Havriliak Negami Research Articles

Processing, Dynamic mechanical thermal analysis, and dielectric properties of barium titanate/cellulosic polymer nanocomposites

High dielectric constant BaTiO3/ethyl cellulose (BT/EC) nanocomposites having BT loadings of up to 13 vol% were fabricated through a simple casting technique. The BT filler powder, synthesized through an ultrasonic‐assisted solid‐state route, was revealed by X‐ray powder diffractometry (XRD) and Raman spectroscopy to be dominantly tetragonal. Scanning electron microscopy (SEM) showed good dispersion of the BT nanoparticles in the EC polymer matrix at lower BT concentrations. However, at higher concentrations, the BT particles form a continuous phase or a “filler network” leading to weak BT/EC interactions. This finding is well supported by the results of the tensile strength and storage modulus. The dielectric properties of the BT/EC nanocomposites were investigated over wide ranges of frequency and temperature. The addition of BT significantly increased the permittivity (ε′) and dielectric loss (ε″) and improved the ionic conductivity of the EC. The electric modulus (M″) results were analyzed in terms of the Havriliak–Negami function through three distinct relaxation mechanisms (namely α, β*, and β relaxations) in the temperature range 30–150°C. The dc conductivity (σdc) results suggest that the BT/EC nanocomposites formed at low BT loading (up to 7.0 vol%) and a temperature of ≤60°C are good candidates for antistatic applications while those formed at higher concentrations and temperatures are recommended for use in electrostatic dissipation applications. POLYM. COMPOS., 38:893–907, 2017. © 2015 Society of Plastics Engineers

Determination of dynamic mechanical properties of carbon black filled rubbers at wide frequency range using Havriliak–Negami model

Abstract An accurate dynamic mechanical model plays a vital role in the engineering application of rubber-like materials. Though many researchers have done work on these models, it is still difficult to fit the model's parameters via dynamic mechanical thermal analysis (DMTA) data, especially for Havriliak–Negami (HN) model. A methodology is proposed to determine the parameters in HN model. The DMTA data of carbon black filled rubber (CBFR) NR100N550 is utilized to verify the methodology in this paper. The time–temperature superposition principle (TTSP) is applied to investigating the viscoelastic properties of CBFR NR100N550 at wide frequency range. The experimental results show that the proposed methodology could be applied to obtaining parameters in HN model. HN model is able to model the dynamic mechanical properties of carbon black filled rubbers at wide frequency range, which are correlated with the chemical structure of the polymers.

A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

This paper presents a unified procedure that can rapidly determine the discrete relaxation and retardation spectra of asphalt concrete. The new procedure involves three consecutive steps: (1) pre-smoothing the complex modulus data with the Havriliak–Negami (HN) model, (2) identifying the discrete relaxation spectrum from the smoothed data with a modified windowing method (MWM) and (3) converting the obtained spectrum into the corresponding discrete retardation spectrum. The HN model adopted furnishes reasonable analytical representations for all the complex modulus components and allows an asymmetrical inflection point for the dynamic modulus and storage modulus master curves on the log–log scale, effectively overcoming the drawbacks of the conventional sigmoidal function in characterizing the asphalt concrete linear viscoelastic (LVE) behavior. Also, the HN model can well predict the phase angle from the dynamic modulus data, substantially extending the application of the old data lacking the phase angle information in the LVE analysis. Additionally, the MWM offers a more appropriate estimation approach for the glassy modulus, successfully avoiding the undesirable spectrum oscillations and negative spectrum lines. A distribution of the time constants with 0.5 decade intervals was implemented in this procedure, completely excluding the waviness in the bell-shaped master curves of the generalized Maxwell (GM) and generalized Voigt (GV) models. Very few parameters are required for the initial inputs in the procedure and no empirical adjustments or selections are required for the GM or GV model constants during the whole computation process. The convergence of the iterations for determining the discrete spectra proved to be very fast.

Dielectric analysis of the interfacial polarization of alkali treated woven flax fibers reinforced epoxy composites

Dielectric measurements were performed on alkali treated flax fibers reinforced epoxy composites in the frequency range 0.1 Hz–1 MHz and the temperature range 40–170 °C. Two common dielectric relaxations were observed for all composites. The first one appearing at low temperatures was attributed to the water dipoles polarization due to the hydrophilic character of flax fibers. The second one observed at high temperatures was identified to the interfacial polarization. Analysis of this latter using the Havriliak–Negami model showed an improvement of the fibers/matrix adhesion by these alkali treatments. The best adhesion was obtained by the leaching treatment.

Impedance Spectroscopy of Nanofluids based on Multiwall Carbon Nanotubes

This work is a contribution to the understanding of the dielectric properties of nanofluids prepared by dispersing multiwalled carbon nanotubes in transformer oil. The dielectric measurements were carried out in the frequency range 100 Hz–1 MHz at constant temperature, T = 300 K, for several volume fractions of the nanotubes in the base fluid. A relaxation phenomenon was induced in the nanofluid comparing to the base fluid. In addition, both the real and imaginary part of the dielectric permittivity changed with volume fraction of the nanotubes. These results suggest that the presence of the nanotubes greatly affect the dielectric properties of the oil as a result of polarization phenomenon induced by these nanoparticles.It was found that the measured effective dielectric permittivity follows the empirical Havriliak–Negami model. Nevertheless to take into account the electrode polarization effects, we rewrote this model, with a new term, which fits accurately the experimental data.

Effect of plasticizers on ionic conductivity and dielectric relaxation of PEO-LiClO4 polymer electrolyte

In this paper, we report the effect of different plasticizers, such as poly ethylene glycol, propylene carbonate, ethylene carbonate and dimethyl carbonate on the ionic conductivity and dielectric relaxation of PEO-LiClO4 solid polymer electrolytes. The highest ionic conductivity is obtained for polymer electrolyte plasticized with poly ethylene glycol. The temperature dependence of ionic conductivity follows the well known Vogel–Tamman–Fulcher relation which indicates a strong coupling of ionic and segmental motions for all compositions. The experimental data for the complex dielectric permittivity and electric modulus have been studied using Havriliak–Negami function for the understanding of ion dynamics. Maximum dielectric strength is obtained for polymer electrolyte plasticized with poly ethylene glycol. The modulus data have been analyzed using non-exponential Kohlrausch–Williams–Watts (KWW) function. It is observed that the non-exponential parameter β is quite lower than unity, suggesting highly a non-exponential relaxation exists in these materials. The temperature dependence of relaxation times obtained from dielectric and modulus formalisms also follow Vogel–Tamman–Fulcher relation for all plasticizers in the compositions.

Thermal and dielectric properties of polycarbonatediol polyurethane

ABSTRACTThe dielectric relaxation behavior of segmented polyurethane has been studied using Broad‐Band Dielectric Spectroscopy in the frequency domain, 10−2 to 108 Hz, and in the temperature range of −120 to 140°C. The spectra show three secondary processes (δ, γ, and β) followed by the α relaxation and conductive processes. The Havriliak‐Negami (HN) phenomenological equation was used in order to characterize all the processes. The δ, γ, and β relaxations are probably associated with (i) local motions of the main chain (ii) motions of the carbonate group in the soft phase and (iii) reorientational motions of water molecules. The microphase separated morphology associated with soft and hard domains is reflected in the dielectric spectra, at high temperatures, by the presence of the Maxwell‐Wagner‐Sillars (MWS) interfacial polarization process. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 42007.

Mechanical properties of bulk polydimethylsiloxane for microfluidics over a large range of frequencies and aging times

The dynamic mechanical characterization of polydimethylsiloxane (PDMS) over a large range of frequencies (10−2 < f < 105 Hz) and long aging times at room temperature (4 h < tv < ~60 000 h) has been presented. Three samples with different curing conditions have been studied and three different techniques, dynamic mechanical analysis at different temperatures, nano-indentation and scanning micro-deformation microscopy, have been used. Although the three techniques work at different scales and at different frequencies all the results match the same master curve. As expected, the storage and the loss moduli greatly increase with the frequency. Moreover, these moduli moderately increase with the aging time tv depending on the curing temperature. A simple model which takes the frequency and the aging time into account, and which is based on the Havriliak–Negami model, has been presented and identified. Hence, values of the relaxed and instantaneous moduli at tv = 0 and tv = ∞ are proposed. Only the relaxed moduli depend on the curing conditions and moreover it has been shown that the tangent of the phase lag is independent of the aging time and thus of the curing process.

Ionic conductivity and dielectric permittivity of PEO-LiClO4 solid polymer electrolyte plasticized with propylene carbonate

We have studied ionic conductivity and dielectric permittivity of PEO-LiClO4 solid polymer electrolyte plasticized with propylene carbonate. Differential scanning calorimetry and X-ray diffraction studies confirm minimum volume fraction of crystalline phase for the polymer electrolyte with 40 wt. % propylene carbonate. The ionic conductivity exhibits a maximum for the same composition. The temperature dependence of the ionic conductivity has been well interpreted using Vogel-Tamman-Fulcher equation. Ion-ion interactions in the polymer electrolytes have been studied using Raman spectra and the concentrations of free ions, ion-pairs and ion-aggregates have been determined. The ionic conductivity increases due to the increase of free ions with the increase of propylene carbonate content. But for higher content of propylene carbonate, the ionic conductivity decreases due to the increase of concentrations of ion-pairs and ion-aggregates. To get further insights into the ion dynamics, the experimental data for the complex dielectric permittivity have been studied using Havriliak–Negami function. The variation of relaxation time with temperature obtained from this formalism follows Vogel-Tamman-Fulcher equation similar to the ionic conductivity.

Effect of the carbohydrate composition of bleached kraft pulp on the dielectric and electrical properties of paper

The effects of hemicellulose removal from bleached birch kraft pulp by alkaline extraction with sodium hydroxide on the dielectric, electrical and electrostatic properties of paper material have been examined. The hemicellulose content, particularly the xylan content, of birch kraft pulp has an effect on the dielectric constant and on the dielectric loss factor. The real part of the dielectric constant increases with decreasing content of hemicellulose in papers containing the extracted birch kraft pulp. Hemicellulose removal by alkaline extraction increases the direct and alternating current electrical conductivity and changes the electrostatic properties of the paper. Dielectric relaxation spectra at different temperatures analysed using the Havriliak–Negami relaxation model revealed that the dielectric properties are determined by at least two relaxation processes which are affected by the hemicellulose content. The first relaxation process originates in the polarizable groups of cellulose and hemicellulose and the second is attributed to the water–polymer structures formed during the interaction of cellulose and hemicelluloses with moisture. Both relaxation processes are compared quantitatively.

Matrix fractional systems

This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole–Cole, Davidson–Cole, and Havriliak–Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.

Anomalous diffusion approach to non-exponential relaxation in complex physical systems

We derive the relaxation function from the simple model of two-state systems under memory effects caused by the subordination. The non-exponential relaxation is shown to result from subordination by inverse infinity divisible random processes. The wide class of such random processes includes ordinary α-stable, tempered α-stable, exponential, gamma processes and many others as particular cases. This approach generalizes the Cole–Cole, Cole–Davidson and Havriliak–Negami laws well known in experimental physics of relaxation. The presented considerations discover a direct (one-to-one) relationship between the method of random relaxation rates and the anomalous diffusion approach based on subordination of random processes that are applied for the theory of relaxation phenomena. Moreover, it is found that the space and time clusterizations are responsible on equal foots for power-law memory effects in relaxation of complex physical systems.

Characterization of poly(ethylene 2,6-naphthalate)/polycarbonate blends by DSC, NMR off-resonance and DMTA methods

The poly(ethylene 2,6-naphthalate) (PEN)/polycarbonate (PC) blends with the weight ratio of homopolymers 50/50 wt./wt. were prepared by injection molding using the Engel machine ES. One mixture was synthesized without the compatibilizer and the second with the compatibilizer SMAC (Samarium acetylacetonate hydrate). The influence of the compatibilizer on the physical and mechanical properties of the PEN/PC blends was investigated. The thermal properties of the new synthesized blends were studied by the differential scanning calorimetry (DSC). The molecular dynamics of the polymer blends was studied by the off-resonance NMR. The correlation times of the internal motions and the spectral density function amplitudes were estimated on the basis of the dispersion of the spin–lattice relaxation time T1ρoff in the rotating frame off-resonance. The rheological properties of the studied blends were investigated by dynamic mechanical thermal analysis (DMTA). The temperature dependencies of the storage modulus G′, of the loss modulus G″ and of the loss tangent (tanδ) were analyzed in order to evaluate the relaxation processes in the studied systems. The analysis of the DMTA data revealed the existence of two primary (α1 and α2) and two secondary (β and γ) relaxation processes in the blend of PEN/PC 50/50 wt./wt. and one primary (α) and two secondary (β and γ) relaxation processes in the blend of PEN/PC 50/50 wt./wt. with the compatibilizer. The motional parameters for the above – mentioned relaxation processes were calculated using the Havriliak–Negami formalism. The comparative analysis of the DSC, NMR off-resonance and DMTA results led to the clarification of the molecular motion in the PEN/PC 50/50 wt./wt. blends.

Microstructure evolution, dielectric relaxation and scaling behavior of Dy-for-Fe substituted Ni-nanoferrites

Dy-substituted nickel nanoferrites have been investigated in order to explore the possibility of Dy-for-Fe substitution in nickel ferrites, as well as the effect of the substitution on the microstructural and electrical properties. The samples were prepared by a simple citrate nitrate auto-ignition method. Rietveld analysis of the X-ray diffraction profiles confirmed the Dy-for-Fe substitution in this spinel ferrite. A slight increase in lattice parameter and microstrain due to incorporation of Dy is observed. The transmission electron microscopy also confirmed the high crystallinity of the prepared samples. It has been found that the doped samples show ionic conductivity 1 to 2 orders greater than that of the undoped sample at a particular temperature. In addition, the doped sample shows lower dielectric loss than the undoped sample. The frequency dependence of the dielectric permittivity has been analyzed using the Havriliak–Negami formalism. The time-temperature superposition principle has been established by the scaling of different spectra.

Dynamics of poly(methyl methacrylate)–montmorillonite nanocomposites: A dielectric study

The effect of varying amounts of montmorillonite (MMT) filler (in weight ratios of 100/0, 100/5, and 100/10) on the molecular dynamics and polarization of atactic poly(methyl methacrylate) (PMMA) is investigated using broad-band dielectric spectroscopy from 10−2 to 106Hz and at temperatures from 30 to 140°C. The experimental data were analyzed with the sum of Havriliak–Negami (HN) functions and a power-law conduction term. The characteristic frequency, activation energies, and dielectric strength of PMMA/MMT nanocomposites were analyzed. As MMT content increases, a Maxwell–Wagner–Sillars (MWS) relaxation emerges in the nanocomposites and the α-relaxation contributed by main-chain movements above Tg occurs at lower temperatures as silicate layers in MMT segregate PMMA chains into smaller domains. The characteristic frequency of β-relaxations is influenced by the mergence with the α-relaxation above Tg. Further, the strength of the β-relaxation is stable as a function of temperature in both pure PMMA and the PMMA/MMT nanocomposites whereas, in the nanocomposites, the strengths of the α- and MWS relaxations increase significantly with temperature up to approximately 120°C.

Dielectric relaxation of gamma irradiated muscovite mica

In the present research, the dielectric relaxation of gamma irradiated muscovite mica was studied in the frequency range of 0.1Hz–10MHz and temperature range of 653–853K, using the dielectric permittivity, electric modulus and conductivity formalisms. The dielectric constants (ϵ′ and ϵ′′) are found to be high for gamma irradiated muscovite mica as compared to the pristine sample. The frequency dependence of the imaginary part of complex electric modulus (M′′) and dc conductivity data conforms Arrhenius law with single value of activation energy for pristine sample and two values of activation energy for gamma irradiated mica sample. The experimentally assessed electric modulus and conductivity information have been interpreted by the Havriliak–Negami dielectric relaxation explanation. Using the Cole–Cole framework, an analysis of real and imaginary characters of the electric modulus for pristine and gamma irradiated sample was executed which reflects the non-Debye relaxation mechanism.

Pyroelectricity enhancement of PVDF nanocomposite thin films doped with ZnO nanoparticles

A thin film of pyroelectric composite with 0–3 connectivity was fabricated from zinc oxide (ZnO) nanopowder and polyvinylidene fluoride (PVDF) with different volume fraction from 0–0.25 wt%. The dielectric and pyroelectric properties of the samples were investigated. It was found that the presence of a small amount of ZnO nanoparticles (0.25 wt%) has significantly increased the pyroelectric coefficient of the PVDF by 25%. Furthermore, the nanocomposite films required lower poling field to form polar-δ phase compared to pure PVDF thin films. Analysis of the complex permittivity in a wide range of frequency was carried out indicating that the dielectric constant and loss of PVDF/ZnO nanocomposite thin films increase when doped with ZnO. Havriliak-Negami (HN) empirical function has been employed to obtain the α-relaxation time of the nanocomposite thin films before and after poling. The α-relaxation time does not vary with the increase of ZnO wt%; however, the effect of poling has lengthened the relaxation time of the thin films. FTIR and XRD results supports the fact that the addition of ZnO nanoparticles into PVDF polymer thin films do not cause any significant effect on the structure of the PVDF thin films. In fact, ZnO nanoparticle has enhanced the overall pyroelectricity of PVDF by facilitating the poling process in the composites and led to phase transformation of PVDF from α- to δ-phase as supported by a marked reduction of (100) x-ray diffraction intensities.

A molecular interpretation of Maxwell–Wagner–Sillars processes

Broadband Dielectric Relaxation Spectroscopy was used to molecularly interpret Maxwell–Wagner–Sillars (MWS) relaxation processes, termed a ζ process, in a heterogeneous laminate configuration with different insulators. The ζ process is due to associated non-covalently bound dipoles that assist in charge migration where the role of the insulator is to allow subsequent discharge away from the material of interest in order for relaxation to occur. The temperature dependent dynamics were characterized in terms of the relaxation time, effective dipole moment and relative molecular associations which were extrapolated from fits of the Havriliak–Negami (HN) equation. The dynamics of the anomalous relaxation process showed a dependence on the properties of the insulator. The ζ process was activated at non phonon timescales. The effective dipole moment of the ζ process phenomenologically had an exponential dependence on temperature and a frictional resistance parameter was introduced. The relative molecular associations through inter and intra cluster interactions depended on characteristics of the insulator and material.

A systematic study on electrical properties of the BaTiO3–epoxy composite with different sized BaTiO3 as fillers

The epoxy composites consisting of BaTiO3 fillers with size of 100nm and 200nm were prepared, respectively. The thermo-mechanical and electrical properties of BaTiO3–epoxy composites were investigated using complex permittivity, electric modulus and ac electrical conductivity. The effects of filler size on the structure, filler–matrix interface and properties were discussed. The Havriliak–Negami model was used to analyze the dielectric relaxation of composites. The results show that larger filler tends to exhibit enhanced dynamic modulus and higher Tg because of the increase of effective volume fraction. The tetragonal phase formation in the BaTiO3 is important to achieve enhanced permittivity of the composite. The relaxation responses of composites revealed by electric modulus and complex permittivity show that the Maxwell–Wagner–Sillars (MWS) polarization and tetragonal phase transition of BaTiO3 affect the dielectric responses of composites. The conduction process is not only related with the barrier hopping but also tunneling effect of electrons. Based on the electrical properties of BaTiO3–epoxy composite with 100nm BaTiO3 at GHz, a compact band-pass filter with significant area reduction was designed and fabricated. The measured results show that the BaTiO3–epoxy composite is promising for advanced wireless device applications.

Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media

In this paper, an accurate finite-difference time-domain (FDTD) scheme for modeling time-domain wave propagation in arbitrary dispersive biological media is proposed. The main drawback occurring in the conventional FDTD implementation for such materials is the approximation of the fractional derivatives appearing in the relevent time-domain permittivity model. To overcome this problem, we propose a novel FDTD scheme based on the direct solution of the time-domain Maxwell equations by using the Riemann-Liouville operator for fractional differentiation. The feasibility of the proposed method is demonstrated by simulating the transient wave propagation in general bulk and slab dispersive materials with dielectric spectrum described by Cole-Cole, Cole-Davidson, and Havriliak-Negami formulas. In particular, the comparison between the numerical results and those evaluated by using an analytical method based on the Fourier transformation and the matrix formulation for lossy layered media demonstrates the accuracy of the proposed FDTD scheme in a broadband frequency range.