Jump relaxation model

Figure 53. Frequency-dependent conductivity of RbAg4ls at 129 K. (More precisely a- represents the real part of the complex conductivity.) As the continuous line shows, the jump-relaxation model in Ref.278-280 can well describe the behavior in the hopping regime.278 Reprinted from K. Funke, Prog. Solid St Chem., 22 (1993) 111-195. Copyright 1993 with permission from Elsevier.

Figure 55 sketches the situation. The realistic potential includes lattice potential and interaction potential. Two functions are crucial in the description of the jump relaxation model, developed and refined by Funke et al.217"219 (i) the probability W(t) that no correlated backward jump has occurred at time t (-W being the backward jump rate) and (ii) g(t) describing the positional mismatch (-g measuring the stabilization rate). The basic assumption of the jump relaxation model is... 

A Modified Jump Relaxation Model for Fragile Glass-Forming Ionic Melts, Z. Phys. Chem. 206, 101-116. 

The alternative viewpoint was to assume that the site potentials of the ions were not static, but varied in time, thus reflecting their changing momentary arrangements and interactions. This view led to the so-called Jump Relaxation Models, which are based on simple rate equations for the ion dynamics [8, 9, 28], The solid lines included in Fig. 2 and Fig. 5 have been derived from the most recent model version, called the MIGRATION concept [29]. 

Ti is a time related to the initial site relaxation rate T2, while p = x x can be expressed in terms of the ratio of the initial back-hopping rate (1/x ) and the initial site-relaxation rate (I/X2) in accordance with the jump-relaxation model (see Sections 6.4 and 6.5). 

The real component of the conductivity spectra in the framework of the jump relaxation model and polymer segmental motion... 

Components of the overall potential (a) and hopping dynamics (b) in the jump relaxation model. 

The jump relaxation model of Punke is a concept of wide validity [410]. In certain aspects it may be compared to the Debye-Falkenhagen theory [411] of liquid electrolytes. The interaction of the point defects expresses itself in a relatively flat defect potential , that is superimposed on the lattice potential, as shown in Fig. 6.34. 

Fig. 6.35 Frequency dependent conductivity of RbAg4l5 at 129K. (More precisely

Detailed simulations [416] indicate the importance of inhomogeneity effects for the dispersion (cf. static distribution of thresholds and time constants, see also Section 7.3.6). This is of special importance in the case of amorphous systems. While the jump relaxation model explicitly addresses dynamic inhomogeneity effects in the sense of Fig. 6.34, possible static inhomogeneities have to be included in the eflFective defect potential and the relation between jump and relaxation rate. A competent recent review is given in Ref. [418]. 

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