Havriliak-Negami Model Research Articles

Dielectric analysis of unpolymerized and photopolymerized NOA65 in a parallel-plate cell

The flourishing development of liquid crystal research in recent decades has highlighted the importance of polymer materials in enhancing liquid–crystal material and device properties, demonstrating tremendous potential in a wide range of industries. One of the polymer materials widely used in polymer-dispersed liquid crystal is Norland UV-curable optical adhesive (NOA65). This study focuses on the dielectric behavior of the optical adhesive in a parallel-plate cell. Given the broadness and asymmetry of the dielectric dispersion curve, the two-relaxation Havriliak–Negami model was employed to analyze the complex dielectric spectra of NOA65 before and after photocuring. Experimental results indicate that as temperature rises, the dielectric relaxation of NOA65 undergoes a blue shift, leading to an eventual overlap with pseudo-dielectric relaxation at a higher frequency. This brings about an increase in the obtained signal in the dielectric loss spectrum, implying that the observed feature of pseudo-dielectric relaxation is actually superposed or contributed by the intrinsic relaxation signal. Furthermore, as temperature continues to rise, the intrinsic dielectric loss signal of NOA65 becomes untraceable beyond the frequency span within which the pseudo-dielectric relaxation signal lies.

AC conductivity, dielectric and thermal properties of hybrid composite: bagasse cellulose carbon nanofibers composite

AbstractThis study investigates the impact of incorporating carbon nanofibers (CNFs) into sugar cane cellulose at a high weight ratio (6 wt.%). Composite samples were prepared using a hot hydraulic press technique, and their thermal stability was analyzed through thermal gravitational analysis in a nitrogen environment. The results indicate that the cellulose-CNF composite exhibits a simplified single-stage decomposition compared to the more complex behavior observed in pure cellulose. FTIR analysis reveals the presence of –OH bonds, indicating enhanced hydrophilic properties in the composite. Dielectric spectroscopy, conducted over a frequency range of 100 Hz to 1 MHz, explores the effects of CNFs on the relaxation and conduction mechanisms at different temperatures. Parameters such as dielectric permittivity, AC conductivity, electrical modulus, and complex impedance were studied, incorporating Jonscher’s equation, and the Havriliak–Negami model. The interplay between interfacial charge and cellulose crystallinity emerged as a crucial factor in the observed dielectric behavior. Overall, this research provides insights into the thermal and dielectric properties of cellulose/CNF composites, offering potential applications in diverse fields.

Study on the Application of Kramers-Kronig Relation for Polyurethane Mixture.

Polyurethane (PU) mixture, which is a new pavement mixture, exhibits different dynamic properties compared to a hot-mixed asphalt mixture (HMA). This paper analyzed whether the Kramers-Kronig (K-K) relation and thermorheologically simple properties applied to the PU mixture. Based on the results, the PU mixture exhibited thermorheologically simple properties within the test conditions. The time-temperature superposition principle (TTSP) was applicable for the PU mixture to construct a dynamic modulus master curve using the standard logistic sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak-Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The core-core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K-K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results with the test temperatures and loading frequencies. The phase angle of the PU mixture at extremely high or low test temperatures cannot be derived from the dynamic modulus data.

Modelling dielectric behaviour and anomalous relaxation in chromonic liquid crystals

ABSTRACT We discuss the feasibility of applying a frequency-dependent diffusive model to study the dielectric response of complex fluids. The model considers the effect of free and bound particles by solving a non-exponential relaxation behaviour and anomalous diffusion phenomena into a coupled system of differential equations and boundary conditions. To illustrate the potentialities of the model in the data interpretation, we used the experimental results that provide the frequency spectra of a system formed by an aqueous solution of sunset yellow, a chromonic liquid crystal. Our model yields a considerably better adjustment of the experimental data compared to the simple Havriliak-Negami model and provides the relaxation frequency due to the director mode associated with the stack fluctuations about their short axis. Furthermore, we obtained parameters associated with the ion motion nature of the sample, including diffusion coefficient, Debye length and the ionic diffusive regime, which present a similar subdiffusive behaviour found in nematic thermotropic liquid crystals.

Preparation and Characterization of Functionalized Multi-Walled Carbon Nanotubes (f-MWCNTs) Incorporated in Gelatin-Based Hydrogel Nanocomposites

This study prepared gelatin/functionalized multi-walled carbon nanotube (f-MWCNT) nanocomposites with different f-MWCNT concentrations using a simple solution casting method. For each f-MWCNT concentration of the gelatin/f-MWCNT nanocomposites, permittivity parameters were measured at five different locations on the sample surface. Cole–Cole graphs were obtained by plotting the imaginary permittivity as a function of the real permittivity. The Havriliak–Negami model was used to obtain the value of alpha, since the shape is a quasi-skewed semicircle. The average relaxation time was τ = 12.6 ps and was roughly constant with the addition of f-MWCNTs. Fourier-transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM) images showed increased interactions between the carbon nanotubes and polymers.

Dielectric Terahertz Characterization of Microwave Substrates and Dry Resist

Microwave fabrication and design techniques are commonly employed in the terahertz (THz) domain. However, a characterization of commercially available microwave dielectric materials is usually lacking at sub-THz and THz frequencies. In this work, we characterized four substrates by Rogers and an Ordyl dry resist between 0.2 and 2 THz, in terms of relative permittivity and loss tangent. The reflectance spectra of the investigated materials were retrieved by means of THz time-domain spectroscopy in reflection mode and post-processed according to a transmission-line model in which the materials’ parameters are fit by means of the Havriliak–Negami variation of the Debye model. The relative permittivity of the investigated materials showed negligible frequency dispersion in the sub-THz and in the THz range. In terms of the loss tangent, the Rogers substrates revealed a more pronounced frequency-dispersive behavior among different materials, as dictated by the Havriliak–Negami model. The Ordyl resist was dispersive in the 0.2–1.2 THz range and presented a nearly constant loss tangent value between 1.2 and 2 THz. These results may represent a reference for the development of innovative components for THz and sub-THz emerging applications.

The Effectiveness of the Havriliak-Negami Model in Predicting the Master Curves of the Asphalt Blends with SBS Triblock Copolymer and Organic-Montmorillonite at Different Temperatures and Frequencies

The Effectiveness of the Havriliak-Negami Model in Predicting the Master Curves of the Asphalt Blends with SBS Triblock Copolymer and Organic-Montmorillonite at Different Temperatures and Frequencies

CuO:V2O5 driven alterations in dielectric, ferroelectric and structural properties of Barium Zirconate Titanate ceramics

This study focuses on the properties of Vanadium and Copper co-doped Barium Zirconate Titanate (BZT) for potential technological applications. Various doping ratios of CuO:V2O5 were used to synthesize the materials, and X-ray diffraction (XRD) confirmed a tetragonal phase in all samples. The grain density and dimensions decreased with higher concentrations of V2O5 and CuO. FTIR spectra confirmed the compositional structure and bonding of the samples. The impedance analysis indicated that higher doping concentrations facilitated charge conduction at grain boundaries. Dielectric relaxation was studied using the Havriliak–Negami model and electrical modulus behavior was analyzed. Activation energy values from Arrhenius fitting matched those from impedance data, suggesting the same type of charge carriers. The study revealed that elevated levels of V concentration induced charge carriers to exhibit hopping behavior, thereby enhancing conductivity. Conversely, higher Cu concentration impeded hopping, leading to a swift rise in activation energy.

Electrospun Microstructured Biopolymer Fibers Containing the Self-Assembled Boc–Phe–Ile Dipeptide: Dielectric and Energy Harvesting Properties

Hybrid biomaterials were engineered using the electrospinning technique, incorporating the dipeptide Boc–L-phenylalanyl–L-isoleucine into microfibers composed of biocompatible polymers. The examination by scanning electron microscopy affirmed the morphology of the microfibers, exhibiting diameters ranging between 0.9 and 1.8 µm. The dipeptide self-assembles into spheres with a hydrodynamic size between 0.18 and 1.26 µm. The dielectric properties of these microfibers were characterized through impedance spectroscopy where variations in both temperature and frequency were systematically studied. The investigation revealed a noteworthy rise in the dielectric constant and AC electric conductivity with increasing temperature, attributable to augmented charge mobility within the material. The successful integration of the dipeptide was substantiated through the observation of Maxwell–Wagner interfacial polarization, affirming the uniform dispersion within the microfibers. In-depth insights into electric permittivity and activation energies were garnered using the Havriliak–Negami model and the AC conductivity behavior. Very importantly, these engineered fibers exhibited pronounced pyroelectric and piezoelectric responses, with Boc–Phe–Ile@PLLA microfibers standing out with the highest piezoelectric coefficient, calculated to be 56 pC/N. These discoveries help us understand how dipeptide nanostructures embedded into electrospun nano/microfibers can greatly affect their pyroelectric and piezoelectric properties. They also point out that polymer fibers could be used as highly efficient piezoelectric energy harvesters, with promising applications in portable and wearable devices.

Dielectric and energy harvesting properties of functionalized composite nanofibers consisting of Boc-Phe-Leu self-assembled dipeptide inclusions in biocompatible polymeric matrices

Hybrid bionanomaterials were produced through electrospinning, incorporating the dipeptide Boc-l-phenylalanyl-l-leucine into nanofibers of biocompatible polymers. Scanning electron microscopy confirmed the uniformity of the nanofibers, with diameters ranging from 0.56 to 1.61 µm. The dielectric properties of the nanofibers were characterized using impedance spectroscopy, assessing temperature and frequency dependencies. Notably, the composite micro/nanofibers exhibited semiconducting dielectric behavior with bandgap energies of 4–5 eV, and their analysis revealed increased dielectric constant with temperature due to enhanced charge mobility. The successful incorporation of the dipeptide was verified by Maxwell–Wagner interfacial polarization, and the Havriliak–Negami model disclosed insights into electric permittivity. Furthermore, the fibers demonstrated pyroelectric and piezoelectric responses, with Boc-Phe-Leu@PLLA nanofibers having the highest piezoelectric coefficient of 85 pC/N. These findings highlight the influence of dipeptide nanostructures on dielectric, pyroelectric, and piezoelectric properties, suggesting the potential of polymeric micro/nanofibers as efficient piezoelectric energy generators for portable and wearable devices.Graphical

Mechanical treatment of aluminum plate surfaces for improvements of capacitance and dielectric permittivity

The surface mechanical alloying (SMA) technique achieved high capacitances, improved capacitance (C) and dielectric permittivity (ε′) of mixed Aluminum/fiber-glass ‘Al/F-glass’ formed on aluminum plates. The radiofrequency RF range 0.1–106 Hz was applied on the Al/F-glass on Al plates, acting as parallel electrodes sandwiching the mixed ceramic Al/F-glass as dielectric. Capacitance increase observed after surface alloying on treated Al with small 1.5 balls than 6 mm balls on Al-plate & 1 A l-plate 2 respectively, giving twice the permittivity constant of the annealed Al. Deformation micro-scale cavities in Al surfaces played important role in raising capacitance and permittivity values; Interpreted as condensers inside a condenser caused capacitance increase according Maxwell-Wagner-Sillars effect. Dielectric relaxation model Havriliak-Negami Model was used to examine the occurrence of the Maxwell-Wagner-Sillars effect in alloyed Al/F-glass surfaces on Al plates, which confirms micro-cavities important role due to pre-treatment of Al surfaces.

A Wideband Non-Contact Voltage Sensing

A non-contact voltage sensing is one of the non-intrusive and galvanic methods for observing signal waveform. Frequency degradation due to the dielectric relaxation of PVC is a technical issue for the wideband (100 Hz ∼ 100 MHz) sensing. In this paper, reconstruction of the frequency response using Havriliak-Negami (HM) model is discussed.

Parameter Determination of the 2S2P1D Model and Havriliak-Negami Model Based on the Genetic Algorithm and Levenberg-Marquardt Optimization Algorithm.

This study utilizes the genetic algorithm (GA) and Levenberg-Marquardt (L-M) algorithm to optimize the parameter acquisition process for two commonly used viscoelastic models: 2S2P1D and Havriliak-Negami (H-N). The effects of the various combinations of the optimization algorithms on the accuracy of the parameter acquisition in these two constitutive equations are investigated. Furthermore, the applicability of the GA among different viscoelastic constitutive models is analyzed and summarized. The results indicate that the GA can ensure a correlation coefficient of 0.99 between the fitting result and the experimental data of the 2S2P1D model parameters, and it is further proved that the fitting accuracy can be achieved through the secondary optimization via the L-M algorithm. Since the H-N model involves fractional power functions, high-precision fitting by directly fitting the parameters to experimental data is challenging. This study proposes an improved semi-analytical method that first fits the Cole-Cole curve of the H-N model, followed by optimizing the parameters of the H-N model using the GA. The correlation coefficient of the fitting result can be improved to over 0.98. This study also reveals a close relationship between the optimization of the H-N model and the discreteness and overlap of experimental data, which may be attributed to the inclusion of fractional power functions in the H-N model.

Influence of bedrock on viscoelastic responses and parametric back-calculation results for asphalt pavements and prediction of bedrock depth under FWD tests

Structural evaluation with a falling weight deflectometer (FWD) plays an essential role in the maintenance and rehabilitation of highways. Research on the influence of bedrock on the results of FWD tests and dynamic back-calculations for asphalt pavements has been a hot topic. In this study, the viscoelastic characteristics of the asphalt surface layer were described by the modified Havriliak-Negami (MHN) model rather than the layered elastic theory computing framework. The effects of bedrock on the deflection time history curves of viscoelastic asphalt pavement under the FWD test were investigated and analyzed by the spectral element method with fixed-end boundary conditions (B-SEM). The effects of bedrock on parametric back-calculation results for the viscoelastic asphalt surface layer and other elastic layers were explored by dynamic back-calculations. To exclude the impact of bedrock and improve the back-calculation accuracy, support vector regression optimized by the gravitational search algorithm (GSA-SVR) was adopted to predict bedrock depth. The viscoelastic responses and dynamic parametric back-calculation results were significantly influenced by bedrock beneath asphalt pavements, and the influence decreased (but was not eliminated) with increasing depth of bedrock. The GSA-SVR model provided excellent predictions of bedrock depth, and it can be applied for pavement performance assessment in road projects.

Dielectric constant, dielectric loss, conductivity, capacitance and model analysis of electronic electroactive polymers

In this study, the dielectric constant, dielectric loss, conductivity and capacitance of the electronic electroactive polymer (EEAP) were systematically tested experimentally, and the effects of different frequencies, effective voltages, electrode types, and specimen thicknesses on the dielectric relaxation properties of polymers were analyzed, and finally the Debye, Cole-Cole and Havriliak-Negami functions were used to model the dielectric constants. The experimental results show that the dielectric constant of the polymer depends strongly on the frequency, especially in the low frequency stage from 10−1 to 100 Hz. The effect of different effective voltages on the dielectric properties is basically identical, and the accuracy of the test can be improved at this AC voltage avoiding the effect of electrostatic stress. At the same effective voltage and thickness, the polymer with G-C electrodes shows the best electrical parameters, the composite electrode form of G-C electrodes contributes to the conductive properties of the polymer and can be applied to the later design of actuators. Compared with the Debye model, the errors of the experimental and calculated values of the Cole-Cole and Havriliak-Negami models are smaller, 1.1102 and 0.7130, respectively. The dielectric behavior of EEAPs differs from that of epoxy materials, probably due to the influence of electric dipole moments, bound charges, and dipole effects. The paper has some reference value for further revealing the dielectric properties and relaxation time distribution of the polymer, and provides guidance for the later application of EEAP materials in flexible robots.

Extended RC Impedance and Relaxation Models for Dissipative Electrochemical Capacitors

Electrochemical capacitors are a class of energy devices in which complex mechanisms of accumulation and dissipation of electric energy take place when connected to a charging or discharging power system. Reliably modeling their frequency-domain and time-domain behaviors is crucial for their proper design and integration in engineering applications, knowing that electrochemical capacitors in general exhibit anomalous tendency that cannot be adequately captured with traditional integer-order-based models. In this study we first review some of the widely used fractional-oder models for the description of impedance and relaxation functions of dissipative resistive-capacitive system, namely the Cole-Cole, Davidson-Cole, and Havriliak-Negami models. We then propose and derive new q-deformed models based on modified evolution equations for the charge or voltage when the device is discharged into a parallel resistive load. We verify our results on anomalous spectral impedance response and time-domain relaxation data for voltage and charge obtained from a commercial supercapacitor.

HR MAS NMR, dielectric impedance and XRD characterization of polyethylene oxide films for structural phase transitions

The amorphous/crystalline phase transition behavior of PEO films prepared by spin casting method was studied. According to X-ray diffraction (DELTA) analysis, PEO film has a semicrystalline nature at room temperature. The amorphous to crystalline nature of PEO increases with temperature until reaching an amorphous state at 333 K. 1H NMR spectra of PEO in the temperatures between 298 K and 323 K exhibit two main peaks at around 1.132 ppm and 3.174 ppm with very different widths, where the narrow component can be assigned to the mobile polymer chains in the amorphous phase, whereas the broad component is assigned to the more rigid molecules in the crystalline phase. The calculated activation energies from the Arrhenius fit of the Γ1 data of the crystalline and amorphous phases are comparable and found to be 0.252 eV and 0.221 eV, respectively. Form fitting dielectric loss (ε″) and the electrical modulus (M″) data with the Havriliak-Negami model with addition of the electrical conductivity term in the case of ε″, it was deduced that the inverse relaxation time (τ−1), dielectric strength (Δε) and electrical conductivity (σ) follow an Arrhenius-like behavior plot versus reciprocal temperature.

Dielectric properties of microcrystalline cellulose/multi-wall carbon nanotubes multi-scale reinforced EVA/VeoVa terpolymer

Dielectric analyses were investigated on vinyl resin emulsion based on ethylene vinyl acetate/vinyl ester of versatic acid terpolymer (EVA/VeoVa) and its composites reinforced with microcrystalline cellulose and multi-wall carbon nanotubes. Dielectric spectra were measured in the frequency range from 10-1 Hz to 107 Hz and the temperature interval from -35°C to 130°C. Three dielectric relaxations were identified for the matrix. The first one, appearing at lower temperatures and higher frequencies, was associated with secondary β relaxation. The second one appearing above the glass transition temperature was attributed to the α relaxation due to the main glass transition of the terpolymer. The third dielectric relaxation appearing at higher temperatures and lower frequencies was attributed to α’ relaxation originating from the motion of more repeat units compared to the α one. The addition of the reinforcements into the matrix gave rise to three additional dielectric phenomena originating either from microcrystalline cellulose or matrix/reinforcement interfaces. Analyses of secondary dielectric relaxations at low temperatures by using the Havriliak-Negami model and those at high temperatures according to an adequate equivalent circuit model allowed probing reinforcement/matrix interactions. This dielectric study was complemented by the thermal, structural and morphological analyses based on differential scanning calorimeter (DSC), X-ray diffraction (XRD) and scanning electron microscope (SEM), respectively

Dynamic conductivity of multilayer graphene during pulsed mechanical activation of a composite (polypropylene - graphene nanoplatelets)

Polymer composite films of polypropylene and graphene nanoplatelets were subjected to mechanical activation . Electrical current pulses are observed during this process. Fourier transforms of the signals are fitted to Havriliak-Negami model and the Kubo model for multilayer graphene. The calculated frequency dependences of conductivity are in good agreement with the experimental results. Relaxation processes and changes in the local geometry of graphene sheets under the influence of elastic waves are responsible for the effects. • Thin films of polypropylene and graphene nanoplatelets are subjected to mechanical activation. • Electrical current pulses are observed. • Fourier transforms of the signals are described by the Kubo model for multilayer graphene.

Dielectric Dispersion Response of Binary Mixtures of n-Butanol and Valeronitrile

Complex permittivity spectra of various concentrations (0.0 → 1.0) of n-Butanol and its mixtures with Valeronitrile were obtained in the radio and microwave frequency range (0.2 GHz to 20 GHz) using Vector network analyzer (VNA). Complex permittivity data points were fitted into Havriliak-Negami Model. CNLS fitting using LEVMW software used to obtain dielectric parameters. Excess static dielectric constant and excess inverse relaxation time for the binary mixtures were calculated and fitted in Redlich-Kister polynomial to derive the binary coefficients and standard deviations. Variation of these parameters were discussed in terms molecular interaction between molecular species.