Classic electrochemical theory

This paper attempts to model and define the conditions under which platinum Eh measurements are likely to reflect the true electrical potential of aqueous solutions. The double layer at the surface of the electrode is modeled as a fixed capacitor (C jj), and the rate at which an electrode equilibrates with a solution (i.e. the rate at which C jj is charged) is assumed to be proportional to the electrical current at this interface. The current across the electrode/solution interface can be calculated from classical electrochemical theory, in which the current is linearly proportional to the concentration and electron-transfer rate constant of the aqueous species, and is exponentially proportional to the potential across the interface. 

To date, it has been documented that ILs can be adsorbed onto various electrode surfaces. For example, Nanjundiah et al. found that several ILs used as electrolytes can induce double-layer capacitance phenomena on the surface of an Hg electrode and obtained the respective capacitance values for various ILs. Hyk and Stojek have also studied the IL thin layer on electrode surfaces and suggested that counterions substantially influence the distribution of IL. Kornyshev further discussed IL formations on electrode surfaces, suggesting that IL studies should be based on modern statistical mechanics of dense Coulomb systems or density-functional theory rather than classical electrochemical theories that hinge on a dilute-solution approximation. There are three conventional models that describe the charge distribution of an ion near a charged surface the Helmholtz model, the Gouy-Chapman model, and the Stern model. In the case of ILs, it remains controversial which model can best explain and lit the experimental data. 

The interpretation of phenomenological electron-transfer kinetics in terms of fundamental models based on transition state theory [1,3-6,10] has been hindered by our primitive understanding of the interfacial structure and potential distribution across ITIES. The structure of ITIES was initially studied by electrochemical and thermodynamic analyses, and more recently by computer simulations and interfacial spectroscopy. Classical electrochemical analysis based on differential capacitance and surface tension measurements has been extensively discussed in the literature [11-18]. The picture that emerged from... 

Abruna HD (1991) X-ray Absorption Spectroscopy in the Study of Electrochemical Systems. In Electrochemical Interfaces. Abruna HD (ed) VCH Publishers, New York Albertini G, Carsughi F, Casale C, Fiori F, La Monaca A, Musci M (1993) X-ray and neutron small-angle scattering Investigation of nanophase vanadium-titanium oxide particles. Phil Mag B 68 949-955 Alexandrowicz Z (1993) How to reconcile classical nucleation theory with cluster-cluster aggregation. Physica A 200 250-257... 

We now turn to the hierarchy of electron-transfer rate theories that have developed since the 1950s, starting with classical Marcus theory of homogeneous reactions and the development of eq. 4.4. In later sections we shall consider theories of nonadiabatic ET, which allow the identification and evaluation of the prefactor A in eq. 4.4, and also electrochemical ET, which differs from homogeneous reactions in that an electronic conductor is one of the reactants . 

Mercury electrodeposition is a model system for experimental studies of electrochemical phase formation. On the one hand, the product obtained is a liquid drop, corresponding very well with the liquid drop model of classical nucleation theory. Besides, electron transfer is fast [61] and therefore the growth of nuclei is controlled by mass transport to the electrode surface [44]. On the other hand, the properties of the mercuryjaqueous solution interface have been the object of study for over a century and hence are fairly well understood. The high overpotential for proton reduction onto both mercury and vitreous carbon favor the study of the process over a wide range of overpotentials. In spite of the complications introduced by the equilibrium between the Hg +, Hg2 " ", and Hg species, this system offers an excellent opportunity to verily the fundamental postulates of the electrochemical nucleation theory. In fact, the dependence of the nucleation rate on the oxidation state of the electrodepositing species is fiiUy consistent with theory critical nuclei appear with similar sizes and onto similar number densities of active sites... 

The classical nucleation theory, based on Gibbs thermodynamics statements, uses the macroscopic properties characteristic of bulk phases, such as free energies and surface tensions, for the description of small clusters. Contradictory results arose in early studies of electrochemical nucleation [9], where the size of a critical mercury nucleus on a platinum substrate amounted to only a few atoms, with properties that could substantially differ... 

The striking quantitative contradiction between the classical nucleation theory and the experimental data accompanies the studies of electrochemical nucleation since the time of Thomfor and Volmer [2.29] who were the first to obtain a surprisingly low value for the size of a critical mercury nucleus on a platinum substrate. The problem has been successfully solved by the atomistic theory of the nucleation rate [2.10-2.12, 2.33, 2.62-2.66], which answers the question how to interpret the experimental data on electrochemical nucleation The next Section contains a survey of these theoretical considerations. 

The dominant tendency of my studies has been not so much to obtain and describe organic compounds but... to penetrate their mechanisms.. . . For undertaking this kind of problem, the classic methods of organic chemistry are far from sufficient. Physicochemical procedures become more and more necessary. I have been led to use especially optical methods (the Raman effect and ultraviolet spectra) and electrochemical techniques (conductibility, electrode potentials, and especially polarography).. . . The notion of reaction mechanism led almost automatically to envisioning the electronic aspect of chemical phenomena. From 1927, and working in common with Charles Prevost, I have directed my attention on the electronic theory of reactions." 56... 

Under pro tic conditions, aromatic hydrocarbons and compounds with activated double bonds usually undergo Birch-Kke reactions [172]. The reaction sequence has been elucidated by the classical work of Hoijtink [15-17, 173, 174], who used the HMO theory to rationalize both chemical and electrochemical steps. 

The rate constants, k+ and k of the forward and backward reactions are finally derived from (12) and (13) according to the transition-state theory, i.e. assuming that the transition and the initial states, on the one hand, and the transition and final states, on the other, are in equilibrium (Glasstone et al., 1941). Thus, estimating the partition function of these three states in the classical way gives (18) and (19), where p is the reduced mass of the two reactants in the homogeneous case and m the mass of the reactant in the electrochemical case. 

A major fallacy is made when observations obeying a known physical law are subjected to trend-oriented tests, but without allowing for a specific behaviour predicted by the law in certain sub-domains of the observation set. This can be seen in Table 11 where a partial set of classical cathode polarization data has been reconstructed from a current versus total polarization graph [28], If all data pairs were equally treated, rank distribution analysis would lead to an erroneous conclusion, inasmuch as the (admittedly short) limiting-current plateau for cupric ion discharge, albeit included in the data, would be ignored. Along this plateau, the independence of current from polarization potential follows directly from the theory of natural convection at a flat plate, with ample empirical support from electrochemical mass transport experiments. 

The small area of a microelectrode, with its proportionately low capacitance, allows its use at very short time scales compared to the time scale used with a classical voltammetric electrode. As we have seen earlier in this chapter, when microelectrodes are used at short time scales, the current follows the behavior expected for diffusion in one dimension. Thus, the development of high-speed voltammetric methods with microelectrodes was a logical step, and has greatly expanded the scope and capabilities of electrochemical techniques [41]. Rapid electrochemical methods allow evaluation of the larger rate constants of rapid heterogeneous and/or homogeneous reactions. For example, theories of hetero-... 

A classical approach72 to unravelling the mechanism of electrochemical reactions and to identifying the rate-determining step (RDS) is based on testing the validity of possible sequences of reaction stages according to the elementary theory of electron transfer. As opposed to disc voltammetry, one does not look for direct evidence such as the presence of intermediate components. As a consequence, more reaction sequences appear to be theoretically possible, which in the ideal case can be dismissed, all but one on the basis of experimental evidence. It should be pointed out that neither does the identification of intermediates by means of electrochemical or non-electrochemical techniques automatically lead to the true reaction mechanism. It is only an aid in the sense that identified intermediates must occur in a postulated reaction mechanism and that hence the number of possible mechanisms can be reduced. 

---