B3a Rotating Disk and Ultramicroelectrode Voltammetry

If the speed of the electrochemical experiment is so fast that the electron transfer step does not remain at equilibrium, the shapes of steady state voltammograms are controlled by kinetics as well as diffusion. A simple electrode reaction with slow kinetics with respect to the measurement time, for example,

Figure 11.7 Steady state voltammogram at 7 mV s 1 of 1 mM ferrocene at a carbon microdisk electrode of 6 jam radius in acetonitrile with no added supporting electrolyte. The solid line shows experimental data with points computed from regression analysis using the model in Table 11.4. The dashed line was computed after mathematical removal of iRu from the data. (Adapted with permission from [6], copyright by VCH.)

Figure 11.7 Steady state voltammogram at 7 mV s 1 of 1 mM ferrocene at a carbon microdisk electrode of 6 jam radius in acetonitrile with no added supporting electrolyte. The solid line shows experimental data with points computed from regression analysis using the model in Table 11.4. The dashed line was computed after mathematical removal of iRu from the data. (Adapted with permission from [6], copyright by VCH.)

can be characterized by the apparent standard heterogeneous electron transfer rate constant, k°' in cm s"1, and a, the electrochemical transfer coefficient [1, 2],

The electrochemical transfer coefficient is a number between 0 and 1, which is related to the symmetry of the energy barrier to electron transfer. A symmetric energy barrier is characterized by a = 0.5. The apparent standard heterogeneous electron transfer rate constant (k°') is characteristic of the rate at which electrons are exchanged between electrodes and elec-troactive compounds at the formal potential E°'. The value of k°' is called an apparent value because it is highly dependent on experimental conditions such as type of electrolyte, electrode materials, method of surface preparation, electrode contaminants, and surface funtionality. Values of A:0' > 10 cm s 1 are considered to be very large and are characteristic of electrochemi-cally reversible systems, except for exceeding short experimental time frames. Values smaller than about 10 6 cm s"1 denote very slow electron transfer reactions.

A common model can be used for rotating disc voltammetry (RDV) and ultramicroelectrode steady state voltammetry when the electrode reactions are controlled by a mixture of electron-transfer kinetics and diffusion. The model is summarized in Table 11.5. The models for the two techniques differ in the definitions of the mass transfer coefficients and the limiting currents. Limiting currents can be used to estimate the diffusion coefficients needed for computing k°'.

Table 11.5 Models for Obtaining Electron Transfer Rate Constants from RDV and Ultramicroelectrode Voltammetry

Assumptions: Rotation disk or microelectrode voltammogram controlled by electrode kinetics and diffusion; a does not depend on E Regression equation:

i = i'i/(l + 9+ k'ff) + b4E + b5\ e = exp[(E - E°')(F/RT)\, k' = kjk°' (reductions) ff = exp[(£ - E° )(F/RT)a] (reductions)

8 = exp[-(£ - E0')(F/RT)\\ k' = kjk°' (oxidations) 6' = exp[-(£ - E°')(F/RT)a] (oxidations) R = gas constant, F = Faraday's constant, T = temperature in Kelvins; k,„ = mass transfer coefficient

Regression parameters: Data:

i'i E°' a k' b4 b5 i vs. E Special instructions: Keep (F/RT) fixed; definitions of km depends on method: RDV km = Do/So; k°' = DtJSok' and <, = 0.62nFADa3(Dll2v~ "6C; So = 1.61 Di'V'2 v 1/6

steady state disk microelectrode; approximately: k°' = 1.226 and i'i = 4nFD0Cr r = microdisk radius; D0 = diffusion coefficient of reactant; S0 = diffusion layer thickness; a> = angular velocity; v = kinematic viscosity; obtain Da values from limiting currents [1, 2]

The model in eq. (11.5) has been used for RDV on conventional solid disk electrodes for a number of redox couples with intermediate values of k°'. Results have been summarized briefly [5], A good signal to noise ratio is essential for the success of the method, because background currents on solid electrodes can be large and have irregular shapes.

The model's use is now illustrated in more detail for oxidation of ferrocy-anide at a carbon microdisk electrode of radius 6 /¿m. A graphical representation of regression analysis onto the model in Table 11.5 show a good fit to the data (Figure 11.8a). The deviation plot was random (Figure 11.8b). Although k°' will depend on the method of electrode pretreatment, results agree well with other determinations of k°' for the ferri/ferrocyanide redox couple on similarly pretreated carbon electrodes (Table 11.6). The upper limit of k°' estimations with this method is about 1 cm s"1 for electrodes with radii of 1-10 fim.

E, VOLT

Figure 11.8 (a) Steady state voltammogram at 10 mV s [ of 0.5 m/W potassium ferrocyanide at a carbon microdisk electrode of 6 /nm radius in 0.5 M KN03. The solid line shows experimental data with points computed from regression analysis using the model in Table 11.5. (b) The residual plot from the analysis in (a). (Reproduced with permission from [6], copyright by VCH.)

Table 11.6 Results of Regression Analysis for Ferri/Ferrocyanide Couple Compared to Published Data for Comparably Pretreated Surfaces

Method

106Z>, cm2!"1

102k°', cm s"1

E°', V/SCE

Electrode/ electrolyte

Reference

c disk"

7.0

2.3

0.189 ± 0.004

6 /xm<7

[6]

Microelectrode

0.5 M KNOj

CV

7.6C

Pt, 1 M KC1

[8]

CV

3

0.21

GCd, 2M KC1

[9]

NPV on GC"

6.9 ± 0.5

3.0 ± 0.9

0.218 ± 0.007

0.5 M KNOj

[10]

electrode

a Electrochemically pretreated carbon microdisk, steady state conditions. b Conventionally polished glassy carbon using 1.1 mM potassium ferricyanide in 0.5 M KN03 (extensively polished and cleaned glassy carbon may give values 3 to 4 times larger than those quoted for ferrocyanide, see [11].

c M KC1 has viscosity within 2% of 0.5 M KN03, and should give comparable D values. d Conventionally polished and electrochemically pretreated.

a Electrochemically pretreated carbon microdisk, steady state conditions. b Conventionally polished glassy carbon using 1.1 mM potassium ferricyanide in 0.5 M KN03 (extensively polished and cleaned glassy carbon may give values 3 to 4 times larger than those quoted for ferrocyanide, see [11].

c M KC1 has viscosity within 2% of 0.5 M KN03, and should give comparable D values. d Conventionally polished and electrochemically pretreated.

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