Dielectric relaxation applications

The dielectric (e ) and loss (e") constants are important properties of interest because these two parameters, among others, determine the suitability of a material for a given application. Dielectric relaxations are studied to reduce energy losses in materials used in practically important areas of insulation and mechanical strength. 

Since we are interested in this chapter in analyzing the T- and P-dependences of polymer viscoelasticity, our emphasis is on dielectric relaxation results. We focus on the means to extrapolate data measured at low strain rates and ambient pressures to higher rates and pressures. The usual practice is to invoke the time-temperature superposition principle with a similar approach for extrapolation to elevated pressures [22]. The limitations of conventional t-T superpositioning will be discussed. A newly developed thermodynamic scaling procedure, based on consideration of the intermolecular repulsive potential, is presented. Applications and limitations of this scaling procedure are described. 

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... 

Several methods are successfully applicable in this field, e.g. dielectric relaxation methods 164>, IR investigations in the near, fundamental, and far IR regions 165>, RAMAN spectroscopy 166>, NMR spectroscopy 32-34-16 ), and ultrasonic absorption i 8-i70). 

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... 

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. 

In the case of those noncrystalline solids that are of sufficiently high electrical condnctivity that dielectric relaxation proscribes the application of the transit time ontlined earlier, the experimental configuration displayed in Fig. 3.1(c) may be of the valne. Here, carriers of both species are excited in equal and uniform concentration across the active area of a specimen film fitted with coplanar electrodes. For step-function illumination, the rate of increase of photocurrent with time is linearly proportional to the carrier generation rate and the carrier drift velocity (and at times sufficiently short that recombination may be neglected). Thus, under the assumption that one species of carrier dominates the behavior, its mobility may be determined. 

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. 

As recalled in the Appendix, the rate of tensile relaxation is principally controlled by the slowest modes, while that for dielectric relaxation is most commonly dominated by the fastest modes. Hence, Eq. (49) may not be without interest in certain physical applications. 

Onsager Theory for C(t) for Non-Debye Solvents. Generally solvents have more complex dielectric responses than described by the Debye equation (Eq. (18)). To obtain the time dependence of the reaction field R from Eqs. (12, (15), (16) and (7) an appropriate model for dielectric behavior of a specific liquid should be employed. One of the most common dielectric relaxation is given by the Debye-type form, which is applicable to normal alcohols. 

For si and sll, Davidson et al. (1977a, 1981) performed NMR spectroscopy and dielectric relaxation measurements where applicable, in order to estimate the barriers to molecular reorientation for simple hydrates of natural gas components, except carbon dioxide. Substantial barriers to rotation should also affect such properties as hydrate heat capacity. 

Current applications have so far avoided these more detailed formulations of the dielectric relaxation, and the scheme of decomposition into collective modes is simplified to two terms only, which here we denote as fast and slow ... 

This electro-optical effect, commonly observed as transient changes in optical birefringence of a solution following application, removal, or reversal of a biasing electric field E(t), has been used extensively as a probe of dynamics of blopolymer solutions, notably by O Konski, and is a valuable tool because it gives information different in form, but related to, results from conventional dielectric relaxation measurements. The state of the subject to 1975 has been comprehensively presented in two review volumes edited by O Konski (25). The discussion here is confined to an outline of a response theory treatment, to be published in more detail elsewhere, of the quadratic effect. The results are more general than earlier ones obtained from rotational diffusion models and should be a useful basis for further theoretical and experimental developments. 

The situation changed dramatically with the application of picosecond and, later, faster techniques. One stimulating study was that of Kosower and Huppert [41]. They found that the reaction time for a particular intramolecular charge transfer in a series of alcoholic solvents was equal to the respective slowest longitudinal dielectric relaxation time of the solvent. It was later pointed out that this equality of the reaction and dielectric relaxation times would apply for barrierless reactions (AG a 0) or, more precisely, for the reactions where the relevant solvent dielectric relaxation, or its fluctuation, are the slow step, i.e., slower than the reaction would be in the absence of any slow solvent relaxational process. 

In the writing of this chapter we have not sought to cover every aspect of the dielectric relaxation of complex materials. Rather, our aim has been to demonstrate the usefulness of dielectric spectroscopy for such systems, using its application to selected examples as illustrations. 

Several comprehensive reviews on the BDS measurement technique and its application have been published recently [3,4,95,98], and the details of experimental tools, sample holders for solids, powders, thin films, and liquids were described there. Note that in the frequency range 10 6-3 x 1010 Hz the complex dielectric permittivity e (co) can be also evaluated from time-domain measurements of the dielectric relaxation function (t) which is related to ( ) by (14). In the frequency range 10-6-105 Hz the experimental approach is simple and less time-consuming than measurement in the frequency domain [3,99-102], However, the evaluation of complex dielectric permittivity in the frequency domain requires the Fourier transform. The details of this technique and different approaches including electrical modulus M oo) = 1/ ( ) measurements in the low-frequency range were presented recently in a very detailed review [3]. Here we will concentrate more on the time-domain measurements in the high-frequency range 105—3 x 1010, usually called time-domain reflectometry (TDR) methods. These will still be called TDS methods. 

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... 

The basic theory of dielectric relaxation behaviour, pioneered by Debye, begins with a macroscopic treatment of frequency dependence. This treatment rests on two essential premises exponential approach to equilibrium and the applicability of the superposition principle. In outline, the argument is as follows. 

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... 

In the particular application to dielectric relaxation, fit) is the aftereffect function following the removal of a constant field [8]. The solution of Eq. (93) rendered in the frequency domain yields the Cole-Davidson equation [Eq. (10)] [28],... 

In the context of dielectric relaxation, we remark that the area of applicability of these results is restricted to the low-frequency range, as defined... 

As far as comparison with experimental data is concerned, the fractional Klein-Kramers model under discussion may be suitable for the explanation of dielectric relaxation of dilute solution of polar molecules (such as CHCI3, CH3CI, etc.) in nonpolar glassy solvents (such as decalin at low temperatures see, e.g., Ref. 93). Here, in contrast to the normal diffusion, the model can explain qualitatively the inertia-corrected anomalous (Cole-Cole-like) dielectric relaxation behavior of such solutions at low frequencies. However, one would expect that the model is not applicable at high frequencies (in the far-infrared region), where the librational character of the rotational motion must be taken... 

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