Cole-Cole Equation Research Articles

Microwave dielectric properties of aqueous potassium iodide solutions as a function of temperature

The complex dielectric permittivity of aqueous KI solutions was studied for molalities of 0.50–4.01 m and temperatures of 288–323 K in the region of water dielectric permittivity dispersion. The values of high-frequency of dielectric permittivity (e) and dielectric losses (e″) were obtained at seven frequencies ranging between 7.5 and 25 GHz. The low-frequency electrical conductivity of the aforementioned solutions was measured for calculating ionic losses. A single relaxation process is observed in these solutions, fitted by the Debye or Cole-Cole equation with small distribution parameters. The static dielectric constant and dielectric relaxation time were studied as functions of temperature and concentration; the activation enthalpy of dielectric relaxation was calculated. The temperature dependence of the static dielectric constant was found to disappear in highly concentrated solutions. The structure-breaking effect on water caused by K+ and I− ions was affirmed, this effect disappearing in going to elevated temperatures.

Rheological behaviors of doughs reconstituted from wheat gluten and starch

Hydrated starch-gluten reconstituted doughs were prepared and dynamic rheological tests of the reconstituted doughs were performed using dynamic strain and dynamic frequency sweep modes. Influence of starch/gluten ratio on rheological behaviors of the reconstituted doughs was investigated. The results showed that the reconstituted doughs exhibited nonlinear rheological behavior with increasing strain. The mechanical spectra revealed predominantly elastic characteristics in frequency range from 10(-1) rad s(-1) to 10(2) rad s(-1). Cole-Cole functions were applied to fit the mechanical spectra to reveal the influence of starch/gluten ratio on Plateau modulus and longest relaxation time of the dough network. The time-temperature superposition principle was applicable to a narrow temperature range of 25°C ~40°C while it failed at 50°C due to swelling and gelatinization of the starch.

Dielectric Relaxation and Water Activity in Aqueous Solution of D-Psicose

Hydration behavior of a rare sugar, D-psicose, was investigated based on measurements of the dielectric relaxation and the water activity in its aqueous solutions. Dielectric relaxation spectra in the frequency domain were obtained from time domain reflectometry. The dielectric relaxation time was then determined by fitting the spectra to a Cole-Cole type equation and used to evaluate the average hydration number representing the average number of water molecules forming a complex with a sugar molecule at infinite dilution. The concentration dependence of the dielectric relaxation time in aqueous solutions of all examined sugars generated a single master cur ve. The average hydration number of psicose was found to be identical with that of fructose. Only slight differences were noticeable among the concentration dependences of the water activity of monosaccharides. The equilibrium constant of hydration of sugar was calculated by considering material balances in an aqueous solution of sugar and using experimentally obtained values of the average hydration number and the water activity. The equilibrium constant values increased in the order of glucose < fructose � psicose < trehalose < sucrose < maltose. The present results suggest that both fructose and psicose interact with water in a similar manner.

Confirmation of water mechanism in zeolite electrorheological fluid by dielectric spectroscopy

Zeolite electrorheological(ER) liquids with different amounts of adsorbed water were measured by dielectric spectroscopy, and the dielectric parameters of every system were fitted by Cole-Cole equation. The permittivity of the dispersed particle was found to increase with adsorbed water increasing, however, the dielectric increment of the ER liquid was independent on the adsorbed water. Considering the relationship between interfacial polarization and ER effect, the previous permittivity mechanism of adsorbed water was confirmed to be unsuitable to zeolite ER liquids. Based on analyzing the relaxation times of different systems, the dielectric loss mechanism was proposed to explain the positive effect of adsorbed water on the ER behavior of zeolite/oil suspension.

Investigation of Collective Relaxation Modes of (S)-(+)-4′-[4-(1-methylheptyloxycarbonyl)] biphenyl 4-[3-(octanoyloxy)prop-1-oxy]benzoate by Dielectric Spectroscopy

In the present work, we are reporting thermal, optical and dielectric properties of (S)-(+)-4′-[4-(1-methylheptyloxycarbonyl)] biphenyl 4-[3-(octanoyloxy)prop-1-oxy]benzoate. This compound possesses Iso- SmA*– SmC*α – SmC* –SmC*γ–SmC*A–Cr phase sequences upon cooling. Dielectric properties of this compound have been investigated under planar anchoring of samples in the frequency range of 1 Hz to 10 MHz with temperature and bias electric filed. Various relaxation modes active in SmC* sub-phases have been observed and their parameters have been analyzed by fitting theoretical Cole-Cole equations. In the SmA* phase, soft mode relaxation has been observed. In chiral tilted smectic subphases (viz. SmC*α, SmC*, SmC*γ) two relaxation modes are observed in different frequency ranges. In the SmC*A phase two modes have been observed due to antiferroelectric ordering.

Dielectric and Electrical Conductivity Relaxation in 0.5Li2O-0.5Na2O-2B2O3 Glasses

The frequency and temperature dependence of the dielectric constant, electric modulus and electrical conductivity of the transparent glasses in the composition 0.5Li2O-0.5Na2O-2B2O3 (LNBO) were investigated in the 100 Hz - 10 MHz frequency range. The dielectric data have been analyzed using Cole-Cole equation with an addition of the conductivity term. The electrical conductivity was found to be obeying Jonscher's universal law. The dielectric constant and the loss for the as-quenched glasses increased with increasing temperature, exhibiting anomalies in the vicinity of the glass transition and crystallization temperatures. The bulk DC conductivity at various temperatures was extracted from the electrical relaxation data. Conductivity plots were not found to follow Summerfield scaling due to mixed alkali effect. The imaginary part of electric modulus spectra was modeled using an approximate solution of Kohlrausch-Williams-Watts (KWW) relation. The stretching exponent, {\beta}, was found to be 0.56 and temperature independent.

Dielectric analysis of poly(diallyldimethylammonium chloride) aqueous solution coupled with scaling approach

Dielectric measurements were carried out on aqueous solution of poly(diallyldimethylammonium chloride) (PDADMAC) with different concentrations at room temperature. Additionally, for selected solutions the temperature dependence of dielectric relaxation spectroscopy (DRS) was examined in the range of 5-70 degrees C. The dielectric relaxation in the order of around MHz was observed, and the dielectric parameters were determined from the dielectric spectra by fitting data with the Cole-Cole equation. The dielectric parameters showed strong dependences on concentration and on temperature, respectively, and these dependences are analyzed by the scaling theory. From the analysis of concentration dependence of dielectric parameters, the dielectric relaxation is assigned to the localized fluctuation of uncondensed counter-ions over the distance between chains in dilute solution and correlation length in semi-dilute solution, respectively, and the solvent quality parameter for the uncharged polyelectrolyte chain is evaluated. By the analysis of temperature dependence of dielectric parameters, we find that: the physical meanings of the typical lengths of uncondensed counter-ions are not influenced by temperature; in semi-dilute solution, the highly extended length of the chain (correlation length) increases and the end-to-end distance of the chain decreases with increasing solution temperature; in the change process of dielectric relaxation of PDADMAC solution induced by the increase of temperature, the increment of ionic diffusion coefficient and decrement of permittivity of the solvent medium are the major factors. The enthalpy and entropy of activation of the dielectric relaxation are experimentally determined by the dependence of relaxation time on temperature, individually.

Dielectric relaxations in chitosan solution with varying concentration and temperature: analysis coupled with a scaling approach and thermodynamical functions

The dielectric properties of chitosan in an aqueous solution with no added salts have been measured as a function of concentration and temperature in the frequency range from 40 Hz to 110 MHz, respectively. After reducing the contribution of the electrode polarization effects, the dielectric spectra of chitosan semidilute solutions show two relaxations at 100 kHz and MHz, respectively. The observed two dielectric relaxations have been strictly analyzed using the Cole-Cole function and the possible relaxation mechanisms were attributed to the fluctuation of condensed counterions and free counterions, respectively. The dependence of the dielectric increment and relaxation time on concentration was interpreted in light of the scaling properties of polyelectrolyte solutions. It was found that the dependence of relaxation time on the Cp follows the expected exponents of the scaling laws, both in the low-frequency and high-frequency cases. The good agreement between experimental results and theoretical analysis suggests that the low- and high-frequency relaxation mechanisms are the fluctuation of condensed counterions and free counterions, respectively. In addition to this, this analysis gives further support to the scaling approach of the dynamic behavior of polyelectrolytes. The temperature dependence of the dielectric spectrum of chitosan solutions showed that the low- and high-frequency dielectric increment generally decreases with the rise of temperature, which is considered to be due to the acceleration of the reorientation motion of the counterions. Moreover, the thermodynamic parameters, such as activation free energy Ea, activation enthalpy change ΔH and activation entropy change ΔS of low- and high-frequency were calculated from the relaxation time, and discussed from the microscopic thermodynamical view.

Microwave Dielectric Study of an Oligomeric Electrolyte Gelator by Time Domain Reflectometry

The dynamics of water molecules in aqueous solutions of an oligomeric electrolyte gelator, poly[pyridinium-1,4-diyliminocarbonyl-1,4-phenylene-methylene chloride] (1-Cl) was characterized by microwave dielectric measurements using the time domain reflectometry method. The dielectric dispersion and absorption curves related to the orientational motion of water molecules were described by the Cole-Cole equation. Discontinuities were observed in the concentration dependence of the dielectric relaxation strength, Deltaepsilonh, as well as in the Cole-Cole parameter, betah. These discontinuities were observed between the samples with concentrations of 6 and 7 g/L 1-Cl/water, which correspond to a change in the transparency. Such a discontinuity corresponds to the observation of the critical concentration of gelation. The interaction between water and 1-Cl molecules was discussed from the tauh-betah diagram. As 1-Cl carries an amide group, it could be expected that 1-Cl may interact hydrophilically with water, but the present result suggests that 1-Cl interact hydrophobically with water.

Dynamic dielectricity of multiferroic spinel CdCr2S4

Dynamic dielectric properties were studied on the newly discovered multiferroic spinel, CdCr2S4. Two single crystals, grown under the same condition but from different batches were used, which showed identical behavior. Frequency-dependent dielectric constant as a function of temperature (ϵ'(ω)) exhibits relaxation behavior only below ferromagnetic transition temperature, TC ∼ 84 K, which indicated that the charge dipoles were associated with ordered magnetic spins. By fitting with extended Debye model (Cole-Cole equation), the relaxation characteristic time (τ) at different temperatures was obtained. When 55 < T < 84 K, the τ value decreases with decreasing temperature. It is somehow unusual as it doesn't obey the thermal activation model (Arrhenius law). These results suggest that the relaxation behavior is strongly affected by spin not by thermal fluctuation. Different ac voltages were also selected to study the field effect on the relaxation behavior. For Vac = 20 V, ϵ'(ω) dramatically changes and τ value becomes difficult to obtain as T < 55 K, suggesting that some unknown phases could exist below 55 K. Complex relaxation behavior below TC could be originated from the coupling among spin, lattice and dipole via exchangestriction.

Dielectric Relaxation Behavior of Anionic Surfactant SDBS Micellar Solutions

The dielectric relaxation behavior of the sodium dodecyl benzene sulfonate (SDBS) surfactant was investigated in a concentration range from 0.1 to 80 mmol·L-1 by dielectric relaxation spectroscopy (DRS) method. Near the critical micelle concentration (CMC) of SDBS, significant relaxation phenomena of SDBS solutions around the frequency 107 Hz were observed. The dielectric data of the overall concentration were fitted by using the Cole-Cole equation, which revealed information about the relationship between dielectric parameters and concentration. Although the relaxation increment (△e) increased with the concentration of SDBS (cs), this change exhibited two kinds of linear relationship, which intersected at an inflexion near 36 mmol·L-1. On the other hand, the curve of relaxation time (τ0) and concentration reached the lowest point at 45 mmol·L -1. Based on the spherical micelle model, the dielectric phenomena are due to the amount of bound Na+ counter-ions and the change in micellar volume.

Dielectric Cytometry with Three-Dimensional Cellular Modeling

We have developed what we believe is an efficient method to determine the electric parameters (the specific membrane capacitance Cm and the cytoplasm conductivity κi) of cells from their dielectric dispersion. First, a limited number of dispersion curves are numerically calculated for a three-dimensional cell model by changing Cm and κi, and their amplitudes Δɛ and relaxation times τ are determined by assuming a Cole-Cole function. Second, regression formulas are obtained from the values of Δɛ and τ and then used for the determination of Cm and κi from the experimental Δɛ and τ. This method was applied to the dielectric dispersion measured for rabbit erythrocytes (discocytes and echinocytes) and human erythrocytes (normocytes), and provided reasonable Cm and κi of the erythrocytes and excellent agreement between the theoretical and experimental dispersion curves.

Cole–Cole, linear and multivariate modeling of capacitance data for on-line monitoring of biomass

This work evaluates three techniques of calibrating capacitance (dielectric) spectrometers used for on-line monitoring of biomass: modeling of cell properties using the theoretical Cole-Cole equation, linear regression of dual-frequency capacitance measurements on biomass concentration, and multivariate (PLS) modeling of scanning dielectric spectra. The performance and robustness of each technique is assessed during a sequence of validation batches in two experimental settings of differing signal noise. In more noisy conditions, the Cole-Cole model had significantly higher biomass concentration prediction errors than the linear and multivariate models. The PLS model was the most robust in handling signal noise. In less noisy conditions, the three models performed similarly. Estimates of the mean cell size were done additionally using the Cole-Cole and PLS models, the latter technique giving more satisfactory results.

Theoretical model analysis of molecular orientations in liquid protein dielectrics

In this study, some theoretical model functions have been used to explain the molecular behaviour of four different types of proteins; human haemoglobin, Insulin, egg-white lysozyme and &#946 - globulin molecules in solution. The results of the computational fitting procedures showed that the dielectric dispersion of the protein molecules generally followed the Debye and Cole-Cole functions. The dielectric parameters obtained from the dispersions, relating to the structural and electrical properties of the molecules were tabulated. The relationships between the dispersion amplitude &#916 and the molecular dipole moment &#956 of the proteins and also between the relaxation time &#964 and the energy of activation &#916H of the molecules have been highlighted. The molecular interpretation of the polarization effects responsible for the dielectric dispersions have been discussed. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 15-20

Fractional Wavelet for R-Wave Detection in ECG Signal

In this paper, we propose a method for the R-wave detection of the QRS complex of the ECG signal using a fractional wavelet. This fractional wavelet is defined, in this context, as the second derivative of the Cole-Cole distribution function of relaxation times, which is widely used in mathematical modeling of fractional order systems. In order to reduce the noise level for the ECG data, our detection algorithm incorporates the proposed fractional wavelet whose parameters are obtained by maximizing the signal-to-noise ratio of the ECG. The scales of this wavelet are chosen based on the spectral characteristics of the ECG. The proposed algorithm performances were evaluated using the MIT-BIH arrhythmia database. The numerical results show that the proposed algorithm achieved a detection rate of about 99.56%.

Synthesis of Havriliak-Negami functions for time-domain system identification

Fractional differentiation models have proven their usefulness in representing high dimensional systems with only few parameters. Generally, two elementary fractional functions are used in time-domain identification: Cole-Cole and Davidson-Cole functions. A third elementary function, called Havriliak-Negami, generalizes both previous ones and is particularly dedicated to dielectric systems. The use of this function is however not very popular in time-domain identification because it has no simple analytical impulse response. The only synthesis method of Havriliak-Negami elementary functions proposed in the literature is based on diffusive representation which sets restrictive conditions on fractional orders. A new synthesis method, with no such restrictions, is developed in this paper. For that purpose Havriliak-Negami function is first split into a Davidson-Cole function and a complementary one. Both functions are then synthesized in a limited frequency band using poles and zeros recursive distribution developed by Oustaloup (1995). As an example, this Havriliak-Negami function is used for a thermal system modeling.

Dielectric relaxation behaviour of liquid crystals with opposite orientation of -COO ester group in molecular core

AbstractDielectric measurements were performed for two smectogens, being structurally analogous with the opposite space orientation of the-COO ester group in the molecular core, using a HP4192A impedance analyser. Gold coated electrode cells of different thicknesses were used. Temperature dependences of the relaxation frequency fR and the inverse of the dielectric strength Δε′┴ −1 obtained by fitting experimental values of perpendicular components, i.e., the real ε′┴ and the imaginary ε″┴ parts of the complex dielectric permittivity to the Cole-Cole equation as well as the investigation of modification of relaxation processes under bias were determined for the SmC*, SmA*, and N* phases of studied compounds. One can conclude, on the basis of the above results, that dielectric relaxation processes observed by us in the studied compounds are similar to those of the soft and Goldstone mode typically observed by others in the SmC*, SmA*, and N* phases. It is concluded from acomparison of their properties with other related compounds that the link between the biphenyl moiety and-COO ester group is closely related to the stability of smectic phases.

Ac conductivity and its scaling behavior in borate and bismuthate glasses

In the present work, ac conductivity measurement and its compositional dependence scaling analysis are studied on lithium and sodium based borate and bismuthate glasses in the frequency range from 20 Hz to 1 MHz at different temperatures. The measured conductivity data of these glasses are analyzed using Cole-Cole type impedance response function, Jonscher’s universal power law and Dyre’s random free energy barrier model. To get a consistent stand point on ion dynamics, different microscopic models and theories proposed for the ion conduction mechanism in disordered ionic solids are discussed and compared. Universality features of ac conductivity and its scaling behavior are discussed. The compositional dependence scaling behavior in borate and bismuthate glasses are studied using Jonscher’s power law hopping frequency ωp and minimum jump frequency γmin in Dyre’s random free energy barrier model. The scaling results are compared and reported.

Dielectric Model and Theoretical Analysis of Cationic Reverse Micellar Solutions in CTAB/Isooctane/n-Hexanol/Water Systems

Dielectric relaxation spectra of CTAB reverse micellar solutions, CTAB/isooctane/n-hexanol/water systems with different concentrations of CTAB and different water contents, were investigated in the frequency range from 40 Hz to 110 MHz. Two striking dielectric relaxations were observed at about 10(4) Hz and 10(5) Hz, respectively. Dielectric parameters were obtained by fitting the data using the Cole-Cole equation with two Cole-Cole dispersion terms and the electrode polarization term. These parameters show different variation with the increase of the concentration of CTAB or the water content. In order to explain the two relaxations systematically and obtain detailed information on the systems and the inner surface of the reverse micelles, an electrical model has been constituted. On the basis of this model, the low-frequency dielectric relaxation was interpreted by the radial diffusion of free counterions in the diffuse layer with Grosse model. For the high-frequency dielectric relaxation, Hanai theory and the corresponding analysis method were used to calculate the phase parameters of the constituent phases in these systems. The reasonable analysis results suggest that the high-frequency relaxation probably originated from the interfacial polarization. The structural and electrical information of the present systems were obtained from the phase parameters simultaneously.

Effect of dc electric field on conductivity and giant permittivity of KxTiyNi1−x−yO

Activation energies (Ea) for electrode and grain boundary (GB) conduction are found to be greater than that of the bulk conduction. This implies that both electrode and GB act as two insulating barriers affecting conductivity and dielectric relaxations in KxTiyNi1−x−yO. Decrease in Ea for electrode conduction above T&amp;gt;295K leads to relatively greater loss due to the dc-charge transportation between electrodes and dielectric. The Cole-Cole equation has been modified to explain ε′ over a wide range of frequency (10–107Hz). Impedance spectroscopic study has also been employed to distinguish electrode relaxation from GB relaxation.