Measuring Surface Related Currents using Digital Staircase Voltammetry
Cyclic Voltammetry (CV) is unarguably the most popular electrochemical technique. It owes its well deserved reputation to its ability to deduce reaction mechanisms with relatively low cost equipment and quick experimentation. Since the very highly cited paper by Nicholson and Shain1 the technique has been the centerpiece of any electrochemical study.
CV involves sweeping the potential linearly between two limits at a given sweep rate while measuring current. The sweep rate chosen can be varied from few microvolts per second to millions of volts per second.
Electrochemical instrumentation has evolved vastly since the days of Nicholson and Shain. Currently, most manufacturers (including Gamry) make digital instruments with digital signal generators. These signal generators approximate the linear sweep with a staircase of variable step sizes and durations.
Early in the development of digital instruments (early 1990s), there have been reports analyzing the effects of using staircases instead of true ramps. In staircase voltammetry, current can be sampled at various points during the step. Two of the report investigated and tabulated the effects of this choice of sampling time. Another report suggested the use of heavy analog filtering either on the applied or on the recorded signal as a way of eliminating the difference. The author demonstrated that through appropriately chosen analog filters, a ramp can be approximated by a staircase and the measured response is not adversely affected.
A later study employed simulations to show that provided the potential steps are small enough, a staircase signal generated similar results as the linear ramp. The author investigated different coupled chemical reaction mechanisms including EC, CE, ECE, etc in addition to surface bound reactions like amalgamation and adsorption.
In this note, we will investigate the differences between data taken using a true analog ramp and a staircase using selected systems. We will show that, for experiments where faradaic reactions of solution species are studied, approximating a ramp with a staircase is adequate.
However, in experiments where faradaic reactions of surface species are involved, or when capacitance is measured, care has to be taken as there can be remarkable differences in the results. We will further introduce oversampling as an alternative solution and show that the oversampled and averaged data does not differ from that measured using the analog ramp.
Polycrystalline Platinum in Sulfuric Acid
CV of polycrystalline platinum in dilute sulfuric acid produces strikingly different results depending on how the current is sampled. A typical voltammogram of polycrystalline platinum in sulfuric acid using a true analog ramp is shown on Figure 2.
Figure 3 Polycrystalline Pt in sulfuric acid using staircase voltammetry with current sampled immediately prior to the step compared to the analog sweep.
There are several distinct regions in the CV profile. Starting from the negative end of the voltammogram, the first region of up to about 0.1 V is the adsorption (reductive peaks) and desorption of hydrogen. From 0.1 V to about 0.6 V no faradaic reactions occur. The third region is the oxide formation region starting at about 0.6 V6. The reduction of platinum oxide (negative currents) occurs at about 0.5 V. This voltammetry has been well studied and understood. The H-adsorption region, in particular, is often used as a tool to deduce the electrochemically active area of the Pt electrode.
Typically, in staircase voltammetry, a current reading is acquired immediately prior to the next step7. This method of sampling discriminates against any capacitive or surface bound reactions. The current due to any capacitive charging or faradaic current confined to the surface, decays in the initial part of the step and does not contribute to the measured current. Therefore, the hydrogen adsorption region is not well defined with the staircase voltammetry as shown in Figure 3.
Gamry employs a unique sampling mode to eliminate this difference. Instead of sampling the current at the end of the step where all the capacitive and surface related current has decayed, one can sample the current throughout the step and average. This way, the current due to capacitive and surface related effects are measured as well as any persistent effects throughout the step. This sampling mode is given the name “Surface Mode” in Gamry’s Framework Software. When surface mode sampling is used, structure in the data is recaptured as shown on Figure 4.
Double layer capacitance:
Another example where staircase voltammetry has to be scrutinized is the study of double layer capacitance (or capacitors in general).
With a pure capacitor, the current response to an applied ramp can be shown to be v • C where v is the sweep rate and C is the capacitance. The effect of series resistors (either stray or intentionally added) can also be shown to be confined to the initial rise time. The steady state current (even when the resistance is considered) is a good measure of the capacitance.
Due to the reasons mentioned in the previous section, when calculating a capacitance from a staircase voltammogram, one has to pay attention to the step size and length compared to the time constant of the system.
We will illustrate the problem with a 36.2 μF capacitor. Its capacitance is the correct order of magnitude for cm2 sized electrodes. At 100 mV/s, the expected steady state current for this capacitor is 3.6 μA (36 μF x 0.1 V/s)
The voltammetry with an analog signal generator (at 100mV/s, 33.3 Hz sampling) is compared to the data with the classically sampled staircase voltammogram (100mV/s, 3mV step) in Figure 5. The time constant of the 36μF capacitor is many orders of magnitude smaller than the step duration used in the experiment. Therefore the measured current in the staircase voltammogram is much lower than that of the analog sweep.
Using Gamry’s surface mode sampling recovers the expected 3.6μA as shown on Figure 6 (with the same hardware settings used for Figure 5).
Supercapacitors and Mostly Faradaic Currents
Difference between staircase voltammetry and analog sweeps isn’t always as striking. In this section, we will investigate two such cases.
The first is the case of electrochemical capacitors. Due to theit large capacitance, the time constants for the currents to decay after a step are comparable to the typical step duration. Therefore, the difference between the analog sweep and the staircase is not as pronounced as shown in Figure 7.
As a second example, we will use the Fe2+/3+ redox couple. In the typical CV experiment where the faradaic current is dominant, the effect is insignificant. As shown on Figure 8, the peak current does not depend on the mode of sampling at all. The only part of the voltammogram that is dependent on the mode of sampling is the region where the only current measured is the charging of the double layer capacitance. At potentials around -300mV vs. SCE, the difference due to sampling mode can be seen.
Staircase voltammetry can be used instead of an analog sweep for a number of different electrochemical measurements. In cases where surface confined effects are important (like the H-adsorption or the double layer capacitance) care has to be taken for the choice of step height and duration. In those measurements, oversampling and averaging can be employed in order to eliminate the differences caused by the use of a staircase signal.
Generally, in a digital sweep the standard convention is to acquire one data point at the very end of the stepError: Reference source not found. Gamry calls this method “Fast” mode, see Figure 9. This method of sampling discriminates against any capacitive or surface bound reactions. The current due to any capacitive charging or faradaic current confined to the surface decays in the initial part of the step and does not contribute to the measured current.
With “Surface” mode, Gamry enables a unique sampling method to eliminate the differences between a staircase and a true ramp. In surface mode, the data is sampled throughout the duration of the step and averaged. This allows capturing both capacitive effects and any faradaic effects confined to the surface.
For the experiments used in this application note a Gamry Reference 3000 was used with the PHE200 and the VFP600 software packages. The CV experiments were performed using the internal digital signal generator as well as a true analog signal generator (Model 175 from Princeton Applied Research).
All data were acquired with a 100mV/s sweep rate with 3mV steps when using the Gamry Framework software. When the analog signal generator was used, Gamry’s Virtual Front Panel Software (VFP600) was employed with a sampling rate of 33.3Hz.
The 36 μF capacitor used was Panasonic ECA-1HM330B and the 3F capacitor was NessCap ESHSR0003C0-002R7.
For the three-electrode experiments, Dr. Bob’s cell was used along with a 3mm Pt working electrode, a saturated calomel reference electrode and graphite counter electrode.
For the sulfuric acid experiments Pt working electrode was polished prior to immersion in 1M sulfuric acid.
For potassium hexacyanoferrate experiments an aqueous solution of 10mM potassium ferricyanide and 0.1M potassium chloride was used.
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- The capacitor is labeled 33μF by the manufacturer. The actual capacitance was measured by impedance spectroscopy.