Uniform dielectric coefficient

In the special case of sharp dielectric boundaries the dielectrics is separated into domains of uniform dielectric coefficients. The dielectric coefficient jumps from one value to another along a boundary. Let us denote the surface of the dielectric boundaries by B. Then the induced charge is a surface charge on the dielectric interfaces (if the induced charges around the source charges are not considered), and the volume integral in Eq. (15) becomes a surface integral over the surface B,... 

The simplest polyelectrolyte model of biological relevance is that of a single semiinfinite impenetrable charged plane in equilibrium with a bulk electrolyte solution of known composition. The charged plane also serves as an introduction to the properties of the electric double layer. We simplify the representation of a membrane by assuming that (1) the membrane is impenetrable to ions, (2) the surface charge is uniformly distributed and constant, (3) the electrolyte is modeled as hard-sphere ions of specific size, and (4) the solvent is a structureless continuum described by a uniform dielectric coefficient... 

Sheet Miea. Good quahty sheet mica is widely used for many iadustrial appHcations, particularly ia the electrical and electronic iadustries, because of its high dielectric strength, uniform dielectric constant, low power loss (high power factor), high electrical resistivity, and low temperature coefficient (Table 6). Mica also resists temperatures of 600—900°C, and can be easily machined iato strong parts of different si2es and shapes (1). 

Ordered polymer films made from poly benzthiazole (PBZT) and poly benzoxazole (PBO) can be used as substrates for multilayer printed circuit boards and advanced interconnects to fill the current need for high speed, high density packaging. Foster-Miller, Inc. has made thin substrates (0.002 in.) using biaxially oriented liquid crystal polymer films processed from nematic solutions. PBZT films were processed and laminated to make a substrate with dielectric constant of 2.8 at 1 MHz, and a controllable CTE of 3 to 7 ppm/°C. The films were evaluated for use in multilayer boards (MLBs) which require thin interconnect substrates with uniform controllable coefficient of thermal expansion (CTE), excellent dielectric properties, low moisture absorption, high temperature capability, and simple reliable processing methods. We found that ordered polymer films surpass the limitations of fiber reinforced resins and meet the requirements of future chip-to-chip interconnection. 

The first step in Eq. 3.32 is the result of substituting Eq. 3.26 into Eq.3. 30 the second step is an integration by parts the third step makes use of Eqs. 3.27 and 3.29a and invokes the assumption that the mobile liquid phase is a homogeneous dielectric medium the fourth step is another integration by parts the fifth step is the result of Eqs. 3.27 and 3.28 along with the assumption that the mobile liquid phase has a uniform viscosity coefficient the sixth step involves the identity... 

It is important to point out that sorption of simple ions is not affected only by charge non-uniformity. The non-homogeneity of the dielectric constant in the membrane is also significant. This becomes particularly evident in the case of uncharged hydrophobic membranes of the type commonly used for water desalination by reverse osmosis, where dielectric exclusion of the electrolyte from the membrane phase is the only sorption mechanism in operation 127). If the swollen membrane is treated as a homogeneous phase, the ionic partition coefficient Sj is expected to be... 

Low-Pressure CVD Processes. Low-pressure CVD (LPCVD) (—101 Pa) is the main tool for the production of polycrystalline Si dielectric and passivation films used in Si IC (integrated-circuit) manufacture (1, 20, 21). The main advantage of LPCVD is the large number of wafers that can be coated simultaneously without detrimental effects to film uniformity. This capability is a result of the large diffusion coefficient at low pressures, which... 

At very low temperatures Eq. (1-250) is no longer valid, and one has to use the exact quantum-statistical expression. The quantum equivalent of Eq. (1-250) has been developed in Ref. (317) from the general relation between the second dielectric virial coefficient and the ordinary (thermodynamic) second virial coefficient of an atomic gas in a uniform electric field317,... 

LB films are ideally suited to analysis by the SPR technique. They may easily be deposited onto a silver-coated microscope slide, and produce a uniform reproducible dielectric layer with a thickness of roughly 2-3 nm per layer, dejpending on molecular size and orientation. For such films, the linear optical properties (refractive index and absorption coefficient) and the thickness may be obtained straightforwar y as described. 

At even quite moderate pressures of a few atmospheres the static permittivites of gases show significant deviations from simple linear proportionality to density expected for ideal gases without significant effects of molecular interactions. As with the equation of state for pressure as a function of density these deviations can be described by a virial series in powers of density with second and higher order dielectric virial coefficients. To introduce these in convenient form for theoretical analysis a macroscopic spherical sample in vacuum is assumed with a uniform field (before insertion of the sample) from external chargee. As the macroscopic in the sample is then given by =... 

Basic requirements on feasible systems and approaches for computational modeling of fuel cell materials are (i) the computational approach must be consistent with fundamental physical principles, that is, it must obey the laws of thermodynamics, statistical mechanics, electrodynamics, classical mechanics, and quantum mechanics (ii) the structural model must provide a sufficiently detailed representation of the real system it must include the appropriate set of species and represent the composition of interest, specified in terms of mass or volume fractions of components (iii) asymptotic limits, corresponding to uniform and pure phases of system components, as well as basic thermodynamic and kinetic properties must be reproduced, for example, density, viscosity, dielectric properties, self-diffusion coefficients, and correlation functions (iv) the simulation must be able to treat systems of sufficient size and simulation time in order to provide meaningful results for properties of interest and (v) the main results of a simulation must be consistent with experimental findings on structure and transport properties. 

A third phenomenon depending solely upon dielectric forces is the guest-host or electronic color-switching interaction in which guest pleochroic dyes are incorporated within nematic host materials. The dyes have different absorption coefficients parallel and perpendicular to their optical axes. As illustrated in Fig. 6, the dye molecules can be oriented by the liquid crystal. With zero field, the liquid crystal is in the uniform parallel orientation and the dye mole-... 

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