Dielectric space-independent

Traditional finite difference methods [55, 81] for solving time-dependent second-degree partial differential equations (such as modified diffusion equation) include forward time-centered space (ETCS), Crank-Nicholson, and so on. For time-independent second-degree partial differential equations such as Poisson-Boltzmann equation, finite difference equations can be written after discretizing the space and approximating derivatives by their finite difference approximations. For space-independent dielectric constant, that is, E(r) = e, a tridiagonal matrix inversion needs to be carried out in order to obtain a solution for tp for a given/. 

Here d is the dielectric constant of the medium which we simply assume constant throughout (that is, concentration and electric field intensity independent). Furthermore, p in (1.4a) is the density of the space charge... 

Dielectric measurements on thin films were made using a two-fluid cell technique as per ASTM D 150. The advantage of the two-fluid cell is that measurement of dielectric constant is independent of sample thickness, electrode spacing, and electrode area. Thin films can be stacked to increase testing accuracy. The reproducibility of the dielectric constant measurement using the two-fluid cell was 2%. 

We can see that relaxation time Tm is independent of the sample dimensions and includes only material parameters, namely, specific COTiductivity a and dielectric constant (real part s = s ). This time is called space charge relaxation time. It is the same Maxwell dielectric relaxatimi time we met in Section 7.2.1. Note that time Tm has no relation to the dispersion frequency of ionic conductivity (Ti) neither to Debye dipole relaxation time. 

Molecules containing two or more independent electroactive centres in close proximity, e.g. bimetallic species with substituted phosphine bridging groups, have important electrochemical properties which potentially can be used to elucidate the dielectric properties of the electrolyte medium in use. Such molecules can exhibit successive voltammetric waves the spacing of which is in part determined by coulombic interactions between the centres thus is influenced by the dielectric properties of the electrolyte. 

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