Electrical overlap

In many crystals there is sufficient overlap of atomic orbitals of adjacent atoms so that each group of a given quantum state can be treated as a crystal orbital or band. Such crystals will be electrically conducting if they have a partly filled band but if the bands are all either full or empty, the conductivity will be small. Metal oxides constitute an example of this type of crystal if exactly stoichiometric, all bands are either full or empty, and there is little electrical conductivity. If, however, some excess metal is present in an oxide, it will furnish electrons to an empty band formed of the 3s or 3p orbitals of the oxygen ions, thus giving electrical conductivity. An example is ZnO, which ordinarily has excess zinc in it. 

Except for helium, all of the elements in Group 18 free2e into a face-centered cubic (fee) crystal stmeture at normal pressure. Both helium isotopes assume this stmeture only at high pressures. The formation of a high pressure phase of soHd xenon having electrical conductivity comparable to a metal has been reported at 33 GPa (330 kbar) and 32 K, and similar transformations by a band-overlap process have been predicted at 15 GPa (150 kbar) for radon and at 60 GPa (600 kbar) for krypton (51). 

Another growing apphcation that overlaps the electrically functional area is the use of transparent conductive coatings or tin oxide, indium—tin oxide, and similar materials in photovoltaic solar ceUs and various optic electronic apphcations (see Photovoltaic cells). These coatings are deposited by PVD techniques as weU as by spray pyrolysis, which is a CVD process. 

The individual membrane filtration processes are defined chiefly by pore size although there is some overlap. The smallest membrane pore size is used in reverse osmosis (0.0005—0.002 microns), followed by nanofiltration (0.001—0.01 microns), ultrafHtration (0.002—0.1 microns), and microfiltration (0.1—1.0 microns). Electro dialysis uses electric current to transport ionic species across a membrane. Micro- and ultrafHtration rely on pore size for material separation, reverse osmosis on pore size and diffusion, and electro dialysis on diffusion. Separation efficiency does not reach 100% for any of these membrane processes. For example, when used to desalinate—soften water for industrial processes, the concentrated salt stream (reject) from reverse osmosis can be 20% of the total flow. These concentrated, yet stiH dilute streams, may require additional treatment or special disposal methods. 

Electrostatic Repulsive Forces. As the distance between two approaching particles decreases, their electrical double layers begin to overlap. As a first approximation, the potential energy of the two overlapping double layers is additive, which is a repulsive term since the process increases total energy. Electrostatic repulsion can also be considered as an osmotic force, due to the compression of ions between particles and the tendency of water to flow in to counteract the increased ion concentration. 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

Fig. 5. Electrical resistance as a function of the temperature at the indicated magnetic fields for a single microbundle of carbon nanotubes. The solid line is a fit using the two-band model for graphite (see inset) with an overlap A = 3.7 meV and a Fermi level right in the middle of the overlap (after Langer et at. l9 ).

In 1993, Jorgenson s group improved upon then earlier reverse phase HPLC-CZE system. Instead of the six-port valve, they used an eight-port electrically actuated valve that utilized two 10-p.L loops. While the effluent from the HPLC column filled one loop, the contents of the other loop were injected onto the CZE capillary. The entii e effluent from the HPLC column was collected and sampled by CZE, making this too a comprehensive technique, this time with enhanced resolving power. Having the two-loop valve made it possible to overlap the CZE runs. The total CZE run time was 15 s, with peaks occurring between 7.5 and 14.8 s. In order to save separation space, an injection was made into the CZE capillary every 7.5s,... 

Pseudocapacitance is used to describe electrical storage devices that have capacitor-like characteristics but that are based on redox (reduction and oxidation) reactions. Examples of pseudocapacitance are the overlapping redox reactions observed with metal oxides (e.g., RuO,) and the p- and n-dopings of polymer electrodes that occur at different voltages (e.g. polythiophene). Devices based on these charge storage mechanisms are included in electrochemical capacitors because of their energy and power profiles. 

We can understand the differences in properties between the carbon allotropes by comparing their structures. Graphite consists of planar sheets of sp2 hybridized carbon atoms in a hexagonal network (Fig. 14.29). Electrons are free to move from one carbon atom to another through a delocalized Tr-network formed by the overlap of unhybridized p-orbitals on each carbon atom. This network spreads across the entire plane. Because of the electron delocalization, graphite is a black, lustrous, electrically conducting solid indeed, graphite is used as an electrical conductor in industry and as electrodes in electrochemical cells and batteries. Its... 

Only electric-dipole- and spin-allowed electronic transitions in the proximity of the observed transitions are tabulated. Anticipated overlap with atomic absorptions. 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

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