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Double Potential Step Chronoamperometry (DPSCA)

This article is part of the AfterMath Data Organizer Electrochemistry Guide

Double potential step chronoamperometry is a technique where the potential of the working electrode is stepped forward for a specified period of time, then stepped back for a specified period of time. Current is monitored and plotted as a function of time.

Detailed Description

Like most of the other electrochemical techniques offered by the AfterMath software, this experiment begins with an induction period. During the induction period, a set of initial conditions is applied to the electrochemical cell and the cell is allowed to equilibrate to these conditions. The default initial condition involves holding the working electrode potential at the Initial Potential for a brief period of time (i.e., 3 seconds).

After the induction period, the potential of the working electrode is stepped to a specified potential for a period of time.

After the first step has finished, the potential of the working electrode is stepped back for a specified period of time, usually to the potential prior to the forward step. The experiment concludes with a relaxation period. The default condition during the relaxation period involves holding the working electrode potential at the initial potential for an additional brief period of time (i.e., 1 seconds).

At the end of the relaxation period, the post experiment idle conditions are applied to the cell and the instrument returns to the idle state.

Current is plotted as a function of time, resulting in a chronoamperogram. You may also choose to do some post experiment processing in order to generate Cottrell plots.

Parameter Setup

The parameters for this method are arranged on various tabs on the setup panel. The most commonly used parameters are on the Basic tab which is similar to that for CA with the addition of a Reverse step period box. Additional tabs for Ranges and Post Experiment Conditions are common to all of the electrochemical techniques supported by the AfterMath software. Finally, a Post Experiment Processing tab deals with manipulating the data automatically when the experiment is finished.

Basic Tab

You can click on the “I Feel Lucky” button (located at the top of the setup) to fill in all the parameters with typical default values (see Figure 1). You will no doubt need to change the Potential and Hold time in the Forward step period and Reverse step period boxes to values which are appropriate for the electrochemical system being studied. You may also want to change the Number of intervals in the Sampling Control box.

Figure 1: Basic Setup for Double Potential Step Chronoamperometry.

The Electrode K1 Current Range on the Basic tab is used to specify the expected range of current. If the choice of electrode range is too small, actual current may go off scale and be truncated. If the electrode range is too large, the chronoamperogram may have a noisy, choppy, or quantized appearance.

Some Pine potentiostats (such as the WaveNow and WaveNano portable USB potentiostats) have current autoranging capability. To take advantage of this feature, set the electrode range parameter to “Auto”. This allows the potentiostat to choose the current range “on-the-fly” while the chonoamperogram is being acquired.

The waveform that is applied to the electrode is a simple pulse to the Potential listed in the Forward step period box for the Hold time followed by a step back to the Potential specified in the Reverse step period box. Note that the actual waveform that is measured (see Figure 2, red trace) fluctuates slightly compared to the applied potential (see Figure 2, black trace).

Figure 2: Waveform for DPSCA. Black = applied potential, Red trace = measured potential.

Ranges Tab

AfterMath has the ability to automatically select the appropriate ranges for voltage and current during an experiment. However, you can also choose to enter the voltage and current ranges for an experiment. Please see the separate discussions on autoranging and the Ranges Tab for more information.

Post Experiment Conditions Tab

After the Relaxation Period, the Post Experiment Conditions are applied to the cell. Typically, the cell is disconnected but you may also specify the conditions applied to the cell. Please see the separate discussion on post experiment conditions for more information.

Post Experiment Processing Tab

The Post Experiment Processing Tab (see Figure 3) looks similar to that for CA and allows you to automatically generate Cottrell current, Cottrell charge, DPSCA working curve, or DPSCC working curve plots. Please see the Typical Results and Theory sections of this wiki for more information regarding Cottrell plots and DPSCA/DPSCC working curves.

Figure 3: Post Experiment Processing Options.

Typical Results

The results for a $2.5 \; mM$ solution of Ferrocene in $0.1 \; M Bu_4NClO_4/MeCN$ are shown in Figure 4. Specific conditions include the use of a $2 \; mm$ Pt WE, forward step potential of $0.75 \; V \; vs. \; Ag/AgCl_{(aq)}$ and reverse step potential of $0 \; V \; vs. \; Ag/AgCl_{(aq)}$ .

Figure 4: Double Potential Step Chronoamperogram of a Ferrocene Solution

If you selected to automatically generate Cottrell plots, the plots are under the other plots folder in the Archive navigation panel. Choosing Cottrell current displays a plot of current versus the $t^{-1/2}$ (see Figure 5A). Choosing Cottrell charge displays a plot of charge versus $t^{1/2}$ (see Figure 5B). Note that for the Cottrell Current plot, the level portion in the plot is actually the time prior to the current spike shown in Figure 4. That is, earlier time points are to the right in a Cottrell Current Plot. This is not the case for a Cottrell Charge plot because integrating the current with respect to time gives charge.

Figure 5 : Post experiment processing plots. A – Cottrell Current, B – Cottrell Charge. Conditions as listed in Figure 4.

If you selected to automatically generate DPSCA or DPSCC working curves, they are also under the other plots folder in the Archive navigation panel. The theory for the forward step in DPSCA is the same as the theory for the first step in CA, however the theory for the reverse step is complicated by the first step. The DPSCA working curve (see Figure 6) is a useful way to examine if kinetic complications of the redox species are present. If there are no kinetic complications and both potential steps are to regions of diffusion-limited currents, the actual (see Figure 6, red trace) working curve will overlay the ideal (see Figure 6, black trace) working curve. The ideal working curve is theoretically generated according to the equation

${\frac{-i_r}{i_f}}= 1 - \left(1-\frac{\tau}{t_r}\right)^{1/2}$

where $i_r$ is the reverse current at $t_r$ , $i_f$ is the forward current at $t_f$ and $\tau = t_r-t_f$ . A quick check for a stable system is:

$\frac{-i_r(2\tau)}{i_f(\tau)}=0.293$

Figure 6: DPSCA Working Curve. Actual = red trace, Ideal = black trace. Conditions as listed in Figure 4.

The DPSCC working curve (see Figure 7) is a useful way to examine the charge passed during an experiment and is similar to the Cottrell Charge plot except that it separates the forward (see Figure 7, red trace) and reverse (see Figure 7, black trace) steps. The reverse step is corrected to account for the charge passed during the forward step, making the charge passed in the reverse step linear with respect to time.

Figure 7 : DPSCC Working Curve. Forward – red trace, Reverse – black trace. Conditions as listed in Figure 4.

Theory

As stated in the Theory section of CA, the time-dependent current transient in a diffusion-limited chronoamperometry experiment is governed by the Cottrell² equation

$i=\frac{nFAD^{1/2}C_0^*}{({\pi}t)^{1/2}}$

where $n$ is the number of electrons, $F$ is Faraday's Constant ( $96485 \; C/mol$ ), $A$ is the electrode area ( $cm^2$ ), $D$ is the diffusion coefficient ( $cm^2/s$ ), and $C$ is the concentration ( $mol/cm^3$ ). In DPSCA, the time of the transition must be taken into account. The current transient for the second pulse, provided it produces diffusion-limited currents, is governed by the equation first obtained by Kambara³

$-i_r(t) = \frac{nFAD_0^{1/2}C_0^*}{\pi^{1/2}}\left[\frac{1}{(t-\tau)^{1/2}}-\frac{1}{t^{1/2}}\right]$

where $\tau$ is the transition time and the other parameters are as above. Dividing the reverse current at time $t_r$ by $i_f [latex] at time [latex] t_f$ and keeping $t_r = t_f + \tau$ allows for the generation of a working curve given by the equation

$\frac{-i_r}{i_f} = 1-\left(1-\frac{\tau}{t_r}\right)^{1/2}$

If there are no kinetic complications in the electrode reaction, the actually working curve should fall on an ideal working curve as shown in Figure 6. Note that the deviation at the beginning of the working curve is due to the electronics of the potentiostat.

DPSCA is a technique that is often used to elucidate mechanisms related to coupled homogeneous reactions preceeding or following an electrode reaction. Bard and Faulkner¹ give a more detailed description of using DPSCA to elucidate mechanisms. A brief description will be given here as to what types of mechanisms can be elucidated and how you might apply DPSCA. Several examples are listed in the Application section also.

The simplest coupled homogeneous reactions are Electrochemical-Chemical (EC) and Chemical-Electrochemical (CE).

Application

This example uses DPSCA to calculate the diffusion coefficients for a subtrate ( $D _s$ ) and a product ( $D_p$ ) of an electrode reaction. Hyk et al.⁴ examined the current transients for DPSCA to analyze the reaction $S_s^Z \rightarrow P_p^Z + ne^-$ . The researchers generated equations for dealing with both hemispherical electrodes and disk microelectrodes under diffusion-limited and mixed diffusion-migration. Interestingly, the researchers were able to show that for an uncharged substrate with less than $0.1%$ supporting electrolyte they are able to obtain diffusion coefficients. This is significant because an uncharged substrate with less than 0.1% supporting electrolyte does not lend to calculation of diffusion coefficients by single potential step chronoamperometry.

In this next example, Long et al.⁵ used a slight variant of DPSCA to examine diffusion and self-exchange in a cobalt bipyridine redox polyether hybrid. Films of material, containing supporting electrolyte, were prepared on inter-digitated array electrodes (IDAs). A pulse was generated (equivalent to a double-potential step) on one set of fingers on the IDA while the current was monitored on the second set of fingers on the IDA. Monitoring the time it takes for the pulse to travel from the generator set of fingers to the collector set of fingers allowed for the calculation of diffusion coefficients and self-exchange rate constants between metal centers.

In the final example, Schwarz and Shain⁶ used DPSCA to measure the rate constant for a chemical reaction after an electrochemical reaction, commonly referred to as an EC reaction. The overall reaction for the general process is

$O+e^-\rightarrow R \xrightarrow{k} Z$

where the product $Z$ is electrochemically inactive. In this example, the researchers reduce azobenzene to hydrazobenzene which in turn rearranges to benzidine in acidic solutions. By varying the time of the second step, the researchers were able to determine the rate constant for the reaction of hydrazobenzene rearrangning to benzidine.

References

1. Faulkner, L. R.; Bard, A. J. Basic Potential Step Methods, Electrochemical Methods: Fundamentals and Applications, 2^nd ed.; Wiley: New Jersey, 2000; 156-225.

2. Cottrell, F. G. Z. Physik, Chem., 42, 1902, 385.

3. Kambara, T. Bull. Chem. Soc. Jpn., 1954, 27, 523.

4. Hyk, W; Nowicka, A.; Stojek, Z. Anal. Chem., 2002, 74, pp 149–157.

5. Long, J. W.; Terrill, R. H.; Williams, M. E.; Murray, R. W. Anal. Chem., 1997, 69, pp 5082–5086.

6. Schwarz, W. M.; Shain, I. J. Phys. Chem., 1965, 69, pp 30-40.

Additional Resources

Links: Electrochemist's Guide, AfterMath User's Guide, AfterMath Main Support Page

Related Techniques: Chronoamperometry (CA)

Posted 1/4/2016 in Uncategorized
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Experimental Considerations

This article is part of the AfterMath Data Organizer Electrochemistry Guide

Interdependency of the Potentiostat and Electrochemical Cell

One of the key aspects of electrochemical measurements is that the potentiostat and the electrochemical cell are part of the same electrical circuit. If something is wrong with the cell, then the cell can make the potentiostat appear to have a problem. Or, if something is wrong with the potentiostat, it can cause an unwanted change to occur within the cell. Other kinds of laboratory instrumentation, from the lowly digital balance to more complex spectrophotometers and chromatographic detectors, are relatively immune to changes in the nature of the sample being analyzed and are less likely to cause unwanted changes in the composition of the sample. But the successful user of a potentiostat must always be aware of the significant interdependence between the potentiostat and the sample and plan experiments accordingly.

Part of this awareness is carefully managing the sequence of events before, during, and after an electroanalytical measurement. The initial conditions imposed upon an electrochemical cell (such as the working electrode potential) as well as the instrument settings (such as the current range) can have a direct bearing on the observed results of an electrochemical measurement. Similarly, the continuity of cell control (or lack thereof) after a measurement concludes can directly influence the composition of the portions of the electrochemical cell immediately adjacent to the electrode(s). Indeed, the surface properties of the electrodes themselves can be unwittingly altered by improper cell control.

Minimizing Cell Change for a Successful Electroanalytical Measurement

A strategy for a successful electroanalytical measurement often begins with devising a way to connect the electrodes to the potentiostat without any appreciable changes occurring within the cell. In the jargon of the electroanalytical chemist, this might be as simple as initially poising the working electrode at a potential where no Faradaic current flows. Or, in the jargon of the corrosion scientist, it might be wise to start an experiment with the corrosion sample at or near OCP (Open Circuit Potential, the potential at which there is no current at the working electrode).

The AfterMath software gives you control of the idle conditions which prevail while you are making electrode connections and before an experiment begins. These “pre-experiment” idle conditions can be adjusted at any time while the potentiostat is not doing an experiment. You can choose to hold the working electrode at a given potential under potentiostatic control or alternately, at a given current (usually zero amperes) under galvanostatic control. You may also choose to hold the electrode at OCP if you wish.

Click here for more information about adjusting pre-experiment idle conditions.

The Induction Period

As part of the experimental specifications for an electrochemical technique, AfterMath allows you to specify a period of time during which the cell is allowed to come into equilibrium with the initial signal levels applied to the working electrode(s). The period of time, called the induction period, is brief by default (usually less than 3 seconds); however, you may increase the duration of the induction period or you may skip the induction period if you wish.

Click here for more information about setting up the induction period.

Idle Conditions

This article is part of the AfterMath Data Organizer Electrochemistry Guide

During the time period between experiments, it is usually important to assure that conditions of the electrochemical cell do not allow any unwanted electrochemical processes to occur. A passive approach is to merely disconnect the cell from the instrument (either manually or automatically) and prevent any stray currents in the cell. A more active approach is to keep the cell connected to the instrument and carefully apply the appropriate signal levels to the electrode(s) to prevent any redox processes.

The AfterMath software allows you to control and monitor the condition of the electrochemical cell at any time when the instrument is idle. This control is provided by clicking on the instrument in the Instrument List and viewing the Instrument Status (see below). One of the tabs on the Instrument Status panel is the “Idle” tab. This tab has cell and electrode controls (top half) and also indicators showing cell status (bottom half).

In the example above, the first working electrode is set to a passive mode of operation (open circuit potential). In the status area (bottom half), you can see that the OCP level is $-783.6 \; mV$ and the current has a magnitude of about $3 \; {\mu}A$ . In addition to the passive OCP mode of operation, you may choose three other modes of operation for an electrode: potentiostatic, galvanostatic, and zero-resistance ammeter (ZRA). When a working electrode idles in one of the two active states (potentiostatic or galvanostatic), then you may choose the signal level that is to be actively applied to the electrode. (see below).

In the example above, the first working electrode is idling in potentiostatic mode, and there is no control of any second working electrode (because the Pine WaveNow potentiostat does not support a second working electrode). The setpoint for the first working electrode potential is $40.0 \; mV$ . The actual potential of the first working electrode is monitored in real time in the status area (bottom half) on the Idle tab. You can see that in this example the “live potential” at the first working electrode is actually $39.8 \; mV$ and the “live current” is $42.0 \; mA$ .

NOTE: The availability of the four modes of operation (potentiostatic, galvanostatic, OCP, and ZRA) depends upon the particular instrument model that you are using. Not all instruments support all four modes of operation on all electrodes.

Links: Electrochemist's Guide, AfterMath User's Guide, AfterMath Main Support Page

Related Topics: post-experiment idle conditions, cell switching

Posted 1/4/2016 in Uncategorized

Cyclic Voltammetry (CV)

This article is part of the AfterMath Data Organizer Electrochemistry Guide

Cyclic voltammetry involves sweeping the potential of the working electrode linearly with time at rates typically between 10 mV/s and 1000 V/s. The current is plotted as a function of potential to yield a voltammogram.

Synonyms: Cyclic linear potential sweep chronoamperometry

Detailed Description

After the induction period, the potential of the working electrode is swept linearly at the specified Sweep Rate to a Vertex Potential. Upon reaching the vertex potential, the direction of the sweep is reversed, and the sweep continues back to a Final Potential.

After the sweeping has finished, the experiment concludes with a relaxation period. The default condition during the relaxation period involves holding the working electrode potential at the final potential for an additional brief period of time (i.e., 1 seconds).

At the end of the relaxation period, the post experiment idle conditions are applied to the cell and the instrument returns to the idle state.

Current is plotted as a function of the potential applied to the working electrode, resulting in a voltammogram.

Parameter Setup

The parameters for this method are arranged on various tabs on the setup panel. The most commonly used parameters are on the Basic tab, and less commonly used parameters are on the Advanced tab. Additional tabs for Ranges and post experiment idle conditions are common to all of the electrochemical techniques supported by the AfterMath software.

Basic Tab

You can click on the “I Feel Lucky” button (located at the top of the setup) to fill in all the parameters with typical default values. You will no doubt need to change the Initial Potential, Vertex Potential, Final Potential, and Sweep Rate to values which are appropriate for the electrochemical system being studied.

Figure 1: Basic Cyclic Voltammetry Setup

The Electrode Range on the Basic tab is used to specify the expected range of current. Consider performing cyclic voltammetry (using a $3 \; mm$ GC working electrode and sweep rate = $100 \; mV/s$ ) on a $1 \; mM$ solution of $K_3Fe(CN)_6$ in $0.1 \; M \; KCl$ . If the choice of electrode range is too small (e.g. $10 \; {\mu}A$ ), actual current may go off scale and be truncated (see Figure 2, red trace). If the electrode range is too large (e.g. $5 \; mA$ ), the voltammogram may have a noisy, choppy, or quantized appearance (see Figure 2, black trace). With the adequate electrode range (e.g. $200 \; {\mu}A$ ), the volatammogram has a desirable appearance (see Figure 2, green trace)

Some Pine potentiostats (such as the WaveNow and WaveNano portable USB potentiostats) have current autoranging capability. To take advantage of this feature, set the electrode range parameter to “Auto”. This allows the potentiostat to choose the current range “on-the-fly” while the voltammogram is being acquired.

Figure 2 : Influence of Current Range Choice on Voltammogram Quality

The actual waveform that is applied to the electrode is linear but not truly analog (see Figure 3A). The flat portions at the beginning and end of the waveform are the induction and relaxation periods, respectively. A typical two segment sweep starts at an initial potential, sweeps to a vertex potential, and then returns to a final potential. The sweep is not perfect; in reality is consists of many small steps (see Figure 3B, black trace) which are generated using the maximum available resolution of the potentiostat’s digital-to-analog converter (DAC).

Figure 3: Cyclic Voltammetry Waveform Details: Total waveform (A), Zoom of waveform showing steps (B)

While cyclic voltammograms are typically two segments or one cycle, it is possible to choose any number of segments for an experiment. If you choose any odd number of segments greater than two (see Figure 4), the parameters that must be entered are a little different than the two segment case. You must choose an Initial Potential, Upper Potential, Lower Potential, and Final potential. You must also choose whether the Initial direction is rising (sweep towards Upper Potential) or falling (sweep towards Lower Potential). If the Initial direction is rising, the Final potential must be different than the Lower potential. If the Initial direction is falling, the Final potential must be different than the Upper potential.

Figure 4: Three Segment Cyclic Voltammetry

If you choose any even number of segments greater than two (see Figure 5) the parameters that must be entered are the same as the three segment case. You must choose an Initial Potential, Upper Potential, Lower Potential, and Final potential. You must also choose whether the first sweep is initially rising (sweep towards Upper Potential) or falling (sweep towards Lower Potential). If the Initial direction is rising, the Final potential must be different than the Upper potential. If the Initial direction is falling, the Final potential must be different than the Lower potential.

Figure 5: Four Segment Cyclic Voltammetry

Advanced Tab

The Advanced Tab for this method (see Figure 6) allows you to change the behavior of the potentiostat during the induction period and relaxation period. By default, the potential applied to the working electrode during the induction and relaxation period will match the initial potential and final potential, respectively, as specified on the Basic Tab. You may override this default behavior, and you may also change the durations of the induction and relaxation periods if you wish.

Other important parameters on the Advanced tab are found in the Sampling Control area. This area contains two parameters, Alpha and Threshold which control when and how samples are acquired during the sweep portion of the experiment.

Figure 6: Advanced parameters for Cyclic Voltammetry

As mentioned previously, the waveform applied to the electrode (see Figure 3) is not truly linear. The actual waveform is a staircase of small potential steps. The duration of each small step is called the step period, and the step period is automatically chosen to take full advantage of the resolution of the potentiostat’s digital-to-analog converter.

The Alpha parameter controls the exact time within the step period at which the current is sampled. A alpha value of zero means the current is sampled at the start of the step period, immediately after a new potential step is applied. An alpha value of 100 means the current is sampled at the end of the step period, immediately before the next potential step is applied.

Changing alpha will have little effect on the voltammogram for a freely diffusing species in solution; however, variations in alpha can dramatically influence the results for surface bound species, especially when using older potentiostats with low DAC resolution (i.e., 12-bit).

Newer potentiostats (such as the WaveNow and WaveNano portable USB potentiostats) have 16-bit DAC resolution, so voltammograms acquired using these instruments are less influenced by the choice of alpha value. Nevertheless, researchers who use digital potentiostats to study surface-confined electrochemical systems (rather than freely diffusing species in solution) should be aware of the influence of this parameter. Further details can be found in the literature¹ and in a related article about CBP Bipotentiostat Interface Boards.

The Threshold parameter helps you to limit the amount of data retained as the voltammogram is acquired. The threshold parameter controls the interval between samples as the potential is swept from one limit to another. By default, a data point is acquired every time the sweep moves 5 millivolts. You can change the threshold from 5 millivolts to a smaller interval (if you want to acquire more data) or to a greater interval (if you want to acquire less data).

Again, consider performing cyclic voltammetry (using a $3 \; mm$ GC working electrode and sweep rate = $100 \; mV/s$ ) on a $1 \; mM$ solution of $K_3Fe(CN)_6$ in $0.1 \; M \; KCl$ . Extreme values for the threshold parameter can lead to undesirable results (see Figure 7). A smaller threshold value, typically less than or equal to 5 millivolts, produces smoother curves and larger data files (see Figure 7, red trace, interval = $1 \; mV$ ). If you set the threshold parameter to zero, then the maximum number of data points is acquired (and the size of the resulting data file will be quite large). If you set the parameter to a very large interval (e.g. $100 \; mV$ ), then the number of points acquired will be so small that the voltammogram appears sharp and jagged (see Figure 7, black trace). Intermediate intervals can also be seen in Figure 7 (gold – $10 \; mV$ , blue = $50 \; mV$ ).

Figure 7: Influence of Sampling Threshold on Voltammogram Quality

Ranges Tab

AfterMath has the ability to automatically select the appropriate ranges for voltage and current during an experiment. However, you can also choose to enter the voltage and current ranges for an experiment. Please see the separate discussions on autoranging and the Ranges Tab for more information.

Post Experiment Conditions Tab

After the Relaxation Period, the Post Experiment Conditions are applied to the cell. Typically, the cell is disconnected but you may also specify the conditions applied to the cell. Please see the separate discussion on post experiment conditions for more information.

A principle result of interest from a cyclic voltammogram is the peak current of the voltammogram. The peak current increases with the sweep rate (see Figure 8, conditions are $1 \; mM$ solution of $K_3Fe(CN)_6$ in $0.1 \; M \; KCl$ with sweep rates = $20$ , $50$ , $100$ , $250$ , and $500 \; mV/s$ for red, gold, green, blue, and black traces, respectively). The peak current is proportional to the square root of the sweep rate (see Figure 8 insert).

Figure 8: Influence of Sweep Rate on a Cyclic Voltammogram
(inset – current vs square root of sweep rate)

The peak current can be obtained by right-clicking on the trace and selecting Add Tool » Peak Height (see Figure 9). This places a peak measurement tool on the voltammogram (not always in the correct place, see Figure 10), and you can move the position of the peak tool using the control points on the tool.

Figure 9: Initial Placement of Peak Height Tool on Voltammogram

Figure 10: Right-Click to Change the Tool Properties

An important part of measuring the peak current is to use the proper baseline. In general, a small portion of the voltammogram leading up to the peak is used as the baseline. This small portion is extrapolated underneath the peak.

Right-clicking on one of the peak tool’s control points will bring up a dialog box where you can change the properties of the tool (see Figure 11). On this dialog box, there is a drop-down menu where you can choose the type of baseline. In this example, the “Free Sloped” baseline type was used. You can then manipulate the tool to draw the desired baseline and obtain an accurate peak height (see Figure 12).

Figure 11: Selection of Baseline

Figure 12: Extrapolation of Baseline for Peak Height Tool

Theory

A brief summary of the theory of cyclic voltammetry will be covered here. Randles² and Sevcik³ contributed to the development of the theory for cyclic voltammetry, however, credit for the modern treatment and notation goes to Nicholson and Shain⁴. Additionally, Bard and Faulkner⁵ provide a nice summary and description of cyclic voltammetry.

Consider a reaction, $O+e \;{\rightleftharpoons}\;R$ , with a formal potential $E^{\circ}$ . If a potential sweep is started sufficiently more positive than $E^{\circ}$ and swept negatively a non-faradaic current will initially flow. As the potential of the electrode approaches $E^{\circ}$ , $O$ begins getting reduced to $R$ creating a concentration gradient and therefore flux (mass transfer) to the surface increases. As $E$ passes $E^{\circ}$ , the concentration of $O$ at the surface of the electrode is nearly zero and mass transfer is at a maximum. The current will begin to tail off as the potential is swept to the vertex potential upon which the sweep is reversed.

The concentration of $R$ at the surface of the electrode is now very high and oxidation can proceed once $E$ begins to approach $E^{\circ}$ . An inverse of the process described above happens resulting in a similarly shaped but inverted $i-E$ curve. Ideally, the peak-to-peak separation for the reduction and oxidation waves should be $59 \: mV$ for a one-electron electrochemically reversible process. Additionally, the peak height $i_p$ in amperes $(A)$ can be described by the Randles-Sevcik equation, shown below,

$i_p=0.4463NFAC({nF{\upsilon}D}/RT)^{1/2}$

where $n$ is the number of electrons, $F$ is Faraday’s Constant $(96485 \:C/mol)$ , $A$ is the electrode area, $D$ is the diffusion coefficient, $C$ is the concentration, $R$ is the universal gas constant $(8.314 J/mol{\cdot}K)$ , $T$ is the absolute temperature $(K)$ and ${\upsilon}$ is the sweep rate. At $25^{\circ}C$ , with $A$ in $cm^{2}$ , $D$ in $cm^{2}/s$ , $C$ in $mol/cm^{3}$ and ${\upsilon}$ in $V/s$ , the above equation simplifies to

$i_p=2.69\times10^5n^{3/2}AD^{1/2}C\upsilon^{1/2}$

A good rule of approximation is $i_p$ will be appoximately $200\:{\mu}A/cm^{2}{\:}area/mM$ .

Application

Cyclic voltammetry is used extensively and the following two examples highlight its usefulness.

The first example shows that you can calculate electron transfer rate constants using cyclic voltammetry. The theory for calculating electron transfer rate constants from cyclic voltammetry was originally developed by Nicholson⁶ but the example here is from more recent work by Weber and Creager⁷. Ferrocene was irreversibly adsorbed in the form of a self-assembled monolayer to a Au surface using a long-chain alkylthiol. Varying the sweep rates gave increasingly larger $E_{peak} - E^0$ values ( $\eta$ , overpotential), with $E_{peak}$ being the oxidation or reduction peak and $E^0$ being the formal potential for ferrocene in this system. Rate constants were then calculated from these overpotentials. The authors went on to compare the experimentally obtained voltammograms to theoretically calculated voltammograms and from these were comparisons were also able to obtain reorganization energies.

In the second example, Duah-Williams and Hawkridge used cyclic voltammetry to study the temperature dependence of the kinetics of $CN^-$ dissociation from the cyanomyoglobin complex ( $Mb(II)CN$ )⁸. By comparing the experimentally obtained cyclic voltammograms to theoretically calculated cyclic voltammograms, they were able to estimate the dissociation rate, $k_f$ , by varying the sweep rate and monitoring the disappearance of an oxidation wave, associated with $Mb(II)CN$ as $CN^-$ dissociated. This is a good example of how cyclic voltammetry can give information, such as a dissociation constant, that has been traditionally been measured by NMR.

References

1. He, P. Anal. Chem., 1995, 67, 986-992.

2. Randles, J. E. B.; Trans. Faraday Soc., 1948, 44, 327-338.

3. Sevcik, A. Coll. Czech. Chem. Commun., 1948, 13, 349-377.

4. Nicholson, R. S.; Shain, I. Anal. Chem., 1964, 36, 706-723.

5. Faulkner, L. R.; Bard, A. J. Potential Sweep Methods, Electrochemical Methods: Fundamentals and Applications, 2^nd ed.; Wiley: New Jersey, 2000; 226-260.

6. Nicholson, R. S. Anal. Chem., 1965, 37, 1351-1355.

7. Weber, K.; Creager, S. E. Anal. Chem., 1994, 66, 3164-3172.

8. Duah-Williams, L.; Hawkridge, F. M. J. Electroanal. Chem. 1999, 466, 177-186.

Additonal Resources

Links: Electrochemist’s Guide, AfterMath User’s Guide, AfterMath Main Support Page

Related Techniques: Linear Sweep Voltammetry (LSV), Staircase Voltammetry (SCV)

Posted 1/4/2016 in Uncategorized