Dielectric constant response function

Now, as already mentioned in Section 1.3, the h of that section s Eq. (6) is of just the same form as the well-known Cole-Cole dielectric dispersion response function (Cole and Cole [1941]). In its normalized form, the same / function can thus apply at either the impedance or the complex dielectric constant level. We may generalize this result (J. R Macdonald [1985a,c,d]) by asserting that any IS response... 

The dielectric constant is also affected by stmctural changes on strong heating. Also the value is very rank dependent, exhibiting a minimum at about 88 wt % C and rising rapidly for carbon contents over 90 wt % (4,6,45). Polar functional groups are primarily responsible for the dielectric of lower ranks. For higher ranks the dielectric constant arises from the increase in electrical conductivity. Information on the freedom of motion of the different water molecules in the particles can be obtained from dielectric constant studies (45). 

Fig. 2. Wave functions and energy levels for the solvated electron in (a) methylamine (MeA) and (b) hexamethylphosphoramide (HMPA). The potential V(r) and wavefunction are based upon the model of Jortner (101) and computed using values of the optical and static dielectric constants of the two solvents. The optical absorption responsible for the characteristic blue color is marked by h v and represents transitions between the Is and 2p states. The radius of the cavity is 3 A in MeA, and —4.5 A in HMPA. 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

As used here, a DC model is characterized entirely in terms of dielectric constants (e) of the pure solvent (i.e., in the absence of the solute and its cavity) and the structure of the molecular cavity (size and shape) enclosing the solute [3], We confine ourselves to dipolar medium response, due either to the polarizability of the solvent molecules or their orientational polarization1 [15,16]. Within this framework, in its most general space and time-resolved form, one is dealing with the dielectric function s(k, >), where k refers to Fourier components of the spatial response of the medium, and oj. to the corresponding Fourier components of the time domain [17]. In the limit of spatially local response (the primary focus of the present contribution), in which the induced medium polarization (P) at a point r in the medium is specified entirely by the electric field (E) at the same point, only the Tong wavelength component of s is required (i.e., k = 0) [18,19]. 

The van der Waals interaction depends on the dielectric properties of the materials that interact and that of the medium that separates them. ("Dielectric" designates the response of material to an electric field across it Greek Si- or Si a- means "across.") The dielectric function e can be measured experimentally by use of the reflection and transmission properties of light as functions of frequency. At low frequencies, the dielectric function e for nonconducting materials approaches a limit that is the familiar dielectric constant. The dielectric function actually has two parts, one that measures the polarization properties and the other that measures the absorption properties of the material. 

Dielectric test methods are used to measure the cure of epoxy adhesives between two conducting electrodes. This method is especially appropriate for metal-to-metal joints because the substrates themselves can be used as the electrode. The adhesive is treated as a capacitor during the test. Its response (dielectric constant, dissipation factor, etc.) over a range of electrical frequencies is measured as a function of curing time. 

Dipole scattering does not require an atomistic theory. A phenomenological theory suffices, which includes a response function dependent on dielectric constants. The cross-section for dipole scattering based on these assumptions is given in Eqs, 3.7 and 3.9 of Ibach and Mills./61/ These formulae include plane-wave reflection coefficients from the surface, which are solutions of the standard LEED problem. Since dipole scattering involves essentially only forward scattering, it is not necessary in practice to adopt the spherical-wave picture of our step 2 (cf. section 3.4.3), the plane-wave approach is adequate in this situation. 

Fig. 11. Hydration dependence of dielectric response at 25 GHz. Dielectric constant (e ) and loss (s") of packed lysozyme powder as a function of water content. Frequency, 25 GHz temperature, 25°C. (From Harvey and Hoekstra, 1972.)... 

Since hydration of the skin has been shown to be the primary variable influencing the skin s impedance [7,10,11,18], one can speculate that the time variation in the skin s impedance may be a strong function of the time variation of the skin s hydration. The reason for the skin s profound dependence on hydration results from the skin s hydroscopic nature [15] coupled with water s significant impact on the skin s dielectric constant [12]. The skin s hydroscopic characteristic is speculated to be in part due to the presence of amino acids in the skin [15]. Hydration probably influences the skin s dielectric constant because the following components are sensitive to an electric field [7] (a) The keratin protein chains contained in the stratum comeum have a dipole moment. Thus, as the stratum comeum becomes more hydrated, the keratin becomes more flexible and responsive to an applied electric field, (b) As the stratum comeum becomes more hydrated, the ions in the stratum comeum become freer to move and thus more responsive to an applied electric field. 

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