Havriliak Negami Research Articles

The Havriliak–Negami susceptibility as a nonlinear and nonlocal process

A theoretical substantiation of the Cole–Cole, Cole–Davidson and Havriliak–Negami types of susceptibilities is presented. These types of susceptibility are shown to be a manifestation of weak nonlocality and nonlinearity. The Debye susceptibility corresponds to linear and local relaxation, the Cole–Cole susceptibility being linear and nonlocal; the Cole–Davidson susceptibility is nonlinear and local and the Havriliak–Negami susceptibility corresponds to nonlinear and nonlocal relaxation.

Dielectric properties of monocrystal diglycine nitrate near the phase transition point in the frequency range 1 Hz-10 MHz

In this paper, the dielectric properties of the polar cut of the monocrystal of diglycine nitrate (DGN), depending on the temperature, the frequency of the applied external field and the measuring time, were studied. Using the Havriliak—Negami equation, an approximation of the experimental frequency dependencies of permittivity was made. For each temperature point, a relaxation time spectrum is obtained. The temperature dependence of relaxation time values near the Curie point was found.

The effect of irregularity on the dielectric dispersion characteristics of spherical cellular suspension

The dielectric dispersion characteristics of cellular suspensions are fundamentally determined based on the analogy to composite dielectric materials when periodically and discrete arrangement of cells is assumed. However, under native physiological conditions, when flocculation and clamping events usually occur, those assumptions are usually not valid. In the framework of this study, an examination of irregularity effect on the dispersion characteristics of spherical cellular suspensions is presented. Here, the permittivity spectra of the suspensions have been determined by both measurements of living K562 cell suspensions and finite numerical simulations. Based on the measured and simulated spectra, the dispersion characteristics of the suspensions, for several destinies and arrangements of cells, have been quantitatively analyzed using the Havriliak–Negami empirical formula. Generally, a strong correlation between the low dispersion characteristics was observed as the concentration and density of the cells was increased. In addition, all characteristics found to be significantly deviated in comparison to the characteristics of a periodically arrayed suspension. However, when low-dense arrangement was assumed, the correlation found to be much lower when all characteristics found to be less perturbated. Based on a simple model of interacting cells, it is suggested that those deviations are related to intercellular interactions between adjacent cells.

Semi-interpenetrating polymer networks based on polyurethane and poly(2-hydroxyethyl methacrylate): Dielectric study of relaxation behavior

Abstract The study of molecular dynamics by broadband dielectric spectroscopy (BDS) is presented for polyurethane (PU), poly(2-hydroxyethyl methacrylate) (PHEMA) and for semi-IPNs based on PU and PHEMA synthesized by photopolymerization. The dielectric properties were performed in wide range of frequencies and temperatures with the goal to establish the relation between the relaxations and the structure. Five relaxation phenomena were finally detected for PHEMA : γ -, β sw -, β-relaxations at low temperatures and α-relaxation at 150 °C at high frequencies plus ionic conductivity relaxation which starts at 0 °C. For semi-IPNs the overlapping of γ- and β sw -relaxations of PHEMA (−125/−75 °C), then with increasing the temperature α-relaxation in PU (−75/0 °C), next ionic conductivity relaxation which starts at 0 °C, and finally the α-relaxation of PHEMA (+125/+170 °C) were detected. The α-relaxation of PHEMA in semi-IPNs shifts to lower temperatures and became broader with increasing amount of PU due to incomplete phase separation in the system and formation of interphases. The dielectric relaxation phenomena were fitted with Havriliak–Negami equation. Activation energy, τ o and α parameters were calculated. For α-relaxations corresponding dielectric characteristics have been determined from Vogel–Fulcher–Tammann equation. The relaxation map for investigated PU, PHEMA and semi-IPNs was built.

Copolymerization of α‐cyanovinyl acetate with acrylonitrile and methacrylonitrile: Synthesis, characterization, and study of their dielectric behavior

AbstractIn the frame of a research aiming at developing new dielectric polymers containing CCN substituent with strong dipole moment, the radical copolymerization of cyano (nitrile) monomers and an α‐cyanovinyl acetate (CVA) as the comonomer, initiated by AIBN is described. Methacrylonitrile (MAN) and acrylonitrile (AN) were chosen as the cyano monomers. The homopolymer of CVA was also prepared and the corresponding yield was close to 60%. All these polymers were characterized by 13C NMR, IR, DSC, and TGA. The percentages of incorporation of AN and MAN in the copolymers were 36 and 56%, respectively. These products showed high glass transition temperatures, Tg, ranging between 124 and 142°C. The thermogravimetry analyses showed that these copolymers are stable up to 200°C. Dielectric spectroscopy analysis revealed a weak relaxation β process below Tg. The α relaxation phenomena have also been characterized around the Tg and associated to the cooperative movements of the polar groups (CN). The values of dielectric relaxation increment were calculated at 150°C using the Havriliak–Negami equation and indicated that these polymers exhibit interesting dielectric properties comparatively to similar cyano materials. The α‐activation energies were also calculated. New statistic copolymers based on CVA were characterized. The values of the intensity of α relaxation show the potential application of such materials in the domain of electronics. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Dielectric relaxation study ofN-methyl formamide with glycols using time domain reflectometry technique

The dielectric relaxation study that is static dielectric permittivity (∈0) and relaxation time (τ) of amide of N-methyl formamide (NMF) with increasing volume percent propylene glycol (PLG) and BLG has been carried out at different temperatures. The time domain reflectometry (TDR) technique has been used to measure reflection coefficient in frequency range of 10 MHz to 20 GHz. The dielectric parameters have been obtained by fitting experimental data with the Havriliak–Negami equation. The experimental observation shows that the static dielectric permittivity and relaxation time decreases with increasing temperature. The experimental observation also shows that the static dielectric permittivity decreases and relaxation time increases with increasing percentage volume of Propylene glycol (PLG) and Butylene glycol (BLG) in NMF. The nature of (ϵ0) and (τ) is same for the temperature ranges (20, 30, and 40°C). The thermodynamic parameters enthalpy (ΔH) and entropy (ΔS) of the binary mixture are also reported in this work.

Dielectric dispersion study of Mn-doped PLZT (8/65/35)

Mn-modified Pb0.92La0.08(Zr0.65Ti0.35)O3 (PLZT) was prepared chemically by a coprecipitate method using their respective nitrate salts and isopropoxides. Differential thermal analysis (DTA) and X-ray analysis clearly show the formation of PLZT single rhombohedral phase for samples calcined beyond 750 °C. Uniform grain distribution was observed from scanning electron microscopic (SEM) studies and grain size was found to increase with Mn doping up to x = 0.08 and then decreased. Dielectric measurement shows the decrease in peak transition temperature (TC) with Mn doping up to x = 0.12 and then increase along with a sharp rise in dielectric maxima. A diffuse dielectric dispersion is observed in all the compositions. A detailed dispersion study was carried out using the Vogel–Fulcher empirical relation, a universal relaxation law and the Havriliak–Negami function. The Vogel–Fulcher relation fitting parameters of activation energy and freezing temperature were found to decrease with Mn doping up to x = 0.12, which was expected to be the cause of the variation of TC. The exponent m of the universal relaxation law was found to increase with Mn doping and also with increasing temperature, which suggests an enhanced conducting nature of the composition. In the Havriliak–Negami function, the Cole–Cole fitting parameter α was found to increase and β was found to decrease with Mn doping and also with temperature, which suggests that the dispersion behavior changed from Cole–Cole type to Cole–Davidson type with Mn doping in PLZT. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermodynamic and dielectric studies of liquid crystalline compound (S)-(+)-4-(1-methylheptyloxycarbonyl)phenyl 4′-(6-octanoyloxyhex-1-oxy)biphenyl-4-carboxylate

Dielectric spectroscopy of a newly synthesized antiferroelectric material (S)-(+)-4-(1-methylheptyloxycarbonyl)phenyl 4′-(6-octanoyloxyhex-1-oxy)biphenyl-4-carboxylate has been carried out over a frequency range 0.1 Hz to 35 MHz for a planar anchoring geometry of sample molecules. Material possesses paraelectric SmA* and ferroelectric SmC* phases along with antiferroelectric Sm phase. Generalized Havriliak–Negami equation has been applied to analyze the acquired dielectric data and consequently various dielectric parameters have been determined. SmC* phase shows two relaxation modes separated by about two decades of the frequency. The mode lying at the higher side of the frequency spectrum relates with Goldstone mode. Low-frequency mode with higher dielectric strength as compared to that of the Goldstone mode apparently seems due to the domain formation in the SmC* phase. SmA* phase shows single relaxation mechanism related with the soft mode. Two weak modes of dielectric relaxation have been detected in the Sm phase and these are related with the antiferroelectric ordering of the molecules in the phase.

Study of supercooled orientationally disordered binary solid solutions II: cyclohexyl derivatives, neopentanol and neopentylglycol

The main aim of the present investigation is to see how various relaxation processes including the chair-chair transformation (as found by earlier researchers at room temperature in mechanical relaxation spectroscopy) in cyclohexane derivatives evolve as the temperature is lowered. For this purpose, four remarkable (two-component) solid solutions that are orientationally disordered are investigated, where the first three systems are hydrogen (H-) bonded pairs, and the fourth is a non-H bonded pair. The former group is the two-component system of cyclohexanol (CHXOL) + 2,2-dimethyl-1-propanol or neopentanol (NPOL); cyclohexanol (CHXOL) + cycloheptanol (CHPOL) & neopentanol (NPOL) + neopentylglycol (NPGOL) systems, and the lone non H-bonded pair that has been studied is cyanocyclohexane (CNCH) and cyclohexylchloride (CHC). In all these cases, the liquid mixtures on cooling form orientationally disordered phases which are a solid solution of the corresponding pure phases. The feature is common to all the four systems studied here, but in CHXOL + CHPOL, the phase I of CHXOL beyond x(m) > or = 0.1 only forms a solid solution (designated as S(I')) with the phase I of CHPOL. In CNCH + CHC the solid phase is stable for the concentration range 0 < or = x(m) < or = 0.4 (without transition to any other phase). The above solid phase I (or I') has been investigated at low temperatures and for several concentrations, by means of dielectric spectroscopy and differential scanning calorimetry (DSC). Depending upon the concentration, this phase reveals a glass transition in the temperature range 116-150 K and associated with this is a pronounced relaxation process identifiable with the so called alpha-process. The dielectric spectra of this process is found to follow the Havriliak-Negami (HN) equation. In context of the binary system study here, the analysis of the various parameters obtained show an isomorphic relationship between the phases of the pure components through a continuous change of parameters. Another process of much smaller magnitude designated as the alpha'-process was also found in systems consisting of cyclohexyl derivatives above the glass transition temperature T(g) which kinetically freezes around 170 K. This process interestingly, is also non-Arrhenius in nature, becomes increasingly weaker with increase in the second component, and may be identified with (axial) chair-(equatorial) chair transformation. In addition in all these systems, a weak high-frequency process and a clear sub-T(g) process, are found which are designated as the beta- & gamma-processes respectively. The beta-process may be identified with Johari-Goldstein (JG) or beta(JG) process as it is found to follow the predictions of the coupling model proposed by Ngai. However, the identification of the gamma-process with internal degrees of freedom are fraught with some problems in the interpretation of the experimental data that are highlighted. The kinetic freezing of the various dielectric processes have been critically examined in relation to the T(g) found in the DSC experiments.

Molecular dynamics of an epoxy resin modified with an epoxidized poly(styrene–butadiene) linear block copolymer during cure and microphase separation processes

Molecular dynamics of diglycidyl ether of bisphenol A (DGEBA) epoxy resin modified with an epoxidized poly(styrene-b-butadiene) (SepB) linear block copolymer has been monitored during cure and microphase separation process by dielectric relaxation spectroscopy (DRS) for wide frequency and temperature ranges. Different primary and secondary relaxation processes have been analyzed for neat components and ternary mixture. Relaxational behaviour has been modelled with Havriliak–Negami, Vogel–Fulcher–Tammann and Arrhenius equations and fitting parameters and their evolution have been obtained. The retention of the epoxidized poly(butadiene) (PepB) block in the epoxy-rich phase during all the polymerization process, previously detected by our group with atomic force and transmission electron microscopies, has been confirmed by dielectric relaxation spectroscopy. The evolution of molecular dynamics during the polymerization process of the epoxy resin in the ternary system indicates a change in the trend of the main relaxation at times that agree with phase separation detected by rheology.

The electrorheological efficiency of polyaniline particles with various conductivities suspended in silicone oil

Electrorheological (ER) behavior of silicone oil suspensions of particles of polyaniline protonated to various doping levels with ortho-phosphoric and tetrafluoroboric acids has been studied. The dynamic yield stress obtained by extrapolation of shear stress to zero shear rate using Herschel–Bulkley equation was used as a criterion of the ER efficiency. At a same molar concentration of doping acids, various protonation effects appeared and the dependences of the yield stress on the acid concentration differed. The comparison of the yield stresses with dielectric characteristics calculated from the Havriliak–Negami equation revealed that the particle conductivity, in contrast to particle permittivity, dominates the polarization process especially at higher protonation degrees. Consequently, particle conductivity or dielectric relaxation time proved to be the parameters providing the common dependences of the yield stress regardless of the way of polarization.

Dielectric behaviour of copolymers based on 2,2,2-trifluoroethyl methacrylate and cyano co-monomers

In the frame of a research aiming at developing new dielectric polymers containing C CN and C F substituents with strong dipole moment, statistical copolymers based on cyano monomers such as acrylonitrile (AN), methacrylonitrile (MAN), methylvinylidene cyanide (MVCN) and 2,2,2-trifluoroethylmethacrylate (MATRIF), were synthesized and characterized. Elemental analysis has shown that the molar percentages of AN and MAN in the copolymers were 45 mol.%, while only 5 mol.% of MVCN was incorporated in the poly(MVCN- co-MATRIF) copolymer. These copolymers exhibit glass transition temperatures, T g, in the range of 70–90 °C. The dynamic dielectric analyses and their complex permittivities of these copolymers were studied versus the temperature and the frequency. Evidence of an α-relaxation phenomenon in the glass transition region, which is confirmed by the Vogel–Fulcher–Tammann (VFT) temperature dependence of the relaxation times, was assigned to the cooperative reorientation motions of the cyano groups. The values of dielectric strength (Δ ε) for the copolymers based on MATRIF were determined by Havriliak–Negami (HN) fitting from the dispersion curves, and can be related to the polarity of the monomer unit and to the packing of the macromolecular chains. These relaxations are sometimes overlapped by conduction phenomena due to ionic impurities at low frequencies and high temperatures dipolar losses. In the glassy state, the permittivity values of AN and MAN copolymers show an increase of polarity which makes them candidates for some applications amongst advanced electrical materials such as dielectric layer for capacitors.

Ultrasonic Energy Transfer and Stress Concentrations in a Single-Fiber Composite with Absorbing Interface Layer

Elastic wave scattering from coated and layered cylindrical scatterers encased in an elastic matrix is reviewed. Interaction of time harmonic monochromatic longitudinal and shear ultrasonic waves with a single fiber coated by homogeneous dissipative (polymeric) materials and embedded in an unbounded elastic matrix is studied using the classical method of eigenfunction expansion. The novel features of Havriliak—Negami model is employed to include the effect of hysteresis-type of compressional and shear waves' absorption in the interphase material by introduction of proper frequency-dependent complex moduli. The pertinent integrals for the time-averaged total fiber energy induced by the elastic waves refracted along the fiber are derived and numerically evaluated. The numerical results reveal the important effects of the absorptive fiber—matrix bond as well as interphase thickness on fiber/matrix energy transfer and dynamic stress concentrations. The calculated results may be interpreted in the context of phenomena observed in acousto-ultrasonic (AU) experiments on fiber reinforced composite materials by correlating certain parameters in the frequency spectrum of the detected waveform to mechanical characteristics of the dissipative interface layer. Limiting cases are considered and good agreements with well-known solutions are established.

Study of secondary relaxation in disordered plastic crystals of isocyanocyclohexane, cyanocyclohexane, and 1-cyanoadamantane

In the present communication, dielectric relaxation investigations on three interesting supercooled plastic crystalline substances, i.e., isocyanocyclohexane (ICNCH), cyanocyclohexane (CNCH), and 1-cyanoadamantane (CNADM) are reported. All of these have the main dipole moment situated in their side group- C[Triple Bond]N or- N[Triple Bond]C. Differential scanning calorimetry (DSC) was also employed as a supporting technique. Glassy crystal were easily formed in the first two samples by slowly cooling the plastic phase, but in CNADM it was formed by rapidly quenching the room temperature plastic phase. In addition to the so called alpha process that can reasonably be described by a Havriliak-Negami (HN) shape function, a secondary (or beta) relaxation process is found in all the materials. The beta process in CNADM has an activation energy (DeltaE(beta)) of about approximately 13.8+/-1 kJmol, and is present even in the corresponding ordered crystalline phase, i.e., in its monoclinic phase. On the other hand, the magnitude of DeltaE(beta) in both the isomers of cyanocyclohexane, i.e., ICNCH and CNCH, is similar and is about 21.1 and 23.4 kJmol, respectively. Unlike CNADM, the cyclohexane derivatives are capable of exhibiting additional intramolecular process due to chair-chair conversion (i.e., in addition to the rotational motion of the side group- C[Triple Bond]N or- N[Triple Bond]C). Therefore, the secondary process of these systems is compared to that occuring in the binary liquid glass formed by dispersing a small quantity of these dipolar liquids in nearly nonpolar orthoterphenyl (OTP). Measurements were also made in the supercooled binary mixures of other cyclohexyl derivatives like cyclohexylchloride and cyclohexylbromide with OTP which lack a flexible side group. The sub-T(g) relaxation process exhibited in all these cases have almost similar activation energy as in case of pure ICNCH and CNCH. These observations together with the fact that the activation energy for this process is much below that of chair-chair conversion which is about 43 kJmol leads us to the conclusion that sub-T(g) relaxation process in the binary mixtures is JG type, and perhaps beta relaxation process in phase I of ICNCH and CNCH is also similar. With the help of semiemperical calculations of the dipolemoments for the axial and equitorial confirmers, it is concluded that the process associated with the chair-chair may not be dielectrically very active and, hence, should be relatively weaker in magnitude. The beta process in CNADM has an activation energy (DeltaE(beta)) of about 13.8+/-1 kJmol, and is present even in the corresponding ordered crystalline phase indicating that it may not be characteristic of the glass formation of phase I. The molecular structure of CNADM is such that it does not possess other intramolecular degrees of freedom of the type equitorial to axial (or chair-chair) transformation. Our experimental finding that JG relaxation for CNADM dispersed in glassy OTP matrix is about 31 kJmol, indicating that the well resolved sub-T(g) process in CNADM is due to the small side group, i.e., -C[Triple Bond]N and JG relaxation in phase I of CNADM is perhaps not resolvable or too small to be detected.

Dielectric relaxation in amorphous linear aliphatic copolyesters

In order to contribute to a more extensive body of experimental knowledge concerning the relaxation processes in glass-forming amorphous polymers, broad-band frequency dielectric measurements have been carried out on two examples of a model amorphous polar polymer system. The system consists of a linear random copolyester with one-to-one mole ratios of adipic acid and succinic acid coupled with glycol units. In one example, ethylene glycol is the coupling unit and in the other it is trimethylene glycol The subglass β relaxations as well as the primary α regions were characterized and emphasis was placed on phenomenological description of the coalescence of the two regions with increasing temperature. Each subglass process was found to be complex in the sense of exhibiting two partially resolved components. One component is a typical extremely broad-in-frequency subglass relaxation and the other component is weaker, narrower in frequency and occurs at lower frequency isothermally or higher temperature isochronally. Tentative assignments of the source of the β process components are made. Phenomenological analysis of the α– β coalescence region invoking the Havriliak–Negami and Cole–Cole functions and utilizing numerical regression indicates that the merging process is optimally described as the β process losing relaxation strength and its presence being expressed as increased skewing in the primary relaxation.

Solid polymer electrolytes based on polyethylene oxide and lithium trifluoro- methane sulfonate (PEO–LiCF 3SO 3): Ionic conductivity and dielectric relaxation

Polymer electrolytes consisting of polyethylene oxide (PEO) and LiCF 3SO 3 were synthesized by solution casting method as a function of EO/Li ratio. An increase in the glass transition temperature of the polymer electrolytes with increasing Li salt content suggested the coordination of the Li ions to the oxygen atoms of polymer backbone. Dielectric spectroscopic studies were performed to understand the ion transport process in polymer electrolytes. The dc conductivity showed a maximum for EO/Li ≈ 24. The ac conductivity analysis revealed the existence of nearly constant loss (NCL) contribution at lower temperatures. The dielectric loss spectra showed the presence of one relaxation for all compositions, which is associated with the motions of the Li ion coordinated polymer segments. The relaxation has been characterized by the empirical Havriliak–Negami (H–N) equation. The temperature dependence of the relaxation times and the conductivity followed the Vogel–Tamman–Fulcher (VTF) equation yielding qualitatively similar pseudoactivation energies, which suggested strong coupling between the ionic conductivity and the segmental relaxation in the polymer electrolytes.

Dynamic viscoelastic effects on sound wave scattering by an eccentric compound circular cylinder

The classical method of separation of variables in conjunction with the translational addition theorem for cylindrical wave functions are employed to obtain an exact solution for two-dimensional interaction of a harmonic plane acoustic wave with an infinitely long (visco)elastic circular cylinder which is eccentrically coated by another (visco)elastic material and is submerged in an ideal unbounded acoustic medium. The novel features of Havriliak–Negami model for dynamic viscoelastic material behaviour are used to take the rheological properties of the coating (and/or core) material into consideration. The analytical results are illustrated with numerical examples in which a steel rod eccentrically coated with (an eccentric steel shell filled with) dissipative materials of distinct viscoelastic properties is insonified by plane sound waves at selected angles of incidence. The effects of incident wave frequency, angle of incidence, core eccentricity and dynamic viscoelastic material properties on the backscattered form function spectra are examined. Limiting cases are considered and fair agreements with available solutions are obtained.

Local dynamics in epoxy coatings containing iron oxide nanoparticles by dielectric relaxation spectroscopy

AbstractNanocomposites of photocurable epoxy resin and epoxy‐modified iron oxide magnetic nanoparticles were analyzed by dielectric relaxation spectroscopy to study the local dynamics at temperatures well below the glass‐transition temperature. Two secondary processes were detected, β and γ processes, but the second one was just detected at lower temperatures in the high‐frequency part of the spectra and moved out of the frequency range at higher temperatures. Data were fitted to the Havriliak–Negami and Arrhenius models, and the obtained parameters were analyzed. Relaxation times of the β secondary relaxation did not change with the nanoparticle content, but the relaxation strength increased. The increase could not be explained when we took into account the molecular origin of the relaxation. The presence of ferromagnetic nanoparticles enhanced the internal field and increased the relaxation strengths. Transmission electron microscopy images showed that the nanoparticles were well dispersed in the matrix, without magnetic agglomerates. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 2008

The modified relaxation time function: A novel analysis technique for relaxation processes. Application to high-temperature molybdenum internal friction peaks

The modified relaxation time (MRT) function, which is based on a general linear viscoelastic formalism, has several important mathematical properties that greatly simplify the analysis of relaxation processes. In this work, the MRT is applied to the study of the relaxation damping peaks in deformed molybdenum at high temperatures. The dependence of experimental data from these relaxation processes with temperature are adequately described by a Havriliak–Negami (HN) function, and the MRT makes it possible to find a relation between the parameters of the HN function and the activation energy of the process. The analysis reveals that for the relaxation peak appearing at temperatures below 900K, the physical mechanism is related to a vacancy-diffusion-controlled movement of dislocations. In contrast, when the peak appears at temperatures higher than 900K, the damping is controlled by a mechanism of diffusion in the low-temperature tail of the peak, and in the high-temperature tail of the peak the creation plus diffusion of vacancies at the dislocation line occurs.

Analysis of the AC electrical data in the Davidson–Cole dielectric representation

The representation of the AC electrical data in the complex plane reveal two major classifications of the relaxation processes known as ideal (Debye) and non-ideal (non-Debye) types. The non-Debye relaxation has been empirically observed via Cole–Cole (C–C), Davidson–Cole (D–C), and Havriliak–Negami (H–N) responses. Each of these non-Debye relaxations is visualized with an equivalent circuit similar to the ideal relaxation. Both ideal and C–C relaxations reveal semicircular behavior in the complex plane while D–C and H–N relaxations deviate from the usual semicircular loci known as skewed behavior. The extracted equivalent circuit elements are essentially non-Debye for both D–C and H–N relaxations possessing complexity in the relaxation time. The analytical method of extracting these elements in conjunction with the empirical parameters of the D–C relaxation is described using conventional (real) domain and complex domain. The curve fitting procedure provided extremely small error for the complex domain analysis. The behavior of the D–C relaxation function and the depression parameter β are also discussed using ωτ=1 and ωτ≠1 corresponding to the maximum of the imaginary part of the impedance ( Z * ) or permittivity ( ε *).