Understanding cyclic voltammetry: Electron Transfer Mechanism
Cyclic voltammetry (CV) is a widely used electrochemical technique for analyzing the charge transfer of a redox-active specie during a linearly cycled potential sweep. It provides valuable information about interfacial processes, redox thermodynamics, diffusion coefficients, electrode surface properties, and charge-transfer kinetics. However, despite its popularity, CV is often misunderstood due to the simultaneous occurrence of multiple processes, complicating the interpretation of voltammograms.
Let's consider the following redox reaction:
\begin{equation} Fe^{2+}\underset{k_b}{\overset{k_f}{\rightleftharpoons}}Fe^{3+}\end{equation}
The rate of this reaction can be described phenomenologically as:
\begin{equation}r=k_f[Fe^{2+}]-k_b[Fe^{3+}]\end{equation}
In the classical chemical kinetics, the kinetic constant depends exponentially with temperature according to the Arrhenius equation:
\begin{equation}k=A\exp\left(-\frac{Ea}{RT}\right)\end{equation}
This equation tells us that the rate constant increases exponentially with temperature, emphasizing the importance of thermal energy in overcoming the activation barrier. In electrochemistry the situation is slightly different. The rate constant for an electrochemical reaction depends on the applied potential (voltage), which provides the energy needed for the charge transfer reaction to occur at the electrode surface. This relationship is given by the Butler-Volmer equation, which describes the kinetics as a function of the difference between the applied potential and the equilibrium potential.
\begin{equation}k_f=k_0\exp\left(\frac{\alpha nF(E-E_0)}{RT}\right) \end{equation}
\begin{equation} k_b=k _0\exp\left(-\frac{(1-\alpha)nF(E-E_0)}{RT}\right)\end{equation}
In these equations, kf represents the rate of oxidation, while kb represent the rate of reduction. Here, k0 is the global charge transfer constant, F is the faraday constant, n denotes the number of charges being transferred, and α is the dimensionless transfer coefficient. E is the applied potential, E0 is the equilibrium potential, which is the potential at which the rates of oxidation and reduction are equal.
The figure below illustrates how the rates of oxidation and reduction change exponentially with the applied potential. When the polarization is more negative than E0, reduction is favoured. Conversely, when the polarization is more potive than E0, oxidation is favoured. However, it's important to note that both processes occur at all potentials. Changing the polarization favours one process over the other, but it doesn't mean that the other process ceases to exist.
Another key aspect of these redox processes is that the charge transfer process only occurrs at the interface between the electrode and the electrolyte solution. When the applied potential is far from the equilibrium potential (E0), the rate of oxidation is very high, rapidly consuming all Fe2+ ions near the interface. As a result, a concentration gradient is generated, causing Fe2+ ions to diffuse from the bulk solution to the interface, leading to the formation of a diffusion layer. This diffusion layer has a concentration gradient that differs from the bulk solution. Tipically, the length of this layer is about 400 micrometers. The following animation illustrates this behaviour.
- Concentration of Fe2+ and Fe3+
- Diffusion coefficient of Fe2+ and Fe3+ (DFe(II) and DFe(III), respectively): Observe how diffusion affects the symmetry of the CV. Note that slider values are on a logarithm scale.
- The global transfer charge constant (k0): Determine when the redox process is reversible or irreversible. The slider values for k0 are also on a logarithm scale.
- The length of the bulk solution (x) in mm: Explore the changes in the CV as the length of the bulk becomes shorter than the diffusion layer.
- 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 number of charges being transferred (n): This value can be fractional as it relates to the moles of charges transferred.
By adjusting these parameters, you can gain a deeper understanding of the factors influencing cyclic voltammetry and diffusion layers in electrochemical systems. In addition, the plot can be exported as csv files.
- Stephens, L.I., Mauzeroll, J.; Desmytifying Mathematical Modeling of Electrochemical Systems. J. Chem. Educ. 2019, 96, 10, 2217-2224. https://doi.org/10.1021/acs.jchemed.9b00542.
- 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
- 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
- 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
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