Exploring Cyclic Voltammetry: Unraveling the Dynamics of Chemical Reactions Coupled with Electron Transfer

In many cases, electrochecial systems are more complex than a simple interfacial electron transfer and may involve coupled chemical reactions. The presence of homogeneous chemical reactions in conjuction with the electrode process can significantly impact the electrochemical response of the system. In this blog, we will explore the scenario where a homogeneous first-order reaction is followed by an interfacial electron transfer, as described by the following sequence reactions:

\begin{equation} A\underset{k_b}{\overset{k_f}{\rightleftharpoons}}B + e^- \end{equation}

\begin{equation} B + H^+\overset{k_1}{\rightarrow}BH \end{equation}

Here k₁  is the homogeneous rate constant, and the species BH is considered electroinactive within the potential region under study. Additionally, we assume that the proton concentration is much higher than that of species B, allowing the homogeneous reaction to be approximated as a first-order reaction.

Examples of this type of mechanism are the oxidation of 1,4-aminiphenol in protic media

or the dissoctiaton of a ligand from a metal complex:

\begin{equation} [ML_n]^+\underset{k_b}{\overset{k_f}{\rightleftharpoons}}[ML_n]^{2+} + e^- \end{equation}

\begin{equation} [ML_n]^+ \overset{k_1}{\rightarrow}[ML_{n-1}] + L\end{equation}

In electrochemical literature,  "C" typically denotes a chemical step, while  "E" represents an electrochemical reaction. Therefore, the reaction sequence described above falls under  what is known as the EC mechanism. When diffusion is the dominat mode of mass transport, the governing equations for this meachanism are: 

\begin{equation} \frac{\partial [A]}{\partial t}=D_A\left(\frac{\partial^2 [A]}{\partial x^2}\right)\end{equation}

\begin{equation} \frac{\partial [B]}{\partial t}=D_B\left(\frac{\partial^2 [B]}{\partial x^2}\right) - k'_1[B]\end{equation}

In these equations, D represents the diffusion coefficient of the  respective species, while k'₁ is the apparent first-order rate constant defined as k'₁=[H⁺]k₁. The rate of electron transfer at the interface is governed by the Butler-Volmer equation, which we discused in detail in a previous post. Due  to the coupled chemical reaction, the concentration of B decreases, leading to a reduced current during the reduction of B to produce A. The animation below illustrates how the cyclic voltammogram is influeced by an increase in pH while maintaing a constant value k₁.

When the rate of conversion of B to C is low, the behaviour of the EC mechanism closely resembles that of a stable reversible electron transfer reaction. However, as the rate incereases, the reduction peak begins to dimisnish because the chemical reaction depletes B. When the chemical reaction rate becomes significantly high, the electron transfer process transitions from being reversible to irreversible. Consequently, the oxidation peak shifts  to more negative potentials  and its height increases. 

The following animation illustratess how the diffusion layer evolves when the pH decreases for species A and C. It cleary shows that at low pH levels, nearly all species A is converted to C. As a result, the concentration of A approaches zero, while C reaches the intial concentration of A.  

The following app simulates a cyclic voltammogram under the EC mechanism, providing insigths into how different parameters influence the outcome.The app outputs both the voltammogram and the layer of species A and C, allowing you to explore various scenarios. The adjustable parameters include:

• Diffusion coefficient of A and B (DRe and DOx, respectively): See how diffusion impacts the symmetry of the CV. Here it is assumed that the diffusion coefficient of C is equal to that of B. Note that slider values are on a logarithm scale.
• The charge transfer coefficient (α): The influence of alpha is significant at low values of k0 but becomes neglegible at high values of k0.
• The concentration of A ([Re]): Adjust the initial concentration of species A to observe its effect on the voltammogram.
• The global transfer charge constant (k0): Determine wheter the redox process is reversible or irreversible. Like diffusion coefficients, the slider values for k0 are also on a logarithm scale.
• The length of the bulk solution (x) in mm: Explore how the CV changes when the  bulk length becomes shorter than the diffusion layer.
• First order kinetic constant (k1): Control the rate at which B converts to C.
• The pH: Since the proton concentration is significantly higher than that of B, pH is treated as a parameter.

By adjusting these parameters, you can gain a deeper understanding of the factors that influence cyclic voltammetry and diffusion layers in electrochemical systems. In addition, the plot can be exported as csv files.

References

1. Compton, R.G, Laborda, E. Ward, K.R. (2014) Understanding Voltammetry: Simulation of Electrode Processes. Imperial College Press., 2014.  https://doi.org/10.1142/p910 
2. Bard, A.J., Faulkner, L.R., White, H.S. (2022) Electrochemical Methods: Fundamentals and Applications. (3rd ed). John Wiley & Sons. https://doi.org/10.1023/A:1021637209564
3. D. Britz and J. Strutwolf (2016)  Digital Simulation in Electrochemistry. (4th ed.). springer. https://doi.org/10.1007/978-3-319-30292-8
4. Molina, A., Compton, R.G., et al.; Effects of convergent diffusion and charge transfer kinetics on the diffusion layer thickness of spherical micro- and nanoelectrodes, Phys. Chem. Chem. Phys. 2013, 15, 7106–7113. https://doi.org/10.1039/C3CP50290B
5. Elgrishi, N., Dempsey, J.L., et al.; A practical Beginner's Guide to Cyclic Voltammetry. J. Chem. Educ. 2018, 95, 2, 197-206. https://doi.org/10.1021/acs.jchemed.7b00361

If you want to cite this blog post use: Robayo, I. (2024). Exploring Cyclic Voltammetry: Unraveling the Dynamics of Chemical Reactions Coupled with Electron Transfer. Available at: https://electrochemeisbasics.blogspot.com/2024/08/exploring-cyclic-voltammetry-unraveling.html [Accessed Date Accessed].