Stretched exponential relaxations, amorphous

The long-pathway rearrangement processes expected for fragile materials at low temperatures are expected to be rare, to involve a local disruption of the otherwise well-structured amorphous medium, and to be relatively long-lived on the usual molecular time scale. These features all contribute to a substantial lengthening of the mean relaxation time /rci(7 ), Eq. (36), with declining temperature. Furthermore, the landscape diversity of deep traps and of the configuration space pathways that connect them should produce a broad spectrum of relaxation times, just as required by stretched-exponential relaxation functions, Eq. (34). 

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. 

A supercooled hquid or amorphous sohd can be driven out of (restricted) equihbrium in a wide variety of ways, and the kinetics of relaxation back to (restricted) equihbrium subsequently followed. This variety includes sudden temperature or pressure changes, mechanical working, application of a polarizing electric field, and irradiation with energetic particles. As mentioned in Section I, the linear-response relaxation kinetics of supercooled liquids as monitored by any of several properties is observed to follow a Kohlrausch-Wilhams-Watts (KWW) stretched exponential form [see Eq. (2)],... 

Dielectric relaxation and photon correlation spectroscopic measurements (to be discussed later) have found that the stretched exponential time correlation fimction of the Q -relaxation of amorphous polymers, exp[ — it/Taf"], has Pa that varies from polymer to polymer. For example, PS and PIB have Pa equal to 0.36 and 0.55 respectively. It was recognized that this difference in the stretched exponent Pa of PIB and PS is the origin of their contrasting viscoelastic properties 12,IQ, 121,122). 

In practice dielectric relaxation curves for polymers (1-5) and glass-forming liquids (eg. Fig. 1) are far broader than that for an SRT process. Numerous empirical relaxation fiinctions have been proposed for this behavior (1,2,5). One function is the stretched exponential function of Kohlrausch, Williams, and Watts (KWW) (4-6), that is widely apphed to dielectric and other relaxation data for amorphous polymers ... 

The local segmental relaxation or a-relaxation in amorphous polymers is fitted well by the empirical KWW stretched exponential function (see also Eq. (2.9)),... 

A further feature of dielectric relaxations in amorphous polymers is that the a (or ctfi) relaxations are well-described by the stretched-exponential or Kohl-rausch-Williams-Watts function [21-23]... 

The decay of the transient photoinduced absorption signal in oxygenated films has been fitted using a stretched exponential temporal decay fit) excitation wavelength of 605 nm (2.0 eV). This type of non-exponential carrier relaxation is frequently encountered in systems exhibiting dispersive transport, such as hydrogenated amorphous silicon [158,159]. The temperature dependence of the parameters and t... 

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