Frequency-dependent permittivity

The chemical nature of the metal appears in Equation (2.333) via the frequency-dependent permittivity emet(w), evaluated at the imaginary frequency iw. For simple metals, the Drude form is often reasonable ... 

Dielectric relaxation — Dielectric materials have the ability to store energy when an external electric field is applied (see -> dielectric constant, dielectric - permittivity). Dielectric relaxation is the delayed response of a dielectric medium to an external field, e.g., AC sinusoidal voltage, usually at high frequencies. The resulting current is made up of a charging current and a loss current. The relaxation can be described as a frequency-dependent permittivity. The real part of the complex permittivity (e1) is a measure of how much energy from an external electric field is stored in a material, the imaginary part (e") is called the loss factor. The latter is the measure of how dissipative a material is to an exter-... 

A third general issue regards the dynamic coupling between solute and solvent. To accurately model excited states formation and relaxation of molecules in solution, the electronic states have to be coupled with a description of the dynamics of the solvent relaxation toward an equilibrium solvation regime. The formulations of continuum models which allow to include a time dependent solvation response can be formulated as a proper extension of the time-independent solvation problem (of equilibrium or of nonequilibrium). In the most general case, such an extension is based on the formulation of the electrostatic problem in terms of Fourier components and on the use of the whole spectrum of the frequency dependent permittivity, as it contains all the informations on the dynamic of the solvent response [10-17],... 

The theory starts from description of the dielectric loss spectra, frequency-dependent permittivity of the solvent e uj), in the framework of the Debye model [86], in which the reorientation of the solvent dipoles gives the main contribution to the relaxation of solvent polarization ... 

Figure 11 shows a representation of e"(o)) = f(e ( o)), called an Argand diagram, for 0.48 M NaClO in a PC-DME mixture (20 weight % PC). Data analysis of the precedingly determined frequency-dependent permittivities of the solvent mixture without NaClO yielded two relaxation regions, one attributable to DME (relaxation time T = 4.7 ps) the other to PC (relaxation time t = 22 ps). The shifts of solvent relaxation times with reference to those of the two pure solvents, t(DME) = 3.6 ps and t(PC) = 39 ps, is correlated to the change in viscosity. Addition of the... 

The main assumption in all these approaches is that the characteristic sizes of the single-phase regions are much larger than the Debye screening length (26). Provided that the dielectric permittivity and electric conductivity of the individual phases are known, the MW models enable us to calculate the total frequency-dependent permittivity of the system. 

The so-called Hanai equation (8,9) gives the complex (frequency dependent) permittivity of an emulsion as... 

Under the action of an alternating electric field, the electrical response of a system having dipolar interaction may be characterized by the complex permittivity e = s ((o) — ie"(ro) as discussed above. Methods to measure the frequency-dependent permittivity use coaxial lines. The cell of our... 

The representation (6.69) of e s indicates that this quantity includes contributions from all the resonance frequencies (C0 =P ) of the frequency dependent permittivity (6.68). Moreover it also is determined by some dissipative properties of the material reflected in the spectral function (,(p)) and also in the optical permittivity =n p,), [6.6, 6.29]. 

Table 6.1 Elements of electric network models for the (complex) admittance function Y=Y(p) and the frequency dependent permittivity t, = of a sorption system.

After the very early work by Michaels et al., the next frequency-dependent permittivity spectra of solid polyelectrolyte materials were only pubhshed in 2001 by Durstock and Rubner, who studied PEM prepared by the layer-by-layer technique [27]. The investigated PEM were made of the polycation poly(allylamine hydrochloride) (PAH) and the polyanions PAA or PSS. The authors investigated very systematically the influences of parameters like pH, temperature, salt content, and RH (wet and dry PEM) on the real and imaginary part of the permittivity. 

In the above discussion of the frequency dependent permittivity, the analysis has been based on either the single particle rotational diffusion model of Debye, or empirical extensions of this model. A more general approach can be developed in terms of time correlation functions [6], which in turn have to be interpreted in terms of a suitable molecular model. While using the correlation function approach does not simplify the analysis, it is useful, since experimental correlation functions can be compared with those deduced from approximate theories, and perhaps more usefully with the results of molecular dynamics simulations. Since the use of correlation functions will be mentioned in the context of liquid crystals, they will be briefly introduced here. The dipole-dipole time correlation function C(t) is related to the frequency dependent permittivity through a Laplace transform such that ... 

The origin of a frequency dependent permittivity is molecular motion associated with a dipole moment. In an oriented fluid, induced or permanent dipole moments contribute differently to the components of the permittivity tensor similarly the effects of molecular motion as reflected by the frequency dependence of the permittivity will also be different for different components. 

Since in ferroelectric polymers ohmic oooductivity may be frequency dependent, the tan 6 represenution is not recommeiKled. The dielectric transition may be represented by the frequency-dependent permittivity related to the imaginary part of the actually measured admittance (V ) and by the frequency-dependent AC conductivity related to the real part V as... 

For time-dependent electrical perturbation, the typical assumption is that the metal nanoparticle behaves as a dielectric, characterized by a frequency-dependent permittivity ( >). Permittivities experimentally determined on bulk sample are almost invariably used. They need to be corrected with terms depending on the particle size. In fact, when the size of the metal particle has the same order of magnitude of the mean free path of conduction electrons in the bulk of the solid (tens of nanometers), it is necessary to take into account the scattering of the electrons at the metal particle surface. This is one aspect of a more general class of phenomena, known as quantum size effects. They are tightly related to the confinement of electrons in the metal particle and hence to the loss of the band structures typical of a bulk metal. Since this phenomenon regards mainly the valence... 

Since the frequency-dependent permittivity is related to a relaxation function in the time domain (see equation 10), another way of introducing an empirical modification to the SRT function is to modify the relaxation function itself. A general procedure used for many years in relaxation theory is to express 0(f) as a discrete set of exponential decay functions or as an integral over a continuous distribution of such decay functions so that... 

Frequency-dependent conductivity C(m) and frequency-dependent permittivity e(co) are complex quantities with real and imaginary parts. Thus, complex... 

The optical properties of all linear optical materials can be described by the complex, frequency-dependent permittivity or dielectric constant ... 

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