Electrochemistry and solid-state physics

Constant phase elements (CPEs) have been used in bioimpedance models since the late 1920s. A CPE can be modeled by a resistor and capacitor, both having frequency-dependent values, in such a way that the phase angle is frequency independent. A CPE is mathematically simple, but not so simple as to realize with discrete, passive components in the real world. A particular type of CPE is the Warburg element, known from electrochemistry and solid state physics. It is diffusion controlled with a constant phase angle of 45° (Warburg 1899). 

Brumleve TR, Buck RP (1978) Numerical solution of the Nemst-Planck and Poisson equation system with applications to membrane electrochemistry and solid state physics. J Electrotmal Chem 90 1-31... 

Interface and colloid science has a very wide scope and depends on many branches of the physical sciences, including thermodynamics, kinetics, electrolyte and electrochemistry, and solid state chemistry. Throughout, this book explores one fundamental mechanism, the interaction of solutes with solid surfaces (adsorption and desorption). This interaction is characterized in terms of the chemical and physical properties of water, the solute, and the sorbent. Two basic processes in the reaction of solutes with natural surfaces are 1) the formation of coordinative bonds (surface complexation), and 2) hydrophobic adsorption, driven by the incompatibility of the nonpolar compounds with water (and not by the attraction of the compounds to the particulate surface). Both processes need to be understood to explain many processes in natural systems and to derive rate laws for geochemical processes. 

Stefan Christov performed and also promoted profound scientific studies in the field of quantum electrochemistry, physical chemistry, theory of chemical reactions, and solid-state physics [36 3]. His contributions related to hydrogen evolution reactions, corrosion phenomena, and electron transfer reactions are well known to those who work in these particular scientific fields. The same is valid also for the so-called Christov s characteristic temperature related to the transition rate of over- and under-barrier tunneling reactions. 

Various disciplines such as colloid chon.istry, electrochemistry, electron microscopy, and solid state physics come together in the investigation of metallic nano-particles in solution. In the studies described above, photo- and radiation chemical methods play an important role in both the preparation of nano-particles and the initiation of surface chemical processes. In fact, the field of free radical chemistry has been enriched by the studies on the interaction of radicals with the surface of finely dispersed metals. The examples mentioned here are to give the reader an impression of the many aspects which one encounters in these investigations. For more details and aspects, the reader s attention is called to recent reviews. ... 

Chen, S. and Sommers, J.M. (2001) Alkanethiolate-protected copper nanopartides spectroscopy, electrochemistry, and solid-state morphological evolution. Journal of Physical Chemistry E, 105, 8816-20. 

While the structure of metals and metal surfaces belongs to solid state physics, a basic understanding is essential for many electrochemical processes, particularly those involving adsorption. A thorough treatment of this topic is beyond the scope of this book. Many metals that are used in electrochemistry (Au, Ag, Cu, Pt, Pd, Ir) have a face-centered cubic (fee) lattice, so we will consider this case in some detail. For other lattice structures we refer to the pertinent literature [1] and to Problem 1. 

This method is undisputedly the most important innovation in this field since the advent of the surface science founding methods AES and XPS in the 1960s [14]. It has revolutionized surface structure determination and is an extremely powerful method for investigating 2D molecular pattern formation. Applications also include biology, electrochemistry, solid state physics, as well as atomic and molecular manipulation. Although most of the studies... 

Refs. [i] West AR(1984) Solid state chemistry and its applications. Wiley, Chichester [ii] Kittel C (1996) Introduction to solid state physics, 7th edn. Wiley, Chichester [Hi] Rickert H (1982) Electrochemistry of solids. An introduction. Springer, Berlin [iv] Chebotin VN (1982) Physical chemistry of solids. Khimiya, Moscow... 

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. 

The measured potential Vm, and thus jEf and K. can be varied through external polarization. Vm is the applied potential when the electrode is externally polarized and is the open-circuit potential without external polarization. When the semiconductor has no excess charge, there is no space charge region and the bands are not bent. The electrode potential under this condition is called the flatband potential Vn,. The flatband potential is an important quantity for a semiconductor electrode because it connects the energy levels of the carriers in the semiconductor to those of the redox couple in the electrolyte and it connects the paramete s that can be experimentally determined to those derived from solid-state physics and electrochemistry. It can generally be expressed as... 

The introduction of in-situ infrared spectroscopy to electrochemistry has revolutionised the study of metal/electrolyte interfaces. Modnlation or sampling techniques are applied in order to enhance sensitivity and to separate snrface species from volume species. Methods such as EMIRS (electrochemicaUy modulated IR spectroscopy) and SNIFTIRS (subtractively normalised interfacial Fonrier Transform infrared spectroscopy) have been employed to study electrocatalytic electrodes, for example. There have been surprisingly few studies of the semiconductor/electrolyte interface by infrared spectroscopy. This because up to now little emphasis has been placed on the molecnlar electrochemistry of electrode reactions at semiconductors because the description of charge transfer at semiconductor/electrolyte interfaces is derived from solid-state physics. However, the evident need to identify the chemical identity of snrface species should lead to an increase in the application of in-situ FTIR. 

In most books on electrochemistry k and Uj are used as symbols for conductivity and mobility, respectively. In order to have the same symbols throughout this book, we are using here those which were introduced in the solid state physics chapter). 

Finally, it turns out that the new definitions of electronic chemical potential, //, and hardness, rj, in DFT are actually old concepts in both solid-state physics and electrochemistry. In these fields it is often convenient to think of solids as havng electrons which are relatively free to move about, and which are independent components rather than appendages of the atoms. 

An understanding of the mechanisms of the reactions in electrodics is provided by physical electrochemistry through the analysis of the electronic and ionic phases. For the first phase, the electronic character of the metals is important and hence solid state physics comes into focus. The quantal characteristic of the metal conductor defines the surface structure properties that are dealt by quantum electrochemistry. The concept of quantum particles is one of the main considerations of this chapter. The properties of the dual nature of this corpuscular wave produce equivocal understanding even in electrocatalysis. When a beam of electrons passes through a solid, the effective mass is the real quantity to be considered in the calculations, since the interactions of the electron with a nucleus are shielded by strong electrostatic interactions. 

The use of experimental physics and the implementation of new theoretical concepts and methods from solid-state physics or statistical mechanics to electrochemistry contributed to the development of surface electrochemistry. This was particularly important for a better understanding of the electric double layer or, more generally speaking, of the solvent structure near a charged metal (by shifting the Fermi level upward or downward). Important results came from computer simulations of the electric double layer that yielded new information about the spatial distribution of ions and water molecules toward the electrode surface [30]. 

As its name suggests, photoelectrochemistry is a hybrid of electrochemistry and photochemistry, and it also incorporates aspects of solid state physics, photophysics... 

Photovoltaic (PV) cells are physical devices that operate on the principles of solid-state physics. Another class of device - one that is capable of splitting water - is based on photo-electrochemical reactions, which take place at electrodes that are light-sensitive. Photo-electrochemistry may serve to generate d.c. electricity (via dye-sensitized solar cells) and this can then be used to electrolyze water (as with PV cells). Alternatively, light illuminating an electrode may reduce water directly to hydrogen - a process known as photolysis . These two processes are described next. 

The characteristic temperature proves to be very useful in the study of all tunneling phenomena depending on temperature. Therefore, it is widely used in chemistry, electrochemistry, solid state physics, and biophysics /20,64,66,67/9/119-129/. It provides the possibility of a determination of three temperature ranges ... 

As corrosion protection by active coatings such as Zn-rich [3], Mg-rich [11], or CP-coatings relies on electrical communication with the underlying metal, the nature of any intervening oxide layer will likely play an important role. As discussed in Section 15.6.3, the electrodeposition of CP films on oxideforming metals is also greatly influenced by the electrical properties of the oxide layer. A detailed understanding of oxide films requires aspects of materials science, solid-state physics, and electrochemistry, and such a discussion is beyond the scope of this chapter. For a detailed discussion of oxide films and their properties, the reader is referred to Ref. [16]. In this section, we provide a brief overview of the... 

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