Cole-Cole Equation Research Articles

Dielectric analysis of chitosan gel beads suspensions: Influence of low crosslinking agent concentration on the dielectric behavior

Dielectric measurements were carried out for the suspensions of chitosan gel beads (CGB) crosslinked with glutaraldehyde (GA), ranging in crosslinking time from 1 to 180 min at six fixed low GA concentrations over a frequency range from 40 to 110 MHz. The distinct dielectric relaxations observed in the frequency range of 10 4–10 5 Hz were explained by the effects of the interfacial polarization. By fitting the experimental data with Cole-Cole equation the dielectric parameters of the suspensions were obtained, and the phase parameters were calculated using Hanai's method. The influence of crosslinking on the dielectric spectra of CGB was investigated by viewing the crosslinking time dependencies of conductivity increment (Δ κ), relaxation frequency ( f 0 ), permittivity of CGB ( ε i ), conductivity of CGB ( κ i ) and conductivity of continuous media ( κ a ) at six fixed GA concentrations. Some information were gained, such as, thinner electric double layer, particle with rougher surface and more compact gel backbone with increasing crosslinking time. The basic information obtained can provide valuable references for the preparation of CGB and the application to more extensive fields such as controlled-release technology of medicament.

Static and Dynamic Dielectric Properties of Mesogenic n-Nonyloxycyanobiphenyl (9OCB)

The dielectric properties of n-nonyloxycyanobiphenyl in the isotropic (I), nematic (N) and smectic A (SA) phases were investigated. The dielectric relaxation spectra, recorded in the frequency range 50 kHz - 100 MHz, were analyzed with use of the Cole-Cole equation. An anomalous temperature behavior of the static permittivity, the rotational diffusion exponent and the activation energy of mesogenic molecules rotating around their short axis, observed in the vicinity of the phase transitions, are discussed.

Dielectric relaxation in BaTi0.85(Fe1∕2Nb1∕2)0.15O3 perovskite ceramic

A polycrystalline sample of BaTi0.85(Fe1∕2Nb1∕2)0.15O3 is synthesized by high temperature solid state reaction technique. This sample crystallizes in cubic pervoskite structure at room temperature. The dielectric properties have been investigated at temperature range from 80to450K at various frequencies (100–107Hz). Frequency dielectric dispersion phenomena in a BaTi0.85(Fe1∕2Nb1∕2)0.15O3 ceramic has been analyzed by impedance spectroscopy in the temperature range from 250to450K. The Cole-Cole relaxation equation modified by introducing the conductivity was used to describe the experimental dielectric spectra of a high permittivity. Excellent agreement has been obtained in wide frequency domain (100–107Hz) between the measured and calculated permittivities in the 250–450K temperature range. The dielectric relaxation frequency obeys the Arrhenius behavior with activation energy of 0.181eV. A separation of the grain and grain boundary properties has been achieved using an equivalent circuit model. The different parameters of this circuit have been determined using impedance and modulus spectroscopy studies. The inner grain conductivity also obeys the Arrhenius low behavior with activation energy of 0.183eV. The dielectric relaxation and the inner grain conductivity have thus similar activation energies which suggest a link between these two phenomena.

Dielectric and Mechanical Relaxational Behavior of Poly (Chlorobenzyl Methacrylate)s

Dielectric relaxational behavior of poly(monochlorobenzyl methacrylate)s (PMClBM) and poly(dichlorobenzyl methacrylate)s (PDClBM) has been analyzed. The study was carried out by determining the components of the complex dielectric permittivity *. Two relaxation processes, labelled as α and β relaxations, which were analyzed in terms of the Havriliak-Negami and Cole-Cole equations, respectively, have been experimentally observed. The relative position of the chlorine substitute in the benzyl ring determines the characteristic parameters of the relaxations. Complementary dynamic mechanical measurements on these polymers have been carried out. The relationship between the macroscopic measurements with the dipolar moment of the relaxing entities has been analyzed in terms of the Onsager-Kirkwood-Fröhlich equation.

Dielectric spectra of disordered ferroelectric systems: Polycrystals and composites

The dielectric spectra of heterogeneous systems that have very large dielectric constants and exhibit the Maxwell-Wagner relaxation are analyzed. The spectra of the disordered systems are found to be of a non- Debye type, and attempts to fit them using either the Cole-Cole or Davidson-Cole equations sometimes fail to produce satisfactory results. Experimental spectra of disordered systems are proved to be close to the spectra obtained by computer simulation of statistical mixtures and ferroelectric ceramics. A new formula is suggested to describe the dielectric relaxation in polycrystalline and composite materials, and reasons for the non-Debye nature of the dielectric spectra are examined.

Pore geometry of Permo-Triassic sandstone from measurements of electrical spectroscopy

Abstract In order to provide an indirect method of estimating the hydraulic properties of sandstone aquifer rocks, electrical spectroscopy measurements were made on Permo-Triassic Sandstone over the frequency range 0.0001–1000 Hz. Samples from several boreholes across Britain are shown to exhibit a phenomenon called electrical relaxation, which we have modelled using a generalized Cole-Cole equation. The Cole-Cole parameters correlate well with other hydrogeologically important parameters determined using mercury injection capillary pressure and nitrogen adsorption techniques. Of greatest importance is that the relaxation time, τ, is strongly related to the dominant pore-throat size from which intergranular permeability may be estimated. A normalized version of the chargeability appears to be related to the surface conductivity and this gives the possibility of estimating the pore surface area to volume ratio, a value that is important in determining both permeability and sorption. The potential uses of electrical spectroscopy in hydrogeology and many other fields, including geology and petroleum petrophysics, are only now becoming apparent, and further advances are certain.

In vitro and in vivo measurement for biological applications using micromachined probe

We developed a small-sized micromachined probe for the measurement of biological properties using microelectromechanical systems (MEMS) technology. We also experimentally showed the suitability of the micromachined probe for biological applications through in vivo, as well as in vitro measurements of various types of tissue. We measured the permittivities of 0.9% saline and the muscle and fat of pork using the micromachined probe after liquid calibration. The measured permittivities of 0.9% saline and pork agreed well with both the expected values of the Cole-Cole equation along with the measured values obtained through the use of a 1-mm-diameter open-ended coaxial probe. We also performed in vivo measurements of breast cancer tissue implanted in an athymic nude mouse to show the suitability of the small-sized micromachined probe for practical biological applications. Through the obtained data, the capability of the micromachined probe of distinguishing different tissue types from one another was shown. The actual aperture size of the micromachined probe is only 240 /spl mu/m /spl times/ 70 /spl mu/m and, therefore, we can extract the biological information from very small biological tissues and drastically decrease the invasiveness of this method through the implementation of the small probe created through the use of MEMS technology.

Charge transport mechanism of vanadium pentoxide xerogel-polyaniline nanocomposite

The nanocomposites of conducting polyaniline are prepared by intercalating into the layers of vanadium pentoxide (V2O5) xerogel. The intercalation is confirmed by the observation of lattice expansion of V2O5 xerogel. Dc conductivity of the gel follows Arrhenius type temperature dependence while the nanocomposites exhibit three dimensional variable range hopping. The ac conductivity and dielectric properties are extensively studied at low temperature up to the frequency of 10 MHz. Two semicircles in Cole-Cole plot of impedance are found for the nanocomposites. The ac conductivity spectra reveal three frequency regions. The frequency exponent in the lower frequency region is nearer to 2. The dielectric response exhibit broad spectra which are analyzed by Cole-Cole distribution function. The peak frequency of dielectric spectra appears at the first cross over frequency of conductivity spectra.

Radio and Microwave Spectroscopy of 0.2PMN-0.4PSN-0.4PZN Relaxor Ceramics

Dielectric spectroscopy results of 0.2PbMg 1/3 Nb 2/3 O 3 -0.4PbSc 1/2 Nb 1/2 O 3 -0.4PbZn 1/3 Nb 2/3 O 3 ceramics are reported for 200 < T < 450 K and 20 Hz < v < 11 GHz. Dielectric constant is very high (more than 12000) in the vicinity of the peak. Anomalous broad dielectric relaxation has been observed near and below the temperature of the maximum permittivity, T m (at 1 kHz). The distribution of relaxation times have been calculated directly from the dielectric spectra. At higher temperatures than the maximum permittivity, T m the distribution of the relaxation times is symmetrically shaped (Cole-Cole function satisfactory describes the dielectric response). At lower temperatures, the distribution of relaxation times becomes asymmetrically shaped. On further cooling the second maximum appears.

Dynamical excitation and anelastic relaxation of ferroelastic domain walls inLaAlO3

The ferroelastic domain processes responsible for low-frequency anelasticity in ${\mathrm{LaAlO}}_{3}$ have been investigated using dynamical mechanical analysis in three-point bend geometry combined with in situ optical observations under dynamic stress at high temperature. Transformations in the types of collective motion of domain walls have been observed optically. For low temperatures and small forces, the anelastic response is dominated by rapid advancement/retraction of combs of ${100{}}_{\mathrm{pc}}$ needle domains. At higher temperatures, lateral translation/rotation of ${110{}}_{\mathrm{pc}}$ twins also contributes to the response. Needle tips are pinned by a broad range of potentials, such that the ratio of mobile to static needle tips increases steadily with increasing temperature. For large forces, three distinct peaks in the relaxation spectrum can be resolved. A small low-temperature peak in the mechanical loss is attributed to the rapid saturation of weakly pinned needles. The dominant intermediate-temperature loss peak is attributed to the gradual relaxation of the comb as a whole. A third high-temperature loss peak occurs at the end of the domain-freezing regime and the beginning of the saturation regime. Activation energies for domain-wall motion of 95, 85, and 86 kJ/mol were determined for samples subjected to low, intermediate, and high forces, respectively. Cole-Cole plots of the response at small forces show a linear section at intermediate frequency and a depressed semicircle at low frequency. The semicircular portion is very well described by the Cole-Cole equation with a broadening exponent \ensuremath{\mu}. Physically, this model corresponds to a Debye-like relaxation process with a distribution of activation energies (domain-sliding regime). The broadening of the relaxation peak is a function of temperature, with \ensuremath{\mu} decreasing from 0.7 at 130 \ifmmode^\circ\else\textdegree\fi{}C to 0.5 at 205 \ifmmode^\circ\else\textdegree\fi{}C. This corresponds to an increase in the full width at half maximum of the activation-energy distribution from 9 to 21 kJ/mol. Fits to the entire data set suggest a parabolic temperature dependence of \ensuremath{\mu} with maximum at \ensuremath{\sim}120 \ifmmode^\circ\else\textdegree\fi{}C. A number of physical processes are suggested to explain this phenomenon. The linear portion of the Cole-Cole plots provides evidence for a dynamic ``transition'' between the domain-sliding and thermally activated creep regimes with increasing frequency.

Study of the SmCa * phase by dielectric measurements

The aim of our work was to make precise dielectric measurements to confirm the existence of the SmCα∗ phase in non-fluorinated compound 2 and in bicomponent mixtures composed of compounds 2 and 1 with partially fluorinated terminal chain. From the linear temperature dependences of relaxation frequency fR and the inverse dielectric strength Δ˜−1 obtained by fitting experimental values $\\varepsilon^{\\prime}_{\\bot}$ and $\\varepsilon^{\\prime\\prime}_{\\bot}$ to the Cole-Cole equation, the SmCα∗ phase was detected in compound 2 and the mixture of 0.9 mole fraction of compound 2 due to the changes of the slopes observed at SmA ⇒ SmCα∗ and SmCα∗ ⇒ SmC∗. The relaxation processes observed in the SmCα∗ phase of investigated systems are strongly modified under bias, thus they are probably connected with the ferroelectric-like structure of this phase.

Detection of a Heat Stress-Mediated Interaction between Protein and Phospholipid Membrane Using Dielectric Measurement

The dielectric response of lipid bilayer membrane vesicles (liposomes) prepared using either phosphatidylcholine from egg (EPC) or 1-palmitoyl-2-oleoyl- sn -glycero-3-phosphocholine (POPC) was analyzed at a frequency range of 0.1 to 100 MHz. A marked dielectric dispersion for EPC and POPC liposome suspensions was observed above 1 MHz. An appropriate analysis of the dielectric dispersion curve was performed using the Cole-Cole equation and the Debye equation and was found to provide a method for the determination of dielectric parameters. Among the dielectric parameters, the characteristic frequency of a second dispersion around 50 MHz varied corresponding with changes in the test conditions. Of particular note is that an anomalous change in the characteristic frequency in the presence of protein corresponded to the degree of hydrophobic interaction between proteins and liposomes. The value of the frequency around 50 MHz, as well as the decrease in permittivity over the frequency range tested, are indicators of the interaction between proteins and liposomes.

Detection of a heat stress-mediated interaction between protein and phospholipid membrane using dielectric measurement

The dielectric response of lipid bilayer membrane vesicles (liposomes) prepared using either phosphatidylcholine from egg (EPC) or 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine (POPC) was analyzed at a frequency range of 0.1 to 100 MHz. A marked dielectric dispersion for EPC and POPC liposome suspensions was observed above 1 MHz. An appropriate analysis of the dielectric dispersion curve was performed using the Cole-Cole equation and the Debye equation and was found to provide a method for the determination of dielectric parameters. Among the dielectric parameters, the characteristic frequency of a second dispersion around 50 MHz varied corresponding with changes in the test conditions. Of particular note is that an anomalous change in the characteristic frequency in the presence of protein corresponded to the degree of hydrophobic interaction between proteins and liposomes. The value of the frequency around 50 MHz, as well as the decrease in permittivity over the frequency range tested, are indicators of the interaction between proteins and liposomes.

Dielectric Relaxation Behavior of a Ferroelectric Liquid Crystal "Felix SCE9"

We report the dielectric relaxation behavior of a room temperature ferroelectric liquid crystalline material (code name Felix-SCE9) which undergoes paraelectric SmA--ferroelectric SmC* phase transition around T C = 64 - 0.1°C. All measurements have been performed using thin (∼10 w m) indium-tin-oxide coated cell in the frequency range 10 Hz to 1 MHz. The influence of the bias field, applied parallel to the smectic layers, on the parameters characterizing the Goldstone mode in the ferroelectric SmC* phase has been analyzed. Relaxation frequency of the Goldstone mode increases with increasing bias field. Dielectric increments ( j l ) and relaxation frequencies ( x ) of the para and ferroelectric phases are estimated from the fits of the Cole-Cole function of the dielectric spectrum. Thermal variations of dielectric increment and relaxation times suggested a first order SmC*-SmA transition (Tc ∼ 64°C) in Felix-SCE9. Experimental frequency and temperature dependent dielectric constant data follow the generalized Landau theoretical model.

Dielectric response of some biological tissues.

The dielectric properties of two freshly excised mice tissue samples (kidney, skeletal muscle) and also freshly excised Ehrlich solid tumor were measured in the frequency range from 20 Hz to 100 kHz using RLC bridges. The data were fitted to a summation of multiple Cole-Cole dispersion and also to the constant power law which is related formally to the fractal geometries of tissues using a genetic algorithm for optimization developed by the author. The data were in good agreement with the Cole-Cole equation for the three samples.

Detection of aggregates in magnetic colloids

The toroidal technique is used in the determination of the complex, frequency dependent magnetic susceptibility, , of four magnetic fluids consisting of colloidal suspensions of magnetite in water with corresponding saturation magnetisation of 134 G, 107 G, 90 G and 30 G. Plots of the susceptibility components against f (Hz) over the frequency range 10 Hz to 1 MHz, are shown to have approximate Debye-type profiles with the presence of Brownian relaxation being indicated by the frequency, f max , of the maximum of the loss-peak in the profiles. Corresponding calculations of particle hydrodynamic radius indicate the presence of aggregation. An estimate of the aggregate size distribution in the samples is determined by fitting the measured susceptibility profiles to susceptibility profiles generated by the Debye equations modified by Frohlich, Cole-Cole, Normal and Lognormal distribution functions. The fits obtained from the four fitting functions are found to be similar and thus it is concluded that none of these functions offers any particular advantage over the other functions.

Dielectric response of cells and liposomes and its utilization for evaluation of cell membrane-protein interaction

The dielectric measurements of an Escherichia coli ( E. coli) cell suspension and liposome suspensions were carried out in the frequency range between 0.1 and 100 MHz to detect the heat stress-mediated interaction between proteins and cell membranes. The dielectric relaxation dispersion was observed to be above 1 MHz. The dielectric parameter (amplitude of dispersion, Δε) based on the Cole-Cole equation was anomalously changed with increasing temperature. The value of Δε of liposomes was varied at various temperatures depending on the type of protein present. The change in Δε of liposomes correlated with the amount of protein translocated across the phospholipid membrane. The changes in the value of Δε of E. coli cells with temperature variation was similar to those of liposomes in the presence of proteins, suggesting that the variation in dielectric parameters reflected the interaction between the phospholipid membrane and proteins. It was found that the dielectric measurement could be utilized for the detection of the interaction between proteins and liposomes.

Dielectric Response of Cells and Liposomes and Its Utilization for Evaluation of Cell Membrane-Protein Interaction.

The dielectric measurements of an Escherichia coli (E. coli) cell suspension and liposome suspensions were carried out in the frequency range between 0.1 and 100 MHz to detect the heat stress-mediated interaction between proteins and cell membranes. The dielectric relaxation dispersion was observed to be above 1 MHz. The dielectric parameter (amplitude of dispersion, Δε) based on the Cole-Cole equation was anomalously changed with increasing temperature. The value of Δε of liposomes was varied at various temperatures depending on the type of protein present. The change in Δε of liposomes correlated with the amount of protein translocated across the phospholipid membrane. The changes in the value of Δε of E. coli cells with temperature variation was similar to those of liposomes in the presence of proteins, suggesting that the variation in dielectric parameters reflected the interaction between the phospholipid membrane and proteins. It was found that the dielectric measurement could be utilized for the detection of the interaction between proteins and liposomes.

Relaxation time distribution function

The distribution function of relaxation time in disordered dielectrics has been calculated in the random field theory framework. For this purpose, we first consider the dynamics of single two-orientable electric dipole in a random electric field E in a disordered ferroelectric. The obtained dependence τ(E) made it possible to express the relaxation time distribution function F(τ) via the random field distribution function f(E). This function has been calculated self-consistently in the random field theory framework. Nonlinear random field contribution and effects of spatial correlations between the dipoles have also been taken into account. It was shown that nonlinear contribution of random field gives asymmetric shape of F(τ), while in linear case it is symmetric. Comparison of calculated F(τ) curves with those extracted from empirical Cole-Cole (CC), Davidson-Cole (DC), Kohlrausch-William-Watts (KWW) and Havriliak-Negami (HN) functions had shown, that they correspond to mixed ferroelectric-dipole glass (ferro-glass) phase with coexistence of short and long-range order. Different forms of F(τ) are determined by linear (CC) or nonlinear (DC, KWW, HN) contributions of random field.

Relaxation time distribution of deuterated dipole glass

We have shown that none of the well-known relaxation functions such as the Cole-Cole, Cole-Davidson and KWW functions are satisfactory to describe the observed dielectric relaxation behavior of the deuterated rubidium-ammonium dihydrogen phosphate dipole glass (DRADP-x). The correlated domain model of Chamberlin was in qualitative agreements with the experimental observations of the dipole glass for (i) a long tail at lower frequency side, (ii) increase in the asymmetry of the dielectric loss spectrum with decreasing temperature.