### Detailed Description

Like most of the other electrochemical techniques offered by the AfterMath software, Differential Pulse Voltammetry (DPV) 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 from the Initial potential to the Final potential. The forward step is determined by the Step height and the reverse step is determined by subtracting the Step increment from the Step height. Cyclic Differential Pulse Voltammetry (CDPV) is a variant where the potential of the working electrode is cycled between an Upper baseline potential and a Lower baseline potential.

After the pulse sequence 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.

Differential 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

For DPV, 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 may need to change the Initial baseline potential and Final baseline potential, to values which are appropriate for the electrochemical system being studied.

Figure 1: Basic setup tab for DPV.

For CDPV, 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 2). You may need to change the Number of segments, Initial baseline potential, Upper baseline potential, Lower baseline potential and Final baseline potential, to values which are appropriate for the electrochemical system being studied. The Final baseline potential is greyed out for the two segment case.

Figure 2: Basic setup tab for CDPV.

Though two segments would be typical for CDPV, 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. You must choose an Initial baseline potential, Upper baseline potential, Lower baseline potential, and Final baseline potential. You must also choose whether the Initial direction is rising or falling . If the Initial direction is rising, the Final baseline potential must be different than the Lower baseline potential. If the Initial direction is falling, the Final baseline potential must be different than the Upper baseline potential.

If you choose any even number of segments greater than two the parameters that must be entered are the different from the two segment case. You must choose an Initial baseline potential, Upper baseline potential, Lower baseline potential, and Final baseline potential. You must also choose whether the Initial direction is rising or falling . If the Initial direction is rising, the Final baseline potential must be different than the Upper baseline potential. If the Initial direction is falling, the Final baseline potential must be different than the Lower baseline potential.

The waveform that is applied to the electrode in DPV is a sequence of pulses (see Figure 3). The total length of each pulse in the sequence is determined by the Period. The potential of the working electrode is stepped according to the Height for the period of time specified by the Width . The potential of the working electrode is then stepped back but only by the Height minus the Potential increment. The current is sampled at two points in each pulse. The first point is just prior to stepping the potential of the working electrode, and the second point comes at the end of each period just prior to stepping the potential of the working electrode back to begin the next pulse period. The waveform that is applied to the electrode in CDPV is identical to DPV on forward sweeps. On reverse sweeps in CDPV, the pulses are inverted.

Figure 3: DPV Waveform. Orange trace – Applied potential. Black squares – First current sample point. Note that the second current sample point is at the end of each pulse. A: Full waveform. B: Zoom of Waveform.

The Advanced Tab for this method 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.

Additionally, common to both DPV and CDPV, you can choose to invert the pulses during the experiment. Theoretically, the results will be the same since it is the differential current that is plotted. Please see the Theory section for more information.

### Ranges Tab

Though AfterMath has the ability to automatically select the appropriate ranges for voltage and current during an experiment it is best to manually select the current range for any pulse technique. 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.

### Typical Results

Below are the typical results for DPV for the oxidation of a $1.4 \; mM$ solution of $K_4Fe(CN)_6$ in $0.1 \; M$ phosphate buffer (see Figure 4, specific parameters are: $pH = 6.8$, $3 \; mm$ GC WE, period = $100 \; ms$, width = $10 \; ms$, height = $50 \; mV$, potential increment = $10 \; mV$).

Figure 4:Differential Pulse Voltammogram of a Potassium Ferrocyanide Solution in Phosphate Buffer

Below are the typical results for CDPV for the oxidation and reduction of $K_4Fe(CN)_6$ in $0.1 \; M$ phosphate buffer (see Figure 5, specific parameters were: $pH = 6.8$, $3 \; mm$ GC WE, period = $100 \; ms$, width = $10 \; ms$, height = $50 \; mV$, potential increment = $10 \; mV$). Crosshair tools have been added to show that peak positions and peak heights should be identical in CDPV for a fully reversible system.

Figure 5 : Cyclic Differential Pulse Voltammogram of a Potassium Ferrocyanide Solution in Phosphate Buffer

### Theory

The following is a brief introduction to the theory of DPV. Please see Bard and Faulkner1 for a more complete description. Please see Drake et al.2 for a complete description of CDPV.

DPV is a technique that is designed to minimize background charging currents. The waveform in DPV is a sequence of pulses, where a baseline potential is held for a specified period of time prior to the application of a potential pulse. Current is sampled, at time ${\tau}'$, just prior to the application of the potential pulse. The potential is then stepped by a small amount (typically $<100 \; mV$) and current is sampled again, at time $\tau$ 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.

Consider a reaction $O + e^- \rightarrow R$, where $O$ is reduced in a one electron step to $R$. At values sufficiently more positive than $E^{0'}$ 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 $E^{0'}$ the baseline potential is reducing $O$ at a maximum rate. The application of a small potential step (towards more negative values) is unlikely to increase the rate of reduction and hence the differential current is again small. Only at potentials around $E^{0'}$ will the differential current be significant. The period during the application of the baseline potential has $O$ being reduced at some rate. The potential step (to more negative values) increases the rate of reduction and hence the differential current will be significant. Under normal conditions (pulse height $<100 \; mV$) the height of the peak can is given by the equation

$({\delta}t)_{max} = \frac{nFAD_O^{1/2}C_O^*}{{\pi}^{1/2}({\tau}-{\tau}')} \left({\frac{1-\sigma}{1+\sigma}}\right)&s=3$

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 ($cm^2/s$), $C_O^*$ is the concentration of electroactive species ($mol/cm^3$) and $\sigma$ is given by

$\sigma = \left(\frac{nF}{RF}\frac{{\Delta}E}{2}\right)$

where ${\Delta}E$ is the pulse height, $T$ is the temperature ($K$) and $R$ is the Universal Gas Constant ($8.314 \; J/K mol$).

As mentioned in the Advanced parameters tab, the direction of the pulse should not affect the results. Consider the reaction above $O + e^- \rightarrow R$, where $O$ is reduced in a one electron step to $R$ . At values sufficiently more positive than $E^{0'}$ no faradaic current flows before the potential step (towards more positive values). The change in current due to the potential step is also insignificant enough to cause faradaic current. Thus, the differential is very small. At values significantly negative of $E^{0'}$ the baseline potential is reducing $O$ at a maximum rate. The application of a small potential pulse (towards more positive values) does not decrease the rate of reduction and hence the differential current is again small. Only at potentials around $E^{0'}$ will the differential current be significant. The period during the application of the baseline potential has $O$ being reduced at some rate. The potential step (to more positive values) decreases the rate of reduction and hence the differential current will be significant. Hence, the direction of the potential step has no effect on the differential current observed.

### Application

The first example uses DPV to examine the pH dependence of redox potential for a electron and proton transfers in trytophan and tyrosine. Sjödin et al.3 used the pH dependence of the redox potential to calculate ${\Delta} G$ values for different reaction pathways and thus determine that the mechanism can be a one step or two steps depending on several factors.

The second example uses DPV to examine the quantized double layer charging of hexanethiolate-coated monolayer-protected $Au_{140}$ clusters (AuMPCs). Miles and Murray used DPV to resolve 13 individual peaks related to $AuMPC$ core charging over a $3 \; V$ window in $CH_2Cl_2$ at lowered temperatures. Though peaks are visible using CV, DPV provides the necessary resolving power, by suppressing background currents, to separate out all 13 peaks. This is a wonderful example highlighting the power of DPV.