Complex susceptibility, dielectric relaxation

Usually, the exponents a and (3 are referred to as measures of symmetrical and unsymmetrical relaxation peak broadening. This terminology is a consequence of the fact that the imaginary part of the complex susceptibility for the HN dielectric permittivity exhibits power-law asymptotic forms Im e (( ) coa and Im s (co) co aP in the low- and high-frequency limits, respectively. 

Besides mechanical viscoelastic experiments, one can also perform dielectric relaxation measurements, which constitute another well-established technique in polymer physics. Dielectric relaxation is related to the frequency-dependent complex dielectric susceptibility, e (co). One usually focuses on Ae (co), which is introduced as follows ... 

Complex dielectric susceptibility data such as those in Figure 15.6 provide a detailed view of the dynamics of polar nanodomains in rls. They define relaxation frequencies, /, corresponding to the e (T) peak temperatures Tm, characteristic relaxation times, r = 1/tu (where uj = 2nf is the angular frequency), and a measure of the interaction among nanodomains as represented by the deviation of the relaxation process from a Debye relaxation. Analysis of data on pmn and other rls clearly shows that their dipolar relaxations cannot be described by a single relaxation time represented by the Debye expression... 

In the present section, it is demonstrated how the linear response of an assembly of noninteracting polar Brownian particles to a small external field F applied parallel and perpendicular to the bias field Fo may be calculated in the context of the fractional noninertial rotational diffusion in the same manner as normal rotational diffusion [8]. In order to carry out the calculation, it is assumed that the rotational Brownian motion of a particle may be described by a fractional noninertial Fokker-Planck (Smoluchowski) equation, in which the inertial effects are neglected. Both exact and approximate solutions of this equation are presented. We shall demonstrate that the characteristic times of the normal diffusion process, namely, the integral and effective relaxation times obtained in Refs. 8, 65, and 67, allow one to evaluate the dielectric response for anomalous diffusion. Moreover, these characteristic times yield a simple analytical equation for the complex dielectric susceptibility tensor describing the anomalous relaxation of the system. The exact solution of the problem reduces to the solution of the infinite hierarchies of differential-recurrence equations for the corresponding relaxation functions. The longitudinal and transverse components of the susceptibility tensor may be calculated exactly from the Laplace transform of these relaxation functions using linear response theory [72]. 

The temperature-modulated mode of operation has been well known for many decades in calorimetry [33], but became well established only during the 1990s, when commercial DSC was modified this way [34], The idea is to examine the behavior of the sample for periodic rather than for isothermal or constant-heating-rate temperature changes. In this way it is possible to obtain information on time-dependent processes within the sample that result in a time-dependent generalized (excess) heat capacity function or, equivalently, in a complex frequency-dependent quantity. Similar complex quantities (electric susceptibility, Young s modulus) are known from other dynamic (dielectric or mechanical) measurement methods. They are widely u.sed to investigate, say, relaxation processes of the material. 

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