The difference current between a forward and reverse pulse is plotted as a function of potential to yield a voltammogram.

### Detailed Description

Like most of the other electrochemical techniques offered by the AfterMath software, Square Wave Voltammetry (SWV) 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 through a series of forward and reverse pulses from the Initial potential to the Final potential. The forward step is determined by the Square amplitude and the reverse step is determined by subtracting the Square increment from the Square amplitude. Cyclic Square Wave Voltammetry (CSWV) is a variant where the potential of the working electrode is cycled between an Upper potential and a Lower 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.

Difference current between the forward and reverse pulses 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 SWV, 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 potential and Final potential, to values which are appropriate for the electrochemical system being studied.

Figure 1 : Basic setup for SWV.

The waveform that is applied to the electrode is a series of forward and reverse pulses (see Figure 2) each having an amplitude of Square amplitude and incremented according to the Square increment. The total time for the forward and reverse pulses is the Square period. Using the sample waveform below, the first pulse is $25 \; mV$ in the positive direction for $5 ms$. The current is sampled (red squares) during the forward pulse at the time obtained by subtracting the Sample width from $1/2$ of the Square period. The potential of the working electrode is then stepped to $-25 \; mV$ for $5 \; ms$. The current is then measured (black squares) at the time obtained by subtracting the Sample width from the Square period.

Figure 2: Zoom of waveform for SWV.

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.

### 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

Typical results for a $1 \; mM$ solution of Ferrocene in $0.1 \; M \; Bu_4NClO_4/CH_2Cl_2$ are shown below (see Figure 3, specific SWV parameters were: $25 \; mV$ square amplitude, $2 \; mV$ square increment, $10 \; ms$ square period, $1 \; ms$ sample width). Also included are plots of the forward (see Figure 4A) and reverse (see Figure 4B) currents. Notice that the each looks like a typical LSV curve, with the forward being an oxidation and the reverse being the reduction. Please see the Theory section for more information.

Figure 3:Square Wave Voltammogram of a Ferrocene Solution

Figure 4: A) Forward current and B) Reverse current of a Ferrocene Solution

Below is an example for CSWV of a $1 \; mM$ solution of Ferrocene in $0.1 \; M \; Bu_4NClO_4/CH_2Cl_2$ (see Figure 5, specific parameters were: $25 \; mV$ square amplitude, $2 \; mV$ square increment, $10 \; ms$ square period, $1 \; ms$ sample width). Peak potentials are marked with a Crosshair tool to show that the anodic and cathodic peaks appear at nearly the same potential.

Figure 5 : Cyclic Square Wave Voltammogram for a Ferrocene Solution

### Theory

The following is a brief introduction to the theory of SWV. SWV was invented by Ramaley and Krause1. Please see Bard and Faulkner2, Osteryoung and O'Dea 3 or Osteryoung and Osteryoung4 for additional information on the technique. CSWV, originally developed by Xinsheng and Guogang5, and recently revived by Helfrick and Bottomley6, is covered in the literature also.

SWV combines the aspects of several pulse voltammetric methods, including the background supression and sensitivity of DPV, the diagnostic value of NPV, and the ability to interrogate products directly in the manner of RNPV.

Consider a reaction $O + e^- \rightarrow R$, where $O$ is reduced in a one electron reaction to $R$ with formal potential, $E^{0}$. An initial potential is applied to the electrode that is significantly more positive than $E^{0}$. No significant faradaic current flows upon the application of forward pulse towards more negative values. Current is sampled at a specified point during the forward pulse.

The reverse pulse consists of stepping the potential of the working electrode to more positive values and the current is sampled near the end of the reverse pulse. The difference current is calculated by subtracting the reverse current from the forward current.

As the potential of the working electrode approaches $E^{0}$ a faradaic current flows due to reduction of $O$. Upon application of the reverse pulse, a faradaic current flows in that effectively oxidizes the $R$ was was produced during the forward pulse. In other words, the rate of reduction slows compared to the forward step, hence an anodic current flows. Once the potential of the working electrode is sufficiently more negative of $E^{0}$ the current is diffusion-limited in both the forward forward and reverse pulses and the difference current is small.

SWV's strengths lie in diagnostics, meaning that it is not typically used for quantitation. It is possible however, to calculate peak height using the equation

${\Delta}i_p = \frac{nFAD_O^{1/2}C_O^*}{{\pi}^{1/2}t_p^{1/2}}{\Delta}{\psi}_p$

where $n$ is the number of electrons, $F$ is Faraday's Constant ($96485 \; C/mol$), $A$ is the electrode area ($cm^2$), $D_{0}$ is the diffusion coefficient of species $O$ ($cm^2/s$), $C_O$ is the concentration of species $O$ ($mol/cm^3$), $t_p$ is the experimental time scale ($1/2$ Square period – Sample window), and ${\Delta}{\psi}_p$ is a Dimensionless Peak Current parameter (see Table 1).

Table 1. Dimensionless Peak Current (${\Delta}{\psi}_p$) vs. SWV Operating Parametersa

 $n{\Delta}E_i/mV$$n{\Delta}E_i/mV$ $n{\Delta}E_a/mV$$n{\Delta}E_a/mV$ $1$$1$ $5$$5$ $10$$10$ $20$$20$ $0^b$$0^b$ $0.0053$$0.0053$ $0.0238$$0.0238$ $0.0437$$0.0437$ $0.0774$$0.0774$ $10$$10$ $0.2376$$0.2376$ $0.2549$$0.2549$ $0.2726$$0.2726$ $0.2998$$0.2998$ $20$$20$ $0.4531$$0.4531$ $0.4686$$0.4686$ $0.4845$$0.4845$ $0.5077$$0.5077$ $50$$50$ $0.9098$$0.9098$ $0.9186$$0.9186$ $0.9281$$0.9281$ $0.9432$$0.9432$ $100$$100$ $1.1619$$1.1619$ $1.1643$$1.1643$ $1.1675$$1.1675$ $1.1745$$1.1745$

${\Delta}E_a$ = Square amplitude

$^b{\Delta}E_a = 0$ corresponds to SCV

${\Delta}E_i$ = Square increment

### Applications

The first application uses SWV to monitor binding events associated with electrochemical sensors. White and Plaxco7 developed redox-tagged electrochemical sensors from electrode-bound oligonucleotides. Tuning the frequency of the voltammetric measurements allows the researchers to amplify both the unbound and target-bound signals, essentially, making an “On/Off” sensor.

The second example used several electrochemical techniques, SWV among them, to monitor metal dissociation events. Chakrabarti et al.8 combined RDE with anodic stripping voltammetry to distinguish between labile and nonlabile complexes in extremely low concentrations in aqueous solutions and in precipitation samples. The authors then showed that DPV, SCV and SWV all give similar dissociation constants but SWV's sensitivity was two orders of magnitude higher than SCV. This is a nice example of how SWV compares with other electrochemical techniques.