Electrochemical thermodynamic voltage

Figure 7. Ternary schematic of the overall thermodynamic voltage of an electrochemical cell...

When the circuit is open and no current flows, the activity of each reactant on the electrode surface is equal to its activity in the bulk. The Nemst thermodynamic voltage expression can be written in terms of the bulk activity, or the concentrations in the ideal solution simplification, and yields the open-circuit voltage (OCV) for the overall electrochemical reaction [Eq. (3.3)] of hydrogen combustion. 

If the thermodynamic, voltage, and current efficiencies are, respectively, 93%, 51%, and 95%, the total efficiency of an electrochemical energy conversion system (without heat exchange) is... 

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Such effects are observed inter alia when a metal is electrochemically deposited on a foreign substrate (e.g. Pb on graphite), a process which requires an additional nucleation overpotential. Thus, in cyclic voltammetry metal is deposited during the reverse scan on an identical metallic surface at thermodynamically favourable potentials, i.e. at positive values relative to the nucleation overpotential. This generates the typical trace-crossing in the current-voltage curve. Hence, Pletcher et al. also view the trace-crossing as proof of the start of the nucleation process of the polymer film, especially as it appears only in experiments with freshly polished electrodes. But this is about as far as we can go with cyclic voltammetry alone. It must be complemented by other techniques the potential step methods and optical spectroscopy have proved suitable. 

The information from electrochemical voltage spectroscopy (EVS) on thermodynamic parameters is in essence the same as that obtained by cyclic voltammetry. 

At present, intercalation compounds are used widely in various electrochemical devices (batteries, fuel cells, electrochromic devices, etc.). At the same time, many fundamental problems in this field do not yet have an explanation (e.g., the influence of ion solvation, the influence of defects in the host structure and/or in the host stoichiometry on the kinetic and thermodynamic properties of intercalation compounds). Optimization of the host stoichiometry of high-voltage intercalation compounds into oxide host materials is of prime importance for their practical application. Intercalation processes into organic polymer host materials are discussed in Chapter 26. 

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. 

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. 

The thermodynamic criterion for spontaneity (feasibility) of a chemical and electrochemical reaction is that the change in free energy, AG have a negative value. Free-energy change in an oxidation-reduction reaction can be calculated from knowledge of the cell voltage ... 

The electric work W required for an electrochemical process in a practical electrolytic cell will be larger than AG °. For example, the indicated value of AG° in Equation (3) corresponds to a thermodynamic standard potential difference of ° = 1.23 V, while the voltage typically applied to the cell of Figure 3.1.1 is approximately U- 1.8 V. 

If both electrode processes operate under standard conditions, this voltage is E°, the equilibrium standard electrode potential difference. Values of E and E° may be conveniently measured with electrometers of so large an internal resistance that the current flow is nearly zero. Figure 3.1.6 illustrates the measurement and the equilibrium state. The value of E° is a most significant quantity characterizing the thermodynamics of an electrochemical cell. Various important features of E and E° will be addressed in the following chapters. 

The cell voltage U is the sum of the voltage which is thermodynamically and kinetically necessary for performing the electrochemical reaction Uec (about 3 V at BDD anode) and the voltage drop A U due to the resistance of the electrolyte. For parallel plate electrodes this voltage drop is given by ... 

---