Electrochemical systems chemical potential

For the first purpose we choose a chemical reaction system with some ionic species, as for example the minimal bromate reaction, for which we presented some experiments in Chap. 10. The system may be in equilibrium or in a nonequilibrium stationary state. An ion selective electrode is inserted into the chemical system and coimected to a reference electrode. The imposition of a current flow through the electrode coimection drives the chemical system (CS) away from its initial stationary state to a new stationary state of the combined chemical and electrochemical system (CCECS), analogous to driving the CS away from equilibrium in the same maimer. A potential difference is generated by the imposed current, which consists of a Nernstian term dependent on concentrations only, and a non-Nernstian term dependent on the kinetics. We shall relate the potential difference to the stochastic potential for this we need to know the ionic species present and their concentrations, but we do not need to know the reaction mechanism of the chemical sj tem, nor rate coefficients. 

When considering the thermodynamics of nucleation and the mechanism of the elementary acts of single ions attachment and detachment to and from a growing cluster or a crystal surface, it proves convenient to work not with molar but with molecular quantities. For that reason the molecular unit to be used in Chapters 1 and 2 ofthis book will be not a mol but uparticle - atom, ion or molecule - and aU physical quantities like chemical and electrochemical potential, electric charge etc. will be referred to this unit. In what follows we consider the conditions that characterize the thermod5Uiamic equilibrium in chemical and electrochemical systems. 

The chemical potential now includes any such effects, and one refers to the gmvochemicalpotential, the electrochemical potential, etc. For example, if the system consists of a gas extending over a substantial difference in height, it is the gravochemical potential (which includes a tenn m.gh) that is the same at all levels, not the pressure. The electrochemical potential will be considered later. 

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). 

The analysis of thermodynamic data obeying chemical and electrochemical equilibrium is essential in understanding the reactivity of a system to be used for deposition/synthesis of a desired phase prior to moving to experiment and/or implementing complementary kinetic analysis tools. Theoretical and (quasi-)equilibrium data can be summarized in Pourbaix (potential-pH) diagrams, which may provide a comprehensive picture of the electrochemical solution growth system in terms of variables and reaction possibilities under different conditions of pH, redox potential, and/or concentrations of dissolved and electroactive substances. 

The electrochemical potential of single ionic species cannot be determined. In systems with charged components, all energy effects and all thermodynamic properties are associated not with ions of a single type but with combinations of different ions. Hence, the electrochemical potential of an individual ionic species is an experimentally undefined parameter, in contrast to the chemical potential of uncharged species. From the experimental data, only the combined values for electroneutral ensembles of ions can be found. Equally inaccessible to measurements is the electrochemical potential, of free electrons in metals, whereas the chemical potential, p, of the electrons coincides with the Fermi energy and can be calculated very approximately. 

In electrochemical systems, many restrictions exist in the use of metal catalysts. Most metals other than the expensive noble metals are unstable at anodic potentials and cannot be nsed for anodic processes. The catalytic activity and selectivity of metal catalysts basically are determined by their chemical nature and are rarely open to adjustments. 

Furthermore, fixing the chemical potential of some of the atoms of the system corresponds to the electrochemical situation of potentiostatic control, since the chemical potential of the atoms can be written as... 

Focusing on the example of a sohd/gas interface, in the following, we will describe how to evaluate the stabihty of non-electrochemical interfaces, which are not influenced by a potential apphed externally or caused by an inhomogeneous ion distribution within the system. In the case that both the solid and the gaseous phase are present in macroscopic quantities, we have already seen in the previous section that each of these reservoirs is characterized by its chemical potential fifT, pi), which for the non-electrochemical interface is a function of temperature and partial pressure. 

Related Polymer Systems and Synthetic Methods. Figure 12A shows a hypothetical synthesis of poly (p-phenylene methide) (PPM) from polybenzyl by redox-induced elimination. In principle, it should be possible to accomplish this experimentally under similar chemical and electrochemical redox conditions as those used here for the related polythiophenes. The electronic properties of PPM have recently been theoretically calculated by Boudreaux et al (16), including bandgap (1.17 eV) bandwidth (0.44 eV) ionization potential (4.2 eV) electron affinity (3.03 eV) oxidation potential (-0.20 vs SCE) reduction potential (-1.37 eV vs SCE). PPM has recently been synthesized and doped to a semiconductor (24). 

An electrochemical system differs from a chemical system in the presence of an additional variable. In a chemical system, the variables are temperature (T), pressure (p) and composition ( tj, the chemical potential of component i). In an electrochemical system, in addition to T,p and (tj, its electrical state is an additional variable. Since an electrochemical system consists of two electron conductors in contact with an ionic conductor (electrolyte), the electrical state is measured by the electrode potential . 

Again it seems not necessary to discuss the considerations of the chemical versus electrochemical reaction mechanism. It is clear from the extremely negative standard potential of silicon, from Eqs. (2) and (6), that the Si electrode is in all aqueous solutions a dual redox system, characterized by its OCP, which is the resultant of an anodic Si dissolution current and a simultaneous reduction of oxidizing species in solution. The oxidation of silicon gives four electrons that are consumed in the reduction reaction. Experimental results show clearly that the steady value of the OCP is narrowly dependent on the redox potential of the solution components. In solutions containing only HF, alternatively alkaline species, the oxidizing component is simply the proton H+ or the H2O molecule respectively. 

Nickel(II) complexes with a variety of tetraaza macrocycles have been found to undergo facile one-electron redox reactions. Such reactions have been accomplished by means of both chemical and electrochemical procedures. The kinetic inertness and thermodynamic stability of the tetraaza macrocyclic complexes of nickel(II) make them particularly suitable systems for the study of redox processes. A very extensive summary of the potentials for the redox reactions of nickel(II) complexes with a variety of macrocycles is given in ref. 2622. 

In chemically homogeneous ionic crystals, may be the only driving force. In inhomogeneous systems, the electrochemical potential gradient Vrij = Vnt+ZjF-Vtp acts upon the mobile charged species i. The additivity of Vp, and stems from the very small electric charge number needed to establish the internal electric field, which is on the order of 1 [V/cm]. These charges are too small to interfere with the concentrations that determine the chemical potentials p,. 

For the sake of completeness, Figure 4-5 illustrates the more general situation of isothermal, isobaric matter transport in a multiphase system (e.g., Fe/Fe0/Fe304 / 02). A sequence of phases a, (3, y,... is bounded by two reservoirs which contain both neutral components (i) and electronic carriers (el). The boundary conditions imply that the buffered chemical potentials (u,(R)) and the electrochemical potentials (//el(R)) are predetermined in R] and Rr. Depending on the concentrations and mobilities (c/, b), c, 6 ) in the various phases v, metallic conduction, semiconduction, or ionic conduction will prevail. As long as the various phases are thermodynamically stable and no decomposition occurs, the transport equations (including the boundary conditions) are well defined and there is normally a unique solution to the transport problem. 

With electrochemical methods, we determine thermodynamic potentials of components in systems which contain a sufficiently large number of atomic particles. Since the systematic investigation of solid electrolytes in the early 1920 s, it is possible to change the mole number of a component in a crystal via the corresponding flux across an appropriate electrolyte (1 mA times 1 s corresponds to ca. 10 s mol). Simultaneously, the chemical potential of the component can be determined with the same set-tip under open circuit conditions. Provided both the response time and the buffer capacity of the galvanic cells are sufficiently small, we can then also register the time dependence of the component chemical potentials in the reacting solids. ... 

This partial molar change of free energy is called the chemical potential of species i. If this species is charged (i.e., an ion) it is called the electrochemical potential of species i because the change of the free energy of the system includes a component of electrical work. 

Recent developments in the field of sensing airborne chemicals using electrochemical sensors and sensor arrays are reviewed. Such systems detect, Identify, and quantify potential chemical hazards to protect the health and safety of workers and citizens. The application discussed In this review article Is single chemicals at part-per-million levels in air. The sensor system consists of an array of sensors used In four modes of operation, and the data are Interpreted by a computer algorithm. Pattern recognition techniques are being used to understand the information content of the arrays and to focus future experimental work. 

Electrochemistry deals with charged particles that have both electrical and chemical properties. Since electrochemical interfaces are usually referred as electrified interfaces, it is clear that potential differences, charge densities, dipole moments, and electric currents occur at these interfaces. The electrical properties of systems containing charged species are very important for understanding how they behave at interfaces. Therefore, it is important to have a precise definition of the electrostatic potential of a phase [1-6]. Note that what really matters in electrochemical systems is not the value of the potential but its difference at a given interface, although it is illustrative to discuss its main properties. 

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