Electrochemical systems, thermodynamics

Regarding the electrode/electrolyte interface, it is important to distinguish between two types of electrochemical systems thermodynamically closed (and in equilibrium) and open systems. While the former can be understood by knowing the equilibrium atomic structure of the interface and the electrochemical potentials of all components, open systems require more information, since the electrochemical potentials within the interface are not necessarily constant. Variations could be caused by electrocatalytic reactions locally changing the concentration of the various species. In this chapter, we will focus on the former situation, i.e., interfaces in equilibrium with a bulk electrode and a multicomponent bulk electrolyte, which are both influenced by temperature and pressures/activities, and constrained by a finite voltage between electrode and electrolyte. 

The industrial economy depends heavily on electrochemical processes. Electrochemical systems have inherent advantages such as ambient temperature operation, easily controlled reaction rates, and minimal environmental impact (qv). Electrosynthesis is used in a number of commercial processes. Batteries and fuel cells, used for the interconversion and storage of energy, are not limited by the Carnot efficiency of thermal devices. Corrosion, another electrochemical process, is estimated to cost hundreds of millions of dollars aimuaUy in the United States alone (see Corrosion and CORROSION control). Electrochemical systems can be described using the fundamental principles of thermodynamics, kinetics, and transport phenomena. 

Determining the cell potential requites knowledge of the thermodynamic and transport properties of the system. The analysis of the thermodynamics of electrochemical systems is analogous to that of neutral systems. Eor ionic species, however, the electrochemical potential replaces the chemical potential (1). 

This equation links the EMF of a galvanic cell to the Gibbs energy change of the overall current-producing reaction. It is one of the most important equations in the thermodynamics of electrochemical systems. It follows directly from the first law of thermodynamics, since nF% is the maximum value of useful (electrical) work of the system in which the reaction considered takes place. According to the basic laws of thermodynamics, this work is equal to -AG . 

The EMF values of galvanic cells and the electrode potentials are usually determined isothermally, when all parts of the cell, particularly the two electrode-electrolyte interfaces, are at the same temperature. The EMF values will change when this temperature is varied. According to the well-known thermodynamic Gibbs-Helmholtz equation, which for electrochemical systems can be written as... 

In this chapter, we will give a general description of electrochemical interfaces representing thermodynamically closed systems constrained by the presence of a hnite voltage between electrode and electrolyte, which will then be taken as the basis for extending the ab initio atomistic thermodynamics approach [Kaxiras et ah, 1987 Scheffler and Dabrowski, 1988 Qian et al., 1988 Reuter and Scheffler, 2002] to electrochemical systems. This will enable us to qualitatively and quantitatively investigate and predict the structures and stabilities of full electrochemical systems or single electrode/electrolyte interfaces as a function of temperature, activi-ties/pressures, and external electrode potential. 

Before we will discuss the electrochemical system, it is important to define the properties and characteristics of each component, especially the electrolyte. In the following, we assume macroscopic amounts of an electrolyte containing various ionic and nonionic components, which might be solvated. In the case that this bulk electrolyte is in thermodynamic equilibrium, each of the species present is characterized by its electrochemical potential, which is defined as the free energy change with respect to the particle number of species i ... 

Now having specified the bulk electrode, the bulk electrolyte, and the interface between them, our aim in this section is to quantify the atomistic structure of the interface and derive an expression that allows us to evaluate its stabUity. Based on (5.5), we wUl extend the ab initio atomistic thermodynamics approach to electrochemical systems. 

Although the extended ab initio atomistic thermodynamics approach provides an exact expression for the interfacial stability, the formalism requires self-consistent modeling of the entire electrochemical system, or electrode/electrolyte interface, exceeding presently available computational capabilities. Therefore, certain assumptions had to be made that reduce the effort to the calculation of the electrode surface only. Even with this simplified approach, which has been applied to the two examples discussed in this chapter, the qualitative behavior can be reproduced. 

Jacob T, Scheffler M. 2007. Extended ab-initio atomistic thermodynamics for electrochemical systems. Submitted for publication. 

Parsons, R., Thermodynamic methods for the study of interfacial regions in electrochemical systems, CTE, 1, 1 (1980). 

THL. 28.1. Prigogine, P. Mazur et R. Defay, Bilans thermodynamiques locaux dans les systemes electrochimiques (Local thermodynamic balances in electrochemical systems), J. Chim. Phys. 50, 146-155 (1953). 

For this reaction AG° = —235.76 kj/mol and A/T = —285.15 kj/mol. Fuel cells follow the thermodynamics, kinetics, and operational characteristics for electrochemical systems outlined in sections 1 and 2. The chemical energy present in the combination of hydrogen and oxygen is converted into electrical energy by controlled electrochemical reactions at each of the electrodes in the cell. 

More recently, the use of a pyridinium mediator in an aqueous p-GaP photo-electrochemical system illuminated with 365 nm and 465 nm light has been reported [125], In this case, a near-100% faradaic efficiency was obtained for methanol production at underpotentials of 300-500 mV from the thermodynamic C02/methanol couple. Moreover, quantum efficiencies of up to 44% were obtained. The most important point here, however, was that this was the first report of C02 reduction in a photoelectrochemical system that required no input of external electrical energy, with the reduction of C02 being effected solely by incident fight energy. 

For engineering purposes, thermodynamic calculations are useful in several respects. First, they tell us whether a proposed electrochemical system can proceed spontaneously in a given direction. Second, they tell us the maximum work that can be derived from a given cell or, conversely, the minimum work that must be expended... 

Potentiometry has found extensive application over the past half-century as a means to evaluate various thermodynamic parameters. Although this is not the major application of the technique today, it still provides one of the most convenient and reliable approaches to the evaluation of thermodynamic quantities. In particular, the activity coefficients of electroactive species can be evaluated directly through the use of the Nemst equation (for species that give a reversible electrochemical response). Thus, if an electrochemical system is used without a junction potential and with a reference electrode that has a well-established potential, then potentiometric measurement of the constituent species at a known concentration provides a direct measure of its activity. This provides a direct means for evaluation of the activity coefficient (assuming that the standard potential is known accurately for the constituent half-reaction). If the standard half-reaction potential is not available, it must be evaluated under conditions where the activity coefficient can be determined by the Debye-Hiickel equation. 

Since about 1989, Homo and coworkers have published a series of papers on their network thermodynamic method of simulation. Only a few of these will be cited here. In the first, the 1989 work, the method is described [309], and again in 1992-4 [271,305,306], adding cyclic voltammetry. In the 1994 paper [305], there is a good description of the method, and an indication how it can be adapted to a multitude of different electrochemical systems. A Chinese group has also used this method [205,208,209,210]. 

Consider the electrochemical system shown in Fig. 19 consisting of three Pt-solution interfaces in room-temperature solutions. The middle chamber is separated from the outer chambers by a porous membrane that limits mass transport, allowing the solutions to remain at different pH. Chamber A represents a NHE reference electrode the pH is zero and hydrogen gas is present at 1 atm. At this Pt-solution interface, the HER reaction is in thermodynamic equilibrium. A... 

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