Electrolyte interface theory

The Temperature and Potential Dependence of Electrochemical Reaction Rates, and th Real Form of the Tafel Equation Theoretical Aspects of Semiconductor Electrochemistry Theories for the Metal in the Metal-Electrolyte Interface Theories of Elementary Homogeneous Electron-Transfer Reactions Theory and Applications of Periodic Electrolysis... 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

By tradition, electrochemistry has been considered a branch of physical chemistry devoted to macroscopic models and theories. We measure macroscopic currents, electrodic potentials, consumed charges, conductivities, admittance, etc. All of these take place on a macroscopic scale and are the result of multiple molecular, atomic, or ionic events taking place at the electrode/electrolyte interface. Great efforts are being made by electrochemists to show that in a century where the most brilliant star of physical chemistry has been quantum chemistry, electrodes can be studied at an atomic level and elemental electron transfers measured.1 The problem is that elemental electrochemical steps and their kinetics and structural consequences cannot be extrapolated to macroscopic and industrial events without including the structure of the surface electrode. 

Electrochemical impedance spectroscopy leads to information on surface states and representative circuits of electrode/electrolyte interfaces. Here, the measurement technique involves potential modulation and the detection of phase shifts with respect to the generated current. The driving force in a microwave measurement is the microwave power, which is proportional to E2 (E = electrical microwave field). Therefore, for a microwave impedance measurement, the microwave power P has to be modulated to observe a phase shift with respect to the flux, the transmitted or reflected microwave power APIP. Phase-sensitive microwave conductivity (impedance) measurements, again provided that a reliable theory is available for combining them with an electrochemical impedance measurement, should lead to information on the kinetics of surface states and defects and the polarizability of surface states, and may lead to more reliable information on real representative circuits of electrodes. We suspect that representative electrical circuits for electrode/electrolyte interfaces may become directly determinable by combining phase-sensitive electrical and microwave conductivity measurements. However, up to now, in this early stage of development of microwave electrochemistry, only comparatively simple measurements can be evaluated. 

The popular and well-studied primitive model is a degenerate case of the SPM with = 0, shown schematically in Figure (c). The restricted primitive model (RPM) refers to the case when the ions are of equal diameter. This model can realistically represent the packing of a molten salt in which no solvent is present. For an aqueous electrolyte, the primitive model does not treat the solvent molecules exphcitly and the number density of the electrolyte is umealistically low. For modeling nano-surface interactions, short-range interactions are important and the primitive model is expected not to give adequate account of confinement effects. For its simphcity, however, many theories [18-22] and simulation studies [23-25] have been made based on the primitive model for the bulk electrolyte. Ap-phcations to electrolyte interfaces have also been widely reported [26-30]. 

The beginning of the twentieth century also marked a continuation of studies of the structure and properties of electrolyte solution and of the electrode-electrolyte interface. In 1907, Gilbert Newton Lewis (1875-1946) introduced the notion of thermodynamic activity, which proved to be extremally valuable for the description of properties of solutions of strong electrolytes. In 1923, Peter Debye (1884-1966 Nobel prize, 1936) and Erich Hiickel (1896-1981) developed their theory of strong electrolyte solutions, which for the first time allowed calculation of a hitherto purely empiric parameter—the mean activity coefficients of ions in solutions. 

Figure 2.11 According to the Gouy-Chapman theory, the capacity of the electrode/electrolyte interface should be a cosh function of the potential difference across it (see text). Concentration of electrolyte in (b) > than that in (a).

Largely through the painstaking work of Grahame in the 1940s, electrocapillarity effectively established the first experimental basis for the now accepted double layer theory. The basic picture of the electrode/electrolyte interface was thus in place. 

Before describing the application of Raman to the study of the electrode/ electrolyte interface, a brief recap of the theory of Raman spectroscopy may be helpful. 

Surface Potential-pH Characteristics in the Theory of the Oxide-Electrolyte Interface... 

In this article, a brief discussion will be given on the relevance of continuum theory in explaining the rate of electron transfer and the activation of species in solution we will concentrate in particular on molecular and quantum mechanical models of ET reactions at the electrode/electrolyte interface that are needed to replace those based on the continuum approach. ... 

Activation polarization arises from kinetics hindrances of the charge-transfer reaction taking place at the electrode/electrolyte interface. This type of kinetics is best understood using the absolute reaction rate theory or the transition state theory. In these treatments, the path followed by the reaction proceeds by a route involving an activated complex, where the rate-limiting step is the dissociation of the activated complex. The rate, current flow, i (/ = HA and lo = lolA, where A is the electrode surface area), of a charge-transfer-controlled battery reaction can be given by the Butler—Volmer equation as... 

Earlier, Gavach et al. studied the superselectivity of Nafion 125 sulfonate membranes in contact with aqueous NaCl solutions using the methods of zero-current membrane potential, electrolyte desorption kinetics into pure water, co-ion and counterion selfdiffusion fluxes, co-ion fluxes under a constant current, and membrane electrical conductance. Superselectivity refers to a condition where anion transport is very small relative to cation transport. The exclusion of the anions in these systems is much greater than that as predicted by simple Donnan equilibrium theory that involves the equality of chemical potentials of cations and anions across the membrane—electrolyte interface as well as the principle of electroneutrality. The results showed the importance of membrane swelling there is a loss of superselectivity, in that there is a decrease in the counterion/co-ion mobility, with greater swelling. 

Bourrie, G. Trolard, F. Jaffrezic, J.-M. R.G.-A. Maitre,V. Abdelmoula, M. (1999) Iron control by equilibria between hydroxy-Green Rusts and solutions in hydromorphic soils. Geochim. Cosmochim. Acta 63 3417-3427 Bousse, L. Meindl, J.D. (1986) The importance of > /o/pH characteristics in the theory of the oxide/electrolyte interface. In Davis, J.A. Hayes, KF. (eds.) Geochemical processes... 

Boroda YG, Voth GA (1996) A theory of adiabatic electron transfer processes across the semiconductor-electrolyte interface. J Chem Phys 106 6168-6183... 

Solar energy conversion in photoelectrochemical cells with semiconductor electrodes is considered in detail in the reviews by Gerischer (1975, 1979), Nozik (1978), Heller and Miller (1980), Wrighton (1979), Bard (1980), and Pleskov (1981) and will not be discussed. The present chapter deals with the main principles of the theory of photoelectrochemical processes at semiconductor electrodes and discusses the most important experimental results concerning various aspects of photoelectrochemistry of a semiconductor-electrolyte interface a more comprehensive consideration of these problems can be found in the book by the authors (Pleskov and Gurevich,... 

Photoelectrochemistry (PEC) is emerging from the research laboratories with the promise of significant practical applications. One application of PEC systems is the conversion and storage of solar energy. Chapter 4 reviews the main principles of the theory of PEC processes at semiconductor electrodes and discusses the most important experimental results of interactions at an illuminated semiconductor-electrolyte interface. In addition to the fundamentals of electrochemistry and photoexcitation of semiconductors, the phenomena of photocorrosion and photoetching are discussed. Other PEC phenomena treated are photoelectron emission, electrogenerated luminescence, and electroreflection. Relationships among the various PEC effects are established. 

While the ability to treat capture cross sections theoretically is very primitive and the experimental data on capture cross sections are very limited this phenomenological parameter seems to be an appropriate meeting place for experiment and theory. More work in both of these areas is needed to characterize and understand the important role of surface states in electron transfer at semiconductor-electrolyte interfaces. 

Here we have sought to show how currently accessible simulation techniques can be brought to bear on qualitative and quantitative issues in the study of electrode-electrolyte interface. In our view, which we hope is exemplified by the cases described in detail, the firmest and most enlightening conclusions can be drawn when there are very tight links between theory, simulation, and experiment. One hears it said, for example, that there is no need for more theory in electrochemistry because we have the theory. But in the examples cited, we have seen that studies in which careful attention is paid to making simulations quantitatively realistic, qualitative conclusions can emerge which are not part of the currently accepted theoretical picture. This occurred in our studies of the fields near electrodes and also in our discovery of the importance of approach free energy in the kinetic barrier for the cuprous-cupric electron transfer. 

---