Dielectric relaxation high frequency

Anderson J. E., Ullman R. Angular velocity correlation functions and high-frequency dielectric relaxation, J. Chem. Phys. 55, 4406-14, (1971). 

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

Paddison et al. performed high frequency (4 dielectric relaxation studies, in the Gig ertz range, of hydrated Nafion 117 for the purpose of understanding fundamental mechanisms, for example, water molecule rotation and other possible processes that are involved in charge transport. Pure, bulk, liquid water is known to exhibit a distinct dielectric relaxation in the range 10—100 GHz in the form of an e" versus /peak and a sharp drop in the real part of the dielectric permittivity at high / A network analyzer was used for data acquisition, and measurements were taken in reflection mode. 

Frequency dependent complex impedance measurements made over many decades of frequency provide a sensitive and convenient means for monitoring the cure process in thermosets and thermoplastics [1-4]. They are of particular importance for quality control monitoring of cure in complex resin systems because the measurement of dielectric relaxation is one of only a few instrumental techniques available for studying molecular properties in both the liquid and solid states. Furthermore, It is one of the few experimental techniques available for studying the poljfmerization process of going from a monomeric liquid of varying viscosity to a crosslinked. Insoluble, high temperature solid. 

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

In contrast to polystyrene the observed intercepts for PMMA and PEMA in the glassy state remain high with values that are a substantial fraction of those observed in the equilibrium liquid state. Such a result should not be too surprising since it was shown above that a large part of the observed relaxation function above Tg was due to the secondary relaxation. The frequency of maximum dielectric or mechanical loss for the /9... 

In Equation 1, R and V refer to the relaxed (low frequency) and unrelaxed (high frequency) dielectric constants, and AH is the measured activation energy for the y process. The latter was nearly independent of blend composition an average value of 8.7 kcal/mole was used. The integral in Equation 1 was found to be approximately independent of frequency in the range studied. The loss peak in absolute terms is rather weak, and values of eR — V were of the order of 10"2 and less. From these values, it was also possible to calculate the apparent dipolar density, Np2, using the Onsager relation (9) ... 

The shape of the frequency dependence of e" has been compared in Fig. 109 in terms of reduced units s / max an(i ///max> at various temperatures. The peak is asymmetric, being broader on the high-frequency side, especially at 10 °C. A gradual narrowing occurs on both the high- and low-frequency sides with increasing temperature. These results show that the motional processes involved in the dielectric j3 relaxation have a distribution of correlation times and that this distribution becomes narrower as temperature increases. 

Obviously in the limit of low and high frequencies the parameters of the two models determine the frequency dependence of the dielectric loss in the a relaxation [162,163],... 

The dielectric behavior of PMCHI was studied by Diaz Calleja et al. [210] at variable frequency in the audio zone and second, by thermal stimulated depolarization. Because of the high conductivity of the samples, there is a hidden dielectric relaxation that can be detected by using the macroscopic dynamic polarizability a defined in terms of the dielectric complex permittivity e by means of the equation ... 

The transformation performed by this equation is a good way for the analysis of the dielectric relaxations in the zone of high temperatures and low frequencies of the spectrum. 

The high conductivity observed at low frequencies would overlap the existence of another new relaxation (Fig. 2.78) what is very similar to that found for transfer complexes [243, 244] in which some of them have a pronounced semiconductor character. In this kind of compounds, the observation of dielectric relaxations over room temperature is inhibited by the high conductivity observed. To avoid this problem and to detect the conductivity effect, it is possible to use the complex polarizability a defined by equation [182], The transformation defined by equation (2.45), has been applied with good results in the case of dielectric relaxation peaks in terms of a" or tan 8 . 

Figure 1 indicates the dielectric behavior of practically all tissues. Two remarkable features are apparent exceedingly high dielectric constants at low frequencies and three clearly separated relaxation regions a, 3, y of the dielectric constant at low, medium, and very high frequencies. Each of these relaxation regions is in its simplest form characterized by equations of the Debye type... 

The static value s is called the relaxed dielectric constant and the short-time (or high-frequency) value lDO the non-relaxed dielectric constant es — e,x, is called the dielectric strength. They are equal to... 

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-... 

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