Complex Dielectric Spectra Research Articles

Disorder effects on dielectric response of Si irradiated with Ar+

Irradiation induced changes in the complex dielectric spectra of single crystal Si are investigated with spectroscopic ellipsometry. The analysis of microstructural variations resulting from ion irradiation is carried out to establish the existence of a well defined amorphization threshold. Increase in fluence leads to amorphization of the crystal resulting in an order–disorder transition as inferred from peak to peak height of the first derivative spectra. The amorphous volume fraction deduced from a microstructure model using effective medium approximation is found to have a power law behavior. The variations in the critical point (CP) structure in the energy range 1.5 to 5 eV is studied as a function of fluence ranging from 6×1013 to 1×1017 Ar+ ions cm−2. The changes in the nature of the CPs is examined in detail by line shape analysis of the second derivative of the optical spectra above and below the amorphization threshold. Irradiation induced structural disorder and its effect on the interband optical transition, particularly the E1 critical point at 3.4 eV is analyzed in detail. The E1 structure is fitted in the complete fluence range with a 2D CP line shape with a large excitonic phase angle. A red shift of the E1 critical point, decrease in its amplitude, increase in excitonic phase angle and broadening of the line shape are observed with increasing fluence. All these parameters of the E1 CP show distinct behavior above and below the amorphization threshold.

Dielectric properties of the low dimensional vanadium oxides Ba 2V 3O 9 and Sr 2V 3O 9

The dielectric response of the low-dimensional vanadium oxides Ba 2V 3O 9 and Sr 2V 3O 9 has been investigated in the frequency range of 20 Hz–1 MHz. At low frequencies the dielectric response is governed by strong relaxation-like features, which we attribute to Maxwell–Wagner type contact contributions. The analysis of the complex dielectric spectra in terms of an equivalent circuit revealed the intrinsic dielectric constant and dc conductivity of these systems. The frequency-dependent ac conductivity in both systems follows the universal dielectric response behaviour, clearly indicating that hopping of localised charge carriers is the dominating charge-transport process. Also, a newly observed dielectric relaxation process in both systems is reported and we find evidence for a phase transition close to 455 K in both materials.

Dielectric spectroscopy of blood

An experimental investigation of complex dielectric spectra of human blood in the frequency range 30 Hz–30 MHz has been carried out for various blood cell concentrations, temperature and environment. Electrode impedances and other distorting effects have been excluded. The average values of the dielectric constant (DC) ε and conductivity γ of normal heparinized blood for the lowest ( ε 0, γ 0) and the highest frequencies ( ε ∞, γ ∞) are: ε 0=7500; γ 0=4.9 mS/cm; ε ∞=160; γ ∞=9 mS/cm. The characteristic relaxation time τ=0.265 μ s with a Cole–Cole distribution around it; only beta-dispersion is observed in normal blood. The DC of resting blood is considerably larger than that of stirred blood; this is associated with the formation of small aggregates of blood cells. The temperature dependence of the static DC shows a maximum at the temperature 37 °C. According to Fricke–Pauly–Schwan theory the membrane capacity C m of stirred blood at normal concentration is 0.8 μF/cm 2 and depends strongly on concentration of cells and stirring. Damaged and aged cells manifest, in addition to beta-dispersion, a low-frequency alpha-dispersion, which can be explained as a result of the formation of large aggregates of cells.

Analysis of complex dielectric spectra. II: Evaluation of the activation energy landscape by differential sampling

Relaxation phenomena are controlled by thermally activated or by free-volume activated kinetics. Evaluation of the kinetic parameters across the whole experimental window is of prime importance. Techniques that provide information about the entire landscape of activation energies or fractional free volumes are discussed. Emphasis is given to a fine-structure analysis by bivariate differential sampling and its potential for studying the glass transition dynamics in equilibrium and non-equilibrium (physical aging) is shown.

Analysis of complex dielectric spectra. I. One-dimensional derivative techniques and three-dimensional modelling

Several strategies for the analysis of isochronal and isothermal spectra as well as complete three-dimensional (3D) spectra are outlined and applied to data of (glass forming) liquids and polymers. Conduction-free loss spectra are calculated using a compact solution of the Kramers–Kronig transformation and an approximation based on ∂ε ′/ ∂ ln ω . The usefulness of the dielectric modulus for data analysis is also evaluated. Apart from ∂ε ′/ ∂ ln ω , other useful derivatives in the frequency and temperature domain are treated as well. Finally, we describe the evaluation of 3D-relaxation maps by means of 3D fitting.

Hydrogen network fluctuations and dielectric spectrometry of liquids

Complex dielectric spectra of associating liquids are presented and are discussed considering their relaxation properties. Particular emphasis is given to water and aqueous solutions and to alcohols and mixtures of alcohols with dipolar and non-polar solvents. The relaxation properties of the associating systems are examined in the light of a wait-and-switch model of dielectric relaxation in which the relaxation time is governed by the period for which a given ensemble of hydrogen bond partners within the hydrogen network has to wait until favorable conditions for a reorientation of a molecular permanent dipole exist. These conditions are provided by an additional molecule or group which firstly tends to lower the potential energy barrier for reorientation and which secondly, at the same time, offers a site for the formation of a new hydrogen bond. Some experimental findings are discussed in terms of the wait-and-switch model, among them the reduced dielectric relaxation time of water under hydrostatic pressure, effects of negative and hydrophobic hydration of ions, and the influence that water, on the one hand, and n-alkanes, on the other hand, act on the relaxation of alcohols.

Dielectric spectra of bound water in hydrated Ca-smectite

Water contained in larger pores is considered to have the properties of free water, but water associated with colloid surfaces is often called bound water. The objective of this study is to utilize dielectric spectra to elucidate properties of various forms of bound water in Ca-smectite. The <2 μm fraction of Wyoming bentonite was Ca-saturated and prepared as oriented films. The loosely-stacked oriented films were equilibrated above saturated salt solutions to control relative humidity (RH), then compressed with a hydraulic press, and finally packed into coaxial cells. A vector network analyzer was used to indirectly determine the complex dielectric spectra. The gravimetric water contents ranged from 0.209 to 0.421 kg kg −1 for RH ranging from 54% to 98%, and static electrical conductivity (EC) ranged from 0.002 to 0.051 S m −1. Volumetric water contents ranged from 0.203 to 0.506 m 3 m −3, and variable amounts of air were present in the different samples, ranging from 0.040 to 0.438 m 3 m −3. Increased water content increased the EC because of greater continuity of water and lower tortuosity. Both the real and imaginary component of the permittivity were about an order of magnitude smaller at 54% RH than at 98% RH.

Time-Resolved and Backward-Wave Oscillator Submillimetre Spectroscopy of Some Ferroelectric Ceramics and Thin Films

Backward-wave oscillator spectroscopy was applied to the transmission measurements of the complex dielectric spectra in the frequency range 8-33 cm m 1 at temperatures from 10 K to 300 K. The samples under investigation were relaxor PLZT 9.5/65/35 ceramics, antiferroelectric PbZrO 3 ceramics and thin films of Ba x Sr 1 m x TiO 3 (x = 0; 0.1; 1) on sapphire substrates. Room temperature measurements on the same samples were performed using a time-domain terahertz transmission spectroscopy in the range 3-80 cm m 1 . A good agreement of both data sets is obtained. Temperature behavior of the complex permittivity is discussed; both experimental methods are compared.

Dielectric relaxation of hydrogen bonded liquids: Mixtures of monohydric alcohols with n-alkanes

The complex dielectric spectra for mixtures of unbranched monohydric alcohols with n-alkanes have been measured between 1 MHz and 18 GHz at various mole fractions xCnOH of the alcohols (0.2⩽xCnOH⩽1). Within the frequency range of measurements the spectra exhibit two dispersion/loss regions which can be analytically well represented by a Davidson–Cole-type and a Debye-type relaxation term, respectively. The relaxation parameters are discussed in terms of a wait-and-switch model of relaxation, considering also the effect of the nonpolar hydrocarbon groups in the enthalpy of activation of the dielectric relaxation process. This model allows for a consistent description of the dielectric properties of the alcohol/n-alkane mixtures which, depending on the relative length of the hydrocarbon chains, divide into two groups. Structural features of the alcohol/n-alkane mixtures are proposed to account for the characteristic behavior of both groups of liquids as a function of alcohol content.

Composition of foods including added water using microwave dielectric spectra

The added water content of fresh and untreated pork, poultry, fish and prawns was adjusted either by dipping in polyphosphate and salt solutions of known concentrations for controlled periods, or by injection (pork) with polyphosphate and salt solutions. Mixtures were prepared from treated and untreated fish and other foods (milk and flour). Liquid uptake was determined by the weight gain of samples. The proximate composition of the samples was determined: water, fat, protein, NaCl and phosphorus (for polyphosphate content). Complex dielectric spectra of each product were measured at known temperatures and at 31 frequencies in the range 0.2–12 GHz using an automatic network analyser (ANA) and a 3.0 mm open-ended coaxial sensor. The spectra were subjected to various procedures. • Principal component analysis (PCA) using the individual complex components. • Regression of the composition data against the principal components to obtain prediction formulae for composition including liquid uptake (internal cross-validation). • Regression of the composition data against raw spectral data and against other composition variables to obtain similar formulae. In order to design a simpler instrument, the effect on accuracy was studied of reducing the number of frequencies in the spectrum and its range. The slight loss of accuracy engendered by using only five or six frequencies was acceptable. The accuracy of the method in predicting liquid uptake and composition was good. Using one of the compositional variables in the calibration made it equivalent to accuracy obtained by proximate analysis, which was the limiting factor. Measurements on solutions of glycerol, NaCl and water with precisely known composition demonstrated that the intrinsic accuracy of the instrument was far better. A prototype instrument was built and validated using samples of prawns and herring.

Dielectric response of concentrated NaCl aqueous solutions: Molecular dynamics simulations

Molecular dynamics simulations are performed to study the dielectric response of concentrated NaCl aqueous solutions. The extended simple point charge interaction potential for water molecules and the Higgis–Mayer potential for ion–ion interactions are used. The ion–ion and ion–water distributions are examined for 1 M solution at 298, 373 and 473 K. The solvate-separated ion pairs with the Na+–Cl− separation of about 5.0 Å are found to form preferentially at ambient temperature. The close contact pairs with the ion–ion separation of 2.9 Å tend to form in high temperature solution. The 3D water–ion arrangements are revealed with the aid of the spatial distribution function. The Na+–O–Cl− angle in the solvate-separated ion pairs is found to be close to 106°. The correlation times of translations, τT, and rotations, τR, for water molecules in the solvation shells of the cation and anion are determined. The frequency-dependent dielectric permittivity and absorption coefficient for the concentrated NaCl solution are calculated over wide temperature range. The origin of the complex dielectric spectra for concentrated NaCl solution is analyzed.

Dielectric spectroscopy of sedimentary rocks

A physiochemical model for the complex dielectric response of sedimentary rocks is used to invert broadband dielectric spectra for effective grain size distributions. The complex dielectric response of each grain within the “water‐wet” granular matrix is obtained by superimposing the polarization of the electrochemical double layer, which is assumed to surround each grain, with the complex dielectric response of the dry mineral grain. The effective complex dielectric response of the water‐wet matrix (grains and surface phase) is obtained by volume averaging over the entire distribution of particle sizes. The complex dielectric response of the total mixture (water‐wet matrix and bulk pore solution) is obtained using the Bruggeman‐Hanai‐Sen effective medium theory. Studies of Berea sandstone show that the grain size distribution, obtained by inverting the real part of the complex dielectric spectra, is similar to the grain size distribution obtained from optical images of the sample in thin section. The current model, however, does not account for surface roughness effects or the polarization of counterions over multiple grain lengths; therefore the grain size distribution obtained by dielectric spectroscopy is broader than the image‐derived distribution. The dielectric‐derived grain size distribution can be fit with two separate power laws that crossover at R ≅ 1 μm, which corresponds to a relaxation frequency of 2 kHz. The low‐frequency dielectric response (f &lt; 2 kHz) is primarily controlled by the macroscopic grain fraction (mainly quartz grains), which has a fractal dimension of d = 1.84±0.05. The high‐frequency dielectric response (f &gt; 2 kHz) is primarily controlled by the clay size grains and surface roughness, which has a fractal dimension of d = 2.48±0.07. At very low frequencies (f &lt; 0.1 Hz) the dielectric response appears to be controlled by the electrochemical polarization of counterions over multiple grain lengths. A more general model should account for the effects of surface roughness and grain interactions on the dielectric response. It would also be useful to develop a simplified version of this model, perhaps similar in form to the empirically derived Cole‐Cole response, which could be more easily used to model and interpret electrical geophysical field surveys (e.g., induced‐polarization, ground‐penetrating radar, and time domain reflectometery measurements).

Dielectric Relaxation of Cationic Surfactants in Aqueous Solution. 2. Solute Relaxation

The complex dielectric permittivity spectra of octyl-, dodecyl-, and hexadecyltrimethylammonium bromide and of dodecyltrimethylammonium chloride reveal two low-frequency relaxation processes centered around 80 and 250 MHz. These are assigned to the diffusional relaxation of free and bound counterions, respectively, around the charged micelles. It is found that at low concencentrations the model of Grosse is able to rationalize simultaneously the amplitudes and relaxation times of both relaxation processes. The similar model of Pauly and Schwan, which is restricted to the relaxation of the bound counterions, fits the parameters of the 250 MHz process over the entire concentration range. Both models were used to determine the radius and surface conductivity of the micelles. Volume fractions determined from these radii are in good agreement with literature data and with values obtained from the analysis of the water relaxation processes. This shows that the complex permittivity spectra of theses solutions, d...

Dielectric Relaxation of Cationic Surfactants in Aqueous Solution. 1. Solvent Relaxation

Complex dielectric permittivity spectra, ε(ν), in the frequency range 0.09 ≤ ν/GHz ≤ 89 were recorded for aqueous solutions of octyl-, dodecyl-, and hexadecyltrimethylammonium bromide and dodecyltrimethylammonium chloride at room temperature and concentrations c ≤ 1 mol dm-3. Additionally, for selected solutions the temperature dependence of ε(ν) was examined in the range of 0 ≤ ϑ/°C ≤ 65 in order to obtain Eyring activation enthalpies and entropies of the relaxation times. It was found that a superposition of up to five Debye relaxation processes is required for a consistent fit of all spectra. The low-frequency dispersion steps with relaxation times τ1 ≈ 1.5 ns and τ2 ≈ 300 ps can be assigned to the diffusion of free and bound counterions surrounding the charged micelles. The remaining relaxation processes are due to the solvent. As in the pure solvent, a small contribution of fast mobile water molecules, τ5 ≈ 1 ps, can be observed besides the dominating relaxation of the hydrogen bond network of bulk water, τ4 ≈ 8 ps. Additionally, a slower relaxation process, τ3 ≈ 25 ps, is detected which can be attributed to water molecules within the micelles and in the vicinity of the hydrophobic tail of monomeric octyltrimethylammonium ions. From the amplitudes of the water relaxation processes hydration numbers of the surfactant ions and micelles as well as the volume fraction of micelles were calculated.

Low-energy charge dynamics inLa0.7Ca0.3MnO3:THz time-domain spectroscopic studies

Direct experimental estimations of the low-energy ($1.5\sim10$ meV) complex dielectric constants spectrum and its temperature variation have been investigated for La$_{0.7}$Ca$_{0.3}$MnO$_3$ thin films using terahertz time-domain spectroscopy. At low temperatures, a clear Drude-term emerges. With increasing temperature, the scattering rate increases, while the plasma frequency decreases, derived both from a simple Drude model. Finally, a Drude-term submerges well below the insulator-metal transition temperature. On the basis of the present results, low-energy charge dynamics are discussed.

Effect of Penetration Enhancers on the Dynamic Behavior of Phosphatidylcholine Headgroups in Liposomes

The results of a time-domain dielectric spectroscopy (TDDS) study of the effect of two skin penetration modulators on phosphatidylcholine (PC) bilayer vesicles are presented. The complex dielectric permittivity spectra of PC vesicle suspensions were described as the sum of two processes: the interfacial polarization of the bilayer and the reorientation of the zwitterionic PC headgroups in a plane approximately tangential to the bilayer surface. The influence of two additives (Azone and Transcutol) on the structure and dynamic behavior of PC headgroups of the bilayer vesicles was analyzed in terms of the interconnection of the dielectric spectra Cole−Davidson parameter, β, and the correlation factor, g, of the dielectric relaxation Kirkwood cell model. Analytically, these parameters are connected in the proposed model via the spatial distribution of headgroup dipole nonhomogeneities. In terms of the physical modulation of the polar surface phase, it appears that these additives can behave either as enhanc...

Hydrogen Network Fluctuations and the Microwave Dielectric Properties of Liquid Water

A short tutorial is given on interactions of water with electromagnetic fields, particularly in the microwave frequency range. Properties of the water molecule are sketched and attributes of the percolating tetrahedral hydrogen bond network of liquid water are presented. Characteristics in the polarization noise of liquid water are discussed and are related to the dielectric spectrum of water. The principal dielectric relaxation in the microwave region is represented by a Debye-type spectrum, the parameter values of which are given as a function of temperature in tabular form. At 19°C, as an example, the complex dielectric water spectrum is shown in an extended frequency range, also covering the near millimetre and submillimetre wave region up to 2 THz. A wait-and-switch model of dielectric relaxation, as suggested by computer simulation studies, is briefly outlined, in order to illustrate the mechanisms behind the hydrogen network fluctuations.

Dielectric Measurements of Aniline and Alcohol Mixtures at 283, 293, 303, and 313 K Using the Time Domain Technique

Complex dielectric spectra ε*(ω) = ε‘ − j ε‘ ‘, in the frequency range 10 MHz to 10 GHz, have been determined using the time domain reflectometry (TDR) technique at various temperatures and different concentrations of alcohols, viz., ethanol, propan-1-ol, butan-1-ol, hexan-1-ol, and heptan-1-ol + aniline binary mixtures. The static dielectric constant (ε0) and relaxation time (τ) have been obtained. The values of ε0 and τ decrease with an increasing percent of aniline in the alcohol.

Frequency shift in smectic multiple relaxations and the effect of a flexible end chain

The low frequency (LF) dielectric constant was studied as a function of temperature in the Schiff 's base liquid crystalline compounds of N (p - n -alkoxybenzylidene)- p - n -alkylanilines with the applied field parallel to the director to determine the phase transition temperatures and the underlying dipolar association. The low frequency (1 kHz to 10 MHz) complex dielectric spectrum systematically studied in the smectic polymorphs of these compounds implied multiple relaxations. The rotational degrees of freedom were found to be squeezed with the decrease of temperature as the low temperature smectic phases were approached. The ColeDavidson method was used to differentiate the fast dynamics of the rigid core-associated dipole from the slow component of the flexible end chain. A comparative study of the orientational dynamics of the rigid core dipole (type I) was carried out by designing a normalized scale in smectic phases. Arrehenius dependence was used in the estimation of smectic relaxation frequency at a common normalized smectic temperature scale point. The results imply the downward shift of frequency with increase in length of the flexible end chain. The distinct loss of rotational degrees of freedom of the rigid core dipole with increasing chain length suggests its solute particle behaviour in the solvent concentration.

Infrared intensities of liquids XXII: Optical and dielectric constants, molar polarizabilities, and integrated intensities of liquid benzene-d 6 at 25 °C between 5000 and 450 cm -1

This paper presents accurate infrared absorption intensities of liquid benzene-d6 at 25 °C, between 5000 and 450 cm–1. The results are presented as graphs and tables of the real, n, and imaginary, k, refractive index spectra, which are also called the optical constant spectra. The real refractive index is shown between 8000 and 450 cm–1. The absolute errors in the k values are estimated to be ∼3% below, and up to 60%, above, 4700 cm–1, with those in the n values ∼0.25% throughout. The Beer-Lambert molar absorption coefficient spectra, Em(˜ν), and the complex dielectric constant spectra, ɛ′(˜ν) and ɛ″(˜ν), were calculated from the optical constant spectra. To correct for macroscopic dielectric effects, the complex molar polarizability spectra, α′m(˜ν) and α″m(˜ν), were calculated from the dielectric constant spectra under the Lorentz local field. The properties of bands in these different spectra are compared. The imaginary molar polarizability spectra were fitted convincingly to 208 Classical Damped Harmonic Oscillator bands, and the areas under the corresponding ˜να″m bands gave the integrated intensities Cj. These were assigned as far as possible and are tabulated. The transition dipole moments of well assigned transitions, and for the infrared-active fundamentals, under the double harmonic approximation, the dipole moment derivatives with respect to the normal coordinates, were calculated from the values of Cj, and are presented. This appears to be the first extensive measurement of the infrared absorption intensities of liquid benzene-d6. The results are compared with literature data for liquid and gaseous benzene-d6.