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Electrode Kinetics of Electron-Transfer Reaction and Reactant Transport in Electrolyte Solution

WeiweiCaia,bXiaoZhaoa,bChangpengLiubWeiXingaJiujunZhangc     aState Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Changchun, PR China     bLaboratory of Advanced Power Sources, Changchun Institute of Applied Chemistry, Changchun, PR China     cEnergy, Mining and Environment, National Research Council of Canada, Vancouver, BC, Canada

Abstract

In this chapter, to facilitate understanding and preparing the basic knowledge for rotating electrode theory, both the electron-transfer and reactant transport theories at the interface of electrode/electrolyte are presented. Regarding the reactant transport, three transportation modes such as diffusion, migration, and convection are described. A focusing discussion is given to the reactant diffusion near the electrode surface using both Fick's first and second laws. In addition, based on the approach in literature, the kinetics of reactant transport near and within a porous matrix electrode layer and its effect on the electron-transfer process is also presented using a simple equivalent electrode/electrolyte interface.

Keyword

Electrolyte solutionElectrochemical theoryElectrode reaction kineticsMass-transfer processOxygen reduction reaction (ORR)Oxygen solubilityRotating disk electrode (RDE)Rotating ring-disk electrode (RRDE)

Chapter Outline

2.1. Introduction?34

2.2. Kinetics of Electrode Electron-Transfer Reaction?34

2.2.1. Fundamental Chemical Reaction Kinetics?34

2.2.2. Fundamentals of Electrode Reactions (Bulter–Volmer Equation)?35

2.3. Kinetics of Reactant Mass Transport Near Electrode Surface?44

2.3.1. Three Types of Reactant Transport in Electrolyte (Diffusion, Convection, and Migration)?45

2.3.2. Nonsteady-State Diffusion Process of Reactant when the Electrolyte Solution at the Static State?48

2.3.3. Steady-State Diffusion–Convection Process of Reactant?54

2.4. Effect of Reactant Transport on the Electrode Kinetics of Electron-Transfer Reaction?57

2.4.1. Effect of Reactant Transport on the Kinetics of Electron-Transfer Process?57

2.4.2. Effect of Reactant Transport on the Thermodynamics of Electrode Reaction?59

2.5. Kinetics of Reactant Transport Near and within Porous Matrix Electrode Layer?61

2.6. Chapter Summary?64

References?64

Introduction

The current density measured from the rotating electrode is contributed by both the current densities of electrode electron-transfer reaction and the reactant diffusion. In order to obtain the kinetic parameters of these two processes and their associated reaction mechanisms based on the experiment data, both the theories of electrode electron-transfer reaction and reactant diffusion should be studied and understood. In this chapter, the general theories for electrode kinetics of electron-transfer reaction and reactant diffusion will be given in a detailed level, and we hope these theories will form a solid knowledge for a continuing study in the following chapters of this book.

Kinetics of Electrode Electron-Transfer Reaction

Electrochemical (or electrode) reaction kinetics is one kind of the chemical reaction kinetics. To obtain a better understanding of the theory of electrode reaction kinetics, understanding the basic knowledge of chemical reaction kinetics is necessary. In this section, the general chemical reaction kinetics will be presented first for facilitating the fundamental understanding of electrode kinetics and mechanism, particularly, for oxygen reduction reaction (ORR).

Fundamental Chemical Reaction Kinetics

Consider two substances, A and B, which are linked by simple unimolecular elementary reactions: ?kbkfB (2-I) Both elementary reactions at two different directions are active at all times, and the rate of the forward process, vf (mol cm?3 s?1), is f=kfCA (2.1) whereas the rate of the reverse reaction is b=kbCB (2.2) In Eqns (2.1) and (2.2), CA and CB are the concentrations of Substances A and B with a unit of mol cm?3 or M, kf and kb are the reaction rate constants (unit: s?1) for Reactions (2.1) and (2.2), respectively. The net reaction rate (vnet) of A to B is: net=kfCA?kbCB (2.3) At vnet = 0, the net reaction rate is zero; then fkb=K=CBCA (2.4) where K is the equilibrium constant. Equation (2.4) indicates that the kinetics must collapse to relations of the thermodynamic form when reaction time goes to unlimited, otherwise the kinetic picture cannot be accurate. Therefore, Eqn (2.4) is only valid at the state of equilibrium, or a case predicted by reaction thermodynamics. Due to the limitation of reaction time period, it is not easy for a reaction to reach its equilibrium state unless the reaction rates for both directions are extremely high. Therefore, in the study of chemical kinetics, all cases of equilibrium are assumed based on the error tolerance.

Fundamentals of Electrode Reactions (Bulter–Volmer Equation)1

To discuss some basic concepts about the electron-transfer kinetics of electrochemical systems, here we present a simple model reaction as shown in Reaction (4-II). +n?e??kbkfR (2-II) where O and R represent the oxidant and reductant, respectively; n? is the electron-transfer number; kf and kb are the forward and backward reaction rates, respectively. Note that this Reaction (2-II) is an elementary reaction. We use n? to distinguish the electron-transfer number in a simple elementary reaction from that of overall electron-transfer number (n) in a complex reaction such as ORR. For an electrochemical reaction, its reaction mechanism may consist of several such elementary reactions, among which there should be one such elementary reaction as the reaction rate-determining step. The value of n? is normally 1, and for some special cases, it could be 2. For introducing the concept of electrode reaction kinetics, we will focus on such an elementary reaction in this chapter. As shown in Figure 2.1, due to the electron-transfer reaction occuring on the electrode surface, only those oxidant species with a concentration of CO(0,t) and reductant species with a concentration of CR(0,t) on the electrode surface can participate in the reaction. The oxidant species with a concentration of CO(x,t) and reductant species with a concentration of CR(x,t) in the bulk solution have to diffuse to the electrode surface in order to participate the reaction (note that in both these concentration expressions, t is the reaction time). Therefore, there are basically two processes during the reaction: one is the electron-transfer reaction at the electrode/electrode interface, and that other is the reactant diffusion from a bulk solution to the electrode surface. In this section, we will only discuss the former process, that is, the kinetics of electron-transfer process. The reactant diffusion kinetics will be discussed in the latter section of this chapter.
Figure 2.1Schematic of the electrode electron-transfer and reactant diffusion process in an electrochemical system.CO(0,t) is the surface concentration of oxidant species, CR(0,t) is the surface concentration of reductant species, CO(x,t) is the bulk solution concentration of oxidant, and CR(x,t) is the bulk solution concentration of reductant species. In these four expressions of concentration, t is the reaction time. (For color version of this figure, the reader is referred to the online version of this book.) The forward and backward reaction rates (?f and ?b, respectively) for Reaction (2-II) can be expressed...