Coupling model and MIGRATION concept – Equivalence and mutual mapping

Frequency-dependent conductivities of ionic materials with disordered structures display a surprising degree of ‘universality’. To understand the underlying phenomena, two complementary routes have been pursued in the last few decades, one of them being macroscopic, the other microscopic in character. On the macroscopic route, the electric-field-relaxation function, Φ(t  ), is related to the complex electric modulus, M^(ω). On the microscopic route, which is based on linear response theory, a similar relation holds between the time-dependent correlation factor, W(t  ), and the complex conductivity, σ^(ω). As M^(ω) and σ^(ω) are easily transformed into each other, a formal connection exists between Φ(t) and W(t), i.e., between the two complementary treatments. Specific rules of how to construct Φ(t) and W(t) are provided by the coupling model (CM) and by the MIGRATION concept (MC), respectively. The function ΦCM(t) formulated in the CM is particularly elegant and easy to use. On the other hand, functions W(t) as formulated in the MC yield excellent agreement with experimental data. In this contribution, we transform such functions W(t) into realistic field-relaxation functions, ΦMC(t), which are then compared with the corresponding functions ΦCM(t). We find agreement in essential aspects as well as differences in the intermediate-time regime.