The actual waveform that is applied to the electrode is linear but not truly analog (see Figure 2A). The flat portions at the beginning and end of the waveform are the induction and relaxation periods, respectively. For a typical two sweep experiment, the sweep starts at an Initial current and sweeps to a Vertex current, then sweeps to the Final Current. The sweep is not perfect; in reality is consists of many small steps (see Figure 2B, orange trace) which are generated using the maximum available resolution of the potentiostat's digital-to-analog converter (DAC).
Figure 2: CCP Waveform Details Showing A) the Total Waveform and B) a Magnified Waveform that shows the Applied Current (Orange) and Measured Current (Red)
While cyclic current ramp potentiograms 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, the parameters that must be entered are a little different than the two segment case (see Figure 3). You must choose an Initial Current, Upper Current, Lower Current, and Final Current. You must also choose whether the Initial direction is rising (sweep towards Upper Current) or falling (sweep towards Lower Current). If the Initial direction is rising, the Final Current must be different than the Lower Current. If the Initial direction is falling, the Final Current must be different than the Upper Current.
Figure 3: Basic setup for three segment CCP.
If you choose any even number of segments greater than two (see Figure 4), you must enter an Initial current, Upper current, Lower current, and Final current. You must also choose whether the first sweep is initially rising (sweep towards Upper current) or falling (sweep towards Lower current). If the Initial direction is rising, the Final current must be different than the Upper current. If the Initial direction is falling, the Final current must be different than the Lower current.
Figure 4: Basic setup for four segment CCP.
Avanced Tab
The Advanced Tab for this method (see Figure 5) allows you to change the behavior of the potentiostat during the induction period and relaxation period. By default, the current applied to the working electrode during the induction and relaxation period will match the initial current and final current, 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 5: Advanced parameters setup for Cyclic Current Ramp Chronopotentiometry
As mentioned previously, the waveform applied to the electrode (see Figure 2) is not truly linear. The actual waveform is a staircase of small current 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 potential is sampled. A alpha value of zero means the potential is sampled at the start of the step period, immediately after a new current step is applied. An alpha value of 100 means the potential is sampled at the end of the step period, immediately before the next current step is applied. Please see the Advanced Parameter Tab section of CV for an analogous situation in a voltammogram.
The Threshold parameter helps you to limit the amount of data retained as the potentiogram is acquired. The threshold parameter controls the interval between samples as the current is swept from one limit to another. As shown in the example in Figure 3, a data point is acquired every time the sweep moves  . You could change the threshold from to a smaller interval (if you want to acquire more data) or to a greater interval (if you want to acquire less data).
It is likely that you will have to change the default value based on your experimental setup in order to obtain the best possible data. Extreme values for the threshold parameter can lead to undesirable results. A smaller threshold value, typically less than or equal to  , produces smoother curves and larger data files. 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, then the number of points acquired will be so small that the potentiogram appears sharp and jagged. Please see the CV article for an analogous situation in a voltammogram.
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 the user may also specify the conditions applied to the cell. Please see the separate discussion on post experiment conditions for more information.
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Figure 6: Chronopotentiograms Depicting A) Potential vs. Time and B) Potential vs. Current for a Ferrocene Solution.
References
1. He, P. Anal. Chem., 1995, 67, 986-992.
2. Faulkner, L. R.; Bard, A. J. Controlled-Current Techniques, Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New Jersey, 2000; 305-330.
3. Murray, R. W.; Reilley, C. N. J. Electroanal. Chem., 1962, 3, 64-77.
4. Murray, R. W.; Reilley, C. N. J. Electroanal. Chem., 1962, 3, 182-202.
Posted 1/4/2016
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Circuit Switching
Most electrochemical instruments are designed to perform a wide range of electrochemical techniques. Different techniques make use of different portions of the circuitry within the instrument, and this means that circuit switching is likely to occur when configuring the instrument for a particular method.
For example, the feedback loop circuitry for a galvanostatic method actively monitors the working electrode current, but for a potentiostatic method, the feedback circuitry must monitor the working electrode potential. Different feedback paths are switched in and out of the circuit depending upon whether the working electrode is operating in potentiostatic or galvanostatic mode. Still other methods require passive measurement of the open circuit potential, meaning that the active feedback loop must be switched out of the circuit entirely. Circuit switching also occurs when changing the current measurement sensitivity (i.e., the current range) or the amount of stability filtering in the feedback loop (i.e., the response time).
The term cell switching refers to making (or breaking) the connection between the instrument and the external electrochemical cell. In some cases, this switching occurs manually (as you physically connect/disconnect cell cables), but in many cases this switching occurs under software control (via internal instrument relays).
Each time a cell or circuit switching action occurs, the instrument is likely to lose control of the external electrochemical cell for a brief period (typically on the order of a few milliseconds). As the instrument regains control of cell, various current transients may occur at the working electrode. These transients are often harmless and decay away rather rapidly. If your electrochemical system is particularly sensitive, however, these transients may interfere significantly with your experiments.
For systems where such transients are harmless, a one to three second long induction period at the beginning of an experiment assures that the random transients will not affect the data recorded during an experiment. In other cases, special steps (see below) must be taken to prevent such transients.
Minimizing Switching and Transients
The best way to minimize unwanted and potentially harmful current transients is to carefully make sure that the signal applied to the working electrode at the beginning and end of the experiment is exactly the same as the signal applied to the working electrode during the idle periods in between experiments.
When no experiment is being performed, the instrument is said to be in its idle mode. Although the instrument is idle, it can still maintain a steady potential (or current) at the working electrode. The precise signal levels can be adjusted from the Instrument Status window. In general, the idle signal level should be set at a potential (or current) at which your electrochemical system is stable.
When specifying a new experiment to be performed, carefully adjust the initial conditions and the induction period conditions so that they exactly match the idle conditions which prevail before the experiment begins. This means that the initial signal level should match the idle signal level. On those instruments which permit adjustment of the idle current range and idle filtering settings, you should further strive to match the idle filter and range settings so that they match those which will be used during the experiment.
Finally, each electrochemical technique allows you to specify the idle conditions that will prevail after the experiment is completed. These post-experiment idle conditions should also be selected so that they exactly match the final conditions which prevail during the relaxation period at the end of the experiment.
Posted 1/4/2016
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Chronoamperometry is a technique where the potential of the working electrode is stepped for a specified period of time. Current is plotted as a function of time. Chronoamperometry is also known as potential step amperometry.
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 step has finished, 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 a Cottrell plot.
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. Additional tabs for Ranges and post experiment idle 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 box 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 Chronoamperometry Setup
The Electrode 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. 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 CA. Black trace = 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 Processing Tab
The Post Experiment Processing Tab (see Figure 3) allows you to automatically generate Cottrell current or Cottrell charge plots. Please see the Typical Results and Theory sections of this wiki for more information regarding Cottrell plots.
Figure 3: Post Experiment Processing Options.
Typical Results
The results for a  solution of ferrocene in  are shown in Figure 4.
Figure 4: Chronoamperogram of a ferrocene solution using a potential =  and a  Pt WE.
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  (see Figure 5A). Choosing Cottrell charge displays a plot of  (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. The endpoint in a Cottrell Charge plot is the total amount of charge passed during the experiment. Monitoring the charge passed during an experiment is a variant of chronoamperometry called Chronocoulometry. See the Applications section for an example of Chronocoulometry.
Figure 5 : Post experiment processing plots. A – Cottrell Current  , B – Cottrell Charge  . Conditions as listed in Figure 4.
The Cottrell current plot is a useful diagnostic tool to examine that your species of interest is freely diffusion in solution. Upon applying the potential step, the current initially spikes, then begins trail off. As will be explained in more detail in the Theory section, the current during the trailing off period is a diffusion-limited current dictated by the Cottrell equation. Examining the Cottrell Current plot in this region reveals that the current is linear with respect to  (see black ellipse in Figure 6).
Figure 6: Highlight of Diffusion-limited Current in Cottrell Current Plot.
The addition of a Baseline tool to the diffusion limited current region allows for calculation of the diffusion coefficient for the species of interest if the concentration and electrode area are known (see Figure 7). First you will have to delete the region of the Cottrell Plot where current is not diffusion limited. Use the Point Selection Tool to delete the unwanted points of the Cottrell Plot. Next, add a baseline tool by right clicking on the leftover point and select Add Tool » Baseline. Manipulate the control points to provide an adequate fit. AfterMath automatically provides the slope and intercept for the Baseline tool.
Figure 7: Addition of Baseline Tool in Diffusion-limited Current Region.
The slope of the line in the plot is given by the equation
where  is the number of electrons,  is Faraday’s Constant  ,  is the electrode area  ,  is the diffusion coefficient  , and  is the concentration  . In the example above,  is calculated to be  .
Theory
The theory section is split into two segments. The first segment deals with Chronoamperometry (CA) and the second section deals with Chronocoulometry (CC). Chronoamperometry leads to Chronocoulometry natually since charge is obtained by integrating current with respect to time.
Chronoamperometry
The following is a basic description of the theory behind Chronoamperometry. Please see the literature1 for a more detailed description of the technique. Consider a reaction  with a formal potential  . In general, the potential step applied to the working electrode should be sufficiently more negative than such that reduction of  to  is complete at the surface of the electrode (i.e. surface concentration of at the electrode surface is  ). When this occurs, the current is diffusion-limited, much like the current that flows in CV after the potential of the electrode sweeps past  .
When the current is diffusion-limited in CA, the current-time response is described by the Cottrell2 equation
where is the number of electrons, is Faraday’s Constant  , is the electrode area , is the diffusion coefficient  , and  is the concentration . As described in the Typical Results section, plotting  gives a slope that contains the diffusion coefficient, .
Application
In the first example, Tennyson et al.3 used chronoampometry to determine the diffusion coefficients (D) and number of electrons (n) for a series of indirectly connected bimetallic complexes. In this instance, the researchers used microelectrodes to generate steady-state currents. Plotting of the function
  
allows for the calculation of without knowledge of or . Though the experiments are relatively simple and straightforward, the researchers then used these values for more complicated electrochemical experiments that enabled them to determine the degree of electronic coupling between the two metallic centers. Understanding the degree of electronic coupling could allow for facilitation to otherwise inaccessible catalysts and materials.
The next example uses chronoamperometry to measure extremely small diffusion coefficients of redox polyether hybrid cobalt bipyridine molten salts. Crooker and Murray4 performed chronoamperometry on a series of undiluted molten salts and were able to obtain diffusion coefficients as low as  . The researchers went on to obtain heterogeneous rate constants  using CV and were able to show that the reaction remains quasireversible despite small  rates because values are so low.
The next example uses chronoamperometry to directly measure rate constants. Smalley et al.5 examined a series of monolayers terminated with either a ferrocene or ruthenium redox moiety. For monolayers containing more than 11 methylene units, chronoamperometry was used to determine the heterogeneous rate constants . The researchers also determined preexponential factors and found them to be much lower that expected based aqueous solvent dynamics.
The fourth example uses chronocoulometry. Wolfe et al.6 prepared a series of ferrocenated hexanethiolate protected Au nanoparticles. Normallly, TGA would be used to calculate the number of thiolates per nanoparticle. However, in this case, TGA was inconclusive due to a slow loss of mass over the applied temperature range. The researchers instead monitored the charge pass over time for solution of nanoparticles with known concentrations. Knowing the total charge passed and the particle concentration allowed them to determine the number of ligands per nanoparticle. This is a good example of how electrochemistry can be used in place of a more traditional characterization technique.
The final example also uses chronocoulometry, but rather than using it for quantification purposes, the researchers use it to evoke a change in the system. Zhang et al.7 use chronocoulometry with predefined endpoints to produce Ag nanoparticles, confined on a electrode surface, with varying shapes and sizes. By varying the amount of charge passed the researchers were able to show that triangular nanoparticles oxidize first on the bottom edge, followed by triangular tips, followed by out-of-plane height. Since the researchers also coupled spectroscopy to their electrochemical experiments they were also able to show how the SPR band changes with shape evolution. This is a nice example of how electrochemistry can be used to evoke a change in a system rather than simply to monitor changes or determine physical parameters of the system.
References
- Faulkner, L. R.; Bard, A. J. Basic Potential Step Methods, Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New Jersey, 2000; 156-225.
- Cottrell, F. G. Z. Physik, Chem., 42, 1902, 385.
- Tennyson, A. G.; Khramov, D. M.; Varnado, C. D. Jr.; Creswell, P. T.; Kamplain, J. W.; Lynch V. M.; Bielawski, C. W.; Organometallics, 2009, 28, pp 5142–5147.
- Crooker, J. C.; Murray, R. W. Anal. Chem., 2000, 72, pp 3245–3252.
- Smalley, J. F.; Finklea, H. O.; Chidsey, C. E. D.; Linford, M. R.; Creager, S. E.; Ferraris, J. P.; Chalfant, K.; Zawodzinsk, T.; Feldberg, S. W.; Newton, M. D. J. Am. Chem. Soc., 2003, 125, pp 2004–2013.
- Wolfe, R. L.; Balasubramanian, R.; Tracy, J. B.; Murray, R. W. Langmuir, 2007, 23 (4), pp 2247–2254.
- Zhang, X.; Hicks, E. M.; Zhao, J.; Schatz, G. C.; Van Duyne, R. P. Nano Lett., 2005, 5, pp 1503–1507
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| 
and the current has a magnitude of about 
. 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).
. 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 
and the “live current” is 
.
and the signal level for the working electrode has been set to 
.
solution of 
in 
phosphate buffer (see Figure 4, specific parameters are: 
, 
GC WE, period = 
, width = 
, height = 
, potential increment = 
).
, just prior to the application of the potential pulse. The potential is then stepped by a small amount (typically 
) and current is sampled again, at time 
at the end of the pulse. The potential of the working electrode is then stepped back by a lesser value than during the forward pulse such that baseline potential of each pulse is incremented throughout the sequence.
, where 
is reduced in a one electron step to 
. At values sufficiently more positive than 
no faradaic current flows before the potential step (to more negative values). The application of the potential step does not produce an appreciable increase in current. Thus, the differential is very small. At values significantly negative of 
is the number of electrons, 
is Faraday’s Constant (
), 
is the electrode area (
), 
is the diffusion coefficient (
), 
is the concentration of electroactive species (
) and 
is given by
is the pulse height, 
is the temperature (
) and 
).
values for different reaction pathways and thus determine that the mechanism can be a one step or two steps depending on several factors.
clusters (AuMPCs). 
core charging over a 
window in 
at lowered temperatures. Though peaks are visible using 
) on a 
solution of 
in 
. If the choice of electrode range is too small (e.g. 
), actual current may go off scale and be truncated (see Figure 2, red trace). If the electrode range is too large (e.g. 
), the voltammogram may have a noisy, choppy, or quantized appearance (see Figure 2, black trace). With the adequate electrode range (e.g. 
), the volatammogram has a desirable appearance (see Figure 2, green trace)
). 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. 
), 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 – 
, 
, 
, 
, and 
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).
, with a formal potential 
. If a potential sweep is started sufficiently more positive than 
passes 
curve. Ideally, the peak-to-peak separation for the reduction and oxidation waves should be 
for a one-electron electrochemically reversible process. Additionally, the peak height 
in amperes 
can be described by the Randles-Sevcik equation, shown below,
, 
is the absolute temperature 
and 
is the sweep rate. At 
, with 
, 
, 
and 
, the above equation simplifies to
.
values (
, overpotential), with 
being the oxidation or reduction peak and 
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.
dissociation from the cyanomyoglobin complex (
)8. By comparing the experimentally obtained cyclic voltammograms to theoretically calculated cyclic voltammograms, they were able to estimate the dissociation rate, 
, by varying the sweep rate and monitoring the disappearance of an oxidation wave, associated with 
) which are generated using the maximum available resolution of the potentiostat’s digital-to-analog converter (DAC).
Ferrocene in 
, 
OD Pt WE, 
couple, based on a time-based Nernstian relation. As the concentration of 
curve is much like a potentiometric titration with a transition time (analogous to an equivalence point), 
is the sweep rate (
).
is equal to
should give a straight line with slope of 
for a reversibile 
Ferrocene in 
, 
sweep rate ).
has a non-zero y-intercept. This intercept is related to double-layer charging and reduction of adsorbed 
is the charge due to double-layer charging and 
is the charge due to reduction of adsorbed