Dielectric relaxation dispersion

The dashed line through the data points is a fit to the data, by analogy with procedures used for dielectric relaxation dispersion, using the Cole-Cole expression (9) ... 

The dispersion of this waiting time distribution, i.e., its second central moment, is a measure that we can use to define a homogenization time scale on which the dispersion is equal to that of a homogeneous (Poisson) system on a time scale given by the torsional autocorrelation time. The homogenization time scale shows a clear non-Arrhenius temperature dependence and is comparable with the time scale for dielectric relaxation at low temperatures.156... 

Before leaving SD applications of the LRA, it is worth stressing that a different approach has often been taken in relating the electrostatic C i) to pine solvent dynamics. In this approach, the connection is made to solvent dielectric relaxation. Early theories made the connection through the longitudinal dielectric relaxation time," while more recent ones use as input the dielectric dispersion s or its generalization to finite wavevectors, e(k, co). 23.24.29,68,89... 

An alternative approach that was used in the past was to treat the photoelectrochemical cell as a single RC element and to interpret the frequency dispersion of the "capacitance" as indicative of a frequency dispersion of the dielectric constant. (5) In its simplest form the frequency dispersion obeys the Debye equation. (6) It can be shown that in this simple form the two approaches are formally equivalent (7) and the difference resides in the physical interpretation of modes of charge accumulation, their relaxation time, and the mechanism for dielectric relaxations. This ambiguity is not unique to liquid junction cells but extends to solid junctions where microscopic mechanisms for the dielectric relaxation such as the presence of deep traps were assumed. 

The dielectric relaxation of bulk mixtures of poly(2jS-di-methylphenylene oxide) and atactic polystyrene has been measured as a function of sample composition, frequency, and temperature. The results are compared with earlier dynamic mechanical and (differential scanning) calorimetric studies of the same samples. It is concluded that the polymers are miscible but probably not at a segmental level. A detailed analysis suggests that the particular samples investigated may be considered in terms of a continuous phase-dispersed phase concept, in which the former is a PS-rich and the latter a PPO-rich material, except for the sample containing 75% PPO-25% PS in which the converse is postulated. 

Eq. (4), frequency-dependent, such that the limit for a(w) in Eq. (8) becomes physically acceptable. Under conditions appropriate to the correct limit, the normalized real and imaginary parts of the complex permittivity and the normalized dielectric conductivity take on the form depicted in Fig. (1). Here, is the relaxation time in the limit of zero frequency (diabatic limit). Irrespective of the details of the model employed, both a(w) and cs(u>) must tend toward zero as 11 + , in contrast to Eq. (8), for any relaxation process. In the case of a resonant process, not expected below the extreme far-infrared region, a(u>) is given by an expression consistent with a resonant dispersion for k (w) in Eq. (6), not the relaxation dispersion for K (m) implicit in Eq. 

Relaxations observed in polymers show broader dispersion curves and lower loss maxima than those predicted by the Debye model, and the (s" s ) curve falls inside the semicircle. This led Cole and Cole (1941) to suggest the following semi-empirical equation for dielectric relaxations in polymers ... 

Rotational Rdaxation.- As far as small molecules having dimensions of a few angstroms are concerned, the rotational relaxation time t, under ordinary conditions (particularly in aqueous solution at room temperature) has the order of magnitude of 10 —10 s. This corresponds to dielectric dispersion in the microwave range of 1 —10 GHz. Macromolecular particles display dielectric relaxation far below these frequencies. Sudi behaviour is readily e>q>lained by the strong dependence of r, on the lei h of the dipolar axis of the molecule. By calculation of the rotational diffusion coefiident Dx according to hydrodynamic theory and inserting the result in (19) one obtains for spherically shaped dipoles ... 

Review Articles.— Dielectric measurements up to 1956 have been discussed by Nelson, whereas de Broucker6 and Mandel have reviewed the results on dielectric properties of dilute polymer solutions. Work on the pemuttivity of gases as a function of density and pressure is discussed by Cole and Smyth and by Beaume et al., who moreover report some simple theories of the second didectric virial coefiident. Dielectric relaxation phenomena (dispersion and absorption) are discussed in the artides by Cole and Smyth and by Davies and Boudoiuis. A recent artide by Grant deals with stutfles of biological molecules by dielectric methods. 

In addition to the more usual application to solids, dielectric relaxation or dispersion measurements are also used on solutions (and pure liquids). Cook (425) related the relaxation mechanism in water-dioxane mixtures to the rupture of H bonds. Hasted and co-workers (890) found that water-dioxane mixtures had longer relaxation times as the dioxane proportion increased or the temperature was lowered. Both trends are explained by formation of a H bonded complex. Yasumi (2219) found similar effects when large amounts of hexane... 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

In order to demonstrate convincingly that this is a general experimental fact of glass-formers, experimental data for many different materials and (for a particular material) experimental data for several dielectric relaxation times are presented herein. The glass-formers include both molecular liquids and amorphous polymers of diverse chemical structures. All show the property of temperature-pressure superpositioning of the dispersion of the structural a-relaxation at constant xa. 

The dielectric relaxation process of ice can be understood in terms of proton behavior namely, the concentration and movement of Bjerrum defects (L- and D-defect) and ionic defects (HaO and OH ), which are thermally created in the ice lattice. We know that ice samples highly doped with HE or HCl show a dielectric dispersion with a short relaxation time r and low activation energy of The decreases in the relaxation time and... 

The dielectric relaxation processes of matter can be analyzed with an empirical model of dielectric dispersion, for example, the one described by Havriliak-Negami s equation. " We analyzed dielectric data obtained for our samples using a model of complex permittivity k with two dispersions (the main and the low-frequency dispersion of a space charge effect) and conductivity ao (caused by electrode discharge), as follows ... 

Figure 1 For pure bulk ice samples, (a) Temperature dependence of the dielectric relaxation time r and (b) Cole-Cole plots of pure ice crystal (parallel to the c-axis) at -10 °C. The dielectric dispersion is of the Debye type (a=0.99, p=1.00).

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