Electrochemical Impedance Spectroscopy as a Tool for Electrochemical Rate Constant Estimation

Electrochemical impedance spectroscopy (EIS) was used for advanced characterization of organic electroactive compounds along with cyclic voltammetry (CV). In the case of fast reversible electrochemical processes, current is predominantly affected by the rate of diffusion, which is the slowest and limiting stage. EIS is a powerful technique that allows separate analysis of stages of charge transfer that have different AC frequency response. The capability of the method was used to extract the value of charge transfer resistance, which characterizes the rate of charge exchange on the electrode-solution interface. The application of this technique is broad, from biochemistry up to organic electronics. In this work, we are presenting the method of analysis of organic compounds for optoelectronic applications.


Introduction
Redox rate of the electroactive compound is an important parameter characterizing its ability to undergo oxidation or reduction processes and predict its behavior in the presence of strong oxidizing or reducing agents or under applied potential. However, most of the electrochemical techniques are only able to qualitatively describe the kinetics of the redox process. Among various electrochemical techniques employed for redox active compounds, characterization cyclic voltammetry (CV) is the most prevailing method for quick and sufficient electrochemical characterization of various soluble species 1,2,3 . The CV technique has broad applications, e.g., energy levels estimations 4,5,6 , the charge carriers analysis supported by spectroscopies 7,8,9,10 , up to surface modifications 11,12,13 . Like every method, CV is not perfect and to increase the applicability and quality of results, the connection with another spectroscopic technique is important. We already present several investigations where the electrochemical impedance spectroscopy (EIS) technique was employed 14,15,16 but in this work, we intended to show step-by-step how to reinforce the CV technique by EIS.
The EIS output signal consists of two parameters: real and imaginary parts of impedance as functions of frequency 17,18,19,20 . It allows estimation of several parameters responsible for charge transfer through the electrode-solution interface: double layer capacitance, solution resistance, charge transfer resistance, diffusion impedance and other parameters depending on system investigated. Charge transfer resistance was an object of high attention since this parameter is directly related to the redox rate constant. Even though oxidation and reduction rate constants are estimated in solution, they may generally characterize the ability of a compound for charge exchange. EIS is considered to be an advanced electrochemical technique requiring profound mathematical understanding. Its main principles are described in modern electrochemistry literature 17,18,19,20,21,22,23 .  NOTE: A typical voltammogram is presented in Figure 1.

Basic Preparation of an Electrochemical Experiment
2. Determine the potential value from the CVA obtained. Note the potential values when maxima of positive (anodic peak) and negative (cathodic peak) current appear and calculate the average value. 3. Add 10 mg of ferrocene by spatula into the working solution and deaerate it by argon bubbling for 5 min. This is necessary for mixing and complete dissolution of the ferrocene added. NOTE: The ferrocene amount is not precise. However, adding less than 1 mg or more than 20 mg would complicate estimation of equilibrium potential. 4. Register the CVA of the working solution within the potential range from −1.0 V to +1.0 V and scan rate 100 mV•s −1 . A small reversible peak of ferrocene will appear as shown in Figure 1. 5. Determine the potential value of ferrocene reversible oxidation from the CVA obtained. Note the potential values when maxima of positive (anodic peak) and negative (cathodic peak) current appear and calculate the average value. 6. Put another portion of the solution prepared at step 1.1 into the cell and clean the electrodes by repeating the procedure described in 1.2-1.7.

Registration of Impedance Spectrum
NOTE: An example of the setup in software is shown in Figure 2; any other software or device also can be used. However, the setup arrangement may differ in different software, although the main principles remain the same. Use the EIS in a staircase mode, i.e. potentiostatic spectra are registered automatically one after another.
1. In the software, choose a potential range of 0.2 V covering the reversible peak in CVA. Example: A reversible oxidation peak was detected on CV at 0.7 V. The potential range for CV should be then from 0.6 V to 0.8 V. The spectra will be registered with the increment of 0.01 V, i.e. at 0.61 V, 0.62 V, etc. 2. Register the EIS automatic measurement procedure under following conditions advised.
1. Enter the following input values: initial potential 0.6 V; finish potential 0.8 V; potential increment: 0.01 V; frequency range: from 10 kHz through 100 Hz; the number of frequencies in logarithmic scale: 20; wait for a time between the spectra: 5 s, ac voltage amplitude 10 mV, minimal 2 measures per frequency. 2. Click the button Start.
NOTE: In that case, 21 spectra, each containing 41 frequency points will be obtained. The typical set of automatically registered spectra is presented in Figure 3.

Analysis of Impedance Spectrum
1. Launch the program EIS spectrum analyser.
2. Download the spectrum by choosing File | Open.
3. In the right upper sub-window construct an EEC by using left/right mouse click choosing series or parallel connection and necessary element from the context menu: C -capacitor, R -resistor, W -Warburg element. Start from the simplest circuit (Figure 5c). , repeat the procedures 4.2−4.5 using another equivalent electrical circuit (EEC) (Figure 5). 8. Repeat the procedure 4.1-4.7 for all the spectra registered 9. For each spectrum analyzed, write down the calculated value of charge transfer resistance and the corresponding potential that the spectrum was registered at.

Calculation of Redox Rate Constants
1. Put the values of the estimated inverse charge transfer resistance versus potential. A typical potential plot of inverse charge transfer resistance for the reversible process is presented in Figure 6. 1. Change values in cells C7 and C8 manually in order to achieve equality between experimental and simulated graph. NOTE: Change of E 0 moves the bell-like curve along the x axis. Change of k 0 controls the height of the bell-like curve. Thus, varying those two only parameters can be used to find a theoretical model corresponding to experimental results (Figure 6). Parameter α (1) controls symmetry of theoretical peak. However, in real systems asymmetry may be caused by the occurrence of side-process rather than by α. Since it influences resulting k 0 value we recommend not to manipulate α value and leave it to equal 0.5.

Representative Results
The first step is cyclic voltammetry characterization presented in Figure 1. Application of EIS was successful when compounds underwent the fast reversible electrochemical process. Such behavior was often not observed for organic compounds but organic compounds that possess electroconductivity in a solid state was found to be a good specimen for electrochemical kinetic investigation. One such organic compound is shown in the inset of Figure 1.
Registration of impedance spectra was carried out according to the experimental setup (Figure 2), and typical raw resulting data are shown in Figure 3. Analysis of impedance spectra was carried out using special software 24 . The window of the open access program EIS Spectrum analyser 24 during results processing is shown in Figure 4. An EEC used to fit the spectrum is built manually in the right upper sub-window. The calculated EEC parameters (resistances R1 and R2, capacitance C1 and diffusion impedance parameter W1) are shown in a table in the left upper sub-window. The graph in lower left sub-window illustrates fitting of experimental results (red points) with the theoretically calculated data plot (green line).
Several different EEC may fit experimental spectrum depending on the processes that take place on the electrode surface and their rates ( Figure 5). The simplest semi-infinite Warburg element can be used as there is no distortion of solution (e.g. rotating of the electrode mixing) and no electrode coating limiting the diffusion. In case of considerably fast electrochemical reactions, resistance R3 ( Figure 5A) was high enough to be neglected in comparison with other parallel branches of EEC ( Figure 5B). Moreover, when rate of charge transfer (R2) is significantly higher than diffusion, the charge transfer step becomes limiting and an even simpler EEC (Figure 5C) describes the system.
Analysis of impedance spectrum may be performed by various software. Here the basic recommendations for EEC analysis method are discussed. One needs to know that there are numerous fitting algorithms and various ways of error estimation. We present an example of using open access software developed by A. Bondarenko and G. Ragoisha 24 (Figure 4).
Exact estimation of R ct value was the main objective of the work. One of the reasons for the choice of the experimental conditions was an intention to conceal the impact of diffusion. Thus, the solution concentration had to be as high as possible. While acquiring the experimental results shown here, the concentration was limited due to economic reasons. The range of frequencies from 10 kHz to 100 Hz was chosen to eliminate the effect of diffusion as well. Diffusion impedance is inversely proportional to the frequency while resistance is not dependent on the frequency. The effect of resistance in the high-frequency part of the spectrum was higher than in the low-frequency part. Spectra were not registered at the frequencies lower than 100 Hz because these data would be useless for resistance calculation. All the electrochemical results obtained in non-aqueous solvent are presented versus ferrocene-oxidized / ferrocene coupled equilibrium potential. For this reason, steps 2.3 -2.5 are performed.
We considered EIS application to organic molecules characterization. Analysis of other EEC parameters and their potential dependencies in perspective may lead to the revelation of other effects and electrochemical characterization of compounds in solution. Estimation of redox rate constants is useful for describing the kinetics of electroactive compound reduction or oxidation and predicting material behavior in oxidizing or reducing medium.

Disclosures
The authors have nothing to disclose.