Diffusion in Cyclic Voltammetry

Cyclic voltammetry (CV) is an extension of LSV in which the potential at the working electrode is cycled linearly between low (Einitial) and high (Efinal) values as illustrated below.

Due to the pattern created in the potential (E) vs. time (t) plot in figure 18, this waveform is known as the sawtooth potential waveform. The gradient of this waveform denotes the scan rate of the experiment (V/t), which is kept constant throughout.

Figure 18. Sawtooth potential waveform of a cyclic voltammetry (CV) experiment. [77]

The “readout” of a CV experiment shows applied potential on the x axis and resulting current flow on the y axis. The system parameters of a typical experiment are set up so that oxidation reactions at the electrode interface give rise to a positive current and reduction reactions give rise to negative current. The current response on the y axis is routinely divided by the working electrode’s electro-active area so that different sized electrodes may be compared. Therefore current density, j (Acm-2), is usually plotted on the y axis rather than current (A).

Figure 19. A possible CV response for the oxidation and reduction of solution species upon the application of the potential waveform in figure 18. Adapted from reference [73].

Other than Faradaic processes, current in CV experiments may result from non-Faradaic processes: in which no electron transfer occurs at the electrode-electrolyte interface. Non- Faradaic current occurs because of the capacitive nature of the electrode-electrolyte interface and is to do with movement of ions, which occurs in response to the changing charge on the electrode surface as its potential is swept. Consider a working electrode surface with a particular amount of positive charge upon it. Due to electroneutrality there is equal negative charge held in the solution side of the double layer. Increasing the potential at the electrode in a positive potential sweep increases the charge at the electrode surface. To maintain electroneutrality the concentration of negative ions in the double layer must increase. These new ions join the electrolyte double layer from the bulk solution. Flow of current due to this phenomenon is known as double layer charging. [50]

Double layer charging current, 𝑖_𝐷𝐿, is directly proportional to CV scan rate and electrode area and is represented by the equation

𝑖

= 𝐶

𝐴𝜈

where 𝜈(𝑉𝑠−1) is the scan rate of the voltammetric experiment, A(cm2_{) the electrode area and}

𝐶𝐷𝐿 (farad, F) is the double layer capacitance.

A typical CV experiment of an electrode in contact with an electrolyte gives a current response resulting from both non-Faradaic and Faradaic processes. In most cases it is the Faradaic processes that are of interest in electrocatalytic investigations, therefore non-Faradaic charging current must be deducted from the overall current response so that only Faradaic current remains. In platinum electrochemistry, the double layer charging is routinely deducted from the whole current response by a rectangular baseline subtraction. Although this assumes a constant capacitance throughout the CV and is therefore a simplification, this treatment is useful in attaining electrochemical surface areas of electrode surfaces. Attempts at identifying how exactly the capacitance changes with electrode potential for a Pt{111} electrode in contact with a perchloric acid electrolyte can be found here [79, 80]. These studies illustrate the complexities in deconvoluting non-Faradaic and Faradaic processes for a reactive surface such as platinum.

The Faradaic current response for a voltammetric technique such as CV is more complex than the potential described step above. Let’s consider using CV to examine the reduction of O as before. The voltage is initiated at some value that is insignificant to reduce O, EInitial. The

voltage then heads towards EFinal, a value chosen which drives the reaction of O rapidly. This

is performed at sweep rate, ν. Upon reaching a potential value which causes species O to react, current increases exponentially; due to effect of overpotential on the rate constant for the reaction (see 1.2). After this initial exponential increase, the current continues to increase, albeit less than exponentially. A peak in the current is then observed. This peak occurs when the effect of the increasing overpotential balances with the decreasing concentration of O at the electrode surface as it is consumed. At higher potentials the current decreases, as it is now dependent upon the rate of diffusion of O to the surface (i.e. there is a large constant diffusion layer thickness). [50, 73]

For the 1 electron, reversible (i.e. a reaction which can be driven with minimal overpotential) reduction of O, the peak current (ip) is proportional to the scan rate according to the Randles-

Sevcik equation at 298K

𝑖

= 0.4463𝐹𝐴[𝑂]

√(

𝑅𝑇

)

where F is Faraday’s constant, A the electrode area, [𝑂]𝑏 the bulk concentration of O, ν the

scan rate, 𝐷_𝑂 the diffusion coefficient of O, R the gas constant and T the temperature. This illustrates a major distinction between the behaviour of Faradaic and non-Faradaic current in response to scan rate. Faradaic current has a square root dependence upon scan rate whereas capacitive charging has a linear dependency. Therefore, capacitive charging scales greater with scan rate and can mask Faradaic responses at high scan rates.

After reaching EFinal in CV, the potential is turned around. At the start of the reverse sweep a

reduction current is still observed as the potential is still sufficient to reduce species O at a diffusion limiting level. After the current reaches levels which may react R, oxidation current rises as R is consumed at the electrode surface. The processes described above happen in reverse: oxidation current increases exponentially, before peaking and then decreasing due to the consumption of R at the electrode surface.

The table and CV below, illustrate some of the diagnostic tests that may be performed in order to differentiate between reversible and irreversible (requiring significant overpotential to push the reaction) couples.

Table 1 Diagnostic tests for the form of the cyclic voltammetric responses for a reversible and irreversible couple O/R at 298K. [50]

Figure 20. Cyclic voltammogram to define the symbols used in the table above. [50]

Finally the current response for the cyclic voltammetry involving the formation of surface- bound species shall be discussed (adsorption), as this is a major feature of platinum single crystal electrochemistry discussed in the next section. The key difference between reactions

forming surface bound species and reaction which do not is that the current observed at potentials beyond the peak is different. If (as in the O/R couple) R is surface bound, at large negative potentials the current will return to zero and not to a diffusion limiting value, as the reaction is ultimately limited by the number of sites available for adsorption of R on the electrode surface. The figure below illustrates the cyclic voltammetry of the oxidation and reduction of surface bound species at the reversible and irreversible kinetic limits. The differences between these and the CV in figure 20 are obvious. In most real scenarios the current before and after the peak reaches not zero, but the capacitive charging baseline current. The table below illustrates the diagnostic tests for CV responses involving adsorption. Many differences between reactions involving adsorption and those without adsorption can be seen. For example the peak-to-peak separation, ΔEp, for a reversible couple with surface adsorption

is 0mV compared to 59 𝑛⁄ mV without surface adsorption.

Figure 21. CVs for the reversible, (a), and irreversible, (b), O/R couples. These involve the oxidation and reduction of bound species. Note that non-Faradaic charging processes are not included in this simulation. [50]

Table 2 Diagnostic tests for the form of the cyclic voltammetric responses for a reversible and irreversible couple O/R when O and/or R adsorbed at the electrode surface at 298K. [50]