Relaxation time Maxwell, dielectric

Each parallel circuit represents the properties of a single layer. An alternate circuit, the Maxwell model, is shown at the left of Fig. 2. It conventionally describes a relaxation situation and is the usual model applied to describe a discrete or continuous (N = oo) distribution of relaxation times for dielectric materials. As shown, these two circuits can have identical impedances at all frequencies if the relations between their elements are correctly chosen. It is possible to calculate the elements on the left directly from those on the right but the reverse solution cannot be carried out (for N > 1) explicitly and exactly. The following relations are applicable, however ... 

We would expect intuitively that tan 0 emd the Deborah number De are related, since both refer to the ratio between the rates of an imposed process and that (or those) of the system. The exact shape of this relationship depends on the number and nature(s) of the releixation process(es). So let us anticipate [3.6.4 la] for the loss tangent of a monolayer in oscillatory motion, which describes a special case of [3.6,12], namely -tan0 = t]°(o/K°. Here, (o is the imposed frequency, equal to the reciprocal time of observation, t(obs) =< . The quotient K° /t]° also has the dimensions of a time in fact it is the surface rheological equivalent of the Maxwell-Wagner relaxation time in electricity, (Recall from sec. 1.6c that for the electrostatic case relaxation is exponential ith T = e/K where e e is the dielectric permittivity and K the conductivity of the relaxing system. In other words, T is the quotient between the storage and the dissipative part.) For the surface rheological case T therefore becomes The exponential decay that is required for such a... 

Finally, attempts are made on a theoretical basis to explain the unusually large dielectric increments and relaxation times of DNA. The discussion is limited to ionic-type polarizations in this report. The available theories, such as the Maxwell-Wagner theory 29) and the surface conductivity treatment, are reviewed and analyzed. These theories do not explain the dielectric relaxation of DNA satisfactorily. Finally, the counter ion polarization theory is described, and it is demonstrated that it explains most reasonably the dielectric relaxation of DNA. 

If the aqueous phase contains electrolytes, a relaxation due to the Maxwell-Wagner-Sillars effect will be observed. Since the electrolyte is not incorporated in the clathrate structures, an increased electrolyte concentration in the remaining free water will result, thus changing the dielectric relaxation mode. In Fig. 42 we note that the relaxation time r decreases from the initial 1000 100 ps to a final level of 200 20 ps during hydrate formation. The experimental value of 200 ps corresponds roughly to a 3% (w/v) NaCl solution, as compared with the initial salt concentration of 1% (w/v). 

On the other hand, since for the sine-form field dE/dt oc caE the role of permanent conductivity ct decreases with increasing frequency, in the high frequency limit (0 >> 1/tm = 47ta/ a material can be considered as non-conductive. The time Tm = /4tict is called Maxwell dielectric relaxation time. Later we shall meet it again under another name space charge relaxation time . 

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. 

Maxwell space charge relaxation time, 8 and a are dielectric permittivity (real part) and conductivity. 

Interfacial or Maxwell-Wagner polarization is a special mechanism of dielectric polarization caused by charge build-up at the interfaces of different phases, characterized by different permittivities and conductivities. The simplest model is the bilayer dielectric [1,2], (see Fig. 1.) where this mechanism can be described by a simple Debye response (exponential current decay). The effective dielectric parameters (unrelaxed and relaxed permittivities, relaxation time and static conductivity) of the bilayer dielectric are functions of the dielectric parameters and of the relative amount of the constituent phases ... 

Keywords dielectric relaxation, dielectric strength permittivity, dipole moment, polarization, relaxation, conductivity, relaxation time distribution, activation energy, Arrhenius equation, WLF-equation, Maxwell-Wagner polarization. 

The conduction model is thought to be only valid for ER. suspensions in reaction with dc or low frequency ac fields. For high frequency ac fields, the polarization model is dominant [55,56]. As shown in Eq. (25) and (26), once the Wagncr-Maxwcll polarization is taken into account, the parameter P is detennined by the conductivity mismatch in dc or low frequency ac fields, and by the dielectric mismatch in high frequency fields (the low or high frequency is relative to the relaxation time of the Wagner-Maxwell polarization). The parameter p in the conduction model is ... 

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. 

Coming to the present volume, one aim has been to provide a basis on which the student and researcher in molecular science can build a sound appreciation of the present and future developments. Accordingly, the chapters do not presume too much previous knowledge of their subjects. Professor Scaife is concerned, inter alia, to make clear what is the character of those aspects of the macroscopic dielectric behaviour which can be precisely delineated in the theoretical representations which rest on Maxwell s analysis, and he relates these to some of the general microscopic features. The time-dependent aspects of these features are the particular concern of Chapter 2 in which Dr. Wyllie gives an exposition of the essentials of molecular correlation functions. As dielectric relaxation methods provided one of the clearest models of relaxation studies, there is reason to suggest that dipole reorientation provides one of the clearest examples of the correlational treatment. If only for this reason, Dr. Wyllie s chapter could well provide valuable insights for many whose primary interest is not in dielectrics. 

The time dependence of the dielectric properties of a material (expressed by e or CT ) under study can have different molecular origins. Resonance phenomena are due to atomic or molecular vibrations and can be analyzed by optical spectroscopy. The discussion of these processes is out of the scope of this chapter. Relaxation phenomena are related to molecular fluctuations of dipoles due to molecules or parts of them in a potential landscape. Moreover, drift motion of mobile charge carriers (electrons, ions, or charged defects) causes conductive contributions to the dielectric response. Moreover, the blocking of carriers at internal and external interfaces introduces further time-dependent processes which are known as Maxwell/Wagner/Sillars (Wagner 1914 Sillars 1937) or electrode polarization (see, for instance, Serghei et al. 2009). 

The time dependence of the dielectric response can be due to different processes like the fluctuations of dipoles (relaxation processes), the drift motion of charge carriers (conduction processes), and the blocking of charge carriers at interfaces (Maxwell/Wagner/Sillars polarization). In the following subchapters these effects will be discussed from a theoretical point of view. 

The paradox with such a reasoning is that the dielectric relaxation-like model invoked relies on the influence of time (and on the existence of conduction), which modifies the wave pulsation and contradicts the form of Maxwell equations used (no current involved). 

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