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Published in Joseph C. Salamone, Polymeric Materials Encyclopedia, 2020
In the frequency domain, dielectric relaxations are often analyzed using the well-known empirical Havriliak-Negami relaxation function shown in Equation 2: ϵ*(ω)=ϵ∞+ϵs−ϵx(1+(iωτ)a)b
Detection of an emerging contaminant in water by dielectric properties in microwave range
Published in Journal of Microwave Power and Electromagnetic Energy, 2020
Edel-Serafin Hernandez-Gomez, Jose-Luis Olvera-Cervantes, Alonso Corona-Chavez, Benito Corona-Vasquez, Tejinder-Kaur Kataria, Maria-Elena Sosa-Morales
The most common models used to describe the electrical behaviour of either aqueous electrolytic solutions or tissues are the: Debye, Cole–Cole, and Cole–Davidson models. In general, the Debye, Cole–Cole, and Cole–Davidson models can be represented collectively by the Havriliak–Negami relaxation, which is an empirical modification of the Debye relaxation model, accounting for the asymmetry and broadness of the dielectric dispersion curve: and are the dielectric constants under DC and at infinity frequency, respectively. is the DC conductivity. α and β are empirical variables that account for the distribution of the relaxation time and the asymmetry of the relaxation time distribution, respectively, and τ is the characteristic relaxation time of the medium, which is the time required for dipoles to become oriented in the presence of an electric field or the time needed to disorient the dipoles after the electric field is removed (Raju 2003; La-Gioia et al. 2018). The relaxation frequency indicates the frequency in which a group of dipoles of material no longer follows to the electrical field and in which the loss factor reaches a maximum. This frequency occurs at ω = 1/τ (Frohlich 1987; Mehrotra et al. 2017).
Determination of ionic strength due to magnesium sulfate heptahydrate in water by means of its permittivity in the microwave range
Published in Journal of Microwave Power and Electromagnetic Energy, 2020
Edel Serafín Hernández Gómez, José-Luis Olvera-Cervantes, Benito Corona Vásquez, Alonso Corona Chávez, Laura Sol Perez Flores, Tejinder Kaur Kataria
The most common models used to describe the electrical behaviour of either aqueous electrolytic solutions or tissues are the: Debye, Cole-Cole, and Cole-Davidson models. In general, the Debye, Cole-Cole, and Cole-Davidson models can be represented collectively by the Havriliak–Negami relaxation, which is an empirical modification of the Debye relaxation model, accounting for the asymmetry and broadness of the dielectric dispersion curve: