Double dielectric

Fig. 6.11 Double dielectric slab. We first obtain the input impedance Zi- of slab 1 looking left. Next, we find the input impedance Z2- of the second slab when terminated in Zi— From the schematic we then see that the ground plane impedance Zj+ should be added in parallel yielding Z2- IIZ2+, Finally, we add the antenna reactance jX in series and obtain the compensated terminal impedance Z2- Z2+ + jX. ...

Figure 1. Cross-section of (a) a commercial FET chip with a polyimide coating as part of a double dielectric and (b) an advanced multilevel chip with four levels of metal circuitry and polyimide as insulator.

The necessity to calculate the electrostatic contribution to both the ion-electrode attraction and the ion-ion repulsion energies, bearing in mind that there are at least two dielectric ftmction discontinuities hr the simple double-layer model above. 

Here a few core equations are presented from tire simplest tlieory for tire electric double layer tire Gouy-Chapman tlieory [41]. We consider a solution of ions of valency and z in a medium witli dielectric constant t. The ions... 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

Barium sodium niobium oxide [12323-03-4] Ba2NaNb 02, finds appHcation for its dielectric, pie2oelectric, nonlinear crystal and electro-optic properties (35,36). It has been used in conjunction with lasers for second harmonic generation and frequency doubling. The crystalline material can be grown at high temperature, mp ca 1450°C (37). 

Mobility is affected by the dielectric constant and viscosity of the suspending fluid, as indicated in Eq. (22-28). The ionic strength of the fluid has a strong effect on the thickness of the double layer and hence on As a rule, mobility varies inversely as the square root of ionic strength [Overbeek, Adv. Colloid Sci., 3, 97 (1950)b... 

The thickness of the dielectric coating on individual elements is nearly double the above... 

When an electrode potential that is initially settled at the rest potential is shifted to the anodic direction, the electrode system begins to move to a new equilibrium state. The resultant reconstruction of the double layer induces dielectric relaxation, which yields a new potential difference, maintaining electrostatic equilibrium. 

However, a number of examples have been found where addition of bromine is not stereospecifically anti. For example, the addition of Bf2 to cis- and trans-l-phenylpropenes in CCI4 was nonstereospecific." Furthermore, the stereospecificity of bromine addition to stilbene depends on the dielectric constant of the solvent. In solvents of low dielectric constant, the addition was 90-100% anti, but with an increase in dielectric constant, the reaction became less stereospecific, until, at a dielectric constant of 35, the addition was completely nonstereospecific.Likewise in the case of triple bonds, stereoselective anti addition was found in bromination of 3-hexyne, but both cis and trans products were obtained in bromination of phenylacetylene. These results indicate that a bromonium ion is not formed where the open cation can be stabilized in other ways (e.g., addition of Br+ to 1 -phenylpropene gives the ion PhC HCHBrCH3, which is a relatively stable benzylic cation) and that there is probably a spectrum of mechanisms between complete bromonium ion (2, no rotation) formation and completely open-cation (1, free rotation) formation, with partially bridged bromonium ions (3, restricted rotation) in between. We have previously seen cases (e.g., p. 415) where cations require more stabilization from outside sources as they become intrinsically less stable themselves. Further evidence for the open cation mechanism where aryl stabilization is present was reported in an isotope effect study of addition of Br2 to ArCH=CHCHAr (Ar = p-nitrophenyl, Ar = p-tolyl). The C isotope effect for one of the double bond carbons (the one closer to the NO2 group) was considerably larger than for the other one. ... 

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

The origin of the observed correlation was not established, and the relation was not interpreted as causal. It could be argued that a sustained elevated potential due to as-yet unknown microbial processes altered the passive film characteristics, as is known to occur for metals polarized at anodic potentials. If these conditions thickened the oxide film or decreased the dielectric constant to the point where passive film capacitance was on the order of double-layer capacitance (Cji), the series equivalent oxide would have begun to reflect the contribution from the oxide. In this scenario, decreased C would have appeared as a consequence of sustained elevated potential. 

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