Electrochemically reversible couple

Where; n is the number of electrons transferred. This 0.058/n V separation of peak potentials is independent of scan rate for a reversible couple but is slightly dependent on the cycle number and switching potential. When the scan rate is increased the anodic and cathodic peak potentials both increase in proportion to the scan rate. For an irreversible couple, plots of the anodic and cathodic peak potentials versus the scan rate should be linear with intercepts at the origin. The values of ipa and ipc should be similar in magnitude for a reversible couple with no kinetic complications, i.e., ipa/ipc≈ 1.

Electrochemical irreversibility is caused by slow electron exchange of the redox species with the working electrode and is characterised by a separation peak potential that is greater than 0.059/n V and is dependent on the scan rate (see Equation 1.20). In CV the presence of only one peak (ipa or ipc) can be an indication of irreversibility. For quasi-reversible systems, the current is controlled by both the mass transport and charge transfer. Voltammograms of a quasi- reversible system are more extended and exhibit a larger separation in peak potentials compared to the separation peaks in a reversible system [10]. Figure 1.10 shows a typical potential-time excitation signal for voltammetry and a cyclic voltammogram for a reversible process while Figure 1.11 shows cyclic voltammograms for irreversible and quasi-reversible redox processes.

(A) (B)

Figure 1.10: (A) Typical potential-time excitation signal for voltammetry, where

Ei is the initial potential and Ef is the final potential, and (B) is a typical voltammogram for a reversible process.

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(A) (B)

Figure 1.11: (A) Typical voltammogram for an irreversible process and (B) is a

typical voltammogram for a quasi-reversible process.

1.3.4.3 Square Wave Voltammetry

Square wave voltammetry (SWV) is among the most sensitive means for the direct evaluation of concentrations. It can have direct detection limits as low as 10-8 M [33]. The excitation signal in SWV consists of a symmetrical square-wave pulse of amplitude Esw superimposed on a staircase waveform of step height, ΔE, where the forward pulse of the square wave coincides with the staircase step as shown in Figure 1.12. The net current, inet, is obtained by taking the difference between the forward and reverse currents (ifor – irev) and is centered on the redox potential. The peak height is directly proportional to the concentration of the electroactive species. The theory for a reversible system predicts that the resulting current-time behaviour should be symmetrical and almost bell-shaped with a peak at E 1/2. The peak current is a linear function of concentration and the square root

of the square wave frequency. SWV has several advantages including its

excellent sensitivity, the rejection of background currents, and its speed. This method also has several applications including the study of electrode kinetics, determination of some species at trace levels, and its use with electrochemical detection in HPLC [33].

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Figure 1.12: Potential wave form for square wave voltammetry

1.3.4.4 Differential Pulse Voltammetry

Differential pulse voltammetry (DPV) involves the application of small constant pulses (of the same amplitude) superimposed upon a staircase waveform [34]. The current is sampled twice in each pulse period, just before the pulse application and again late in the pulse life, when the charging current has decayed. The first current is subtracted from the second, and this current difference plotted versus the applied potential as shown in Figure 1.13. The resulting voltammogram consists of current peaks, the height of which is directly proportional to the concentration of the corresponding analytes.

Potential (mV) Time (s) Sample Period (if) Sample Period (ir) Quiet Time SW Amplitude Step E Δi = if - ir

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Figure 1.13: Potential wave form for differential pulse voltammetry

1.3.4.5 Electrical Impedance Spectroscopy (EIS)

Electrochemical impedance spectroscopy (EIS) is a sensitive technique, which monitors the electrical response of the system studied after the application of periodic small amplitude of AC signal. Analysis on the system provides information concerning the interface and reactions occurring at it.

EIS data is commonly analysed by fitting the data to an equivalent electrical circuit model. Common electrical elements such as resistors, capacitors and inducers are the most used in the circuit model. A Randles circuit is an equivalent electrical circuit that consists of an active electrolyte resistance Rs in series with the parallel combination of the double-layer capacitance Ddl and an impedance of a faradaic reaction. Figure 1.14 shows the typical Randles Model for EIS characterisation on modified electrodes used in Chapter 4.

Sample Period Sample Period Step E Pulse Amplitude Pulse Period Pulse Width Quiet Time Time (s) Potential (mV)

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Figure 1.14: Impedance circuit (Randles model) for characterisation of modified

electrodes

In Randles model circuit, Rs represents the dynamic solution resistance, Cdl represents the double layer capacitance measured between the electrode and the electrolyte solution, Rct is the charge transfer resistance and Zw is the Warburg element describing the time (frequency) dependence of mass transport.

The impedance data could also be presented using the Nyquist plot, as the results in this thesis were plotted, where the imaginary (Z”) versus (Z’) components of the impedance is plotted. Figure 1.15 represents an example of a Nyquist plot of the Randles impedance with the semi-circle at higher frequencies and the straight line at an angle to the real axis at lower frequencies.

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Figure 1.15: Nyquist plot for oxidation/reduction reaction of 5 mM [Fe(CN)6]3-/4- in 0.1 M KCl (imaginary impedance versus real impedance). Frequency measured from 1Hz to 100 kHz.

Using the model circuit that was previously mentioned in Figure 1.14, the Cdl value could only be calculated after the frequency information is provided. The Warburg impedance could be calculated as shown in Equation 1.21.

ω