Thermodynamics 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. 

Y. Wang, E. O. Barnes, E. Laborda, A. Molina, and R. G. Compton. Differential pulse techniques in weakly supported media. Changes in the kinetics and thermodynamics of electrode processes resulting from the supporting electrolyte concentration, J. Electroanal. Chem. 673, 13 23 (2012). 

Thermodynamic treatments in physical chemistry were effectively identical with the theory of the subjectin the nineteenth century. No oneunderstoodelectron transfer at interfaces at that time (J. J. Thompson did not discover the electron until 1897). But whereas the molecular kinetic approach gradually seeped into many parts of chemistry by the 1930s, the chemistry of electrode processes remained reluctantly bound up with the older thermodynamic viewpoint. The Faraday Society meeting in Manchester, U.K. in 1947 was a turning point in the application of a molecular-level concepts and even of quantum mechanics. By the mid-1950s, research papers in electrode process chemistry (except for those dealing with electroanalytica] themes)10 were fully kinetic. 

As we have seen, acidity and basicity are intimately connected with electron transfer. When the electron transfer involves an integral number of electrons it is customary to refer to the process as a redox reaction. This is not the place for a thorough discussion of the thermodynamics of electrochemistry that may be found in any good textbook of physical chemistry. Rather, we shall investigate the applications of electromotive force (emf) of interest to the inorganic chemist. Nevertheless, a very brief review of the conventions and thermodynamics of electrode potentials and half-reactions will be presented. 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

Figure 14. Conductivities of various Zr02-M203 systems at 800°C.85 Reprinted from T. Takahashi, in Physics of Electrolytes. Thermodynamics and Electrode Processes in Solid State Electrolytes, J. Hladik (ed.), Academic Press, London, Vol. 2, 980-1052, Copyright 1972 with permission from Elsevier.

Whereas for reversible reactions only thermodynamic and mass-transport parameters can be determined, for quasi-reversible and irreversible reactions both kinetic and thermodynamic parameters can be measured. It should also be noted that the electrode material can affect the kinetics of electrode processes. 

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. 

Refs. [i]KahlertH(2002) Potentiometry. In ScholzF(ed)Electroanalytical methods. Springer, Berlin, pp 227-228 [ii] Oldham KB, Myland IC (1994) Fundamentals of electrochemical science. Academic Press, San Diego, p 135 [iii] Damaskin BB, Petrii OA (1978) Fundamentals of theoretical electrochemistry. (In Russian), Vysshaya Shkola, Moscow, p 118 [iv] Brett CMA, Oliveira Brett AM (1993) Electrochemistry. Oxford University Press, p 21 [v] Petrii OA, Tsirlina GA (2002) Electrode potentials. In Bard AJ, Stratman M, Gileadi E, Urbakh M (eds) Thermodynamics and electrified interfaces. Encyclopedia of electrochemistry, vol 1. Wiley-VCH, Weinheim, pp 1-23 [vi] Erdey-Gruz T (1972) Kinetics of electrode processes, p 149 [vii] Hamann CH, Hammett A, Vielstich W (1998) Electrochemistry. Wiley-VCH, Weinheim, p 86... 

VII. Stereoisomeric Effects on Thermodynamics and Kinetics of Electrode Processes... 

VII. STEREOISOMERIC EFFECTS ON THERMODYNAMICS AND KINETICS OF ELECTRODE PROCESSES... 

The rate of a corrosion reaction is affected by pH (via H reduction and hydroxide formation), the partial pressnre of O, (the solubility/concentration of oxygen in solution), fluid agitation, and electrolyte condnctivity. Corrosion processes are analyzed using the thermodynamics of electrode reactions, mass transfer of the cathode reactants O2 and/or H, and the kinetics of metal dissolution reactions [157, 158]. 

Since a thermodynamically reversible electrode process is one in which the the overall reaction rate is a balance between the forward reaction to the product and the back reaction from product back to the original species, both the original species and the products must control the properties of the wave and the potential at which the overall reaction occurs. Thus the half wave potential of the wave, is controlled by the energy difference between the original species and the electrode reaction product. The half wave potential will lie close to the theoretical standard electrode potential for the reaction. 

In a thermodynamically irreversible electrode process the rate of the back reaction, restoring the original species, is negligible. The potential of the reaction is concerned only with the original species and the forward reaction rate and not with the product. The potential could be thought of in terms of an activation energy required to get the reaction going. 

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. 

Similar phenomena such as diffusion potential and thermal diffusion potential in systems where ion transport is involved are also of considerable interest. Coupling of flow of ions relative to solvent is involved in the development of diffusion potential, while in the case of thermal diffusion potential, coupling of flow of ions and energy flow is involved. In such situations, the effective transference number as compared to Hittorf transference number is affected. Interesting experimental results have been reported in the context of galvanic cells (thermo-cells), in which the two electrodes are not at the same temperature where results have been interpreted in terms of thermodynamics of irreversible processes [3]. 

Except for the use of classical thermodynamics in the treatment of galvanic cells at zero current (including thermogalvanic cells, for which some aspects of the thermodynamics of irreversible processes have to be brought in—a, topic not treated here— see Agar s recent review where a complete bibliography will be found) and for the introduction of thermodynamic quantities pertaining to the formation of activated complexes from reactants in electrode processes, little systematic use of thermodynamics has been made in the various areas of electrochemistry concerned with nonzero currents. 

Besides those mentioned in the Introduction we have left out of our presentation a number of topics some which can easily be derived from what has been given in our treatment, such as the examination of the temperature variation of I s and /q s and of the related enthalpies of activation some which, although they are of very great interest and likely to receive considerable clarification from the thermodynamics of irreversible processes, would involve for the moment too much speculation, such as the study of simultaneous overall electrode processes occurring near or far from their reversible electric tensions. In the case, e.g., of two electrode processes with neighboring e.m.f s, linear relations between partial currents and overtensions could be set up and tested experimentally... 

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). 

Cyclic voltammetry is probably the electrochemical technique that is simulated most often, aiming at the analysis of electrode processes with respect to mechanism, kinetics, and thermodynamics of the reaction steps as well as transport properties of the molecules involved. The simulation of processes at (ultra)microelectrodes is also popular and highly important for the analysis of scanning electrochemical microscopy experiments [10]. 

Cyclic voltammetry (CV) is one of the most widely used electrochemical techniques for acquiring qualitative information about electrochemical reactions. Measurement using cyclic voltammetry can rapidly provide considerable information about the thermodynamics of redox processes and the kinetics of heterogeneous electron-transfer reactions, as well as coupled chemical adsorption and reactions. Cyclic voltammetry is often the first experiment performed in an electroanalytical study. In particular, it can rapidly reveal the locations of the redox potentials of the electroactive species. CV is also used to measure the electrochemical surface area (ECSA, m /g catalyst) of electrocatalysts (e.g., Pt/C catalyst) in a three-electrode system with a catalyst coated glass carbon disk electrode as a working electrode [52]. Figure 21.9 shows a typical CV curve on Pt/C. Peaks 1 and 2 correspond to hydrogen electroadsorption on Pt(lOO) and Pt(l 11) crystal surfaces, respectively. The H2 electroadsorption can be expressed as Equation 21.35 ... 

In order to identify EPHs of the cell or electrode reactions from the experimental information, there had been two principal approaches of treatments. One was based on the heat balance under the steady state or quasi-stationary conditions [6,11, 31]. This treatment considered all heat effects including the characteristic Peltier heat and the heat dissipation due to polarization or irreversibility of electrode processes such as the so-call heats of transfer of ions and electron, the Joule heat, the heat conductivity and the convection. Another was to apply the irreversible thermodynamics and the Onsager s reciprocal relations [8, 32, 33], on which the heat flux due to temperature gradient, the component fluxes due to concentration gradient and the electric current density due to potential gradient and some active components transfer are simply assumed to be directly proportional to these driving forces. Of course, there also were other methods, for instance, the numerical simulation with a finite element program for the complex heat and mass flow at the heated electrode was also used [34]. 

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. 

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