Cyclic voltammetry simulation program

The current depends on the electrode potential when the electrode process and not the diffusion is rate limiting:. Figure 1 shows a schematic for the potential energy curves of educts and products for an electrochemical reaction. Species having a high electrochemical rate constant k 0 have only a little rearrangement of either the outer or inner coordination spheres on oxidation and reduction. This means that a lot of energy is necessary to rearrange the sphere.

However, there is another process involved in the electrochemical reaction: the mass transport to or from the electrode. This process is described by the second Fick law:.

From a statistical view, diffusion is a random walk and the time-dependent distance d as a function of time is given by:. This means that diffusion in solution is a slow process. The solution has to be stirred to prevent a diffusion-controlled electrochemical process.

The figure shows the concentration—distance plots at six different parts of the cyclic voltammogram CV.

In this reversible case, the electron transfer reaction is so fast that the well-known Nernstian equation can be used. At the end of the reduction process F , the concentration of the reduction product is maximal again. All simulations were done with DigiElch Professional. Figure 3 shows the surface concentration of the oxidation black curve and reduction products red curve at different potentials.

Starting at Now we turn back to the CV Figure 2 , bottom. The CV can be explained by two processes: the electrochemical reaction and the diffusion of the relevant species to and from the electrode. The electrode used is a macro-electrode in contrast to a micro-electrode with a diameter in the range of micrometres and a rotating electrode with hydrodynamic flow of the electrolyte.

At progressing potential, the oxidation process becomes more thermodynamically favourable and the current increases. The oxidation now is under kinetic control, the concentration of the reactant species in the vicinity of the electrode drops, and the current reaches a maximum point B in the cyclic voltammogram in Figure 2.

Now, the current decreases and the reaction is under diffusion control. In this situation, the diffusion Equation 4 has to be solved. The equation shows that the concentration is a function of both time and space. Initially, the overall concentration of A is the bulk concentration c 0. Figure 4 schematically shows the situation between the electrode and the solution.

According to Eq. The gradient of the concentration is given by:. The goal of the simulations of all these processes is to numerically solve Equations 1 , 4 and 6. For details, see 2. The peak current i. Figure 5 shows the CVs for ten different scan rates 0. Figure 6 shows the Randles-Sevcik plot. The scan rate dependence is caused by the thickness of the diffusion layer.

The lower the scan rate, the greater is the thickness, and the lower is the concentration gradient. This is manifested in the current peak, which is low at low scan rates.

The slopes are the square roots of the diffusion coefficients D Ox and D Red. In this article, we present and interpret three instructive systems to understand the principles of cyclic voltammetry—the main important method in electrochemistry for determining electrode reaction mechanisms, standard electron transfer rate constants, and diffusion coefficients.

We describe CVs that show the behaviour of reversible, quasi-reversible, and irreversible systems the first two are necessary conditions for rechargeables. Based on the theory by Matsuda and Ayabe 10 and Nicholson and Shain 11 , the experimentercan estimate the electron transfer rate constant k 0 , the decisive factor describing the electrode process, from the CVs in a very simple way.

One should note here that electrochemical and chemical irreversibility are different things: chemical irreversibility means that one of the redox partners is removed from the electrode by a chemical reaction; electrochemical irreversibility means that the electron transfer is hindered. In the irreversible and quasi-reversible cases, the theoretical modelling of systems is quite complex.

In practice, the assumption of equal diffusion coefficients of Ox and Red is reasonable. In the case of equal diffusion coefficients, the formal potential E 0 corresponds to the midpoint between the two current peaks in the CV:. At different diffusion coefficients, the midpoint potential depends on the ratio between D A and D B :. Variation in the equal diffusion coefficient is shown in Figure 8. Increasing the diffusion coefficient also increases the current, as indicated by Eq.

In chapter 4, we will develop that chronoamperometry is another method to calculate the diffusion coefficient. Experimental CVs are sometimes difficult to interpret given the plethora of possible processes Table 2 DigiElch Professional provides the opportunity of fitting experimental CVs after assuming a reaction scheme.

Drops of the appropriate solutions were placed on screen-printed electrodes SPEs using a pipette; the substances examined as well as the corresponding concentrations are given for the various experiments.

The reference potential of the silver electrode had a pseudo-potential. That means that the silver did not react much with the aqueous solution but enough to form a low quantity of silver ions. These ions react with the supporting electrolytes, which, in our experiments, contained sulfate to form insoluble silver sulfate. Therefore, the reference potential was approximately defined.

Perdicakis et al. After compensation of the IR drop, the separation between the anodic and the cathodic peaks was about 60 mV and remained constant regardless of the scan rate. This means that the electrochemical reaction is reversible with suitable electrodes see 2. We must point out that the difference between the CVs in Figure 9 and Figure 10 is not the redox system but the electrode.

The redox reaction is quasi-reversible on graphite Figure 9 and reversible on gold Figure This is in good agreement with the fitted values of k 0.

We assume that the gold surface is much more rippled than the graphite surface scanning electrode images, not shown here, confirm that the roughness of the gold surface is pronounced.

Therefore, the electron can transfer much faster. Table 3 shows the fitting parameters on gold and on carbon nanotubes decorated with gold nanoparticles.

The results show that the coherent surface of gold is much more favourable for electron transfer than the graphite surface with the spreaded Au-particles on the nanotubes. Quaternary ammonium bromide is often added to complex Br 2 , thereby preventing the crossover of Br 2. Bennett et al. The group of Compton studied the electrooxidation of bromide in nitrobenzene 20 , Halasz et al. The authors compared sulfuric acid and nitromethane as solvents.

In the acidic solution, the used Pt single crystals do not influence the bromide oxidation because the formed hydrogen suppresses orientation effects. Shin et al. Chronoamperometric measurements revealed that Br - was electro-oxidised to Br 3 - and further to Br- 2. Figure 11 shows a CV and the fitted curve for an assumed ECE mechanism of the bromide oxidation on an Au working electrode.

The fitted values are summarised in Table 4 and the schematic reactions at two different potentials are shown in Figure Figure 11 shows quite a difference between the experimental and the fitted curves especially in the region between the two oxidation processes. Two reasons may be responsible for this difference: The IR drop and the Helmholtz double layer between electrode and solution. Both effects were not considered in the fitting process.

Spectroelectrochemistry is a two-dimensional spectroscopy that combines electrochemical and spectroscopic experiments 24 , 25 , In this arrangement, the absorbed or emitted light can be detected as a function of the applied potential, meaning absorption or emission and electrogenerated chemiluminescence and electrical current can be measured synchronously.

We want to mention the didactical reasons for presenting the two-dimensional spectroscopy to chemistry students: The combination may reduce some misunderstanding of electrochemical processes because electrochemical processes become visible. Figure 13 shows the CV of methylene blue. The redox reaction is a two-electron process 28 :.

Figure 14 shows the absorption at nm as a function of the potential. At about Figure 15 shows the absorption spectra at different potentials. The figure confirms Figure Beginning at about In chronoamperometric CA experiments, the potential is first set to a potential E 0 where no electrochemical activity occurs.

Then, the potential is stepped from E 0 to E 1 where redox activity occurs. You can read how we use them in our privacy policy. DigiElch Electrochemical Simulation Software. Product Details Product Images Manuals.

Product Details Overview DigiElch electrochemical simulation software is able to simulate the most common electrode geometries including thin-layer cells. DigiElch Standard Fast and accurate simulation of the current response for any user-defined mechanism consisting of charge-transfer steps and first- or second-order chemical reactions.

Inclusion of IR-drop and double-layer charging. Simulation of amalgam formation with mercury electrodes. Modeling surface adsorption and redox catalysis reactions on electrode surfaces with unprecedented detail.

The software then executes the numerical solution for the proper set of diffusion equations. The parameters for the cyclic voltammetry experiment must also be entered. It is possible to use the DigiSim software to do a least squares fit to experimental data to obtain kinetic parameters.

DigiSim simulates cyclic voltammetry done with a smooth analog ramp, or a very close approximation to it.