Thermodynamics of electrochemical processes

One of the first quantitative studies of an electrochemical process, specifically, electrolysis, was carried out by Faraday in 1832 [122], Fie obtained two laws that are defined as follows  

The weight of a substance generated by a cathode or anode reaction during an electrolytic process is directly proportional to the amount of electricity passed through the electrolytic cell. 

The weights of diverse substances generated by the same amount of electricity are proportional to the equivalent weights of the substances. 

M is the molecular or atomic weight of the material being transformed 

F is the Faraday number, which is defined as the charge of one equivalent of electrons 

---

We have considered the thermodynamics of electrochemical processes, studied the kinetics of electrode processes, and investigated the effects of the electrical double layer on kinetic parameters. An understanding of these relationships is an important ingredient in the repertoire of the researcher of battery technology. Another very important area of study which has major impact on battery research is the evaluation of mass transport processes to and from electrode surfaces. 

Cyclic voltammetry is the most widely used technique for acquiring qualitative information about electrochemical reactions. The power of cyclic voltammetry results from its ability to rapidly provide considerable information on the thermodynamics of redox processes, on the kinetics of heterogeneous electron-transfer reactions, and on coupled chemical reactions or adsorption processes. Cyclic voltammetry is often the first experiment performed in an electroanalytical study. In particular, it offers a rapid location of redox potentials of the electroactive species, and convenient evaluation of the effect of media upon the redox process. 

The forces Fk involve gradients of intensive properties (temperature, electrochemical potential). The Ljk are called phenomenological coefficients and the fundamental theorem of the thermodynamics of irreversible processes, due originally to Onsager (1931a, b), is that when the fluxes and forces are chosen to satisfy the equation... 

The application of thermodynamic principles to this type of electrochemical processes is discussed in die next section (5.1.2). 

In the first part, Chapters 2-6, some fundamentals of electrode processes and of electrochemical and charge transfer phenomena are described. Thermodynamics of electrochemical cells and ion transport through solution and through membrane phases are discussed in Chapter 2. In Chapter 3 the thermodynamics and properties of the interfacial region at electrodes are addressed, together with electrical properties of colloids. Chapters 4-6 treat the rates of electrode processes, Chapter 4 looking at fundamentals of kinetics, Chapter 5 at mass transport in solution, and Chapter 6 at their combined effect in leading to the observed rate of electrode processes. 

It is important to obtain experimental information on the thermodynamics of electrode processes to ascertain the tendency of a particular reaction to occur under a given set of experimental conditions namely temperature, pressure, system com H)sition and electrode potential. Such information is provided by the standard- or formal-electrode potentials for the redox couple under consideration. Appropriate combinations of these potentials enable the thermodynamics of homogeneous redox processes to be determined accurately. However, such quantities often are subject to confusion and misinterpretation. It is, therefore, worthwhile to outline their significance for simple electrochemical reactions. This discussion provides background to the sections on electrochemical kinetics which follow. The evaluation of formal potentials for various types of electrode-reaction mechanisms is dealt with in 12.3.2.2. 

The relationship between ionic conductivity and Onsager s theory can now be presented in terms of the electrochemical potential. By expressing the force leading to the transport of ions in terms of the gradient of jr,-, one finds important relationships between the diffusion coefficients of the ions, and the molar conductivity and mobility. Furthermore, when the force has the correct Newtonian units, one is also in a position to calculate the rate of entropy production. On the basis of the thermodynamics of irreversible processes, the relationship between the flux of ion i and the force Vp,- is... 

This chapter explains the fundamental principles and applications of electrochemical cells, the thermodynamics OF electrochemical reactions, and the cause and prevention of corrosion BY ELECTROCHEMICAL MEANS. SOME SIMPLE ELECTROLYTIC processes and the QUANTITATIVE ASPECTS OF ELECTROLYSIS ARE ALSO discussed. 

The thermodynamics of corrosion processes provides a tool to determine the theoretical tendency of metals to corrode. Thus, the role of corrosion thermodynamics is to determine the conditions under which the corrosion occurs and how to prevent corrosion at the metal/environment interface. Thermodynamics, however, cannot be used to predict the rate at which the corrosion reaction will proceed [1—6]. The corrosion rate must be estimated by Faraday s law and is controlled by the kinetics of the electrochemical reaction. 

Chapters 1 to 3 describe the theory of corrosion engineering and offer analyzed case studies and solved problems in the thermodynamics of corrosion processes, the relevance of electrochemical kinetics to corrosion, low field approximation theory, concentration polarization, the effects of polarization behavior on corrosion rate, the effect of mass transfer on electrode kinetics, and diffusion-limited corrosion rates. 

This work presents electrochemistry from a macroscopic viewpoint, and is divided into 4 parts the thermodynamics of electrochemical cells, electrochemical kinetics, transport processes, and finally current distribution and mass transfer in electrochemical systems (including porous electrodes and semiconducting electrodes). Problems to solve are presented at the end of each chapter, without the answers. 

The reader who may be somewhat unfamiliar with the thermodynamics of irreversible processes, of which the chemical and electrochemical aspects are of most concern here, will find help, we hope, in our three monographs, in the two monographs of Prigogine, and in the treatise by Prigogine and Defay(in which electrochemistry is not touched, but where the essentials of chemical thermodynamics are clearly presented in terms of affinities and chemical potentials). 

The thermodynamic data determined in the present work, together with the enthalpy measurements in progress, will make it possible to get more insight into the stability of niobium species and correlatively to obtain new routes leading to the optimization of electrochemical processes. 

The practical electrochemical parameters (actual cell capacity, cell voltage, etc.) are strongly related to the theoretical thermodynamic calcnlalions and are usually diminished by a certain factor because of the occurrence of various real-life usage losses. The most important theoretical properties of battery materials (electrochemical potential of the cell, cell s theoretical capacity, and energy) are derived from thermodynamics of the electrode reactions in lithium-ion cell (Table 1.1). A comprehensive, in-depth discussion of thermodynamics of the processes occurring in a lithium-ion cell can be found elsewhere [4]. Some of the most crucial formulas are Usted below. 

The interest in the analysis of the dependencies of equilibrium potential on composition of cathode materials for lithium-metal cells appeared in the late-1970s [2-8] where phase composition and phase transitions of oxides and hal-cogenides of transient metals upon lithiation were discussed. The usefulness of the simultaneous scrutiny of the equilibrium potential together with its tanpera-ture coefficient was first proved in several works [9-13] published soon after. The approach to the calculation of kinetic parameters using the thermodynamic data, which is the subject of this chapter, has been proposed [14-16] later. In early 2000, new interest in the method has arisen, both in the thermodynamics of the processes within the electrodes for lithium-ion cells [17-22] and in the connection between thermodynamic functions and kinetic parameters [23]. In the series of recent works, M. Bazant [24] described the development of the fundamental theory of electrochemical kinetics and charge transfer applied to lithium iron phosphate (LFP). 

In this book we offer a coherent presentation of thermodynamics far from, and near to, equilibrium. We establish a thermodynamics of irreversible processes far from and near to equilibrium, including chemical reactions, transport properties, energy transfer processes and electrochemical systems. The focus is on processes proceeding to, and in non-equilibrium stationary states in systems with multiple stationary states and in issues of relative stability of multiple stationary states. We seek and find state functions, dependent on the irreversible processes, with simple physical interpretations and present methods for their measurements that yield the work available from these processes. The emphasis is on the development of a theory based on variables that can be measured in experiments to test the theory. The state functions of the theory become identical to the well-known state functions of equilibrium thermodynamics when the processes approach the equilibrium state. The range of interest is put in the form of a series of questions at the end of this chapter. 

The thermodynamic treatment of electrochemical processes presented in Sec. 2.2 describes the equilibrium condition of a system but does not present information on nonequilibrium conditions such as current flow resulting from electrode polarization (overvoltage) imposed to effect electrochemical reactions. Experimental determination of the current-voltage characteristics of many electrochemical systems has shown that there is an exponential relation between current and applied voltage. The generalized expression describing this relationship is called the Tafel equation. 

The processes taking place on the surface of the solid are complicated and great in number. We measure a certain common resultant effect as the powder electrode potential. The full mastery of the subject would have to be based on the elaboration of a chemical and physicochemical model of all processes (i.e., giving the chemical equations of reactions in process, indicating the processes of solution, adsorption, desorption, and secondary reactions, etc.) as well as on the classical thermodynamic description, and possibly by thermodynamics of irreversible processes, and chemical and electrochemical kinetics. 

---