General properties dielectric relaxation

The considered model of a straight line of M nanoparticles illustrates only general features of dielectric losses caused by an M nanoparticle cluster in polymer matrix. Actually such cluster is a complex fractal system. Analysis of dielectric relaxation parameters of this process allowed the determination of fractal properties of the percolation cluster [104], The dielectric response for this process in the time domain can be described by the Kohlrausch-Williams-Watts (KWW) expression... 

Dielectric relaxation of complex materials over wide frequency and temperature ranges in general may be described in terms of several non-Debye relaxation processes. A quantitative analysis of the dielectric spectra begins with the construction of a fitting function in selected frequency and temperature intervals, which corresponds to the relaxation processes in the spectra. This fitting function is a linear superposition of the model functions (such as HN, Jonscher, dc-conductivity terms see Section II.B.l) that describes the frequency dependence of the isothermal data of the complex dielectric permittivity. The temperature behavior of the fitting parameters reflects the structural and dynamic properties of the material. 

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

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. 

In chapter 7, several aspects of conductivity and dielectric relaxation were discussed. Various other properties such as shear modulus, viscosity, refractive index, volume, enthalpy etc. also exhibit relaxational behaviour particularly in the glass transition region. In this chapter, few further aspects of relaxation are discussed. Relaxation of generalized stress or perturbation whether electrical, mechanical or any other form is typically non-exponential in nature. The associated property is a function of time. A variety of empirical functions, (/) t), have been used to describe the relaxation. Some of them have already been discussed in chapters 6 and 7. The most widely used function is the Kohlraush-Williams-Watts (KWW) function (Kohlraush, 1847 Williams and Watts, 1970 Williams et al., 1971). It is more commonly referred to as the stretched exponential function. The decay or relaxation of the quantity is given by,... 

The general experimental fact of constant frequency dispersion (or time dependence of the correlation function) of the a-relaxation at constant Ta for different combinations of T and P has an immense impact on glass transition. Although the data were mostly obtained by dielectric relaxation, the same effect was found in some glass-formers by photon correlation spectroscopy. The primary concern of most theories, including those mentioned in the NY Times article, is to explain the temperature and pressure dependences of the structural relaxation time Tq.. In these theories, the dispersion of the structural relaxation is either not addressed, or else considered separately with additional input not involved in arriving at r . Consequently, the frequency dispersion is unrelated to the relaxation time of the structural a-relaxation in these theories, and they are unlikely to be consistent with the T, / -superpositioning property by happenstance. 

The rates of change (slopes of the curves) of many important properties (such as the refractive index, surface tension, and gas permeabilities) as a function of temperature, the value of the dielectric constant, and many other optical and electrical properties, often change considerably at Tg. These changes enable the measurement of Tg by using techniques such as refractometry and dielectric relaxation spectroscopy. Refractometry provides results which are similar to those obtained from dilatometry, because of the correlation between the rates of change of the specific volume and of the refractive index with temperature. Dielectric relaxation spectroscopy is based on general physical principles which are similar to those in dynamic mechanical spectroscopy, the main difference being in its use of an electrical rather than a mechanical stimulus. 

The general approach adopted in this section is to treat bulk and interfacial phenomena separately. First the electrical properties of homogeneous phases are discussed. There are two aspects to this treatment, relating respectively to dielectric relaxation and long-range dc conductivity. 

Solutions to these linear equations of motion have important properties in common, notably (1) the solutions are linear, in the sense that if A and B are solutions to the equations of motion, then A + B is also a solution, (2) every solution to the equations of motion can be written as a linear combination of a set of normal mode solutions, and (3) the time correlation function of the amplitude of each normal mode relaxes exponentially. On the other hand, if the actual equations of motion are not linear, for example because forces between beads depend other than linearly on the particle positions, then (1) the solutions to the equations of motion are in general nonlinear, (2) if A and B are solutions to the equations of motion, then A- -B m general is not a solution, and therefore (3) the true solutions do not admit of a normal mode decomposition. Watanabe and collaborators have systematically explored applications of normal mode descriptions to dielectric relaxation measurements(38,3). 

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