for investigating speciation and organic mechanisms

Another method for resolving overlapping SWV peaks involves peak fitting of their component curves. The symmetric nature of SWV peaks enables composite curves to be fitted to the sum of two independent Gaussian curves, facilitating the measurement of relative concentrations of electroactive species, and thereby proving useful for monitoring the progress of organic reactions.

Case study 12: measuring reaction conversion by fitting SWV curves. In a study by Compton and co-workers ( Fig. 13 ), SWV was used to monitor a halogen exchange reaction of 2,4-dinitrochlorobenzene (2,4-DNCB) in the preparation of 2,4-dinitrofluorobenzene (2,4-DNFB), 42 a reagent used to label N -terminal amino acid groups of polypeptide chains. Since the reactants and products are structurally similar, monitoring this reaction by TLC proved impractical. Both 2,4-DNCB and 2,4-DNFB can be electrochemically reduced and exhibit reversible redox waves with midpoint potentials at −0.51 V and −0.56 V, respectively. The similarity of redox potentials and the asymmetric nature of sweep voltammetry makes peak fitting of their overlapping CV signals impractical for a reaction mixture; however, SWVs of reversible redox species generally result in symmetric peaks that can be readily fit to a Gaussian curve. Using two Gaussian fits to resolve distinct SWV peaks in aliquots from the halogen exchange reaction, absolute concentrations of each reaction component were conveniently determined at regular time intervals, enabling analysis of the conversion of the reaction as a function of time.

4. Spectroelectrochemistry

Case study 13: identifying intermediates by UV-Vis spectroelectrochemistry. As an example of the utility of SEC, Nocera and co-workers utilised UV-Vis spectroscopy to validate the presence of a mixed-valent Ni( I / II ) dimer ( 7 ) as an off-cycle reaction intermediate in a nickel-catalysed cross-coupling ( Fig. 14 ). 48 Dimer 7 was independently synthesised and found to match the UV-Vis absorption profile of the reaction mixture from in situ SEC, providing direct evidence of this species in solution. By the identification of the off-cycle dimer 7 , the authors were able to provide a revised mechanism in which the iridium photocatalyst initiates a self-sustaining Ni( I )/Ni( III ) cycle. Additionally, the authors were able to identify conditions which help to reduce the formation of other off-cycle Ni( II ) species, leading to a 15-fold increase in the quantum yield for the photochemical etherification of aryl halides, a reaction originally reported by MacMillan and co-workers. 49

Case study 14: identifying intermediates by EPR spectroelectrochemistry. As another example of the application of SEC to investigate organic mechanisms, EPR spectroelectrochemistry was used by Mo and co-workers to determine the existence of radical intermediates in an electrochemical Sandmeyer reaction ( Fig. 15 ). 50 It was found that reduction of aryl diazonium 8 forms an aryl radical 9 , which can be trapped by spin-trap 11 to form stable, EPR detectable radical 12 . Conveniently, the time evolution of the EPR signal can be measured during the electrochemical reaction – demonstrating rapid formation of the intermediate radical 9 , trapping by 11 and competitive bromination of the radical in the presence of N -bromosuccinimide (NBS).

Mass spectrometry also provides a valuable tool to determine intermediates and products. Coupling an electrochemical flow cell to an on-line mass spectrometer has been used widely to determine intermediates and products present in solution following a redox reaction, including in studies of possible metabolic oxidation pathways. 51 Alternatively, gaseous or volatile components can be measured by Differential Electrochemical Mass Spectrometry (DEMS) techniques, which have the added capability of directly monitoring rates of product formation. 52 Whilst these mass spectrometry techniques have been primarily utilised in the domain of fuel cells and electrolysis, their future prospects for investigating organic mechanisms are exemplified by a report from the groups of Zare and Chen in which the radical cation of N , N -dimethylaniline was detected, an intermediate with a half-life on the order of a microsecond. 53

5. Rotating disk and ring-disk electrodes

5.1 rotating disk electrodes.

Experiments with an RDE typically use linear sweep voltammetry (LSV): starting at a potential at which no faradaic reaction is occurring, the voltage is then swept over the potential range up to at least 250 mV past the redox potential. Slow sweep rates such as 5 or 10 mV s −1 are often used to ensure steady-state conditions and to reduce capacitive currents ( cf. , Section 3.1).

While LSV is commonly used with RDE, constant potential techniques known as chronoamperometry (CA) can also be useful to measure changes in concentration. In a CA experiment, the potential is stepped to a value in the region of interest for a given redox process and then held for a specific amount of time. The region of interest at which the potential is held is typically one at which the current is in the limiting regime, where the current is limited only by the flux of the redox-active species to the electrode (see also Section 6). Since the limiting current in an RDE experiment is directly related to the concentration of a species in solution, it provides the ability to monitor the concentration of a species in real-time.

Chronoamperometry was performed with varying amounts of the hydroxide base relative to the arylboronic acid substrate, resulting in a “bell-shaped” relationship between the reaction rate constant and the equivalents of hydroxide ( Fig. 16c ). At low hydroxide concentrations, the reactive complex 16 is in low concentration and the reaction is slow. Conversely, at high concentrations of hydroxide the boronate complex 15 is formed, which almost entirely retards the reaction, suggesting that the boronate is unreactive in the catalytic cycle. The work provides strong evidence for the existence of a palladium-hydroxide species ( 14 ) in the dominant catalytic cycle, a result which has been corroborated by several alternative techniques. 59 This insightful work by Amatore et al. was followed with additional investigations combining CA and RDEs to determine the kinetic effects of varying the type of anionic base and countercation in the Suzuki reaction. 60

5.2 Rotating ring-disk electrodes

One such example of the utility of RDE and RRDE is to benchmark heterogeneous catalysts for the oxygen reduction reaction (ORR), 61b,63 since the absence of a homogeneous reaction allows the mass transport to be determined using Koutecký–Levich analysis. 4a ORR can either proceed through a two-electron pathway to form peroxide, or via a four-electron pathway which generates water. Using a RRDE allows detection and quantification of peroxide generated in the ORR at the ring electrode, which enables determination of the number of electrons transferred ( n ), to demonstrate the relative catalyst efficiency for the two-electron pathway against the four-electron pathway. 64

6. Microelectrodes

The advantages of microelectrodes relative to macroelectrodes stem from differences in transport to and from their surfaces. While transport to macroelectrodes occurs perpendicular to the electrode surface (planar diffusion) and edge effects can be ignored, transport to microelectrodes is dominated by edge effects and species are transported to/from the electrode in all directions (radial diffusion) ( Fig. 18b ). Radial diffusion leads to much higher mass transport rates and current densities, which facilitates the measurement of faster processes. This difference in transport is apparent from comparing voltammetry using a macro- and microelectrode ( Fig. 18c ). As discussed in Section 2.1, cyclic voltammetry with a macroelectrode results in a peak current ( i p ) followed by a diffusional tail, since the reactant has to be transported to the electrode from increasingly farther distances. In contrast, the constant flux to a microelectrode from radial diffusion results in a steady-state response with limiting current ( i lim ), much like the limiting current observed with rotating disk electrodes (Section 5.1). Additionally, no peak is observed on the reverse scan since the product of the electron transfer diffuses away from the electrode.

Case study 16: determining rate constants in nonpolar solvents with microelectrodes. As an example of using microelectrodes, in conjunction with their studies on transmetalation ( Fig. 16 ), Amatore and Pflüger utilised a microelectrode to study the rate of oxidative addition of (Ph 3 P) 4 Pd(0) into p -iodotoluene, using toluene as a low dielectric constant solvent ( Fig. 19 ). 67 By measuring the limiting current, which results from the oxidation of Pd(0) as a function of time following the addition of the aryliodide, the variation of Pd(0) concentration over time could be plotted ( Fig. 19c ). Comparing the rate constants obtained with a variety of para -substituted aryliodides enabled the authors to obtain a Hammett correlation with ρ = 2.3 ± 0.2 ( Fig. 19d ). Interestingly, this Hammett rho value was found to be largely independent of the polarity of the solvent, 68 indicating that the transition state of the oxidative addition does not possess significant ionic character.

The proportionality in eqn (5) extends beyond just concentration; i lim is also proportional to the number of electrons transferred in the redox event ( n ) as well as the diffusion coefficient of the redox-active species ( D ). Therefore, knowledge of two of these parameters allows evaluation of the third. Additionally, following the application of a potential step, a large current is initially observed, before rapidly decaying to the steady-state response (limiting current). Since the time dependent i – t response and the steady state current have different dependencies on D and n , it is possible to determine D by recording the current following a single potential step experiment. 69 Knowledge of the diffusion coefficient itself is of significant value in cases where dimers or other higher order complexes may be present.

With the value of D independently calculated by this method, the authors could then determine that the initial reduction is an apparent two-electron process using eqn (5) , which would form the unknown species 20 as a Ni(0) intermediate. Since oxidative addition is postulated to proceed from a Ni( I ) species, this suggests that comproportionation of Ni( II ) species 19 and electrogenerated Ni(0) species 20 may lead to the active Ni( I ) complex in solution. 70

The experiments described above consider the situation in which there is an excess of supporting electrolyte. A unique, especially important and often employed advantage of microelectrodes is the ability to study electrochemical reactions and mechanisms in the absence of any supporting electrolyte. When the supporting electrolyte concentration is lowered, the passage of current through the resistive solution creates an electric field in the solution adjacent to the electrode. For a cathodic reaction (reduction), transport of cationic reactants is enhanced by electrical migration in the field; thus, the limiting current of a positively charged reactant ( A + ) will increase relative to the limiting current in the presence of excess supporting electrolyte ( Fig. 21a and b ). 71 If the reactant is neutral ( A ), the voltammetry displays the same limiting current with and without supporting electrolyte. Finally, in the scenario where the reactant in a cathodic reaction is negatively charged ( A − ), a lower limiting current is observed in experiments without electrolyte.

Case study 18: determining the charge of redox-active species. As an example of the utility of this concept in transition metal catalysis, in extension to the study displayed in Fig. 20 , White and co-workers studied the two-electron reduction of the purported nickel( II ) complex 19 with and without supporting electrolyte. 72 Surprisingly, it was found that the limiting current is higher in the absence of the electrolyte ( Fig. 21c ), indicating that the complex undergoing reduction is presumably a cationic Ni( II ) species, which does not match the supposed neutral structure of complex 19 . Further studies to investigate the precise nature of the Ni( II ) cationic species undergoing reduction are required, but this case study exemplifies the utility of microelectrodes for probing the chemical properties of species in solution.

7. Scanning electrochemical microscopy (SECM)

Case study 19: determining concentration profiles of species in solution. As an illustration of the utility of this technique, Amatore et al. used SECM to monitor the catalytic reduction of aryl halides mediated by benzophenone ( Fig. 22b ). 75 The concentrations of electroactive species close to the substrate electrode are influenced by the electrode redox reaction, further chemical reactions in the solution, and transport processes in solution (for schematic concentration profiles, see Fig. 22c ). When benzophenone reduction occurs in the absence of the aryl halide, chemical reactions in the solution need not be considered. The concentration of the intermediate (benzophenone radical anion, 22 ) is highest at the electrode surface and diminishes towards bulk solution ( Fig. 22d , closed black circles), whereas the reactant (benzophenone, 21 ) displays the opposite trend, being lowest at the electrode surface (typically zero, when the reaction is transport-limited) and increasing to its bulk concentration far away. This control experiment provides information on how species are transported to/from the electrode.

With the introduction of iodobenzene 23 , electron transfer from the benzophenone radical anion to iodobenzene decreases the concentration of 22 , regenerates the reactant mediator and generates a new species (ArI˙ − ), which also diffuses away from the electrode. Subsequent cleavage of the carbon–iodine bond affords an aryl radical, which undergoes further reduction and protonation to yield the protodehalogenated arene. Electrochemical quantification of the product of the redox reaction (the benzophenone radical anion, 22 ) and/or that of any of the following reactions using the tip microelectrode creates a map of the species present at various distances from the electrode, as shown in Fig. 22d and e . Accordingly, it was found that the benzophenone radical anion 22 concentration decreases concomitantly with distance as it reacts with iodobenzene. Additionally, only when the benzophenone radical anion supplied at the electrode is exhausted does the iodobenzene 23 concentration increase above baseline, which occurs further from the electrode (within ∼50 μm, Fig. 22e ) with a 5 mM iodobenzene concentration than with 10 mM (∼30 μm, not shown), as would be expected.

With careful analysis, these concentration profiles can be used to probe the mechanism and measure the reaction rate, and also to identify the presence of intermediates. Importantly, the creation of high concentrations of reactive intermediates close to the electrode as seen here must be considered when designing a synthetic electrochemical reaction, especially when compared with other methodologies, such as photoredox catalysis, which create uniformly low concentrations of reactive intermediates in solution. It is also of note that the steady-state diffusion reaction layer, which is formed by this catalytic mechanism, results in the plateau current response observed in a CV of this EC′ system ( cf. , Section 2.4).

Converting concentration maps to a detailed mechanism often involves creating a model describing the pertinent physical processes (reactions at the electrode/in solution, and transport) and comparing the results to those from experiments (see Section 9). In this process, physical parameters are determined from complementary experiments, and the expected results are calculated for a range of unknown values ( e.g. , varying the reaction rate). The results are then compared with experiments, with a good match implying a plausible scheme has been successfully determined. The physical model is adjusted to reflect the chemical reactivity and can describe processes such as irreversible reactions, dimerisation, and disproportionation. 76 Li and Unwin applied these techniques to measuring the kinetics of electron transfer from a photo-excited *[Ru(bpy) 3 ] 2+ species at a liquid/liquid interface, 77 demonstrating the potential applicability to the field of photoredox catalysis.

Case study 20: identifying very short-lived species in solution. An example of the observation of a short-lived species is the detection of the CO 2 ˙ − radical anion reported by Bard and co-workers ( Fig. 23 ). 78 This radical anion dimerises to form oxalate (C 2 O 4 2− ) with a half-life of 10 ns and a rate constant of (6.0 × 10 8 M −1 s −1 ), making this measurement inaccessible to many conventional techniques. When the SECM electrodes are separated by 0.5 μm, current at the substrate electrode was observed corresponding to re-oxidation of most of the CO 2 ˙ − , which was generated at the tip electrode. However, upon increasing the separation of the electrodes to 10 μm, the substrate electrode current drops to zero as a result of complete dimerisation of the radical anion in the time taken to travel between the two electrodes. SECM is thus an effective way to identify and quantify the reactivity of highly reactive species with short half-lives in solution.

8. Bipolar electrochemistry

Reactions occur at the BPE when the magnitude of Δ U BPE provides sufficient overpotential to simultaneously reduce/oxidise available redox species. Bipolar electrochemistry offers advantages in electrocatalyst screening by allowing arrays of multiple ‘wireless’ electrodes to be incorporated in a single device. For instance, it is reported that by using a BPE array, Crooks and co-workers were able to simultaneously screen 33 different heterogeneous electrocatalyst candidates in about 10 min, 80 a technique which could be applied to rapid screening and optimization in organic redox catalysis at a surface. Additionally, the interfacial potential difference is highest at the ends of the BPE, whilst attenuating gradually towards the middle, generating molecular gradients for material functionalisation. 81

Although BPEs have been investigated in the electrosynthesis of conducting polymers, 82 applications in organic synthesis remain rare, principally due to the difficulty of in situ monitoring of the current.

Case study 21: applications of BPEs in organic chemistry. To overcome this problem, Inagi and co-workers applied split-BPEs in a U-type cell such that the electrical current could be monitored ( Fig. 24b ). 83 An insulator shielding wall was introduced in the middle of the BPEs to further augment the potential drop around the split electrodes. 84 This set-up enabled the optimisation of the oxidative fluorination of triphenylmethane ( Fig. 24c ). 83 Specifically, the supporting CsF electrolyte (and F − source) could be used at concentrations of only 1 mM, whilst typically 100 mM or more supporting electrolyte is often required. Conducting a reaction in a low supporting electrolyte concentration such as this could provide alternative options in both organic synthesis and analysis. 85

9. Electrochemical simulations

In this context, we use modelling to mean the formulation of a physical description of the important phenomena occurring during an experiment. The model allows prediction of the experimental response as a function of the experimental conditions and physical unknowns. Comparison of real and simulated experimental results is performed, with a good match indicating that the model plausibly describes the experiment.

The particulars of the model depend on the experiment, but will frequently describe: reactions at the electrode surface and in solution, the geometry of the electrode, and the transport of species (diffusion/convection/migration). Descriptive parameters (reaction rates, transport parameters, etc. ) may come from complementary experiments or literature values, but if a parameter is unknown it can be varied in the simulation to match experiment. When the mechanism is unknown, hypothesised mechanisms are simulated and the results compared to experimental results.

While forming a model may sound like a daunting task, fortunately, a number of software packages exist in which the transport and other equations are inbuilt, as are the numerical algorithms required to solve them. 87 Additionally, many of the commercially-available potentiostats have integrated simulation and fitting software functions built-in. In the simplest case, modelling is reduced to describing the reactions and choosing the electrode geometry from a drop-down list. The output of the model extends beyond just the experimental measurable (current/voltage), to include quantities that would be challenging to attain experimentally, such as the concentration distribution of species as a function of distance from the electrode surface (see Fig. 22 ). 75

It is important to note that when modelling, the output is only as good as the foundations (assumptions) upon which is it built – chemical knowledge is encoded into the model description. If none of the tested mechanisms fit the data, or the data doesn't correspond to chemical intuition, then an alternative mechanism or other assumption is required. Moreover, if multiple models deliver predictions matching the experimental data, the model alone is insufficient to eliminate either possibility, and experiments to discriminate scenarios might be required.

10. Conclusions

Since this perspective is designed to provide case studies of mechanistic probes, detailed discussions of experimental set-ups and theoretical treatments of the techniques have not been included. For further reading, we direct the interested reader specifically to the following key selected reviews and books:

CV basics and experimental set-up: ref. 5 b and c .

Theory of CV: ref. 4 a (chapter 6).

Coupled chemical reactions: ref. 4 a (chapter 12) and ref. 5 a (chapter 2).

Measurements of catalysis: ref. 4 f and ref. 5 a (chapter 4).

Pulsed voltammetry: ref. 4 a (chapter 7).

Spectroelectrochemistry: ref. 4 a (chapter 17) and ref. 43 b .

RDEs: ref. 4 a (chapter 9).

Microelectrodes: ref. 65 a and b .

SECM: ref. 73 a and b .

Bipolar electrochemistry: ref. 79 a .

Electrochemical simulations: ref. 4 a (Appendix B) and ref. 86 a .

Whilst many of the reactions discussed are electrochemical in nature, it is important to note that these techniques can be applied to study mechanisms in alternative redox processes, including photoredox catalysis. To this end, we envision that electroanalytical tools will become commonplace in studying synthetic organic and organometallic reaction mechanisms in the near future.

Conflicts of interest

Acknowledgements.

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Theoretical and Experimental Cyclic Voltammetry Studies of the Initial Stages of Electrocrystallization

• Published: 25 August 2021
• Volume 2021 , pages 1016–1022, ( 2021 )

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• O. V. Grishenkova 1 ,
• A. V. Kosov 1 ,
• O. L. Semerikova 1 ,
• V. A. Isaev 1 &
• Yu. P. Zaikov 1  

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The problem of the cyclic voltammetry investigation of the initial stages of electrochemical phase formation is considered. Analytical expressions are derived for the cyclic voltammograms and the sizes of the independent new-phase nuclei having formed on an indifferent electrode under linear potential sweep conditions for the cases of instantaneous and progressive nucleation followed by diffusion-controlled growth. The current as a function of the overpotential is found to have different dependences on the scan rate for the given limiting cases of nucleation. The results of a numerical simulation are presented. The logarithmic dependences of the maximum and minimum currents on the scan rate are shown to have a slope of –1/2 if nuclei appear in a narrow time interval long before the reverse, their number does not change when the scan rate changes, and their growth is controlled by diffusion. The slope of the dependences is –3/2 when nuclei form before and after the reverse and their number decreases with increasing scan rate. The possibility of using the proposed criteria for the interpretation of the experimental cyclic voltammograms is analyzed and confirmed for the model system (KNO 3 –NaNO 3 –AgNO 3 melt/iridium substrate/silver) at low concentrations of depositing ions, which provide diffusion control of the process. Both instantaneous nucleation and progressive nucleation are shown to occur in this system, depending on other experimental conditions.

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ACKNOWLEDGMENTS

This work was performed (partly) using the equipment of the Shared Access Center Composition of Compounds at Institute of High-Temperature Electrochemistry, Ural Branch, Russian Academy of Sciences.

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O. V. Grishenkova, A. V. Kosov, O. L. Semerikova, V. A. Isaev & Yu. P. Zaikov

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Grishenkova, O.V., Kosov, A.V., Semerikova, O.L. et al. Theoretical and Experimental Cyclic Voltammetry Studies of the Initial Stages of Electrocrystallization. Russ. Metall. 2021 , 1016–1022 (2021). https://doi.org/10.1134/S0036029521080103

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Received : 04 January 2021

Revised : 16 January 2021

Accepted : 29 January 2021

Published : 25 August 2021

Issue Date : August 2021

DOI : https://doi.org/10.1134/S0036029521080103

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