Thermodynamics electrochemical irreversibility

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... 

Formal potentials can be defined on different levels of conditions Thus the formal potential of the -> quinhydrone electrode may be defined (I) as including (a) the standard potential of the hydroquinone di-anion/quinone system, (b) the two acidity constants of the hydroquinone, and (c) the activity coefficients of the hydroquinone dianion and quinone, or, (II), it may also include (c) the pH value. In the latter case, for each pH value there is one formal potential, whereas in the first case one has one formal potential for all pH values, and an equation describing the dependence of the electrode potential as a function of that formal potential and the individual pH values. Formal potentials are strictly thermodynamic quantities, and no kinetic effects (e.g., by electrochemical -> irreversibility) are considered. 

The electrochemical irreversible reduction of [Cu(sar)]2+ cation in aqueous solution was studied by cyclic voltammetry [293], This cation is kinetically and thermodynamically stable except toward reduction of encapsulated copper(II) ion to copper ion E = - 800 mV vs SCE). After reduction, the coordination number of this copper ion diminishes from six (copper(II)) to four (copper(I)). 

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... 

Nevertheless, voltammetric techniques have long been applied to the study of direct electron transfer processes of biological molecules. Such early voltammetric studies revealed a high degree of electrochemical irreversibility in the direct heterogeneous electron transfer reactions between electrodes and biological molecules. The irreversible nature of direct electron transfer observed in these early studies precluded the accurate and precise characterization of the electron transfer stoichiometry and thermodynamics of biological molecules. The models alluded to above were often used to account for the irreversible electron transfer kinetics observed in these studies. 

Electrochemical irreversibility caused by slow heterogeneous electron-transfer kinetics at the electrode surface can limit the ability of the measurement to yield thermodynamically meaningful potentials. While proton transfer in aqueous solutions is generally very fast, heterogeneous... 

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). 

Van Rysselberghe, J. Chem. Educ. 41 (1964) 486 see also Thermodynamics of Irreversible Electrochemical Processes, pp. 743-747, and Remarks on Nomenclature, pp. 859-861, in The Encyclopedia of Electrochemistry, Ed Hampel, Reinhold Publishing Corp., New York, 1964. 

The total heat flux qT emitted by the MEA is determined by thermodynamic and irreversible heat released in the electrochemical reactions (Section 2.8) ... 

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 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. 

Consider the cyclic voltammetry trace of electrically activated iridium oxide (the so called AIROF) which features reversible reactions (Fig. 3.3). The scan rate is very slow, so the dynamic behavior of the Helmholtz capacitance has a negligible effect on the measured trace. The positive peaks A and B correspond to two distinct oxidation reactions at the surface of the electrode, pertaining to different electrode potentials. The negative peaks C and D correspond to reduction reactions. C matches A and D matches B, as they have similar shape. The reduction potential peak (for example at C, Epc) does not happen at a negative electrode-electrolyte voltage drop, but at a positive one even near to the potential where oxidation potential peak (at A, Epa) is located. If the surface redox reactions are fast and the reaction rate is limited by the diffusion of the reactants in the solution, the difference between the oxidation and reduction peaks is only 59 mV/n for a reaction where n electrons are transferred in the stoichiometry of the reaction. This state is called electrochemical reversibility, which means that the thermodynamic equilibrium in the redox reaction at the surface is established fast at every applied electrode potential. Note that this concept is not the same as the chemical reversibility explained before. A system can be electrochemically irreversible but chemically reversible. As seen in Fig. 3.3, iridium oxide is already electrochemically irreversible even at the very slow potential ramp of 50 mV/s, as the , 4 — is already larger than 59 mV. 

Whenever energy is transformed from one form to another, an iaefficiency of conversion occurs. Electrochemical reactions having efficiencies of 90% or greater are common. In contrast, Carnot heat engine conversions operate at about 40% efficiency. The operation of practical cells always results ia less than theoretical thermodynamic prediction for release of useful energy because of irreversible (polarization) losses of the electrode reactions. The overall electrochemical efficiency is, therefore, defined by ... 

As already stated, other electrochemical techniques have been used to derive thermodynamic data, some of them considered to yield more reliable (reversible) redox potentials than cyclic voltammetry. This is the case, for instance, of second harmonic alternating current voltammetry (SHACV) [219,333], Saveant and co-workers [339], however, concluded that systems that appear irreversible in slow-scan CV are also irreversible in SHACV experiments. We do not dwell on these matters, important as they are. Instead, we concentrate on a different methodology to obtain redox potentials, which was developed by Wayner and colleagues [350-352]. 

These derivatives undergo an irreversible oxidation process. Assuming that such electron removal involves an electrochemically reversible process complicated by fast chemical reactions, a thermodynamic meaning can be assigned to the different peak potential values. 

Figure 10. Kleitz s reaction pathway model for solid-state gas-diffusion electrodes. Traditionally, losses in reversible work at an electrochemical interface can be described as a series of contiguous drops in electrical state along a current pathway, for example. A—E—B. However, if charge transfer at point E is limited by the availability of a neutral electroactive intermediate (in this case ad (b) sorbed oxygen at the interface), a thermodynamic (Nernstian) step in electrical state [d/j) develops, related to the displacement in concentration of that intermediate from equilibrium. In this way it is possible for irreversibilities along a current-independent pathway (in this case formation and transport of electroactive oxygen) to manifest themselves as electrical resistance. This type of chemical valve , as Kleitz calls it, may also involve a significant reservoir of intermediates that appears as a capacitance in transient measurements such as impedance. Portions of this image are adapted from ref 46. (Adapted with permission from ref 46. Copyright 1993 Rise National Laboratory, Denmark.)...

So the product, R, of the electrochemical reduction reacts in the solution with an electroinactive oxidizer, Ox, to regenerate O, etc. If Ox is present in large excess, the chemical reaction is pseudo-first-order in R and O. For thermodynamic reasons, Rc can only proceed if the standard potential of the redox couple Ox/Red is more positive than that of O/R. Then, for Ox to be electroinactive, it is required that its electroreduction proceeds irreversibly, in a potential range far negative to the faradaic region of the 0/R reaction. Thus, Ox being stable for reasons of the slow kinetics of its direct reduction, it can be said that, in the presence of O, it is being catalytically reduced. 

Solid state reactions occur mainly by diffusional transport. This transport and other kinetic processes in crystals are always regulated by crystal imperfections. Reaction partners in the crystal are its structure elements (SE) as defined in the list of symbols (see also [W. Schottky (1958)]). Structure elements do not exist outside the crystal lattice and are therefore not independent components of the crystal in a thermodynamic sense. In the framework of linear irreversible thermodynamics, the chemical (electrochemical) potential gradients of the independent components of a non-equilibrium (reacting) system are the driving forces for fluxes and reactions. However, the flux of one independent chemical component always consists of the fluxes of more than one SE in the crystal. In addition, local reactions between SE s may occur. 

These polymerizations depend upon the ability to oxidize the monomer to a radical cation, whose further reactions lead to polymer. Since the oxidation potentials of the polymers are lower than those of the corresponding monomer, the polymer is simultaneously oxidized into a conducting state so that it is non-passivating. Some of the more important electrochemically-synthesised structures are discussed in more detail below and Chandler and Pletcher U4) have reviewed the electrochemical synthesis of conducting polymers. Detailed discussion in terms of thermodynamic parameters is impossible because the polymerizations are irreversible, so that E0 is undefined for the monomer-polymer equilibrium. 

The values for the redox potential for the couple M3 + /M2+ have been estimated57 using a simple ionic model and available thermodynamic data. The results (Table 2) correlate closely with the ionization potentials for the M2+ ions, and are in good agreement with both chemical observations and other estimates obtained by spectroscopic correlations. Irreversible oxidation of terbium(m) to terbium(iv) in aqueous K2C03-K0H solutions has been observed electrochemically 58 the discovery of an intermediate of mixed oxidation state explains partly the reduction behaviour of terbium(iv) deposits. Praseodymium(iv) and terbium(iv) have also been detected in nitrate solutions. 

In thermodynamic equilibrium, the electrochemical potential of a particle k (juk = Hk + zkeq>, juk = chemical potential,

electrical potential, zk = charge number of the particle, e = elementary charge) is constant. Gradients in jlk lead to a particle flux Jk and from linear irreversible thermodynamics [95] the fundamental transport... 

Fig. 2 distinguishes the domains of immunity, corrosion and passivity. At low pH corrosion is postulated due to an increased solubility of Cu oxides, whereas at high pH protective oxides should form due to their insolubility. These predictions are confirmed by the electrochemical investigations. The potentials of oxide formation as taken from potentiodynamic polarization curves [10] fit well to the predictions of the thermodynamic data if one takes the average value of the corresponding anodic and cathodic peaks, which show a certain hysteresis or irreversibility due to kinetic effects. There are also other metals that obey the predictions of potential-pH diagrams like e.g. Ag, Al, Zn. 

Catalytic reactions in electrochemistry — When the product of an electrochemical reduction reaction is regenerated by a chemical reoxidation, or when the product of an electrochemical oxidation is regenerated by a re-reduction, the regeneration reaction is called a catalytic reaction. For thermodynamic reasons the chemical oxidant (or the reductant) has to be electro-chemically irreversible in the potential range where the catalyst is electroactive. The reduction of Ti(IV) in the presence of hydroxylamine is an example for an oxidative regeneration [i, ii] ... 

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