**5. The inverted rotating disk electrode (IRDE) reactor**

The combination of linear sweep voltammetry with an RDE is a powerful tool to study electrochemical reactions. One limitation to the technique is the presence of gas in some electrochemical systems. The inverted rotating disk electrode (IRDE) is designed to tackle this problem. It allows an investigation of gas evolving reactions, preventing the presence of gas from being an obstacle to a quantitative modeling.

When the RDE set-up is used for the mechanistic study of gas evolution reactions, the formed gas bubbles tend to stick to the downward facing electrode surface and, hence, shield the active electrode surface. In contrast to the classical RDE configuration where the rotating disk is downward facing and positioned at the top of the electrochemical cell, in the IRDE configuration the rotating disk is now placed at the bottom of the cell, facing upwards. As a result, the generated bubbles rise freely and are no longer shielding the electrode surface. The bubbles are detached from the electrode by buoyancy or swept away by the rotational movement of the electrode.

Many industrial electrochemical systems deal with gas evolution, such as, for example, the water electrolysis, the chlorine and chlorate production or the side reactions during the electrowinning or electrodeposition of metals.

#### **5.1 Design and construction of the IRDE reactor**

The electrochemical cell consists of a cylindrical vessel of 74 mm diameter and 200 mm height, with a square water jacket around it. A schematic illustration of the IRDE design is presented in Figure 7 and a picture of the IRDE set-up is shown in Figure 8. The height of the working electrode protruding into the electrolyte is 30 mm. The counter and the reference electrode are located in the upper part of the cell, far away from the rotating electrode in order not to disturb the flow field near the working electrode. Because of the positioning of the reference electrode vs the working electrode, the current-potential data needs to be corrected for the ohmic drop. After emptying the cell, the vessel itself can be removed permitting an easy exchange of the working electrode. The cell is entirely made of plexiglas (polymethylmethacrylate or PMMA) to ensure full optical access to the cell. In this way, the gas bubbles can be characterized in-situ (e.g. bubble size, rise velocity, etc.) by means of optical imaging techniques.

(b) Top view

rotating disk electrode (working electrode)

reference electrode

platina grid (counter electrode)

**5.2 Evaluation of the IRDE reactor for kinetic studies of electrochemical reactions**

Although the change in position of the working electrode from the top to the bottom of the cell seems to be a minor modification, it has to be examined whether the characteristics of mass transfer governing the RDE reactor are also valid for the IRDE reactor. To this purpose, the ferri/ferrocyanide redox system is used. Since theoretically charge transfer parameters are independent of the hydrodynamics, the same parameter values must be found in both the RDE and IRDE configuration. The equations of mass transfer, used for kinetic studies in an RDE configuration, are based on an analytical expression of the velocity field with the assumption of an infinite large electrode disk and bath dimensions. In practice, however, we deal with a finite sized rotating disk and a confined electrochemical cell. Although it is generally accepted that the analytical solution of the flow field derived by Levich (Newman, 1973) describes the velocity field near the electrode surface well, it is nevertheless not evident that the velocity field is described with the same accuracy for the IRDE configuration as for

<sup>39</sup> Modeling and Quantification of Electrochemical Reactions in RDE (Rotating Disk Electrode) and IRDE (Inverted Rotating Disk Electrode) Based Reactors

The analytical modeling utilized for the RDE configuration is applied to the IRDE reactor. The experimental procedure described in section 4.1 is used for the LSV experiments of the ferri/ferrocyanide redox reaction on the IRDE. Eq. 29 is fitted to the mean polarization curves, obtained at 300, 1000 and 1500 rpm. The mean polarization curve is calculated from 11 independently recorded polarization curves. The 95 % confidence intervals of *kox*, *kred* and *αox* obtained at 300, 1000 and 1500 rpm perfectly overlap (not shown). This means that the values of the charge transfer parameters, *kox*, *kred* and *αox*, are independent of the rotation speed, as expected theoretically. The calculated weighted mean values of the model parameters for charge transfer, *kox*, *kred* and *αox*, are respectively 1.03E-08 m/s ± 1.31E-09 m/s, 9.12E-01 ±

Fig. 8. Picture of the IRDE cell.

the RDE configuration.

1.25E-01 m/s and 5.39E-01 ± 7.06E-03.

Fig. 7. Schematic illustration of the IRDE cell.

(a) Front view

#### Fig. 8. Picture of the IRDE cell.

18 Electrochemical Cells

this problem. It allows an investigation of gas evolving reactions, preventing the presence of

When the RDE set-up is used for the mechanistic study of gas evolution reactions, the formed gas bubbles tend to stick to the downward facing electrode surface and, hence, shield the active electrode surface. In contrast to the classical RDE configuration where the rotating disk is downward facing and positioned at the top of the electrochemical cell, in the IRDE configuration the rotating disk is now placed at the bottom of the cell, facing upwards. As a result, the generated bubbles rise freely and are no longer shielding the electrode surface. The bubbles are detached from the electrode by buoyancy or swept away by the rotational

Many industrial electrochemical systems deal with gas evolution, such as, for example, the water electrolysis, the chlorine and chlorate production or the side reactions during the

The electrochemical cell consists of a cylindrical vessel of 74 mm diameter and 200 mm height, with a square water jacket around it. A schematic illustration of the IRDE design is presented in Figure 7 and a picture of the IRDE set-up is shown in Figure 8. The height of the working electrode protruding into the electrolyte is 30 mm. The counter and the reference electrode are located in the upper part of the cell, far away from the rotating electrode in order not to disturb the flow field near the working electrode. Because of the positioning of the reference electrode vs the working electrode, the current-potential data needs to be corrected for the ohmic drop. After emptying the cell, the vessel itself can be removed permitting an easy exchange of the working electrode. The cell is entirely made of plexiglas (polymethylmethacrylate or PMMA) to ensure full optical access to the cell. In this way, the gas bubbles can be characterized in-situ

(b) Top view

(e.g. bubble size, rise velocity, etc.) by means of optical imaging techniques.

reference electrode

water jacket

Å inlet water jacket

platinum grid

RDE

30 mm

(a) Front view

Fig. 7. Schematic illustration of the IRDE cell.

100 mm

outlet Å water jacket

O-ring

gas from being an obstacle to a quantitative modeling.

electrowinning or electrodeposition of metals.

**5.1 Design and construction of the IRDE reactor**

movement of the electrode.

### **5.2 Evaluation of the IRDE reactor for kinetic studies of electrochemical reactions**

Although the change in position of the working electrode from the top to the bottom of the cell seems to be a minor modification, it has to be examined whether the characteristics of mass transfer governing the RDE reactor are also valid for the IRDE reactor. To this purpose, the ferri/ferrocyanide redox system is used. Since theoretically charge transfer parameters are independent of the hydrodynamics, the same parameter values must be found in both the RDE and IRDE configuration. The equations of mass transfer, used for kinetic studies in an RDE configuration, are based on an analytical expression of the velocity field with the assumption of an infinite large electrode disk and bath dimensions. In practice, however, we deal with a finite sized rotating disk and a confined electrochemical cell. Although it is generally accepted that the analytical solution of the flow field derived by Levich (Newman, 1973) describes the velocity field near the electrode surface well, it is nevertheless not evident that the velocity field is described with the same accuracy for the IRDE configuration as for the RDE configuration.

The analytical modeling utilized for the RDE configuration is applied to the IRDE reactor. The experimental procedure described in section 4.1 is used for the LSV experiments of the ferri/ferrocyanide redox reaction on the IRDE. Eq. 29 is fitted to the mean polarization curves, obtained at 300, 1000 and 1500 rpm. The mean polarization curve is calculated from 11 independently recorded polarization curves. The 95 % confidence intervals of *kox*, *kred* and *αox* obtained at 300, 1000 and 1500 rpm perfectly overlap (not shown). This means that the values of the charge transfer parameters, *kox*, *kred* and *αox*, are independent of the rotation speed, as expected theoretically. The calculated weighted mean values of the model parameters for charge transfer, *kox*, *kred* and *αox*, are respectively 1.03E-08 m/s ± 1.31E-09 m/s, 9.12E-01 ± 1.25E-01 m/s and 5.39E-01 ± 7.06E-03.

applied to one electron transfer reactions. Yet the fitting can be extended to other reaction steps, such as chemical or adsorption reactions, or to other measurement techniques, such as, for example, electrochemical impedance spectroscopy, provided that they can be analytically

<sup>41</sup> Modeling and Quantification of Electrochemical Reactions in RDE (Rotating Disk Electrode) and IRDE (Inverted Rotating Disk Electrode) Based Reactors

However, in many cases the electrochemical systems present more complicated reaction mechanisms, including multiple electrochemical or chemical reactions. The reaction model is thus too complex to be translated into analytical equations. Besides, when gas bubbles are involved in the electrochemical process, a new transport model describing the two-phase mass transport is designed (Maciel et al., 2009; Nierhaus et al., 2009; Van Damme et al., 2010). Modeling these complex systems requires a numerical approach. In our group, focus is put on the development of numerical models for such complex systems. Nevertheless, in order to achieve a statistical and accurate parameter estimation, it is clear that also a numerical fitting procedure has to be introduced. This aspect is under development at present in our group.

The strength of the analytical fitting model to quantify the kinetic parameters of an electrochemical reaction is shown. The coupling of statistically founded parameter estimation techniques with LSV/RDE experiments is an important innovative point of the modeling

The fitting methodology requires the proposition of an appropriate mechanism for the studied reaction and its mathematical translation into an expression that analytically describes the voltammogram. This expression depends on the mass and charge transfer parameters of the reaction (rate constants, transfer coefficients and diffusion coefficients). Powerful parameter estimation algorithms are used in the data fitting tool to adjust the values of the model parameters in order to obtain a good agreement between experimental and modeled data. The values of the model parameters that give rise to the best match, characterize the system quantitatively. Moreover, this method provides error estimates of the obtained parameter values. However, it is only after a statistical evaluation of the obtained results, that it is

The application of the analytical modeling for the study of the ferri/ferrocyanide reaction with LSV/RDE experiments demonstrate that the modeling methodology is valid to extract the quantitative mechanism of an electrochemical reaction. In the case of the hexaammineruthenium (III)/(II) reaction, however, the results of the analytical modeling

The IRDE reactor is built to facilitate the study of electrochemical gas evolution reactions. It offers the advantages of the classical RDE set-up, such as well-defined hydrodynamics and mass transport over a wide range of rotation speeds, while the gas bubbles can rise freely and do not shield the electrode surface. It is demonstrated that the IRDE configuration is valid for

It has to be emphasized that for the existing fitting procedure the proposed reaction model describing the reactions taking place must be translated into an analytical equation. It is clear that in the presence of, for example, chemical reactions or gas bubbles, an analytical solution does not exist anymore. Therefore, for further modeling studies a fitting tool that makes use

decided whether the model is able to describe the experiments.

point out the importance of a correct formulation of the reaction mechanism.

kinetic and mechanistic investigations of electrochemical reactions.

of numerical calculation procedures needs to be developed.

formulated.

**7. Conclusions**

strategy.

In Figure 9, the weighted mean values of the charge transfer parameters and their 95 % confidence interval, obtained in the IRDE and the RDE reactors, are compared. It can be seen that the confidence intervals of *kox* perfectly overlap, while a small deviation between the confidence intervals is observed for *kred* and *αox*. However, the deviation between the confidence interval is smaller than 1% for *αox* and smaller than 5% for *kred*. The deviation between the confidence intervals is determined by the difference between the maximum and the minimum values of the respective confidence intervals obtained in the RDE and the IRDE configurations, normalized to the mean value of the respective model parameter obtained in the RDE configuration. The values lie sufficiently close that it is reasonable to assume that the mass transfer characteristics of the RDE are also valid for the IRDE. The estimation of the charge transfer parameters does not depend on the hydrodynamics and mass transport within the electrochemical cell, which in its turn demonstrates that the IRDE is a suitable tool for the mechanistic study of the electrochemical reactions. Moreover, the differences between the values of the rate constants estimated for the RDE and the IRDE reactors narrow the window of values reported in literature (Angell & Dickinson, 1972; Beriet & Pletcher, 1993; Bruce et al., 1994; Jahn & Vielstich, 1962).

Fig. 9. Comparison of the 95 % confidence intervals of the weighted mean of the charge transfer parameters obtained in the IRDE and the RDE configurations.

### **6. Towards the identification and quantification of characteristic parameters of complex electrochemical systems**

In general, an accurate and fully statistical founded solution is the aim of all kinetic and mechanistic studies of electrochemical systems. The proposed analytical fitting model is applied to one electron transfer reactions. Yet the fitting can be extended to other reaction steps, such as chemical or adsorption reactions, or to other measurement techniques, such as, for example, electrochemical impedance spectroscopy, provided that they can be analytically formulated.

However, in many cases the electrochemical systems present more complicated reaction mechanisms, including multiple electrochemical or chemical reactions. The reaction model is thus too complex to be translated into analytical equations. Besides, when gas bubbles are involved in the electrochemical process, a new transport model describing the two-phase mass transport is designed (Maciel et al., 2009; Nierhaus et al., 2009; Van Damme et al., 2010). Modeling these complex systems requires a numerical approach. In our group, focus is put on the development of numerical models for such complex systems. Nevertheless, in order to achieve a statistical and accurate parameter estimation, it is clear that also a numerical fitting procedure has to be introduced. This aspect is under development at present in our group.
