Elsevier

Electrochimica Acta

Volume 259, 1 January 2018, Pages 56-65
Electrochimica Acta

Effect of migration on homogeneous redox electrocatalysis at rotating disk electrode

https://doi.org/10.1016/j.electacta.2017.10.150Get rights and content

Abstract

This work is devoted to the theoretical study of the effect of migration on homogeneous redox electrocatalysis of electrochemical reactions at the rotating disk electrode. The mathematical model involves the Nernst-Planck equations that take into account diffusion, migration, convection, homogeneous chemical reactions, and electroneutrality condition. For the convenience of solving and analyzing the results, the mathematical model was reduced to the dimensionless form. The numerical solution was performed by the finite volume method on the nonuniform grid. Based on the results of computational experiments, for the electrocatalytic reduction of hydrogen peroxide in the presence of ferric ions, three zones were observed in the plane of concentrations of H2O2–H2SO4. These zones differ in the nature of the limiting current: for H+ ions, Fe+2 ions, and hydrogen peroxide H2O2. The dependences of the limiting current on the concentrations of H2SO4 and H2O2 were determined with and without consideration of the ionic migration. It was found that the ionic migration may be ignored only in the cases that the concentration of H2SO4 is significantly higher than that of H2O2. It was shown that the strongest effect of ionic migration is reached on the boundaries between zones that differ in the nature of the limiting current.

Introduction

Electrochemical reaction can be accompanied by homogeneous chemical reaction involving the products of electrochemical reaction [1], [2], [3], [4], [5]. This is so-called EC process. If the products of chemical reaction are nonelectroactive, the chemical reaction has no considerable effect on the current [2]. In the case that the homogeneous chemical reaction yields the reagents for the electrochemical reaction and the oxidation (reduction) of nonelectroactive substance, which is present in the solution, occurs, the homogeneous redox electrocatalysis takes place [6], [7], [8], [9], [10]. This is so-called EC′ process, when the attendant chemical reaction has a pronounced effect on the current.

A special type of EC process involves reaction of B with a nonelectroactive species C in the solution to regenerate A [3]:A+ne-BB+CA+D

This chemical reaction is normally assumed to be uni-directional. A current depending on the regeneration rate of the depolarizer is usually called a catalytic current, the A/B couple acts as a catalyst for the reduction (or oxidation) of C, which is nonelectroactive within the given potential region [3]. In homogeneous redox electrocatalysis, the catalyst couple merely plays the role of an electron carrier by contrast to the chemical catalysis, which involves the transitory formation of catalyst-substrate adduct.

Electrocatalysis is important to many applications in the electrochemistry, because the energy efficiency of any electrochemical cell is determined, in part, by the potentials of the anode and cathode [9], [10], [11]. A large number of works have been devoted to the experimental and theoretical study of homogeneous redox electrocatalysis [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. The theory of catalytic currents can be illustrated by the reduction of hydrogen peroxide in the presence of ferric ions [14], [15]. In this system iron, changing its valence, seems to be the transfer agent for electrons from the electrode to hydrogen peroxide. The slowest stage of the process is the reaction between H2O2 and Fe2+, and therefore the height of the catalytic wave is governed by the rate of this reaction. An increase in the current occurs at the expense of the hydrogen peroxide, which by itself is not reduced electrolytically until much more negative potentials are reached, although chemically it is a more powerful oxidizing agent than ferric iron [3]. On the basis of the reaction layer theory, the equation for the limiting catalytic current was derived [13]. A rigorous solution was presented by Koutecky for polarography [17]. The theory of homogeneous electrocatalysis is most well-developed for polarography [10], [27]; however, in some works, variously shaped electrodes and chemical reactions of various orders were considered [28], [29], [30], [31], [32], [33], [34], [35]. In all works devoted to the theoretical study of homogeneous redox electrocatalysis, the ionic migration was ignored. In many cases, the supporting electrolyte is present in the solution, which almost completely suppresses the migration of electroactive ions. However, in some cases, the concentration of supporting electrolyte can be rather low or it is absent at all [36], [37]. In this case the migration transfer of all types of ions, which are present in the solution, should be taken into account. The methods of numerical solution of Nernst-Planck-Poisson and (or) Nernst-Planck equations simultaneously for all chemical species and for potential have been well developed (see, for example [38], [39], [40], [41], [42], [43], [44], [45], [46]) and can be used to estimate the effect of migration in the electrocatalytic systems.

Along with the dynamic methods [3], when the current varies with the time, the steady-state methods are widely applied [2]. Among them, a rotating disk electrode (RDE) with equally accessible surface is of special importance [47]. Another important merit of RDE is that the diffusion layer thickness and, consequently, a ratio between the thicknesses of diffusion and kinetic layers can be changed rather simply and in a wide range by varying the electrode rotation rate [48].

The methods for calculating the hydrodynamic velocity and transport processes with regard for diffusion, migration, and convection near a RDE have been well developed [49], [50], [51] and can be adapted for solving the problems of homogeneous electrocatalysis.

In the systems with homogeneous redox electrocatalysis of electrochemical reactions (Eq. (1)), the limiting current can be associated with reaching zero concentration of one (or several) reactants of chemical or electrochemical reaction on the surface of RDE. When the composition of initial solution and/or the operation conditions are changed, the type of ions, which control the current (their concentration reaches zero) can change. Therefore, to solve the problem, it is advantageous to split the range of parameters into several zones corresponding to different types of ions that control the current under the given conditions.

The aim of this work is to develop the mathematical model of homogeneous redox electrocatalysis with regard for the migration transfer of ions of all types and to analyze the regularities of ionic transport processes near a rotating disk electrode by the example of the reduction of hydrogen peroxide in the presence of ferric ions.

Section snippets

Mathematical model

For definiteness, we restrict ourselves to the consideration of classical electrocatalytic process of hydrogen peroxide reduction in the presence of iron ions. In accordance with [52], we assume that the following chemical reaction proceeds in the solution:2Fe2++H2O2+2H+k2Fe3++2H2O

The rate of the reaction depends only on the concentrations of Fe2+ and H2O2:q=kcFe2+cH2O2where k is the rate constant of the chemical reaction.

Ferrous ions form on the electrode as a result of electrochemical

Results and discussion

The numerical solution of developed mathematical models was performed by the finite volume method [53] using the home-made software. Fig. 1 gives the scheme of discretization of computational domain. A non-uniform primary grid with the nodes in points 0, 1, , i, , NE was used. The region between the i-th and the (i + 1)-th nodes will be denoted the i-th element. A finite volume is formed around each node; the boundaries of volume are placed in the middle between the nodes of the primary grid.

Conclusions

The effect of migration on the ionic transport in the homogeneous redox catalysis of electrochemical reactions at the rotating disk electrode is theoretically analyzed. The distributions of the concentrations of ions and potential over the diffusion layer and the limiting current densities are calculated for the electrocatalytic reduction of hydrogen peroxide in the presence of ferric ions with and without regard for the ionic migration. The diagrams of the limiting-current zones are

Acknowledgements

The study was funded by RFBR, research project № 16-03-00786.

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