Quantum mechanics, electrode-electrolyte

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. ... 

Nov. 21, 1931, Tbilisi, Georgia, USSR - May 13, 1985) Dogonadze was one of the founders of the new science - electrochemical physics [i]. The main scientific interests of Dogonadze were focused on condensed-phase reactions. His pioneering works of 1958-59 have laid the foundations of the modern quantum-mechanical theory of elementary chemical processes in electrolyte solutions. He developed a comprehensive quantum-mechanical theory of the elementary act of electrochemical reactions of -> electron and -> proton transfer at metal and - semiconductor electrodes [ii—v]. He was the first to obtain, by a quantum-mechanical calculation, the expression for the electron transfer probability, which was published in 1959 in his work with -> Levich. He conducted a number of studies on the theory of low-velocity electrons in disordered systems, theory of solvated electrons, and theory of photochemical processes in solutions. He made an impressive contribution to the theory of elementary biochemical processes [vi]. His work in this area has led to the foundation of the theory of low-temperature -> charge-transfer processes cov-... 

In the first part of this century, electrochemical research was mainly devoted to the mercury electrode in an aqueous electrolyte solution. A mercury electrode has a number of advantageous properties for electrochemical research its surface can be kept clean, it has a large overpotential for hydrogen evolution and both the interfacial tension and capacitance can be measured. In his famous review [1], D. C. Grahame made the firm statement that Nearly everything one desires to know about the electrical double layer is ascertainable with mercury surfaces if it is ascertainable at all. At that time, electrochemistry was a self-contained field with a natural basis in thermodynamics and chemical kinetics. Meanwhile, the development of quantum mechanics led to considerable progress in solid-state physics and, later, to the understanding of electrostatic and electrodynamic phenomena at metal and semiconductor interfaces. 

While an understanding of the molecular processes at the fuel cell electrodes requires a quantum mechanical description, the flows through the inlet channels, the gas diffusion layer and across the electrolyte can be described by classical physical theories such as fluid mechanics and diffusion theory. The equivalent of Newton s equations for continuous media is an Eulerian transport equation of the form... 

For the strong-interaction electron-transfer reactions, substantial quantum mechanical resonance splitting occurs in the activated state, and the electron becomes delocalized—i.e., smeared out between the electrode and the electrolyte phase reactants. The electrode surface has a strong catalytic effect, and such reactions are sensitive to the electrode surface conditions. The theoretical treatments of electron transfer for the strong interaction case are in a very early state (35). 

In addition to the solvent contributions, the electrochemical potential can be modeled. Application of an external electric field within a metal/vacuum interface model has been used to investigate the impact of potential alteration on the adsorption process [111, 112]. Although this approach can model the effects of the electrical double layer, it does not consider the adsorbate-solvent, solvent-solvent, and solvent-metal interactions at the electrode-electrolyte interface. In another approach, N0rskov and co-workers model the electrochemical environment by changing the number of electrons and protons in a water bilayer on a Pt(lll) surface [113-115]. Jinnouchi and Anderson used the modified Poisson-Boltzmann theory and DFT to simulate the solute-solvent interaction to integrate a continuum approach to solvation and double layer affects within a DFT system [116-120]. These methods differ in the approximations made to represent the electrochemical interface, as the time and length scales needed for a fiilly quantum mechanical approach are unreachable. 

Eor ferrocene sites at the end of long alkanethiols self-organized at gold electrodes and diluted with unsubstituted thiols with the redox moiety in contact with the electrolyte (Fig. 4a), Chidsey has reported [34] curved Tafel plots (Fig. 4b), which could be fitted by equations derived from Marcus theory with values of k = 0.85 eV and Z = 6.73 x 10 s"l eV" for a reaction rate of A = 2.5 s at in Fig. 4(b). Similar curvature in Tafel plots has been reported by Faulkner and coworkers [35] for adsorbed osmium complexes at ultramicro-electrodes (UME). The temperature dependence of the rate coefficient could also be fitted from Marcus equation and electron states in the metal and coupling factors given by quantum mechanics. 

Electrochemistry is a background field for a modem theory of ET based on quantum mechanics. A short summary will be given here. Electrochemical systems are heterogeneous systems where the action takes place at the interface of a solid metal or semiconductor called the electrode, and a fluid, ionic conductor called the electrolyte. Electrochemistry started with Galvani, who serendipitously discovered that muscles of an animal may still move shortly after the animal has died, if its muscles come into contact with two different metals at the same time. Later, it was understood that electricity was involved and caused by the two metals rather than by the dead animal. In the year 1800, Volta constructed a pile where the voltage depended on the number of cells and therefore could become high if many cells were piled on top of each other with electrolytes, sucked up in an absorbing material, in between. 

Newer models of the electrode-electrolyte interface, based on quantum mechanics, will not be presented here. By taking account of the electron distribution near the surface, these models can give, in principle, an explanation for the influence of crystal orientation, but at this time they do not offer decisive insight into the variety of... 

One of the most fundamental problems in electrochemical surface science is distribution of the electric potential and the particles at the interface. The classical model which prevailed until about 1980 treated the electrode surface as a perfect and structureless conductor and did not take into account the surface electronic structure. The electrolyte was considered as an ensemble of hard, point ions immersed in a dielectric continuum. This approximation neglected the fine structure of the solvent molecules and the solute as well as their discrete interactions. In recent years, much progress has been made in providing a more realistic model of the solid-liquid electrochemical interface by applying quantum mechanical theories to model the metal... 

It is important in the quantum mechanical treatment of the electrode interface, therefore, to have a good knowledge of the structure of the electrolyte near the electrode, and also, of the electric fields at the interface. 

This section summarizes the quantum mechanical threshold theories of Brodskii and Gurevich for photoelectronic emission from metal electrodes into vacuum and into electrolyte solutions. 

The interface between a solid electrode and a liquid electrolyte is a complicated many-particle system, in which the electrode ions and electrons interact with solute ions and solvent ions or molecules through several chatmels of interaction, including forces due to quantum-mechanical exchange, electrostatics, hydrodynamics, and elastic deformation of the substrate. Over the last few decades, surface electrochemistry has been revolutionized by new techniques that enable atomic-scale observation and manipulation of solid-liquid interfaces, yielding novel methods for materials analysis, synthesis, and modification. This development has been paralleled by equally revolutionary developments in computer hardware and algorithms that by now enable simulations with millions of individual particles, so there is now significant overlap between system sizes that can be treated computationally and experimentally. 

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