Comments on the fitting of Cole-Cole/Havriliak-Negami equation with the dielectric data under the influence of parasitic effects in order to extract correct parameters of the materials

Interplay of Ion-Conduction and Nanoscale Self-Assembly in Amphiphilic Janus-Type Hexa-peri-hexabenzocoronenes

“…Contributions from electrode polarization effects as well as from Maxwell−Wagner−Sillars polarization (the latter in heterogeneous systems) appear at lower frequencies as well-documented in literature. 29,30,32,33 X-ray Scattering. Wide-angle X-ray scattering (WAXS) measurements were made using Cu Kα radiation (λ = 1.54184 nm) with a Bruker D8 ADVANCE 2θ diffractometer, equipped with the detector LYNXEYE XE-T.…”

“…For a capacitance of ∼100 pF, the absolute accuracy in the loss factor tan δ is ∼3 × 10 –5 for frequencies in the range from 10 –1 to 10 6 Hz. The real (ε ′ ) and imaginary (ε ″ ) part of the complex dielectric function, ε * (ω ,T ) = ε′(ω ,T ) – i ε″(ω ,T ), was obtained as a function of frequency, f (= ω/2π), and temperature, T . − At a given temperature, the complex dielectric function can be fitted by the empirical equation of Havriliak and Negami: ε * false( ω , normalΤ false) = ε ∞ + ∑ k normalΔ ε k false( normalΤ false) false[ 1 + false( i · ω · τ HN , normalk false( normalΤ false) ) m k ] n k where Δε k is the dielectric strength, τ HN, k is the characteristic relaxation time of the H–N equation, and the index k indicates the process under investigation. The parameters m k and n k (0 < m k , m k n k ≤ 1) are two shape parameters of the H–N function.…”

Impact of carbon quantum dots on self-assembly and dielectric relaxation modes of a room temperature tri-component fluorinated antiferroelectric liquid crystal mixture

“…The generalized Cole–Cole equation for the complex permittivity ( ε *) is used to fit with the measured data of permittivity ( ε ') and loss ( ε ′′). 49,50 where, ε ′(0) and ε ′(∞) are the low and high frequency limiting values of the relative permittivity. δ ε = ε ′(0) − ε ′(∞) is the dielectric relaxation strength, α i (0 < α i <1) is the distribution parameters and τ (1/ f r ) is the relaxation time.…”

“…The generalized Cole-Cole equation for the complex permittivity (e*) is used to fit with the measured data of permittivity (e') and loss (e 00 ). 49,50 e à ¼ e 0 À je 00…”

“…Different correction terms (at low and high frequencies) were calculated with the acquired fitting parameters and then these terms were subtracted from the measured data to obtain the corrected data. [50][51][52] Corrections for the parasitic effect in the high frequency region were possible only up to 6-7 MHz at the most (until the correction terms are not too large) 52 and therefore in some of the figures, the display of data is only up to 10 MHz despite actual measurements up to 40 MHz.…”