Dielectric constant, local

This shows that the dielectric constant e of a polar solvent is related to the cavity fimction for two ions at large separations. One could extend this concept to define a local dielectric constant z(r) for the interaction between two ions at small separations. 

Effective local dielectric constant on the polyion surface... 

As we have seen, the constant-force images depend on the local dielectric constant. We will now discuss the effect of the dielectric constant by calculating the relation between true and measured heights of a flat parallel film on a surface of different dielectric constant. 

Thus, the electric displacement at r is linearly related to the electric field at positions other than r a local dielectric constant makes D(r) proportional to E(r). If one has planar symmetry, so that only the x-components of D and E are nonzero and these depend on x only,... 

Calculate the capacity of the Helmholtz layer per unit area for an interface of mercury in contact with a 0.0 XM NaF electrolyte. Model the value of the double layer thickness assuming a two-state water model, a positive charge on the electrode, and a local dielectric constant of six. (Bockris)... 

More recently an oil continuous microemulsion technique has been described,16 which allows the study of specific interactions between amino acid side chains and metal ions. Both the metal ion and amino acid are microencapsulated as aqueous droplets in a dispersed phase. The technique is of particular relevance to metalloprotein and metal-membrane interactions where the local dielectric constant can be considerably less than that of bulk water. 

In Equation (12.7), a specifies the geometry while e(U) now denotes the local dielectric constant probed with the tip. 

In addition, the dielectric constant at the pzt top surface was found to be dramatically reduced compared to the bulk value. Our measurements therefore suggest a dead layer to be present. Similar experiments of deducing the local dielectric constant are now necessary for the inner interface. 

An ECT system is composed of three basic components (1) a capacitance sensor, (2) a data acquisition system, and (3) a computer system for reconstruction and viewing. Figure 1 is a sketch of the ECT system with all three components (Warsito and Fan, 2003). The capacitance sensor is made of nr capacitance electrodes distributed around the wall of the process vessel. The ne capacitance electrodes provide up to ne(ne—1)/2 combinations of independent capacitance measurements between the electrode pairs. The capacitance measurements are related to the local dielectric constant (permittivity) filling the process vessel between electrode pairs (Figure 2) (Warsito and Fan, 2001b). The relation between the electric potential and the permittivity distributions follows Poisson equation shown in Equation (1). 

Pratt and co-workers have proposed a quasichemical theory [118-122] in which the solvent is partitioned into inner-shell and outer-shell domains with the outer shell treated by a continuum electrostatic method. The cluster-continuum model, mixed discrete-continuum models, and the quasichemical theory are essentially three different names for the same approach to the problem [123], The quasichemical theory, the cluster-continuum model, other mixed discrete-continuum approaches, and the use of geometry-dependent atomic surface tensions provide different ways to account for the fact that the solvent does not retain its bulk properties right up to the solute-solvent boundary. Experience has shown that deviations from bulk behavior are mainly localized in the first solvation shell. Although these first-solvation-shell effects are sometimes classified into cavitation energy, dispersion, hydrophobic effects, hydrogen bonding, repulsion, and so forth, they clearly must also include the fact that the local dielectric constant (to the extent that such a quantity may even be defined) of the solvent is different near the solute than in the bulk (or near a different kind of solute or near a different part of the same solute). Furthermore... 

Fig. 6.4 Local dielectric constant, ecurrent, calculated according to Eqs. 6.8 and 6.9 [45].

Here, 8 = (z/z ) l/d), / is the local dielectric constant, is the bulk dielectric constant, / is the distance between two charges on the polylectrolyte, and d is the length of the dipole that is formed between one condensed couterion and the closest charged monomer [48]. 

Another possible treatment [9] is to define the Born energy in term of a local dielectric constant e(x) ... 

In conclusion, we suggest that the ion dispersion forces were ignored by most (but by no means all) electrolyte theories mainly because they are important only for separations between ions smaller than about 5 A, and the interactions at these distances are not well-known. It is hard to believe that at these distances the interactions can be accurately described by a sum between a hard-wall repulsion, a Coulomb interaction, and a London attraction. Even if the latter would be true, a correction in the local dielectric constant (because of incomplete screening by water molecules) would render again the van der Waals interactions negligible, up to distances of the order of ion diameters. 

While the field produced by remote dipoles can be treated as screened by a medium with a large dielectric constant (e = 80), the screening of the neighboring dipoles is much weaker. In the present treatment, we will simply assume that Elocal is produced only by the dipoles located within a radius 21 from the given site and that the dielectric constant for them is a constant e". The electric field caused by a neighboring molecule is given by eq 17 (with e" replacing e ). It is important to emphasize that the local dielectric constant e" is smaller than e, the bulk dielectric constant of water. 

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