Dielectric continuous

Rigorous formulations of the problems associated with solvation necessitate approximations. From the computational point of view, we are forced to consider interactions between a solute and a large number of solvent molecules which requires approximate models [75]. The microscopic representation of solvent constitutes a discrete model consisting of the solute surrounded by individual solvent molecules, generally only those in close proximity. The continuous model considers all the molecules surrounding the solvent but not in a discrete representation. The solvent is represented by a polarizable dielectric continuous medium characterized by macroscopic properties. These approximations, and the use of potentials, which must be estimated with empirical or approximate computational techniques, allows for calculations of the interaction energy [75],... 

While research into ULK dielectrics continues apace, other approaches such as the creation of air-gaps have already seen implementation into commercial chips. Intel... 

The cavity immersed in a continuum dielectric continues to attract attention from quantum chemists trying to incorporate solvent effects in their in vacuo calculations [28-41]. Cavity models in a continuum dielectric follow in a simple manner by directly modelling . ... 

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

The are essentially adjustable parameters and, clearly, unless some of the parameters in A2.4.70 are fixed by physical argument, then calculations using this model will show an improved fit for purely algebraic reasons. In principle, the radii can be fixed by using tables of ionic radii calculations of this type, in which just the A are adjustable, have been carried out by Friedman and co-workers using the HNC approach [12]. Further rermements were also discussed by Friedman [F3], who pointed out that an additional temi is required to account for the fact that each ion is actually m a cavity of low dielectric constant, e, compared to that of the bulk solvent, e. A real difficulty discussed by Friedman is that of making the potential continuous, since the discontinuous potentials above may lead to artefacts. Friedman [F3] addressed this issue and derived... 

TABLE 5.17 Dielectric Constant (Permittivity) and Dipole Moment of Various Organic Substances Continued)... 

TABLE 5.18 Viscosity, Dielectric Constant, Dipole Moment, and Surface Tension of Selected Inorganic Substances Continued)... 

There are two general weaknesses associated with capacitance systems. First, because it is dependent on a process medium with a stable dielectric, variations in the dielectric can cause instabiUty in the system. Simple alarm appHcations can be caUbrated to negate this effect by cahbrating for the lowest possible dielectric. Multipoint and continuous output appHcations, however, can be drastically affected. This is particularly tme if the dielectric value is less than 10. Secondly, buildup of conductive media on the probe can cause the system to read a higher level than is present. Various circuits have been devised to minimize this problem, but the error cannot be totally eliminated. 

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