Normal Pulse Voltammetry (NPV)

1. Technique Overview

Normal Pulse Voltammetry (NPV) is a potentiostatic method that offers some advantages to common techniques like Cyclic Voltammetry (CV), in that the waveform is a series of pulses that are increasing in potential amplitude. The way in which the current is measured at each pulse aids in minimizing the measurement of background (charging) current. Related pulse-type methods include Differential Pulse Voltammetry (DPV) and Square Wave Voltammetry (SWV).

Normal Pulse Voltammetry (NPV) is a derivative technique of Normal Pulse Polarography (NPP). NPP is a technique that was traditionally used with Dropping Mercury Electrodes and Static Mercury Dropping Electrodes. The waveform for the two techniques is the same; however, it is appropriate to use the term “Normal Pulse Voltammetry” when referring to the application of the waveform to nonpolarographic electrodes. As with many other methods, users can initially sweep positively (towards an anodic limit) or negatively (toward a cathodic limit) initially. Below, typical NPV waveforms are shown for illustration, using only an increasing positive pulse sequence.

INFO:

Initial sweep direction can be positive-increasing or negative increasing. Not all possibilities have been provided as examples in this article. Users must tailor their parameters to suit their specific electrochemistry. Contact us with any questions or additional assistance.

In the simplest case, when Segments (S_N) = 1 (see Figure 1), increasing potential pulses step from a common baseline in a linear fashion, from an initial to final potential, sampling current at specified intervals (see Figure 7).

Figure 1: Normal Pulse Voltammetry (NPV) One Segment Waveform

Current sampling occurs at the same time in each pulse of the NPV waveform. For each pulse, the current is sampled as a function of the pulse sequence, $i_{sample}(T^*)$ , which is determined as

$T^*=T_{W,\;NP}-T_{S,\;NP}$

(5)

where $T_{W,\:NP}$ is the pulse width and $T_{S,\:NP}$ is the sampling width (see Table 1 and Figure 7). When Segments (SN) = 2 (see Figure 2), increasing potential pulses step from a common baseline in a linear fashion, from an initial potential to vertex potential, at which time the NPV pulses decrease until reaching the final potential. Again, the current is sampled in the same fashion as NPV experiments with other Segment values.

Figure 2: Normal Pulse Voltammetry (NPV) Two Segment Waveform

When Segments (SN) = 3 (see Figure 3), increasing potential pulses step from a common baseline in a linear fashion, from an initial potential to upper potential, then from upper potential to lower potential, and finally from lower potential to final potential. Throughout each segment, the NPV pulses increases/decreases until reaching the next significant potential value supplied to AfterMath. Again, the current is sampled in the same fashion as NPV experiments with other Segment values (see Figure 7).

Figure 3: Normal Pulse Voltammetry (NPV) Three Segment Waveform

2. Fundamental Equations

Consider the reaction

$O + ne^- \rightleftharpoons R$

(6)

where $O$ is reduced in a one-electron reaction to $R$ with formal potential $E^0$ . The application of a baseline potential should be sufficiently positive of $E^0$ such that no faradaic current flows. After a period of time $(\tau^{\prime})$ , typically 100 - 5000 ms, the potential of the working electrode is stepped to a more negative value for a period of time. The total time from the application of the baseline potential through the application of the potential pulse is $\tau$ . The potential pulse is incrementally increased with each cycle. As the potential of the working electrode approaches $E^0$ faradaic current flows due to the reduction of $O$ to $R$ . Upon the application of the baseline potential in the next cycle, $R$ is oxidized back to $O$ . When the potential of the working electrode gets sufficiently negative of $E^0$ , $O$ is reduced to $R$ at a maximum rate and the current levels off to a plateau. The magnitude of this current plateau is given by

$i_{d,RPV} = \dfrac{nFAD_O^{1/2}C_O^*}{{\pi}^{1/2}}\left[{\dfrac{1}{({\tau}-{\tau}^{\prime})^{1/2}}}-{\dfrac{1}{{\tau}^{1/2}}}\right]$

(7)

where the parameters are as described above. Notice that in the Sample Experiments section, there is a slight anodic current flowing at the beginning of the experiment. The magnitude of this current is given by the equation

$i_{d,DC} = \dfrac{nFAD_O^{1/2}C_O^*}{{\pi}^{1/2}{\tau}^{1/2}}$

(8)

where the parameters are as described above. The magnitude of this current is the difference between the NPV and RNPV currents. Bard and Faulkner¹ provide a summary and description of normal pulse voltammetry as do Kissinger and Heinemann².

3. Experimental Setup in AfterMath

To perform a normal pulse voltammetry experiment in AfterMath, choose Normal Pulse Voltammetry (NPV) from the Experiments menu (see Figure 4).

Figure 4: Normal Pulse Voltammetry (NPV) Experiment Menu Selection in AfterMath

Doing so creates an entry within the archive, called NPV Parameters. In the right pane of the AfterMath application, several tabs will be shown (see Figure 5).

Figure 5: Normal Pulse Voltammetry (NPV) Experiment Parameters

As with most Aftermath methods, the experiment sequence is

Induction Period → Pulse Sequence → Relaxation Period → Post-Experiment Idle Conditions

Continue reading for detailed information about the fields on each unique tab.

3.1. Basic Tab

TIP:

Click the AutoFill button on the top bar in AfterMath to automatically fill all required parameters with reasonable starting values. While the values provided may not be appropriate for your specific system, they are reasonable parameters with which to start your experiment, especially if you are new to the method.

The basic tab contains fields for the fundamental parameters necessary to perform an NPV experiment. AfterMath shades fields with yellow when a required entry is blank and shades fields pink when the entry is invalid (see Figure 6).

Figure 6: Normal Pulse Voltammetry (NPV) Basic tab in AfterMath

During the induction period, a set of initial conditions are applied to the electrochemical cell and the cell equilibrates at these conditions. Data are not collected during the induction period, nor are they shown on the plot during this period. Users will define induction period parameters on the Advanced Tab. After the induction period, the potential of the working electrode is stepped through a series of increasing pulses from the Initial potential to the Final potential. The potential is incremented with each successive pulse according to the Pulse increment. Current is measured at the time obtained by subtracting the Pulse sampling width window from the Pulse width. In a typical experiment, Segments = 1 and there is a single series of increasing pulses. Some may want to reverse the pulses (move in the opposite direction), accomplished by adjusting the number of segments to be > 1. By adjusting the number of segments, users can create variants of the NPV technique. Cyclic Normal Pulse Voltammetry consists of cycling (through a series of potential pulses also) the potential of the working electrode between an Upper potential and a Lower potential (Segments = 2 or 3). Reverse Normal Pulse Voltammetry is a variant of NPV where you choose to apply a Baseline potential in a region where the Faradaic current is flowing at a maximal rate ( >200 mV from $E^{0}$ ). Refer to Figures 1, 2, and 3 for examples of such NPV waveforms that vary based on number of segments. The parameter settings for pulse-type experiments are often not as clear as with something more simple like Cyclic Voltammetry (a sweep method ). Refer to Figure 2 above when understanding each parameter of the NPV pulse. Further, clicking "AutoFill" ("I Feel Lucky" in older versions of AfterMath) provides reasonable starting parameters if you are unsure of typical values used in these experiments. Most often, research journal articles describe the NPV pulse sequence used, which can be replicated using AfterMath. The experiment concludes with a relaxation period. During the relaxation period, a set of final conditions (specified on the Advanced tab) are applied to the electrochemical cell and the cell equilibrates at these conditions (set on the Advanced Tab). Data are not collected during the induction period, nor are they shown on the plot during this period. 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. A plot of the typical experiment sequence, containing labels of the fields on the Basic tab, helps to illustrate the sequence of events in an NPV experiment (see Table 1 and Figure 7).

The table below lists the group and field names and symbols for each parameter associated with this experiment. See Table 1

Sweep (Sweep limits)

Segments

$S_N$

Sweep (Sweep limits)

Initial Potential

$E_I$

Sweep (Sweep limits)

Initial Direction

$DIR_I$

Sweep (Sweep limits)

Upper Potential

$E_U$

Sweep (Sweep limits)

Vertex Potential

$E_V$

Sweep (Sweep limits)

Lower Potential

$E_{LOW}$

Sweep (Sweep limits)

Final Potential

$E_F$