Dielectric space-dependent

The measurement of ion activities assumes chemical equilibrium between the PVC membrane and the electrolyte bearing solutions. The time domain chemical and dielectric space charge changes that occur are minimized by membrane composition and sensor design and are considered negligible during the measurement period. Hence, the potential dependence of the ion activity is characterized by the Nemst equation. The following thermodynamic expressions describe the potentials of the... 

These methods can be applied both to the simplified model with constant s, and to models with space dependent s(r )or real charges dispersed in the whole dielectric medium. They aim at solving the Poisson equation (1) expressed as a set of finite difference equations for each point of the grid. The linear system to be solved has elements depending both on e... 

Microwave dielectric heating depends on the ability of an electric field to polarize charges in materials and their inability to follow rapid changes in an electric field space. Total polarization is a sum of several components ... 

Proof.- We study the linear response of the system to an electromagnetic wave at frequency Ct). Introduce a space-dependent local dielectric function s(r,(o) to represent the local dielectric response of both the interior of the solid as well as empty space. The theorem is general enough to accommodate a graded dielectric function as well. In the case of a shape of constant dielectric constant e(r,0>) = j(co) if F is inside the solid and s(r,co) = l if F is outside the solid. The potential field (r) obeys the Laplace equation... 

As matrix inversion is computationally very costly, so this particular technique is limited to one-dimensional problems. Also, the generalization of Eq. (6.102) to space-dependent dielectric constant creates extra numerical difficulties while solving Poisson-Boltzmann equation. 

In order to deal with the case of space-dependent dielectric constant in multidimensional space, alternating direction implicit techniques [82] are developed after revwiting Eq. (6.102) as... 

A through-space electrostatic effect (field effect) due to the charge on X. This model was developed by Kirkwood and Westheimer who applied classical electrostatics to the problem. They showed that this model, the classical field effect (CFE), depended on the distance d between X and Y, the cosine of the angle 6 between d and the X—G bond, the effective dielectric constant and the bond moment of X. 

Now let us examine what would happen to the response of the dielectric if we put an alternating voltage on the capacitor of frequency co. If CO is low (a few Hz) we would expect the material to respond in a similar manner to the fixed-voltage case, that is d (static) = e(co) = e(0). (It should be noted that eo, the permittivity of free space, is not frequency-dependent and that E(0)/eo = H, the static dielectric constant of the medium.) However, if we were to increase co to above microwave frequencies, the rotational dipole response of the medium would disappear and hence e(co) must fall. Similarly, as we increase co to above IR frequencies, the vibrational response to the field will be lost and e(co) will again fall. Once we are above far-UV frequencies, all dielectrics behave much like a plasma and eventually, at very high values, e(co)lto = 1. 

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