Glass Debye relaxation

In summary, the NFS investigation of FC/DBP reveals three temperature ranges in which the detector molecule FC exhibits different relaxation behavior. Up to 150 K, it follows harmonic Debye relaxation ( exp(—t/x) ). Such a distribution of relaxation times is characteristic of the glassy state. The broader the distribution of relaxation times x, the smaller will be. In the present case, takes values close to 0.5 [31] which is typical of polymers and many molecular glasses. Above the glass-to-liquid transition at = 202 K, the msd of iron becomes so large that the/factor drops practically to zero. 

Non-Debye dielectric relaxation in porous systems is another example of the dynamic behavior of complex systems on the mesoscale. The dielectric properties of various complex multiphase systems (borosilicate porous glasses [153-156], sol-gel glasses [157,158], zeolites [159], and porous silicon [160,161]) were studied and analyzed recently in terms of cooperative dynamics. The dielectric response in porous systems will be considered here in detail using two quite different types of materials, namely, porous glasses and porous silicon. 

Thus, the non-Debye dielectric behavior in silica glasses and PS is similar. These systems exhibit an intermediate temperature percolation process associated with the transfer of the electric excitations through the random structures of fractal paths. It was shown that at the mesoscale range the fractal dimension of the complex material morphology (Dr for porous glasses and porous silicon) coincides with the fractal dimension Dp of the path structure. This value can be obtained by fitting the experimental DCF to the stretched-exponential relaxation law (64). 

Relaxation functions for fractal random walks are fundamental in the kinetics of complex systems such as liquid crystals, amorphous semiconductors and polymers, glass forming liquids, and so on [73]. Relaxation in these systems may deviate considerably from the exponential (Debye) pattern. An important task in dielectric relaxation of complex systems is to extend [74,75] the Debye theory of relaxation of polar molecules to fractional dynamics, so that empirical decay functions for example, the stretched exponential of Williams and Watts [76] may be justified in terms of continuous-time random walks. 

Much attention has been given to the relaxation of various properties toward their equilibrium values, especially in the glasses literature. Kohlrausch first proposed a stretched exponential form as a description of viscoelasticity, while Williams and Watts suggested the same form for dielectric relaxation exp[-(t/r) ], where 0 < 9 < 1 and 0 = 1 corresponds to the Debye limit. The master equation solution, Eq. (1.41), has a decaying multiexponential form that could lead to a wide variety of behavior depending upon the system. 

An implicit assumption made in deriving the Debye equations is that of a single relaxation time. In other words, the heights of the barriers are identical for all sites. And while this may be true for some crystalline solids, it is less likely to be so for an amorphous solid such as a glass, where the random nature of the structure will likely lead to a distribution of relaxation times. 

All the above descriptions use the Debye model, characterized by an arc of a circle in the plot e" vs. , and a unique relaxation time. In most cases (polymers, glasses, liquids ), however, the spectrum does not correspond to an arc of a circle and is frequently interpreted in terms of a relaxation time distribution. The latter broadens with increasing temperature. Such distributions can be either intrinsic (disordered compounds) or due to lack of accuracy in the measurements fixed frequency measurements with too-widely spaced intervals, or insensitive apparatus. As we shall see later, protonic conductors give rise to better defined but more complex spectra because of the existence of various protonic and polyatomic species corresponding to fixed or mobile charges strong dipoles lead frequently to ferroelectric phenomena. 

---