Introduction.

This experiment is offered as an alternative Lab #4. If you find this experiment more interesting and at least another student who shares your choice, you should discuss it with the instructor on the last day of your Lab #1 or #2 whichever comes last. No switching will be allowed after that.

Objective: In this lab you will study the cyclic voltametry technique and measure redox potentials of a few compounds.

Cyclic voltammetry is the most widely used technique for acquiring qualitative information about electrochemical reactions. The power of cyclic voltammetry results from its ability to rapidly provide considerable information on the thermodynamics of redox processes and the kinetics of heterogeneous electron-transfer reactions, and on coupled chemical reactions or adsorption processes. Cyclic voltammetry is often the first experiment performed in an electroanalytical study.  In particular, it offers a rapid location of redox potentials of the electroactive species, and convenient evaluation of the effect of media upon the redox process.

Potential Step Voltammetry

Let us begin by discussing what happens near an electrode in a polar solution (water or other highly polar solvent) with high concentration of a background electrolyte (an electrochemically inert salt such as NaCl or tetra butylammonium perchlorate, TBAP; usually added in high concentration ~0.1M to allow the current to pass). If an analyte or reactant , say Fe³⁺(aq), is present at a low concentration (ca. 10^-3 M), its distribution near the electrode surface is initially uniform (see picture to the right). If at time zero a voltage sufficient to initiate electrochemical reaction is applied, a current starts flowing due to the reaction:

Fe³⁺(aq) + e^-(from the electrode) --(k_red)--> Fe²⁺(aq)

The concentration of Fe³⁺(aq) near the electrode will gradually decline and thus the current will decrease in time as well (see Figure to the right).

d[Fe³⁺]dt = Dd²[Fe³⁺]dt²                               (1)

i_c = - nFAk_red[Fe³⁺]_surface                              (2)

|i_c| = nFAk_red[Reactant]_bulk(D/pt)^1/2              (3)

Linear Sweep Voltammetry (LSV)

Now let us assume that the voltage is changed from value V₁ (where electrochemical reaction of interest is thermodynamically unfavorable) to a value V₂ linearly increasing in time (see Figure to the left), opposite to an abrapt change considered above. The voltage scan rate (n) is calculated from the slope of the line. Clearly by changing the time taken to sweep the range we alter the scan rate. The characteristics of the linear sweep voltammogram recorded depend on a number of factors including:

-The rate of the electron transfer reaction(s)
-The chemical reactivity of the electroactive species
-The voltage scan rate, n

In LSV measurements the current response is plotted as a function of voltage rather than time, unlike potential step measurements. For example if we return to the Fe³⁺/Fe²⁺ system

Fe³⁺ + e^- --> Fe²⁺

then the following voltammogram would be seen for a single voltage scan using an electrolyte solution containing only Fe³⁺ resulting from a voltage sweep (see Figure to the right). The scan begins from the left hand side of the current/voltage plot where no current flows. As the voltage is swept further to the right (to more reductive values) a current begins to flow and eventually reaches a peak before dropping. To rationalise this behaviour we need to consider the influence of voltage on the equilibrium established at the electrode surface. If we consider the electrochemical reduction of Fe³⁺ to Fe²⁺, the rate of electron transfer is fast in comparsion to the voltage sweep rate. Therefore at the electrode surface an equilibrum is established identical to that predicted by thermodynamics. You may recall from equilibrium electrochemistry that the Nernst equation

E = E^o + RT/nF ln([Fe³⁺]/[Fe²⁺])                          (4)

predicts the relationship between concentration and voltage (potential difference), where E is the applied potential difference and E^o is the standard electrode potential. So as the voltage is swept from V₁ to V₂ the equilibrium position shifts from no conversion at V₁ to full conversion at V₂ of the reactant at the electrode surface.
The exact form of the voltammogram can be rationalised by considering the voltage and mass transport effects. As the voltage is initially swept from V₁, the equilibrium at the surface begins to alter and the current begins to flow: The current rises as the voltage is swept further from its initial value and the equilibrium position is shifted further towards products (Fe²⁺), thus converting more reactant. The peak occurs, since at some point the diffusion layer has grown sufficiently above the electrode so that the flux of reactant to the electrode is not fast enough to satisfy that required by the Nernst equation. In this situation the curent begins to drop just as it did in the potential step measurements. In fact the drop in current follows the same behaviour as that predicted by the Cottrell equation. The above voltammogram was recorded at a single scan rate. If the scan rate is altered the current response also changes. The figure on the left shows a series of linear sweep voltammograms recorded at different scan rates for the same solution containing only Fe³⁺. Each curve has the same form but it is apparent that the total current increases with increasing scan rate. This again can be rationalised by considering the size of the diffusion layer and the time taken to record the scan. Clearly the linear sweep voltammogram will take longer to record as the scan rate is decreased. Therefore the size of the diffusion layer above the electrode surface will be different depending upon the voltage scan rate used. In a slow voltage scan the diffusion layer will grow much further from the electrode in comparison to a fast scan. Consequently the flux to the electrode surface is considerably smaller at slow scan rates than it is at faster rates. As the current is proportional to the flux towards the electrode the magnitude of the current will be lower at slow scan rates and higher at high rates. This highlights an important point when examining LSV (and cyclic voltammograms), although there is no time axis on the graph the voltage scan rate (and therefore the time taken to record the voltammogram) do strongly effect the behaviour seen.
A final point to note from the figure is the position of the current maximum, it is clear that the peak occurs at the same voltage and this is a characteristic of electrode reactions which have rapid electron transfer kinetics. These rapid processes are often referred to as reversible electron transfer reactions

For the reactions that are 'slow' (so called quasi-reversible or irreversible electron transfer reactions) the voltage applied will not result in the generation of the concentrations at the electrode surface predicted by the Nernst equation. This happens because the kinetics of the reaction are 'slow' and thus the equilibria are not established rapidly (in comparison tothe voltage scan rate). The figure on the left shows a series of voltammograms recorded at a single voltage sweep rate for different values of the reduction rate constant (k_red) In this situation the overall form of the voltammogram recorded is similar to that above, but unlike the reversible reaction now the position of the current maximum, E_p) shifts depending upon the reduction rate constant (and also the voltage scan rate). This occurs because the current takes more time to respond to the the applied voltage than the reversible case.

Cyclic voltammetry consists of scanning linearly the potential of a stationary working electrode, using a triangular potential waveform (see Figure on the right). Depending on the information sought, single or multiple cycles can be used. During the potential sweep, the potentiostat measures the current resulting from the applied potential. The resulting plot of current vs. potential is termed a cyclic voltammogram. The cyclic voltammogram is a complicated, time-dependent function of a large number of physical and chemical parameters.

Figure to the right illustrates the expected response of a reversible redox couple during a single potential cycle. Here it is assumed that only the oxidized form O is present initially. Thus, a negative-going potential scan is chosen for the first half cycle, starting from a value where no reduction occurs. As the applied potential approaches the characteristic E° for the redox process, a cathodic current begins to increase, until a peak is reached. After traversing the potential region in which the reduction process takes place, the direction of the potential sweep is reversed. 

O + e^- --> R

During the reverse scan, R molecules (generated in the forward half cycle, and accumulated near the surface) are reoxidized back to O and an anodic peak results.

R --> O + e^-

The characteristic peaks in the cycle voltammogram are caused by the formation of the diffusion layer near the electrode surface. These can be best understood by carefully examining the concentration-distance profiles during the potential sweep. For example, Figure illustrates four concentration gradients for the reactant and product at different times corresponding to (B) the initial potential value, (D) and (G) to the formal potential of the couple (during the forward and reversed scans, respectively), and (C) to the achievement of a zero reactant surface concentration. Note that the continuous change in the surface concentration is coupled with an expansion of the diffusion layer thickness (as expected in quiescent solutions). The resulting current peaks thus reflect the continuous change of the concentration gradient with the time. Hence, the increase to the peak current corresponds to the achievement of diffusion control, while the current drop (beyond the peak) exhibits a t ^-1/2 dependence (independent of the applied potential).  For the above reasons, the reversal current has the same shape as the forward one. The use of ultramicroelectrodes – for which the mass transport process is dominated by radial (rather than linear) diffusion – results in a sigmoidal-shaped cyclic voltammogram.

Data Interpretation

         The cyclic voltammogram is characterized by several important parameters. Four of these observables, the two peak currents and two peak potentials, provide the basis for the diagnostics developed by Nicholson and Shain (2) for analyzing the cyclic voltammetric response.

Reversible Systems

The peak current for a reversible couple (at 25°C), is given by the Randles-Sevcik equation:

              i_p = (2.69x10⁵) n^3/2ACD^1/2v^1/2                         (5)

where n is the number of electrons, A the electrode area (in cm²), C the concentration (in mol/cm³), D the diffusion coefficient (in cm²/s), and v the scan rate (in V/s).  Accordingly, the current is directly proportional to concentration and increases with the square root of the scan rate. The ratio of the reverse-to-forward peak currents, i_pr/i_pf , is unity for a simple reversible couple. This peak ratio can be strongly affected by chemical reactions coupled to the redox process. The current peaks are commonly measured by extrapolating the preceding baseline current. The position of the peaks on the potential axis (E_p) is related to the formal potential of the redox process.  The formal potential for a reversible couple is centered between E_pa and E_pc:

                   E° =   (E_pa + E_pc)/2                                                      (6)

The separation between the peak potentials (for a reversible couple) is given by:

                  DE_p = E_pa - E_pc = 59mV/n                                              (7)

Thus, the peak separation can be used to determine the number of electrons transferred, and as a criterion for a Nernstian behavior. Accordingly, a fast one-electron process exhibits a DE_p of about 59 mV.Both the cathodic and anodic peak potentials are independent of the scan rate. It is possible to relate the half-peak potential (E_p/2 , where the current is half of the peak current) to the polarographic half-wave potential, E_1/2

                   E_p/2 = E_1/2 ± 29mV/n                                                          (8)

(The sign is positive for a reduction process.) For multielectron-transfer (reversible) processes, the cyclic voltammogram consists of several distinct peaks, if the E^o values for the individual steps are successively higher and are well separated. An example of such mechanism is the six-step reduction of the fullerenes C₆₀ and C₇₀ to yield the hexaanion products C₆₀^6- and C₇₀^6- where six successive reduction peaks can be observed.

The situation is very different when the redox reaction is slow or coupled with a chemical reaction.  Indeed, it is these "nonideal" processes that are usually of greatest chemical interest and for which the diagnostic power of cyclic voltammetry is most useful. Such information is usually obtained by comparing the experimental voltammograms with those derived from theoretical (simulated) ones.

Irreversible and Quasi-reversible Systems

For irreversible processes (those with sluggish electron exchange), the individual peaks are reduced in size and widely separated. Totally irreversible systems are characterized by a shift of the peak potential with the scan rate: 

     E_p = E° - (RT/an_aF)[0.78 - ln(k^o/(D)^1/2) + ln (an_aFn/RT)^1/2]      (9)

where a is the transfer coefficient and n_a is the number of electrons involved in the charge-transfer step. Thus, E_p occurs at potentials higher than E°, with the overpotential related to k° and a. Independent of the value k°, such peak displacement can be compensated by an appropriate change of the scan rate. The peak potential and the half-peak potential (at 25°C) will differ by 48/an mV. Hence, the voltammogram becomes more drawn-out as an decreases.

The peak current, given by:

                 i_p = (2.99x10⁵)n(an_a)^1/2ACD^1/2n^1/2                                  (10)

is still proportional to the bulk concentration, but will be lower in height (depending upon the value of a). Assuming a = 0.5, the ratio of the reversible-to-irreversible current peaks is 1.27 (i.e. the peak current for the irreversible process is about 80% of the peak for a reversible one). For quasi-reversible systems (with 10^-1 > k° > 10^-5 cm/s) the current is controlled by both the charge transfer and mass transport. The shape of the cyclic voltammogram is a function of the ratio k°/(pnnFD/RT)^1/2.  As the ratio increases, the process approaches the reversible case. For small values of it, the system exhibits an irreversible behavior. Overall, the voltammograms of a quasi-reversible system are more drawn out and exhibit a larger separation in peak potentials compared to a reversible system. In Eq.(10), n is equal to the number of electrons gained in the reduction, A is the surface area of the working electrode in cm², D is the diffusion coefficient in cm²/s, n is the sweep rate in V/s, and C is the bulk molar concentration in mole/cm³.

Nonfaradeic current

So far we have only considered faradeic current, i.e., the current resulted from charge transfer at the electrode, but when the potential is changing with time, another nonfaradeic contribution to the current takes place as well. More on that can be found in Lab 14. The easiest interpretation of such current is as due to charging the double layer capacaitance, as given in the figure to the right. Here C_dl is the capacitance of the double layer :

C_dl = ee_oA/d_dl                              (11)

and R_F is the resistance of the Faradaic reaction, in parallel to it. The resistance of the solution to the motion of ions can be represented a series resistance R_cell. As a result, the equivalent electrical circuit for the cell can be presented as shown in the same figure.

In the cyclic voltammetry experiment, the nonfaradeic current appears as hysteresis current proportional to the first power of the sweeping rate, n:

i_nF = (I_a-I_c)/2  = AC_dldE/dt = nAC_dl                         (12)

The double layer capacitance does depend on the applied potential and the electrolyte, as well as, its concentration but we will not delve into that for now.

For more detailed information on the theory of cyclic voltammetry, and the interpretation of cyclic voltammograms, see references.

References

1. Wang, J., Analytical Electrochemistry, Chapter 2, John Wiley & Sons (2000)
2. Nicholson, R.S.; Shain, I., Anal. Chem., 36, 706 (1964).

Last updated 05/05/14.