CHAPTER 3

ELECTROCHEMISTRY

3.1 The Nernst Equation

The Nernst equation describes the fundamental relationship between the potential applied to an electrode and the concentration of the redox species at the electrode surface.¹ If an electrode is at equilibrium with the solution in which it is immersed, the electrode will have a potential, invariant with time, which is thermodynamically related to the composition of the solution. In solution, species O is capable of being reduced to R at the electrode by the following reversible electrochemical reaction.

The Nernst equation relates the potential, E, which is applied to the electrode and the concentrations of species O and R at the electrode surface:

where E = potential applied to electrode

E° ¢ = formal reduction potential of the couple vs. reference electrode

n = number of electrons

[O] = surface concentration of species O

[R] = surface concentration of species R.

The variation in the ratio of the [O] to [R] as a function of potential is the basis of all voltammetric methods. The Nernst equation describes the relationship for reversible equations. In other words, those are systems for which the electrode reaction in the

O + ne- Û R is rapid in both directions. Surface concentration responds instantaneously to any changes in potential (Table 2).²

3.2 Cyclic Voltammetry

Early contributions to cyclic voltammetry were made by investigators including Randles,³ Nicholson and Shain,^4,5 and Kalthoff and Tomsicek.⁶ Cyclic voltammetry is one of the most versatile electroanalytical techniques for the study of electroactive species. Cyclic voltammetry has the capability for rapidly observing redox behavior over a wide potential range. Cyclic voltammetry involves the cycling of the potential of an electrode, which is immersed in an unstirred solution, and measuring the resulting current. The controlling potential applied across these two electrodes is an excitation signal. For cyclic voltammetry, the excitation signal is a linear potential scan with a triangular waveform⁸ (Figure 14). A cyclic voltammogram is obtained by measuring the current at the working electrode during the potential scan. The voltammogram is a display of current versus potential.⁷

Figure 15 is a cyclic voltammogram of 6 mM K₃Fe(CN)₆ in 1 M KNO₃. The scan was initiated at 0.80 V (applied at a) vs. SCE in negative direction at 50 mV/s. The area of the platinum electrode is 2.54 mm². The cathodic current at b to due to the electrode process:

The cathodic current rapidly increases (b-d) until the concentration of [Fe(CN)₆]^3- at the electrode surface approaches zero, and the current peaks at d. The current then decreases (d-g) as the solution surrounding the electrode is depleted of [Fe(CN)₆]^3-. The scan direction is switched to positive at -0.15V (f) for the reverse scan. Anodic current is generated (i-k) when the electrode becomes a sufficiently strong oxidant, and [Fe(CN)₆]^4- can be oxidized by the electrode process:

The anodic current increases until the surface concentration of [Fe(CN)₆]^4- approaches zero and the current peaks (j). The current decays (j-k) as the solution surrounding the electrode is depleted of [Fe(CN)₆]^4-. The magnitudes of parameters including the anodic peak current, (i_pa), cathodic peak current (i_pc), anodic peak potential (E_pa), and cathodic peak potential (E_pic) are elucidated from the cyclic voltammogram.

The formal reduction potential E° ¢ for an electrochemically reversible couple is:

For a reversible redox couple, the number of electrons transferred in the electrode reaction can be determined by the separation between the peak potentials:

The Randles-Sevcik equation for the forward sweep of the first cycle is:

where i_p = peak current, A

n = electron stoichiometry

A = electrode area, cm²

D = diffusion coefficient, cm²/s

C = concentration, mol/cm³

v = scan rate, V/s

Furthermore, i_p increases with v^1/2 and is directly proportional to concentration. This relationship becomes particularly important in the study of electrode mechanisms. The ratio of i_pa to i_pc should be close to one; however, chemical reactions coupled to the electrode process can significantly alter the ratio of peak currents:

3.3 Instrumentation

In cyclic voltammetry, a potentiostat applies a potential to the electrochemical cell and a current to a voltage converter which measures the resulting current. The current is displayed on a recorder as a function of the applied potential (Figure 16).² Operational amplifiers are circuit elements utilized for enforcing a controlled potential at an electrode or for controlling the current through a cell (Figure 17).⁸ The characteristics of an ideal operational amplifier most importantly include:

1. No current through amp...a high input impedance (Z)

ideally Z = ¥

2. E(-) = E (+) This is only true when the op amp is balance

Current loops cause ground problems when a series of instruments are connected to ground separately (use of three-prong plugs). Current loop problems can be eliminated when a series of instruments are connected to ground through one common source (use of three-plug adapters for all instruments expect one). See Figure 18.

Figure 19 illustrates the basic potentiostat used for cyclic voltammetry which incorporates a three-electrode configuration. The potentiostat applies the desired potential between a working electrode and a reference electrode. The working electrode is the place where the reaction being studied takes place. The auxiliary electrode, typically platinum wire, generates the current (polarized) required to sustain electrolysis at the working electrode. The potential of the working electrode is controlled versus a reference electrode such as a Ag/AgCl electrode (Figure 20) which maintains constant potential (polarized).

The half cell constructed may be represented as:

for which the half-reaction is:

The potential of the reference electrode is measured before and after each experiment. During an experiment, the potential of the reference electrode should vary no more than +10mV. The potential of the reference electrode can be easily measured by immersing the reference electrode in a buffer solution of known pH which is saturated with quinhydrone (Figure 21).

quinhydrone = QNH + 2H⁺ + 2e^- Û

for QNH:

and

or

3.4 Ohmic Potential Drop

Also known as iR drop, ohmic potential drop is potential drop due to solution resistance-the difference in potential required to move ions through the solution. The major effects of iR drop in cyclic voltammetry include shift in peak potential, decrease in magnitude of current, and increase in peak separation (Figure 22).⁹ The reactions of interest occur at the surface of the working electrode. Controlling the interfacial potential, specifically, the potential across the interface between the surface of the working electrode and the solution, is imperative.¹⁰ The iR drop effects will become more evident as the scan rate is increased due to increasing current. However, increasing peak separation with increasing scan rate is also characteristic of a quasi-reversible process-the rate of the heterogeneous electron transfer is slow compared to the time scale of the experiment.¹¹

The iR drop or kinetic effects can be distinguished by scan rate studies performed at two different concentrations (the difference should be at least an order of magnitude).¹² The increase in peak separation will be the same if due solely to electron transfer kinetics. The increase in peak separation will be less at the lower concentration if due to iR drop. The iR drop can be minimized by using a three-electrode system. By adding a high concentration of fully dissociated electrolyte to the solution, conductivity will be increased, thereby reducing resistance. Furthermore, the reference electrode tip should be in close proximity to the working electrode surface.

The current can also be decreased in an effort to minimize iR drop.¹³ In a reversible process peak current is directly proportional to the square root of the scan rate; therefore, the use of low scan rates will minimize the current. However, higher scan rates are required for calculation of heterogeneous and homogeneous rate constants. For a reversible process, peak current is also proportional to concentration, so concentrations on the order of 10^-4-10^-3 M analyte solution should be used for cyclic voltammetry. Finally, decreasing the electrode surface area will also serve to minimize iR drop effects. Ohmic potential drop can have a significant influence on electrochemical measurements, and these effects need to be considered during the interpretation of electrochemical data.¹⁴

3.5 Mass Transfer

Mass transfer is the movement of material from one location to another in solution.¹⁵ In electrochemical systems, three modes of mass transport are generally considered including diffusion, convection, and migration. Diffusion removes concentration gradients by the movement of material from a high concentration to a low concentration. Migration is the movement of charged species due to a potential gradient. Electrolysis is carried out with a large excess of inert electrolyte in the solution so the current of electrons through the external circuit can be balanced by the passage of ions through the solution between the electrodes, and a minimal amount of the electroactive species will be transported by migration. Convection is the movement of species due to mechanical forces and usually can be eliminated on a short time scale.

A concentration-distance profile² is shown in Figure 23 for voltammetry of a planar electrode immersed in a stirred solution of species O (1mM). The x-axis is distance from the electrode into solution, and the y-axis is concentration. The vertical line at distance = 0 is the interfacial boundary between the electrode and the solution. The dashed horizontal line is the concentration of R in solution, C_R=O. The continuous horizontal line is the concentration of O in solution, C₀ = 1 mM. Three regions of solution flow can be identified. A thin layer of stagnant solution having a discrete thickness d , called the Nernst diffusion layer, is present immediately adjacent to the electrode surface. Turbulent flow comprises the bulk of solution. Laminar flow, a nonturbulent flow in which adjacent layers slide by each other parallel to the electrode surface, occurs in a region between the Nernst diffusion layer and the solution bulk. Figure 23a illustrates the homogeneous concentration of O and R throughout the solution and up to the electrode surface. Either no potential has been applied or a potential has been applied which is sufficiently positive of E ¢ ° _O,R such that C_O/C_R > 1000. Figure 23b illustrates the conditions when E = E ¢ ° _O,R and equal concentrations of O and R are present at the electrode surface in order to satisfy the Nernst equation. Figure 23c profiles the conditions when a potential has been applied which is sufficiently negative such that C_O/C_R < 0.0001, and effectively, the concentration of O at the electrode surface is zero. The curved lines denote the gradual transition between stagnant and flowing solution.

3.6 The Electrical Double-Layer

The changing arrangement of ions, solvent, and electrons in the interphasial region near the electrode surface has been the focus of considerable investigation.¹⁶ The electrical double-layer is associated with an ideally polarized electrode which is an electrode in which no charge transfer can occur regardless of the potential imposed by an external voltage source. The specific nature of the structure and the interactions of the electrical double-layer should be considered in the interpretation of electroanalytical data. Various models have been proposed describing the interphasial region near the electrode surface.

Helmholtz envisaged a "double layer" in which the excess charge on the metal would be neutralized by a monomolecular layer of ions of opposite charge to that on the metal phase.¹⁷ This model did not account for the possible specific adsorption or random motion of ions. See Figure 24.

The Guoy-Chapan "diffuse-layer model" was derived depicting a distribution of net charge near the electrode surface which diminishes as the interfacial region stretches toward the bulk (Figure 25). The random motion of ions results in a diffuse layer of charge in which the concentration of counter ions is greatest next to the electrode surface and decreases progressively until a homogeneous distribution appears in the bulk electrolyte. Specific adsorption of desolvated ions at the electrode is weak; therefore, the adsorbed inner layer of negative charge only partially shields the positive charge at the electrode. As a result, a layer of solvated anions is present adjacent in the diffuse layer.

Finally, the Gouy-Chapman-Stern model was proposed which accounts for the finite size of ions (Figure 26). Specifically adsorbed anions which are desolvated maintain direct contact with the electrode surface in the inner Helmholtz layer. Electrostatic and chemical interactions between the electrode and the ion govern the nature of specific adsorption. Furthermore, potential profiles as well as the kinetics of interfacial interactions may be significantly altered as the result of specific adsorption. The inner Helmholtz plane (IHP) is considered to pass through the center of specifically adsorbed ions. The metal-ion interactions are strong, and the specifically adsorbed charge may exceed the positive charge on the electrode effectively establishing a layer of solvated cations adjacent in the outer Helmholtz layer. The outer Helmholtz plane (OHP) is considered to be the approximate site for electron transfer. Nonspecifically adsorbed ions which have their primary solvation shells generally reside in the diffuse layer extending some distance from the electrode surface. The thickness of the diffuse layer is dependent upon ionic strength of the buffer, and in dilute electrolyte, the diffuse layer can extend to 100Å. The nature of the diffuse layer can have a significant impact on the rate of electron-transfer since the actual potential felt by a reactant close to the electrode is dependent upon it. Interfacial interactions must be considered in the treatment of electrochemical data even though the exact interfacial structure near the electrode surface is not known.^18,19

3.7 Ferricyanide

A three-electrode potentiostat with a Lucite cell of conventional design was used for all experiments with provision for nitrogen bubbling through a solution volume of approximately 1 mL. The working electrode was a tin-doped indium oxide film deposited on glass (Donnelly Corporation). A new electrode was used for each set of determinations. Pretreatment and cleaning of the working electrode and cell involved successive ultrasonications in Alconox (5 minutes), ethanol (5 minutes), and distilled water (5 minutes). The area of the working electrode was approximately 0.3 cm² in all experiments. A Ag/AgCl reference electrode and a platinum auxiliary electrode completed the cell. The reference electrode was calibrated against saturated quinhydrone in the appropriate buffer before each experiment.

All determinations were carried out under nitrogen (Grade 4.5 from Airco, Inc.) to prevent oxygen interference. The buffer and sample solutions were purged with nitrogen for approximately 10 minutes prior to the beginning of a new series of determinations. Between each scan, initial conditions at the electrode were restored by gently stirring the solution and then allowing approximately two minutes for the solution to come to rest before obtaining the cyclic voltammogram. All scans were initiated in the negative direction. The initial potential was set at 0.80 V and the scan limits at 0.80V and -0.12V. A background of the supporting electrolyte was obtained prior to each experiment. All chemicals were ACS reagent grade and used as received. All water used was purified with a Milli RO-4/Milli-Q system.²⁰ Graphs were drawn with a Hewlett-Packard x-y recorder (model 7015B) which was interfaced to the potentiostat.

The effect of scan rate (v) on cyclic voltammograms of 1 mM K₃Fe(CN)₆ in 0.1M KNO₃ has been observed (Figure 27) at 10, 20, 50, 100, and 200 mV/s. The reversibility of the electrochemical system is indicated by the separation of the peak potentials (D Ep) which is independent of the scan rate v. According to the Randles-Sevcik equation, i_pa and i_pc increase as v^1/2 (Figure 28). A plot of this equation will yield a straight line, the slope of which can be used to determine the diffusion coefficient (D in cm²/s).

Concentration affects the magnitude of the peak current. Figure 29 displays cyclic voltammograms of 6, 8, 10, and 20 mM K₃Fe(CN)₆ in 0.1M KNO₃ at 20mV/s. Figure 30 illustrates that peak current is directly proportional to concentration.

As reported in the literature, a formal potential is a working number that is dependent on the conditions of the experiment. The effect of supporting electrolyte on the cyclic voltammograms of 4 mM K₃Fe(CN)₆ in 1M Na₂SO₄ and 1M KNO₃ is shown in Figure 31.

3.8 References

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New York: John Wiley & Sons, 1980.

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12. Oldman, K.B. Anal. Chem. 1969, 41, 1904-1905.

13. Oldman, K.B. Anal. Chem. 1972, 44, 196-198.

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15. Bockris, J.O’M.; Khan, S.U. Surface Electrochemistry: A Molecular Level

Approach. New York: Plenum Press, 1993.

16. Bowden, E.F.; Hawkridge, F.M.; Blount, H.N. Comprehensive Treatise of Electroanalytical Chemistry. Vol. 10 (S. Srinivasan, Y.A. Chizmadshev, J. O’M. Bockris, B.E. Conway, E. Yeager, Eds.) New York: Plenum Press, 1985.

17. Greef, R.; Peat, R.; Peter, L.M.; Pletcher, D.; Robinson, J. Instrumental Methods in Electrochemistry. New York: John Wiley & Sons, 1985.

18. Riger, P.H. Electrochemistry. New York: Chapman & Hall, 1994.

19. Riley, T.; Tomlinson, C. Principles of Electroanalytical Methods. New York: John Wiley & Sons, 1987.

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J. Chem. Ed. 1983, 60, 772-776.