Debye-like relaxation process

We remark that activation processes that involve crossing of the encaged dipole over an internal potential barrier may also be incorporated into the present model by adding a cos 20 term to the potential in Eq. (15). This may give rise to a Debye-like relaxation process at very low frequencies with relaxation time governed by the Arrhenius law, the prefactor of which may be calculated precisely using the Kramers theory of escape of particles over potential barriers (see Section III). We remark that a cos 20 term in the potential has also been considered by Pofimeno and Freed [41] in their discussion of a many-body stochastic approach to rotational motions in liquids. Their... 

Therefore to analyze the a- and the 6-relaxation of the polymers investigated another method has been employed. This is based on taking the derivative of e with respect to log f i.e. A= de/ Slog This way of analyzing dielectric data was introduced by van Turnhout and Wubbenhorst (van Turahout, J. Wiibbenhorst, M., personal coomunication). It can be shown for Debye-like relaxation processes that... 

To better understand the nature of the two types of dynamics, the Cole-Cole plots were plotted, and they clearly indicate the evolution from FR to SR with the changing temperature. Strikingly, the plots can be nicely fitted by the sum of two modified Debye functions (Figure 3.8b, inset), which is used to explain such a complex relaxation process. Here, the two separated relaxation processes are most likely associated with distinct anisotropic centres, that is, two Dy ions with... 

Clear evidence of L-L transitions has been found only in /-Si modeled by the SW potential [269]. Sastry and Angell [288] performed MD simulations of supercooled /-Si using the SW potential. After cooling at ambient pressure, the liquid (HDL) was transformed to LDL at 1060 K. The Nc in LDL is almost 4, and the diffusivity is low compared with that in HDL. The structural properties of LDL, such as g(r) and Nc, are very close to those of LDA, which indicates that this HDL-LDL transition is a manifestation of the multiple amorphous forms (LDA and HDA) of Si. McMillan et al. [264] and Morishita [289] have also found structural fluctuations between LDL-like and HDL-like forms in their MD calculations for /-Si at 1100 K. Morishita has demonstrated that such a structural fluctuation induces spatial and temporal dynamical heterogeneity, and this heterogeneity accounts for the non-Debye relaxation process that becomes noticeable in the supercooled state [289]. 

In these equations the subscript 1 is used to identify the properties of the matrix, while 2 is used for the particles. These equations are for the special case of a highly insulating matrix of constant dielectric properties containing a small amount of well-dispersed spherical particles that are somewhat conductive. The important aspect of this result is that the particles produce a Debye-like dispersion centered at a frequency of roughly Oj/eq. With a conductivity of, say, 10 7 S/m (Siemens/meter) and 0 = 8.84 x 1CT12 F/m (Farads/meter) the frequency of the MWS dispersion will be around 10 kHz, where it can be easily confused with a dipolar relaxation process. As shown by equation (7-57), the magnitude of the MWS dispersion should increase linearly... 

According to EM theory, the dielectric loss may be contributed by the processes like natural resonance, Debye dipolar relaxation and electron polarization relaxation, etc. In the Debye dipolar relaxation regime, the relative complex permittivity can be expressed as ... 

Figures 20.21c and d show that poly(VCN-a/f-MATRIF) copolymer exhibits a dynamic scenario with four relaxation processes two relaxations are above Tg, merging at low temperatures, while two others are below Tg. The addition of VCN unit increases the dielectric constant as well as the value of calorimetric glass transition Tgi (i) -relaxation (Debye-like and strong, i.e., low fragility index m = 44 [68]) (ii) a2-relaxation (broad and fragile, high fragility index m = 101 [68]), more separated from p-one effect of rigidity of VCN segment (iii) p-relaxation (faster), due to a less efficient packing similar effect for random copolymers based on butyl methacrylate (n-BMA) with styrene (ST) named poly( -BMA-5 fflf-ST) copolymer [123].

After the introduction of the various interrelated response functions and basic concepts like the Debye-process and the derived spectral representations we come now in the second part of this chapter to the description and discussion of actual polymer behavior. In fact, relaxation processes play a dominant role and result in a complex pattern of temperature and frequency dependent properties. 

It can not be described by means of a single Debye process, but more complicated relaxation functions involving distributions of relaxation times (like the Cole-Cole function [117]) or distributions of energy barriers (like log-normal functions [118]) have to be used for its description. Usually a narrowing of the relaxation function with increasing temperature is observed. The Arrhenius temperature dependence of the associated characteristic time is ... 

At 143 K, the loss spectrum shows one more peak in the range 10 -10 Hz which corresponds to a-relaxation. It is due to the slowest cooperative motion. The / -process is the result of the influence of nearest neighbour cage fluctuations on libration, creating diffusion of the encaged molecule from one energy well into another. It has been described by Johari et al. [91] and Williams [92] as a remnant of the liquid-like diffusional reorientation observed at ambient temperatures the loss process first explained by Debye. 

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