**2. Linear sweep voltammetry in combination with a rotating disk electrode**

Linear sweep voltammetry with a rotating disk electrode (LSV/RDE) is a powerful technique for providing information on the mechanism and kinetics of an electrochemical reaction. Since the current density is a measure for the rate of an electrochemical reaction, LSV provides a stationary method to measure the rate as a function of the potential. In other words, the technique is used to distinguish between the elementary reactions taking place at the electrode as a function of the applied potential. Different elementary steps are often coupled, however, the overall current is determined by the slowest process (rate determining step). As a steady state technique, linear sweep voltammetry can only give mechanistic information about rate determining elementary reactions.

To determine a quantitative model for an electrochemical process, first a plausible reaction model is proposed and afterwards combined with a transport model. The combination of both models enables the formulation of the mass balances of the species and the conservation laws, which results in a set of non-linear partial differential equations, where the electrochemical reactions constitute a boundary condition at the electrode. While the reaction model is proper to the reaction under study, the transport model is merely determined by the mass transport of the species in the electrochemical reactor. As a result, it is possible to direct an electrochemical investigation in an adapted experimental reactor (electrochemical cell) under conditions for which the description of the transport phenomena can be simplified, without a loss of precision.

For controlling the mass transport contribution to the overall electrochemical kinetics, a rotating disk electrode possesses favorable features. The RDE configuration provides analytical equations to describe the mass transport and hydrodynamics in the electrochemical cell. It is known that a simplified transport model can be used if an RDE and diluted solutions are used in the experimental set-up. The hydrodynamic equations and the

Experimental Study

> Proposed Model

Analytical model I = f (E, model parameters)

Experimental polarization curves

<sup>25</sup> Modeling and Quantification of Electrochemical Reactions in RDE (Rotating Disk Electrode) and IRDE (Inverted Rotating Disk Electrode) Based Reactors

> Minimization of the cost function

Iestimated = Iexperimental (95% confidence) ?

yes

no

*pijXi* ± *nje* (1)

*<sup>j</sup>* are the rate constants. For an electrochemical

*th* step of

Reliable mechanism and estimated parameters

charge transfer, which can be found in numerous textbooks (Bamford & Compton, 1986; Diard

Consider a uniformly accessible planar electrode, immersed in an electrolyte that contains electroactive species and an excess of inert supporting electrolyte. At the surface an electrochemical reaction is taking place, which has *P* partial heterogeneous electrochemical or chemical reactions with *Nv* electroactive species in the electrolyte or in the electrode material and *Ns* electroactive species present in an adsorbed phase on the electrode surface. *N* is the

et al., 1996; Newman, 1973; Pletcher, 1991; Thirsk & Harrison, 1972; Vetter, 1967).

total number of electroactive species involved in the reaction: *N* = *Nv* + *Ns*. The *j*

*Kj*

*K*� *j*

*N* ∑ *i*=1

with *rij* and *pij* the stoichiometric coefficients, the index *i* refers to the considered species,

reaction, they depend on the electrode potential. *nj* is the number of electrons exchanged in

The global reaction is described by the relations that connect the electrode potential *E* to the faradaic current density *if* , the interfacial concentrations of the volume species *Xi*(0) and the

*th* partial reaction. For an electrochemical reaction *nj* is preceded by a plus sign if the reaction is written in the sense of the oxidation and by a minus sign if written in the sense of

*rijXi* ↔

*N* ∑ *i*=1

Fitting Procedure

Statistical Evaluation

Fig. 1. The four building blocks of the modeling methodology.

the reaction can be written as:

the *j*

the index *j* to the partial reaction. *Kj* and *K*�

the reduction. For a chemical reaction *nj* equals zero.

convective-diffusion equation for a rotating disk electrode have been solved rigorously for the steady state (Levich, 1962; Slichting, 1979). The axial symmetry of the configuration of the RDE reactor and the uniform current distribution allow a one-dimensional description. Moreover, at sufficient flow rate (when natural convection can be ignored), the hydrodynamics in diluted solution are not influenced by changes in concentrations due to electrochemical reactions. The mathematical problem can thus be solved more easily. Levich reduced the equation of convection transport to an ordinary differential equation (Albery & Hitchman, 1971; Levich, 1962; Slichting, 1979).

To model an electrochemical reaction and determine its mass and charge transfer parameters quantitatively, an electrochemical data fitting tool has been developed in our research group. From an analytical approach, it is designed to extract a quantitative reaction mechanism from polarization curves.
