Debye Dielectric relaxation

This approximation requires that cos. This behavior in fact follows from a Debye dielectric continuum model of the solvent when it is coupled to the solute nuclear motion [21,22] and then xs would be proportional to the longitudinal dielectric relaxation time of the solvent indeed, in the context of time dependent fluorescence (TDF), the Debye model leads to such an exponential dependence of the analogue... 

Raicu, V., Sato, T., and Raicu, G. 2001. Non-Debye dielectric relaxation in biological stmc-tures arises from their fractal nature. Phys. Rev. E 64 021916. 

This treatment is oversimplified because, in addition to neglecting inner sphere contributions to the reorganization energy it approximates the dielectric frequency spectrum to a single frequency, 0jo — 1011 s 1, corresponding to the Debye dielectric relaxation which probably varies in the vicinity of the ions. The cathodic current is given by... 

Here td is the so-called Debye dielectric relaxation time. One could view td as a phenomenological time constant which applies to dielectric relaxation measurements, or alternatively for simple causes, involving dielectric relaxation of weakly interacting dipoles, tD is related to the reorientation time constant of the solvent dipole in the laboratory frame. 

Noting the similarity between NMR relaxation and dielectric relaxation effects, Bloembergen, Purcell, and Pound (35) adapted the Debye theory for the latter to the problems of the former to obtain equation (2). 

In the most general sense, non-Debye dielectric behavior can be described in terms of a continuous distribution of relaxation times, G(x) [11]. 

In summary, we must say that unfortunately there is as yet no generally acknowledged opinion about the origin of the non-Debye dielectric response. However, there exist a significant number of different models which have been elaborated to describe non-Debye relaxation in some particular cases. In general these models can be separated into three main classes ... 

Non-Debye dielectric relaxation in porous systems is another example of the dynamic behavior of complex systems on the mesoscale. The dielectric properties of various complex multiphase systems (borosilicate porous glasses [153-156], sol-gel glasses [157,158], zeolites [159], and porous silicon [160,161]) were studied and analyzed recently in terms of cooperative dynamics. The dielectric response in porous systems will be considered here in detail using two quite different types of materials, namely, porous glasses and porous silicon. 

Non-Debye dielectric relaxation was also observed in porous silicon (PS) [25,160,161], PS has attracted much attention recently, mainly due to its interesting optical and electro-optical properties that can be utilized for device applications [164,165], So far, most of the activity in this field has focused on the intense visible photoluminescence (PL) from nano-PS and the underlying physical mechanism that is responsible for the generation of light. In addition, transport and dielectric relaxation phenomena in PS have also attracted... 

Thus, the non-Debye dielectric behavior in silica glasses and PS is similar. These systems exhibit an intermediate temperature percolation process associated with the transfer of the electric excitations through the random structures of fractal paths. It was shown that at the mesoscale range the fractal dimension of the complex material morphology (Dr for porous glasses and porous silicon) coincides with the fractal dimension Dp of the path structure. This value can be obtained by fitting the experimental DCF to the stretched-exponential relaxation law (64). 

Table 7-4. Change of the natural bond order (NBO) charges and of the dipole moment of pNA in the ICT state. The label (Un)relax/(Un)relax means that we do (not) have allowe for solute geometry relaxation/solvent dielectric relaxation. Charges are in a.u. and dipole moments in Debye...

The plot shows a distribution closely around a slope of unity indicated by the solid line in Figure 2 except for the alcohols and nitrobenzene. Such anomaly in alcohols is also reported for other chemical processes and time-dependent fluorescence stokes shifts and is attributed to their non-Debye multiple relaxation behavior " the shorter relaxation components, which are assigned to local motions such as the OH group reorientation, contribute the friction for the barrier crossing rather than the slower main relaxation component, which corresponds to the longitudinal dielectric relaxation time, tl, when one regards the solvent as a Debye dielectric medium. If one takes account of the multiple relaxation of the alcohols, the theoretical ket (or v,i) values inaease and approach to the trend of the other solvents. (See open circles in Figure 2.)... 

Figures 20.21c and d show that poly(VCN-a/f-MATRIF) copolymer exhibits a dynamic scenario with four relaxation processes two relaxations are above Tg, merging at low temperatures, while two others are below Tg. The addition of VCN unit increases the dielectric constant as well as the value of calorimetric glass transition Tgi (i) -relaxation (Debye-like and strong, i.e., low fragility index m = 44 [68]) (ii) a2-relaxation (broad and fragile, high fragility index m = 101 [68]), more separated from p-one effect of rigidity of VCN segment (iii) p-relaxation (faster), due to a less efficient packing similar effect for random copolymers based on butyl methacrylate (n-BMA) with styrene (ST) named poly( -BMA-5 fflf-ST) copolymer [123].

The Maxwell-Wagner dispersion effect due to conductance in parallel with capacitance for two ideal dielectric materials in series Rj Cj - Rj Cj can also be represented by Debye dispersion without postulating anything about dipole relaxation in dielectric. In the ideal case of zero conductivity for both dielectrics (R, — , R —> ), there is no charging of the interfaces from free charge carriers, and the relaxation can be modeled by a single capacitive relaxation-time constant. 

Mozumder (1969b) pointed out that in the presence of freshly created charges due to ionization, the dielectric relaxes faster—with the longitudinal relaxation time tl, rather than with the usual Debye relaxation time T applicable for weak external fields. The evolution of the medium dielectric constant is then given by... 

Relaxation processes are probably the most important of the interactions between electric fields and matter. Debye [6] extended the Langevin theory of dipole orientation in a constant field to the case of a varying field. He showed that the Boltzmann factor of the Langevin theory becomes a time-dependent weighting factor. When a steady electric field is applied to a dielectric the distortion polarization, PDisior, will be established very quickly - we can say instantaneously compared with time intervals of interest. But the remaining dipolar part of the polarization (orientation polarization, Porient) takes time to reach its equilibrium value. When the polarization becomes complex, the permittivity must also become complex, as shown by Eq. (5) ... 

Even if we consider a single solvent, e g., water, at a single temperature, say 298K, depends on the solute and in fact on the coordinate of the solute which is under consideration, and we cannot take xF as a constant. Nevertheless, in the absence of a molecular dynamics simulation for the solute motion of interest, XF for polar solvents like water is often approximated by the Debye model. In this model, the dielectric polarization of the solvent relaxes as a single exponential with a relaxation time equal to the rotational (i.e., reorientational) relaxation time of a single molecule, which is called Tp) or the Debye time [32, 347], The Debye time may be associated with the relaxation of the transverse component of the polarization field. However the solvent fluctuations and frictional relaxation occur on a faster scale given by [348,349]... 

When a constant electric field is suddenly applied to an ensemble of polar molecules, the orientation polarization increases exponentially with a time constant td called the dielectric relaxation time or Debye relaxation time. The reciprocal of td characterizes the rate at which the dipole moments of molecules orient themselves with respect to the electric field. 

The remaining types of polarization are absorptive types with characteristic relaxation times corresponding to relaxation frequencies. Debye, in 1912, suggested that the high dielectric constants of water, ethanol, and other highly polar molecules were due to the presence of permanent dipoles within each individual molecule and that there is a tendency... 

There is no oscillation the polarization merely relaxes toward zero with a time constant t. In the following paragraphs, we shall use (9.35), the basic assumption of the Debye theory, to derive an expression for the dielectric function of a collection of permanent dipoles. 

On physical grounds, relaxation of permanent dipoles is expected to be highly dependent on temperature this is in contrast with Lorentz oscillators, the dielectric behavior of which is relatively insensitive to changes in temperature. Debye (1929, Chap. 5) derived a simple classical expression for the relaxation time of a sphere of radius a in a fluid of viscosity tj ... 

Figure 9.15 Dielectric function of water at room temperature calculated from the Debye relaxation model with r = 0.8 X 10 11 sec, eQcl = 77.5, and e0l, = 5.27. Data were obtained from three sources Grant et al. (1957), Cook (1952), and Lane and Saxton (1952).

Existence of a high degree of orientational freedom is the most characteristic feature of the plastic crystalline state. We can visualize three types of rotational motions in crystals free rotation, rotational diffusion and jump reorientation. Free rotation is possible when interactions are weak, and this situation would not be applicable to plastic crystals. In classical rotational diffusion (proposed by Debye to explain dielectric relaxation in liquids), orientational motion of molecules is expected to follow a diffusion equation described by an Einstein-type relation. This type of diffusion is not known to be applicable to plastic crystals. What would be more appropriate to consider in the case of plastic crystals is collision-interrupted molecular rotation. 

Fig. 1.1 Dielectric dispersion spectra for a polar solvent with a single Debye relaxation process in the micro-wave region and two resonant transmissions in the IR and UV ranges [5 b].

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