An approach to the interpretation of Cole–Davidson and Cole–Cole dielectric functions

Abstract

Assuming that a dielectric sample can be described by Debye's model at each frequency, a method based on Cole's treatment is proposed for the direct estimation at experimental frequencies of relaxation times and the corresponding static and infinite-frequency permittivities. These quantities and the link between dielectric strength and mean molecular dipole moment at each frequency could be useful to analyze dielectric relaxation processes. The method is applied to samples that follow a Cole–Cole or a Cole–Davidson dielectric function. A physical interpretation of these dielectric functions is proposed. The behavior of relaxation time with frequency can be distinguished between the two dielectric functions. The proposed method can also be applied to samples following a Navriliak–Negami or any other dielectric function. The dielectric relaxation of a nanofluid consisting of graphene nanoparticles dispersed in the oil squalane is reported and discussed within the novel framework.

A dielectric and spectrophotometric study of the tautomerization of 2-hydroxypyridine and 2-mercaptopyridine in water

“…Thus, to verify our concern, 3 0 (u) against 3 00 (u)/u, and 3 0 (u) against u3 00 (u) were plotted according to the eqn (12) and (13), which are rearranged versions of Debye equation. 87 3 0 ðuÞ ¼ 3 a þ 1 s 3 00 ðuÞ u (12)…”

Variable-order modeling of nonlocal emergence in many-body systems: Application to radiative dispersion

“…equation. Systems such as these are often accurately captured by fractional differential descriptions due the memory effects imposed by viscoelastic transduction of the incident field [50] [51]. The plots of the real (gray) and imaginary (black) values for the dielectric function are given in (c).…”

Time-Constant-Domain Spectroscopy: An Impedance-Based Method for Sensing Biological Cells in Suspension

“…Once experimental data are collected, complex electrical models are required to decode the underlying electrical processes. Such a task is, in general, performed by fitting the impedance data to the well-known Cole-Cole model [19] and lumped electrical equivalent circuits [20], or in some cases, by comparing experimental data with rigorous theoretical models [21]. This task, however, is not always trivial, and requires some prior knowledge of the sample under study to identify the underlying processes.…”