Cole-Davidson Model Research Articles

Dielectric relaxation study of pyridine-n-propyl alcohol mixture using time domain reflectometry technique

ABSTRACT The Time Domain Reflectometry (TDR) technique was used to analyse the complex permittivity spectra of the Pyridine-n-propyl alcohol mixture across the concentration and temperature range of 10–25°C. The Cole-Davidson model was used to match the Pyridine- n-propyl alcohol complex permittivity spectra. The nonlinear least squares fit approach has been used to obtain the Static dielectric constant (ε0), Relaxation time (τ), Effective Kirkwood correlation factor (geff) Excess permittivity ε 0 E , Thermodynamic parameters (activation enthalpy and activation entropy), and Bruggeman factor (fB). Furthermore, the analysis of excess characteristics and the Bruggeman factor points towards the presence of hydrogen bonding between the pyridine and n-propyl alcohol molecules.

Molecular interaction between thiamine hydrochloride-DMSO binary mixture: a TDR spectroscopic approach

ABSTRACT The dielectric measurements of thiamine hydrochloride (vitamin B1 hydrochloride) and dimethyl sulphoxide (DMSO) binary mixtures have been carried out in the frequency range of 10 MHz to 50 GHz at 25°C, 20°C and 15°C using the TDR technique. The dielectric parameters such as complex dielectric permittivity ɛ*(ω), static dielectric permittivity (ɛs), relaxation time (τ), and asymmetric distribution parameter (β) are obtained by using Cole-Davidson model. These parameters are used to compute thermodynamic properties, Kirkwood correlation factor (geff), and excess molar volume (VE). The heteromolecular H-bonding existing in the binary mixture is explained.

H-bonding interaction study for binary mixtures of methyl cellosolve and ethanol: a dielectric, FTIR spectroscopic and volumetric approach

The dielectric measurement of neat ethylene glycol monomethyl ether (EGMME), neat ethanol and their binary mixtures have been carried out using time domain technique in frequency range of 10 MHz to 50 GHz at the temperature range from 10 °C to 25 °C with a difference of 5 °C. The frequency domain technique within the frequency range of 20 Hz to 2 MHz is used to obtain complex dielectric permittivity ε*(ω), electrical modulus M*(ω), complex electrical conductivity σ*(ω) and loss tangent (tan δ) at 25 °C. The dielectric spectra obtained using TDR technique are fitted in Cole-Davidson model to extract the dielectric parameters such as static dielectric permittivity (ε s), relaxation time (τ) and asymmetric distribution parameter (β). These relaxation parameter values are used to predict intermolecular hydrogen bonding between EGMME and ethanol molecules. Furthermore, the inter-molecular interactions through H-bonding between EGMME and ethanol molecules have been confirmed and discussed using Kirkwood correlation factor, excess permittivity, thermodynamic parameter, Bruggeman factor, excess molar volume, excess dielectric permittivity at high frequency and Fourier transform infrared (FTIR) spectra.

Dielectric relaxation and thermodynamic study of aqueous Glycine using time domain reflectometry technique

Using the Time Domain Reflectometry technique in the frequency range of 10 MHz to 50 GHz, the complex permittivity spectra of Glycine (Gly) with water combination have been determined over the complete concentration range of mole fractions and in temperature range of 10–25 °C. The Cole-Davidson model was used to fit the intricate permittivity spectra for Gly and water.The non-linear least square fit method has been used to compute the static dielectric constant (ε0), relaxation time (τ), effective Kirkwood correlation factor (geff), excess permittivity (ε0E), (1/τ)E excess inverse relaxation time (1/τ)E and Bruggeman factor (fB). An automated density and sound velocity meter, the Anton Paar DSA 5000 M and viscosity with Lovis 2000 M/ME, was used to measure the density, sound velocity, and viscosity of aqueous solutions. FT-IR spectra are used to identify the conformation assessments of hydrogen bonding development between complicated mixtures.

Dielectric Behaviour of Metal Complexes Cu (II), Ni (II) and UO2 ((VI) Of the Ligand Oxaloanilic Acid Hydrazone

Abstract: The dielectric behaviour and molecular structure of metal complexes Cu(II),Ni(II) and UO2((VI) of the ligand oxaloanilic acid hydrazine have been investigated using Time Domain Reflectometry (TDR) technique in the frequency range 10 MHz to 10GHz. Cole-Davidson model has been applied for fitting the complex permittivity spectra [ ε* (ω)]. The parameters εs –the static permittivity, τ- the dielectric relaxation time are evaluated at different temperatures from 2880K to 3330K and are discussed in respect of their molecular structural behaviours. The thermodynamic parameters, such as ΔH* - molar enthalpy, ΔS* - the molar entropy are obtained using Eyring.s rate equation. In the light of such data the possible structures of the present complexes are discussed.

Dielectric relaxation study of aqueous glycol ethers with water using time domain reflectometry technique in the frequency range 10 MHz to 50 GHz

The Complex permittivity spectra of glycol ether (GE) compounds such as ethylene glycol mono-methyl ether (EGME), ethylene glycol ethyl ether (EGEE) and ethylene glycol butyl ether (EGBE) with water mixture over entire concentration range and at 25 °C has been determined using Time Domain Reflectometry technique in the frequency range 10 MHz to 50 GHz. The complex permittivity spectra for GE–water were fitted in Cole–Davidson model. The Static dielectric constant (ε0), Relaxation time (τ), effective Kirkwood correlation factor (g eff), excess permittivity () and Bruggeman factor (fB ) have been calculated by non-linear least square fit method. The intermolecular interactions between GE-water binary mixtures suggest the non-linear behavior of dielectric parameters. The contribution of hydrogen bonding interactions among the solute-solvent mixtures is confirmed by Excess properties and Bruggeman factor.

Broadband dielectric relaxation spectroscopy and molecular dynamics simulation study of paracetamol-propylene glycol solutions

The complex permittivity ε*(ω) = ε′(ω) - ε“(ω) was studied for a series of paracetamol (PCM) – propylene glycol (PG) solutions over the broadband frequency range of 20 Hz to 20 GHz at different temperatures ranging from 293.15 K to 323.15 K. Measurements of the complex permittivity were carried out using Agilent Precision LCR meter E4980A with Agilent 16452A liquid test fixture (for 20 Hz to 2 MHz frequency region) and Anritsu Shockline Vector Network Analyser MS46322A with DAK-3.5 probe (for 200 MHz to 20 GHz frequency region). Obtained broadband frequency dependent dielectric data were analyzed to explore the interaction mechanisms and structural behavior of PCM and PG molecules in mixed state in terms of molar PCM concentration and temperature variation. Temperature dependent dc conductivity response of all solutions exhibited Arrhenius behavior from which activation energy was calculated. Microwave complex permittivity data were fitted to the Cole-Davidson model in order to determine dipolar relaxation parameters of the solutions. Dielectric constant and dielectric loss values at a spot frequency of 2.45 GHz were utilized to determine the microwave heating parameters and analyzed in view of its suitability for the microwave dielectric heating in pharmaceuticals. Molecular dynamics simulation study for selected concentrations of PCM in PG was also conducted in order to understand the actual mechanism of H-bonding interactions in the solutions and to justify the inferences derived from the experimental results.

Dielectric dispersion of Ag/PAN nanocomposites

The dependence of the electric modulus of silver/polyacrylonitrile nanocomposites on the ac field frequency has been studied at different temperatures and AgNO3 content in the base mixture. The observed relaxational maxima on the frequency dependences of the electric modulus’ imaginary part are connected with the interfacial polarization. It was shown that the frequency electric modulus’ experimental points are well-described by the Cole-Davidson model, correspondingly. The values of the relaxation times and the activation energies of these structures have been estimated by this model.

On The Equivalent Impedance of Two-Impedance Self-Similar Ladder Networks

Recurrent ladder network models are encountered in the analysis of many natural systems including wave propagation in transmission lines, porous electrode/electrolyte interfaces and viscoelastic (bio)materials. Here we re-visit the equivalent impedance of self-similar ladder networks composed of two arbitrary impedances recursively arranged, with the goal of correlating the behavior of the whole versus that of the part. We show that the macroscopic and microscopic scales are related via a generally complex-valued parametric scaling factor. We report on two new universal complex numbers that we denote as the Complex Golden Ratios . We also show that a lumped inductor (with its internal series resistance) or a lumped capacitor (with its parallel parasitic resistance) are actually equivalent to an infinite ladder network that involves resistors and imaginary resistors only. Finally, we show that the Cole-Davidson model, widely used in material characterization, naturally arises from the self-similar circuit ladder structure. Comparison with tree networks is also discussed.

Dielectric relaxation and molecular interactions study of saccharides in aqueous solutions

Time domain reflectometry (TDR) technique has been extensively used to study dielectric relaxation and solution properties of carbohydrates. Using TDR techninque, complex permittivity spectra of monosaccharides (d-fructose and d-xylose) and disaccharides (d-maltose monohydrates) were obtained in the frequency range of 10 MHz–50 GHz at various concentrations and temperatures. The static dielectric constant (ε0), dielectric constant at high frequency (ε∞), relaxation time (τ) and relaxation time distribution parameter (β) extracted from the complex permittivity spectra using least squares fit method. The values of static dielectric constant were also verified by LCR meter by dielectric measurement in the frequency range of 20Hz to 2 MHz at 25 °C. The relaxation behavior of aqueous solutions of monosaccharides and disaccharides has been illustrated by using Cole-Davidson model. Activation enthalpy (ΔH), entropy (ΔS) and Kirkwood correlation factor have been determined to study extent of hydrogen bonding. This data might be useful in pharmaceutical, food processing industry and in solubility prediction method in aqueous solution.

Field-enhanced polarization in polytype ferric oxides: confronting anisotropy in dielectric ellipsoid dispersion

An analytic dielectric introspection in two cardinal ferric oxide polymorphs, viz. hematite and maghemite, is conducted using a three-fold line of direction. Firstly, dc field-dependent radio/audio-frequency impedance and dielectric spectra of polycrystalline MIM pellets, comprising near-stoichiometric (meticulously characterized) Fe2O3 nanoparticles, are analysed by employing the Cole–Davidson model, Jonscher’s power law and equivalent circuitry to quantify non-Debye dipolar relaxations, small polaron hopping conduction, grain core–boundary resistivity correlations and field-driven delocalization/de-trapping of carriers. Bias-tuned low-frequency enhancement of the dielectric constant by augmenting Maxwell–Wagner polarization is demonstrated for both samples, a prerequisite for conquering classical energy-storage bottleneck. Secondly, the optical dielectric function and associated parameters are evaluated under a density functional theory + U framework, to physically designate particular resonant absorption, dissipation, electronic polarization and decay. In doing so, a new crystallographically consistent and energetically stable vacancy-ordered maghemite-type supercell is constructed to accomplish reasonable computational cost. Thirdly, intrinsic anisotropy in materials sensitive to photonic excitations is videographed by simulating energy-dispersive evolution of the quadric surface to project real/imaginary dielectric tensors. The authors anticipate that this intensive technique will pictorially demonstrate anisotropic deviations in the dielectric ellipsoid, fostering materials physics over linear and nonlinear dielectrics.

Enhancing the electrical properties of NBT ceramics by the addition of small amounts of Yb

In the present work, the magnetic and electrical properties of ceramic samples of Na0.5Bi0.5−xYbxTiO3 with x = 0.005, 0.010, 0.015 and 0.020 prepared by a solid-state reaction were investigated. X-ray diffraction (XRD) patterns revealed that the addition of Yb3+ ions led to distortions in the rhombohedral perovskite structure. The microstructure morphology investigated by scanning electron microscopy revealed the presence of micro-pores, diminishing the overall mass density of the ceramics for increasing values of x. This behaviour is opposite to the one observed for the mass density determined by using the XRD data. Despite of the contraction in the lattice parameter, the<Ti–O>bond length was found to increase for increasing values of x, shifting the corresponding Raman modes towards lower values of energy. The magnetization and the ac and dc magnetic susceptibilities were measured from 300 K down to 5 K. The magnetic moment associated to the Yb3+ ions added a paramagnetic behavior to the NBT samples that increases for increasing values of x. The electrical permittivity was measured at room temperature by impedance spectroscopy for frequencies (f) in the range 20 Hz–2.0 GHz. The f-dependence for the permittivity was accounted for by using the Cole-Davidson model. It was observed that the addition of the Yb3+ ions enhances the values of the dielectric constants, yielding an increase of about 70% for x = 0.020, while the overall dielectric losses are significantly reduced.

Dielectric relaxation and co-operative dynamics of propylene glycol – Ethanol mixtures using time domain spectroscopy

The dielectric measurement of propylene glycol (PG) – ethanol (ETH) mixtures over whole composition range have been carried out using time domain technique in the frequency range of 10 MHz to 50 GHz. The measurements were carried out at temperatures 25 °C, 15 °C and 5 °C. Dielectric parameters were evaluated by fitting the complex permittivity data in Cole-Davidson model using non linear least square method. Dielectric relaxations and co-operative dynamics of PG-ETH molecules in pure and their mixtures were discussed using Kirkwood correlation factor (geff), excess permittivity (ε0E), thermodynamic parameter.

Relaxation of the dielectric response in thin films of vanadium dioxide

The results of studying the processes of dielectric relaxation in thin nanocrystalline films of vanadium dioxide are presented. The existence of a non-Debye relaxation process was revealed, which is due to the presence of a distribution of relaxators over relaxation times according to the Cole-Davidson model. The activation energy of the dielectric relaxation process was found to be Ep = (0.9 ± 0.1) eV. The observed regularities are explained by a model which views the system as a set of relaxators whose physical parameters have different numerical values due to the Gaussian size distribution of nanocrystallites of the VO2 film. The temperature change in the parameters of the dielectric relaxation process, detected at T = 340 K, indicates that a complex Mott-Peierls semiconductor-metal phase transition occurs at a given temperature in the VO2 nanocrystalline film.

Dielectric relaxation study of aqueous ethylene glycol mono-methyl ether (EGME) with water using time domain reflectometry technique in the frequency range 10MHz to 50GHz

The Complex permittivity spectra of glycol ether (GE) compounds such as ethylene glycol mono-methyl ether (EGME) with water mixture over entire concentration range and in temperature range of 10–25∘C have been determined using Time Domain Reflectometry (TDR) technique in the frequency range 10[Formula: see text]MHz to 50[Formula: see text]GHz. The complex permittivity spectra for EGME-water were fitted in the Cole–Davidson model. The Static dielectric constant ([Formula: see text], Relaxation time ([Formula: see text], effective Kirkwood correlation factor ([Formula: see text], excess permittivity ([Formula: see text], thermodynamic parameters (activation enthalpy and activation entropy) and Bruggeman factor ([Formula: see text] have been calculated by the nonlinear least square fit method. The intermolecular interactions between EGME-water binary mixtures suggest the nonlinear behavior of dielectric parameters. The contribution of hydrogen bonding interactions among the solute–solvent mixtures is confirmed by Excess properties and Bruggeman factor.

Dielectric properties of polyols, at frequency range 0.2–3 GHz and temperature range 293–473 K: an analysis in the frequency and temperature domain

The use of polyols as green solvents in conjunction with microwave heating (MH) has become a very attractive synthetic protocol nowadays. However, among the needs of this area, as well as any other that uses MH, figure the electromagnetic properties of the materials. In this context, the contribution of this work is provide dielectric data of three polyols: glycerol, 1,2-propanediol and 1,3-propanediol. The data are presented in two ways: in frequency domain and in temperature domain (whose parameters were denominated f-dispersion and T-dispersion, respectively). In the frequency domain analysis, f-dispersion parameters were obtained for the Cole–Davidson model – one of Debye's models. From the analysis in this domain, the uncertainty and accuracy of the data was established. In the temperature domain analysis, an empirical model is proposed to represent the complex permittivity as a function of temperature – ɛ*(T) of the polyols. From the analysis in this domain, concluded that the presented model can be applied to other materials. In addition, that can to conclude that the phenomena of thermal runaway and self-limitation of heating are, in fact, subsequent opposite phenomena associated to the variation of the loss factor with the temperature.

Grain shearing models and relevance beyond sediment acoustics

The grain shearing (GS) and viscous grain shearing (VGS) models for saturated, unconsolidated marine sediments fit well to real data. But the models have much further relevance. The inherent convolution is in fact the definition of a non-integer derivative. Therefore, the GS theory is exactly described by the fractional diffusion-wave equation for shear waves and the fractional Kelvin-Voigt wave equation for the compressional mode. Both have been studied extensively in fractional calculus [Pandey and Holm, “Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations,” JASA (2016)]. The GS theory demonstrates that fractional derivatives arise naturally from physical processes and thus are more than just clever mathematics. These derivatives appear in the relaxation modulus, the stress response to a strain step, of the GS process. The variation in time of the viscosity makes it a time variant non-Newtonian process. But when strain and stress change roles, a surprising result appears. The creep response is the Lomnitz law, an empirically defined logarithmic relationship for such diverse materials as igneous rocks and wood [Pandey and Holm, “Linking the fractional derivative and the Lomnitz…,” Phys. Rev. E (2016)]. In the VGS model, the power-law response is exponentially tempered. The relaxation modulus is then that of the Cole-Davidson model, known from dielectric materials. This relationship has yet to be explored [Holm, Waves with Power-Law Attenuation (Springer, 2019), Chap. 8].

Dielectric relaxation and hydrogen bonding interaction of polyethylene glycol dimethyl ether in water mixture

ABSTRACT The complex permittivity spectra of binary mixtures of polyethylene glycol dimethylether [PEGDME: Molecular Weight 250 g.mol−1 & 500 g.mol−1] with water over entire concentrations and at different temperatures (5ºC, 15ºC and 25ºC) have been measured using time domain reflectometry (TDR) technique in the frequency range of 10–30 GHz. The complex permittivity spectra were fitted in Cole–Davidson model using non-linear least square fit method. The dielectric parameters, such as static dielectric constant and relaxation time, have been determined for PEGDME250+ water and PEGDME500+ water mixtures. The hydrogen bonding interactions for the PEGDME250- water & PEGDME500- water mixtures have been discussed through the determination of excess permittivity, Bruggemann factor and thermodynamic parameters.

Dielectric relaxation study of aqueous tetraethylene glycol using time domain reflectometry technique in the frequency range 10 MHz to 50 GHz

The Complex permittivity spectra of Tetraethylene glycol(TTEG)-Water mixture over entire concentration range at variant temperatures (0 °C–25 °C) have been determined by Time Domain Reflectometry technique in the frequency range 10 MHz to 50 GHz. The complex permittivity spectra for TTEG- water were fitted in Cole-Davidson model. The Static dielectric constant (ε0), Relaxation time (τ), effective Kirkwood correlation factor (geff), excess permittivity (ε0E), thermodynamic parameters (activation enthalpy and activation entropy) and Bruggeman factor (fB) have been calculated by non-linear least square fit method. The intermolecular interaction between TTEG-Water binary mixture suggest the non-linear behavior of dielectric parameters. The contribution of hydrogen bonding interactions among the solute-solvent mixtures is confirmed by Excess properties and Bruggeman factor.

Dielectric relaxation and thermodynamic study of polyhydric sugar alcohols in DMSO using TDR technique

The measurement of complex permittivity spectra of binary mixtures of sugar alcohols with DMSO were carried out using picosecond time domain technique at the temperatures ranging from 283.15K to 298.15K. In order to obtain the dielectric parameters, the measured complex permittivity spectra were fitted to the Cole-Davidson model. These dielectric parameters are further used to evaluate the Kirkwood correlation factor and thermodynamic parameters to discuss hydrogen bond formation.