3.6 Cyclic voltammetric study of the ferrocyanide / ferricyanide redox couple.

All electrochemical reactions are governed at least in part by the Nernst equation (Eqn. 3.23). This fundamental expression simply specifies the relationship between the potential of an electrode (E) and the concentrations (C) of the two species (designated O and R) involved in the redox reaction at that electrode:

O + n e- → R (3.22) E = E° + RT

nFln �CO

CR� (3.23)

Where R is the molar gas constant (8.3144 J mol–1 K–1), T is the absolute temperature (K), n is the number of moles of electrons transferred in the balanced equation, F is Faraday’s constant (96,485 C mol-1), and E° is the standard reduction potential for the reaction.

During an electrolytic reduction reaction O gains electron(s) from the electrode, generating R, at potentials (E) less than E° (i.e. at potentials where E < E°). E is the applied potential at the electrode (note: in this experiment E will be accurately controlled using the potentiostat, see later). The value of E - E° is known as the overpotential (η). As the reaction proceeds the electrode potential (E) will vary with the concentrations of reactants (CO) and products (CR) immediately adjacent to the electrode surface according to the Nernst equation. The current (i) generated, due to the flow of electrons, is a quantitative measure of the rate of electrolysis (non-spontaneous oxidation or reduction of a chemical species) at the electrode surface.

Figure 1. Electrolytic reduction at an electrode surface (O + n e- → R).

The Butler-Volmer equation (Eqn. 3.24) describes the relationship between the variables for current (i), potential (E) and concentration (C).

𝑖𝑖𝑛𝑛𝑛𝑛𝑛𝑛

= 𝑘𝑘°{𝐶𝐶𝑂𝑂𝑒𝑒𝑒𝑒𝑒𝑒(−∝ ∅) − 𝐶𝐶𝑅𝑅𝑒𝑒𝑒𝑒𝑒𝑒(1 −∝ ∅)} (3.24)

Where ∅ = nFη/RT, k° is the heterogeneous rate constant, α is the transfer co-efficient (normally ca. 0.5) and A is the area of the electrode. In simple terms this equation states that the rate of electron transfer (measurable by the flow of current) from electrode to reactant (O + n e- → R) will increase as the overpotential (η) becomes increasingly negative (i.e. as the electrode potential (E) moves negatively away from E°). Conversely, the rate of electron

transfer from the reactant to the electrode (R → O + n e-) will increase as the overpotential (η) becomes increasingly positive. Normally current is measured from the point of view of the electrode. ‘Negative’ current is generated if the electrode supplies electrons to a reactant, as in the case of a reduction reaction (O + n e- → R), whilst ‘positive’ current is generated if the electrode gains electrons from a reactant, as in the case of an oxidation reaction (R → O + n e-).

At some point the current (i) resulting from the redox process (known as the faradaic current) will become limited by the rate at which the reactant can diffuse to the electrode and/or the rate that the product diffuses away from the electrode. In this case, the material flux (j) at the electrode–solution interface dictates the maximum current generated, described by Fick’s law of diffusion:

𝑗𝑗 = 𝑛𝑛𝑛𝑛𝑛𝑛 𝐶𝐶−𝐶𝐶′𝛿𝛿

(3.25)

where j is the flux, D is the diffusion co-efficient, C is the concentration in the bulk solution, Cʹ is the concentration immediately adjacent to the electrode and δ is the Nernst diffusion layer thickness. In simple terms Fick’s law of diffusion states that the reactant (and product) will diffuse from regions of high concentration to regions of low concentration at a certain rate (D). This process gives rise to the formation of a diffusion layer (δ) at the electrode surface. The thickness of the diffusion layer will increase with time (t) as the electrolysis reaction proceeds as depicted in Figure 2.

Figure 2. Formation of the Nernst diffusion layer.

The rate (D) at which an electroactive species diffuses toward or away from the electrode surface is specific for each individual chemical species. In this experiment, the diffusion co-efficient (D) of electroactive species, [FeCN6]3-/4- will be determined using an electrochemical technique known as ‘Cyclic Voltammetry’ (CV). A ‘potentiostat’ is used to perform the CV experiment. The potentiostat permits the user to accurately control the potential difference (ΔE) between two electrodes (working electrode and reference electrode), whilst a third electrode, known as the counter electrode, is used to complete the circuit (Fig. 3a).

In a CV experiment the voltage applied to the working electrode is scanned linearly from an initial value, E1, to a predetermined limit, E2 (known as the switching potential), where the

direction of the scan is reversed (Fig. 3b). The current response is plotted as a function of the applied potential producing a cyclic voltammogram (Fig. 3c).

Figure 3. (a) Experimental setup, (b) the potential waveform applied to an electrode during a typical cyclic voltammetric experiment and (c) a typical cyclic voltammogram.

Figure 4. A typical cyclic voltammogram for a reversible redox couple showing parameters Epa, Epc, Ipa and Ipc. Solid arrows indicate direction of scan.

The parameters of greatest interest for a reversible cyclic voltammogram are the anodic peak potential (Epa), the cathodic peak potential (Epc), the anodic peak current (ipa), and the cathodic peak current (ipc) as displayed in Fig. 4. The redox potential (E°ʹ) of the reversible redox couple can be evaluated according to:

E°ʹ = Epa + Epc2

(3.26)

The peak separation (∆Ep) for a reversible, ‘Nernstian’, redox couple provides information about the number of electrons (n) transferred per mole.

∆𝐸𝐸𝑝𝑝 = (𝐸𝐸𝑝𝑝𝑝𝑝 − 𝐸𝐸𝑝𝑝𝑝𝑝) = 0.0592 𝑛𝑛

(3.27)

Quantitative information regarding the concentration of the species undergoing electrolysis is obtained from the peak height (ip) according to the Randles-Sevcik equation:

ip = (2.69 × 105) n3/2 A D1/2 C∗ v1/2 (3.28)

where ip (amperes) is the peak current associated with the anodic (ipa) or cathodic (ipc) scan, n is the number of electrons transferred, A (cm2) is the geometric area of the electrode, C∗ (mol cm−3) is the bulk concentration of species, D (cm2 s−1) is the diffusion coefficient of species and v (V s−1) is the experimental scan rate (dE/dt).

The most straightforward method for determining the diffusion coefficient (D) is to measure the peak current (ip) at several scan rates (v) and then plot ip as a function of v1/2. The slope of the best-fit line can then be used to calculate D:

𝑛𝑛 = (𝑠𝑠𝑠𝑠𝑠𝑠𝑝𝑝𝑠𝑠)2

𝑛𝑛3 (2.69 ×105 𝑛𝑛 𝐶𝐶∗)2 (3.29)

In this experiment you will use CV to determine the redox potential (E°ʹ) and diffusion co-efficients for the ferrocyanide / ferricyanide reversible redox couple:

[Fe(CN)6]3- + e- ⇌ [Fe(CN)6]4- (3.30)

As the peak current (ip) is proportional to concentration (C*) of the electro-active species undergoing electrolysis, the unknown concentration of a ferricyanide solution will also be determined.

Experimental:

1. Prepare a 5 mM standard solution of K3Fe(CN)6 (Mr 329.24 g mol-1) in 0.1 M KNO3 solution using the 100 mL volumetric flask provided.

2. Polish the working electrode (3mm diameter glassy carbon) using the alumina slurry polishing pad, rinse well with DI water and dry.

3. Fill the electrochemical cell with about 8 to 10 mL of the 5 mM solution. 4. Place the working electrode, reference electrode (Ag/AgCl in 1 M KCl) and counter

electrode into the electrochemical cell. Ensure that the electrodes are suspended in solution i.e. that they are not touching the bottom of the cell (see Fig. 4).

Figure 5. Experimental parameters and software functions.

5. Connect the potentiostat cables to the electrodes (red: working electrode, blue: reference electrode and black: counter electrode).

6. Double click on PSTrace 4.6 to open the user interface software. From within the program open the ‘CV_setup’ file located on desktop. Ensure that the parameters match those displayed in Figure 5.

7. Ensure that the software is connected to the potentiostat (EmStat3+). Click on the ‘Play’ button to initiate a scan at 0.1 V s-1. The resulting voltammogram should be similar in shape to that depicted in Fig. 4.

8. Create a personal folder on desktop. Save scan in folder and export to Excel. Save Excel file separately.

9. Repeat step 8 at the following scan rates: 0.2 V s-1, 0.3 V s-1, 0.4 V s-1, 0.5 V s-1.

Results analysis:

Using Excel:

1. Plot the scan at 0.1 Vs-1 and evaluate Epa and Epc from graph. 2. Plot i) ipa vs. v1/2, and ii) ipc vs. v1/2 for each of the scan rates (0.1 V s-1 to 0.5 V s-1)

and evaluate the slope of the best-fit line (note: plot ipc currents as positive values).

Questions:

1. Calculate the redox potential (E°ʹ) for the ferrocyanide / ferricyanide redox couple. Compare the value of ΔEp that you measured to that predicted by the Nernst equation. Is this what you expected? Account for any deviations observed.

2. Calculate the diffusion co-efficients (D) for ferrocyanide (using ipa vs. v1/2) and ferricyanide (using ipc vs. v1/2). Be careful with units! Remember molar concentrations are expressed as mol dm-3. Are the diffusion co-efficient values similar? If so, what does this signify?