Dielectric Mixture Equations Research Articles

Dielectric properties of Pouteria sapota compounds in terahertz frequency range

The analysis and a mathematical approximation of the dielectric properties of Pouteria sapota (Mamey) pulp compounds in the Terahertz (THz) range are presented. Since THz electromagnetic waves show a high sensitivity to detect water content when interacting with organic materials, this technique was used to determine the effective dielectric function (EDF) of a wet and a dry sample from the THz spectrum data. By fitting the EDF to the Landau-Lifshitz-Looyenga (LLL) dielectric mixture equation, the theoretical dielectric functions of each pulp compounds were approximated. The approach proposed here not only considered dry matter and water content in the Pouteria sapota pulp, as has been reported in the literature for organic samples, but also included the contribution of the volatile components (VC) that allowed a better adjustment to the experimental results. The water and VC content increase the value of the real and imaginary part of the calculated EDF of the wet sample. The use of the non-destructive THz spectroscopy technique allows determining the dielectric properties of fruits that have been dehydrated. Therefore, the methodology proposed here can be used as a method of in situ and ex situ quality control in the agri-food industry.

Effective Complex Permittivity of Random Composite Media: PVDF/(Na<sub>1/2</sub>Bi<sub>1/2</sub>)TiO<sub>3</sub>

The present study discusses the fabrication of non-lead ceramic/polymer composites employing (Na1/2Bi1/2)TiO3 (NBT) ceramic powder as a filler and poly(vinylidene fluoride); PVDF as a polymer matrix. The NBT (volume fraction, ϕ = 1) ceramics were synthesized using the conventional mixed-oxide method followed by the high-energy ball milling method whereas (1-ϕ)PVDF/ϕ(Na1/2Bi1/2)TiO3; 0 ≤ ϕ ≤ 0.3 composites were prepared from a melt-mixing process. It was observed that the real and imaginary parts of dielectric permittivity, ac conductivity, and longitudinal piezoelectric charge coefficient increase with the increase in NBT-content. Different dielectric mixing models were presented to determine the effective complex permittivity of the composites. Five dielectric mixture equations have been chosen to test the acceptability of experimental data. It was revealed that theoretical models as given by Bruggman, Rother-Lichtenecker, and modified Rother-Lichtenecker show good agreement with the experimental results of filler-concentration dependent alteration of effective relative permittivity and loss factor of the PVDF/NBT composite. A mathematical model of first-order exponential growth has also been proposed, which fitted excellently the experimental data (r2 > 0.998).

Use of dielectric mixture equations for the characterization of uncleaned peanuts

Dielectric properties measurement plays an important role for peanut quality assessment as it offers a unique characterization for each sample condition. In this study, four dielectric mixture models including linear, quadratic, cubic, and logarithmic equations, were used to characterize the dielectric properties of mixtures of cleaned peanuts and foreign materials. The peanut samples consisted of mixtures of cleaned unshelled peanuts mixed with a single type or multiple types of foreign materials (peanut shells, sticks, raisins (shriveled undeveloped kernels), and stones). The effective dielectric constants of these mixtures of cleaned unshelled peanuts and foreign materials were measured by a free-space-transmission technique at 10 GHz and 23 °C. The effective dielectric constants obtained from the measurements for the mixtures were compared to those calculated by using the four mixture equations. Results for the logarithmic equation provided the best estimates for the dielectric constants of mixtures of unshelled peanuts and foreign materials with a standard error of performance of 2.7%. Therefore, the logarithmic dielectric mixture model can be useful in developing dielectric-based algorithm for foreign material determination.

Effective dielectric properties of Cement/Ba0.06(Na0.5Bi0.5)0.94TiO3 composites: A comparative approach

Lead-free ceramic powder of a morphotropic phase boundary composition Ba0.06(Na0.5Bi0.5)0.94TiO3 (BNBT) was prepared from a solid-state synthesis route. The cement-ceramic (1−ϕ)cement/ϕBNBT; 0 ≤ ϕ 1.0 composites were fabricated. The filler concentration-dependent values of the bulk density and real part of complex permittivity showed an increasing trend of variation while the apparent porosity and imaginary part of complex permittivity followed a decreasing trend. In order to test the acceptability of dielectric mixture equations of the inclusion material in the mixture, five such equations have been chosen. The Bruggeman, and Rother-Lichtenecker equations showed their coherence with minimal deviation from the experimental results of the real part of complex permittivity for the entire measurement range of volume fractions. Also, a first-order exponential growth/decay type of mathematical model was suggested which could fit the experimental data excellently well (r2 > 0.97).

Impedance characterization of elevated temperature carbon dioxide adsorption process on potassium-modified hydrotalcite

The adsorption process is strongly dependent on the dielectric properties of the adsorbent. In this study, electrochemical impedance spectroscopy (EIS) was applied for measuring the dielectric characteristics of CO2 adsorption on hydrotalcite at 400 °C and atmospheric pressure. Compared with the gravimetric method measuring the kinetic properties at different CO2 pressures, EIS proved to be more effective for characterizing the CO2 adsorption process in situ with high sensitivity, distinguishing between physisorption and chemisorption. A model for the dielectric properties of hydrotalcite in the CO2 adsorption process was developed using the kinetic model of CO2 adsorption on hydrotalcite and dielectric mixture equation. The simulation results agree well with the experimental data, demonstrating the potential application of EIS in the study of CO2 adsorption on hydrotalcite.

Electrochemical impedance characterization on catalytic carbon gasification reaction process

The dielectric characteristics of the solid fuels have close relation with gasification process. Electrochemical impedance spectroscopy (EIS), is applied for measuring the dielectric characteristics of solid carbon fuels in catalytic and non-catalytic gasification systems. Compared with kinetic experiments at different gasification temperatures (775, 800 and 825°C) for both catalytic and non-catalytic gasification, EIS spectra is proved to be an effective method to characterize the carbon gasification reaction characteristics in situ with high sensitivity, especially at low carbon conversion ratio. An elementary reaction model for potassium catalyzed carbon gasification combined with a dielectric mixture equation for the simulation of complex permittivity is developed. The modeling results agree well with the experimental data. The dielectric property of catalyzed solid carbon fuels provided by EIS reveals that the polarization intensity contains effective information of gas adsorption and heterogeneous chemical reaction. EIS can possibly be applied as a new methodology in investigating the catalytic carbon gasification reaction and transport processes.

Concentration dependent dielectric properties of Barium Titanate/Polyvenylidene Fluoride (PVDF) and (Bi0.5Na0.5)0.94Ba0.06TiO3/Poly(VDF-TrFE) composite

The present study addresses the problem of quantitative prediction of effective complex relative permittivity of Barium Titanate/Polyvenylidene Fluoride (PVDF) and (Bi0.5Na0.5)0.94Ba0.06TiO3/ Poly(VDF-TrFE) biphasic ceramic-polymer composites. Theoretical results for effective relative permittivity derived from several dielectric mixture equations were fitted to the experimental data taken from the works of Prasad et al. (2010), Wang et al. (2004), Takenaka et al. (1991) and Yamada et al. (1982). The study revealed that out of the different test equations, only a few equations like modified Rother-Lichtenecker equation, Dias-Dasgupta equation or Rao equation for the real part and Bruggeman equation for the imaginary part of complex permittivity well fitted the corresponding experimental results. In the present study, some of the equations were used in their original forms, while some others were modified by choosing suitable shape-dependent parameters in order to get reasonably good agreement with experimental results. Besides, the experimental results have been proposed in the form of a mathematical model using first order exponential growth, which provided excellent fits.

THE USE OF DIELECTRIC MIXTURE EQUATIONS TO ANALYZE THE DIELECTRIC PROPERTIES OF A MIXTURE OF RUBBER TIRE DUST AND RICE HUSKS IN A MICROWAVE ABSORBER

A change in the relative proportions of a mixture of rubber tire dust and rice husks will cause a change in the mixture's electrical permittivity and its ability to absorb electromagnetic energy. An open- ended coaxial probe was used in conjunction with three dielectric mixture equations (the Kraszewski equation, the Landau equation and the Lichtenecker equation) to obtain the dielectric properties of a mixture of rubber tire dust and rice husks (RTDRH) over the frequency range of 7GHz to 13GHz. Lichtenecker's equation for dielectrics proved to be a useful practical formulation for determining the efiective permittivity of homogeneous dielectric mixtures. The efiectiveness of these dielectric mixture equations in determining the efiective permittivity of RTDRH was investigated in this study. A newly developed mixture equation was derived based on these dielectric

Measurement and estimation of aromatic plant dielectric properties. Application to low moisture rosemary

Essential oils are important in the flavour and cosmetic industries. Recently, microwave energy has been applied in different extraction processes to obtain essential oils with quality and yield similar to those obtained using steam distillation, but using less energy and time. The dielectric properties of any given material are of critical importance when seeking to understand its response to applied electromagnetic waves. Nevertheless, data related to aromatic plants are scarce. This paper addresses the measurement and estimation of dielectric properties of herbal matrices as a part of the study of the fundamental phenomenology behind the extraction of essential oils with microwaves. A cavity perturbation system was used to measure the properties of the plant matrix, and dielectric mixture equations were used later to try to reproduce the results obtained. The dielectric properties of partly dried rosemary, rosemary's essential oil and oven-dry plant material were measured at temperatures between 20 °C and 160 °C, and atmospheric pressure, at frequencies of 2450 MHz and 910 MHz. The results show a strong influence of water content on the dielectric properties. A new predictive approach that uses the results from measurements of dielectric properties from the different constituents to obtain effective mixture dielectric properties is proposed. The predicted values of the dielectric constants were better than those of the loss factors.

A comparative approach to predicting effective dielectric, piezoelectric and elastic properties of PZT/PVDF composites

Abstract The present study addresses the problem of quantitative prediction of effective relative permittivity, dielectric loss factor, piezoelectric charge coefficient, and Young's modulus of PZT/PVDF diphasic ceramic–polymer composite as a function of volume fraction of PZT in the different compositions. Theoretical results for effective relative permittivity derived from several dielectric mixture equations like those of Knott, Rother–Lichtenecker, Bruggeman, Maxwell–Wagner–Webmann–Skipetrov or Dias–Dasgupta, Furukawa, Lewin, Wiener, Jayasundere–Smith, Modified Cule–Torquato, Taylor, Poon–Shin and Rao et al. were fitted to the experimental data taken from previous works of Yamada et al. Similarly, the results for effective piezoelectric coefficient and Young's modulus, derived from different appropriate equations were fitted to the corresponding experimental data taken from the literature. The study revealed that only a few equations like modified Rother–Lichtenecker equation, Dias–Dasgupta equation and Rao equation for dielectric and piezoelectric properties while the four new equations developed in the present study of elastic property (Young's modulus) well fitted the corresponding experimental results. Further, the acceptable data put to various regression analyses showed that in most of the cases the third order polynomial regression analysis provided more acceptable fits.

Effective permittivity of random composite media: A comparative study

In the present study, experimental data for effective permittivity of amorphous, polycrystalline thick films, and ceramic form of samples, taken from the literature, have been chosen for their comparison with those yielded by different mixture equations. In order to test the acceptability of dielectric mixture equations for high volume fractions of the inclusion material in the mixture, eleven such equations have been chosen. It is found that equations given by Cuming, Maxwell–Wagner, Webmann, Skipetrov and modified Cule–Torquato show their coherence and minimal deviation from the experimental results of permittivity for all the chosen test materials almost over the entire measurement range of volume fractions. It is further found that Maxwell–Wagner, Webmann, and Skipetrov equations yielded equivalent results and consequently they have been combined together and reckoned as a single equation named MWWS. The study revealed that the Cuming equation had the highest degree of acceptability (errors <±1–5%) in all the cases.

Density-Permittivity Relationships for Powdered and Granular Materials

Relationships between the permittivities of powdered or granular solid materials and their bulk densities (density of the air-particle mixture) are discussed. Linear relationships between functions of the permittivity and bulk density are identified that are useful in determining permittivity of solids from measurements of the permittivity of pulverized samples. The usefulness of several dielectric mixture equations for calculating solid material permittivity from measured permittivity of pulverized samples is also discussed. Results of testing linear extrapolation techniques and dielectric mixture equations on pulverized coal, limestone, plastics, and granular wheat and flour are presented. Recommendations are provided for reliable estimation of solid material permittivities or changes in permittivities of powdered and granular materials as a result of changes in their bulk densities.

DIELECTRIC PROPERTIES OF IN-SHELL AND SHELLED PEANUTS AT MICROWAVE FREQUENCIES

Dielectric properties (..,.. ) of ground samples of in-shell and shelled peanuts (Arachis hypogaea L.) weremeasured for several densities, temperatures, and moisture contents in the range of 300 to 3000 MHz. Dielectric mixtureequations were used to correlate the dielectric properties with density. The coefficients of quadratic and linear dielectricmixture equations are tabulated for 915 and 2450 MHz, for different temperatures and moisture contents. The values of thedielectric constant (..) and loss factor (.. ) of bulk in-shell and shelled peanuts were determined by extrapolation of the firstandsecond-order polynomials that relate .. and .. with density. An equation that determines the dielectric properties ofnominal peanut pods (in-shell peanuts) and kernels (shelled peanuts) as a function of their temperature and moisturecontent was determined by using multiple linear regression.

An impedance model for the estimation of water absorption in organic coatings. Part I: A linear dielectric mixture equation

A capacitance model for the estimation of water uptake in polymeric coatings is presented. The model is based upon a linear combination of the individual capacitances of the polymeric phase, the water and the air contained in the coating. Experimental comparison of the model with gravimetric data has revealed an improvement with respect to the classical equations.

Measurement and calculation of powdered mixture permittivities

The permittivities of pulverized samples of coal and limestone were measured over a range of bulk densities at 11.7 GHz and 20/spl deg/C. The measured values were used, along with particle densities, determined by pycnometer measurements, and the Landau & Lifshitz, Looyenga (LLL) dielectric mixture equation to determine the solid material permittivities. Subsequently, similar measurements were taken on a 35%-65% coal-limestone mixture, and the LLL equation and the complex refractive index (CRI) dielectric mixture equation were used to calculate the permittivities of powdered coal, limestone, and the 35%-65% mixture at various bulk densities. Results compared to the measured permittivities showed that the LLL equation provided much better estimates than the CRI equation, with errors of 0.15% in predicting the dielectric constants of powdered coal, 1.4% in predicting the dielectric constants of powdered limestone, and 0.5% in predicting the dielectric constants of the coal-limestone mixture.

Dielectric Relaxation of Bound Water versus Soil Matric Pressure

The electrical permittivity of soil is a function of the water content, which facilitates water content measurements. The permittivity of soil is also a function of the frequency of the applied electric field. This frequency dependence can be described by the relationship between the dielectric relaxation frequency and the activation enthalpy of the water, which in turn is related to the soil matric pressure. The activation enthalpy or soil matrix pressure is a measure of the binding forces acting on a water molecule in the soil matrix. Each water molecule is differently bound, varying from tightly bound to free water. The permittivity of the bulk soil results from the contribution of all the water molecules in the soil matrix. Therefore, the permittivity of soil as a function of frequency is related to the soil matrix pressure. It is realistic to consider hygroscopic water as ice like. A relatively sharp transition can be observed from free to hygroscopic water at matric pressure – 100 MPa corresponding to relaxation frequency fr ≈ 8 GHz. Therefore, for the interpretation of dielectric data using a dielectric mixture equation, the water content of soil can be split conveniently in “free” water and “hygroscopic” water.

Radio-Frequency: and Microwave Dielectric Properties of Insects

Basic principles and definitions of dielectric properties of materials are presented. Data from the literature on the dielectric properties of insects are briefly reviewed and discussed in relation to insect control by selective dielectric heating. Because early measurements of the dielectric properties of insects were taken on bulk samples of insects (insect and air-space dielectric mixtures), a means for converting the dielectric properties, or permittivities, of bulk samples of particulate materials to those of the solid particles is described. The technique uses the Landau & Lifshitz, Looyenga dielectric mixture equation and information on the bulk densities of air-insect mixtures used for dielectric properties measurements along with the densities of the insects. Such converted data for the dielectric constants and loss factors of the insects are presented and collected for comparison with other measurements of insect tissues and permittivity determinations from more recent microwave measurements of these same parameters. Resulting data are presented for reference, and comparisons are presented and discussed briefly.

New Dielectric Mixture Equation for Porous Materials Based on Depolarization Factors

A change in the relative proportions of the constituents of a porous material like soil will cause a change in its electrical permittivity. The measured permittivity reflects the impact of the permittivities of the individual material constituents. Numerous dielectric mixture equations are published, but none of these equations are generally applicable. A new theoretical mixture equation is derived, using the principle of superposition of electric (E) fields. This mixture equation relates the measured permittivity to a weighted sum of the permittivities of the individual material constituents and includes depolarization factors to account for electric field refractions at the interfaces of the constituents. The depolarization factors are related to physical properties of the material. Most other mixture equations contain one or more empirical factors. The concept of the depolarization factor is comparable with that of the “shape factor” of particles as described by other authors. A special case of the new mixture equation, for which the depolarization factors equals one (no depolarizations), appeared equal to a mixture equation for fluids derived from using thermodynamics. The new mixture equation is compared with other mixture equations. Comparison of the new mixture equation with measured data for glass beads and fine sand was promising. Concluding, depolarization factors in the new mixture equation relate the microstructural and compositional material properties to the measured bulk permittivity of a material. Although not shown, depolarization factors can be calculated from physical material properties.

RF AND MICROWAVE DIELECTRIC PROPERTIES OF STORED-GRAIN INSECTS AND THEIR IMPLICATIONS FOR POTENTIAL INSECT CONTROL

The permittivities of bulk samples of adult insects of the rice weevil, red flour beetle, sawtoothed grain beetle,and lesser grain borer were measured at single frequencies of 9.4 and 11.7 GHz in X-band waveguide at about 23C, andpermittivities of homogenized samples of the same species were measured from 0.2 to 20 GHz at temperatures from 10 to70C with an open-ended coaxial-line probe and network analyzer. Sample densities for the coaxial-line probemeasurements were determined from the X-band measurements with a linear relationship between the cube root of thedielectric constant and sample bulk density determined from permittivity measurements on bulk samples of the adultinsects in a waveguide sample holder taken with the short-circuited line technique. Since linearity of the cube root of thedielectric constant with bulk density is consistent with the Landau & Lifshitz, Looyenga dielectric mixture equation, thisequation was used to calculate estimated dielectric constants and loss factors of the insects from measured permittivitiesand volume fractions determined from measured bulk density and adult insect density determined by air-comparisonpycnometer measurements. Estimated dielectric constants and loss factors of the insects are presented graphically fortemperatures from 10 to 70C, and tabulated data are provided for range information and comparative purposes.

Measurement and Prediction of Dielectric Properties of Biscuit Dough at 27 Mhz

Dielectric properties of baked dough samples of various moisture contents, temperatures and densities were measured at 27 MHz with a parallel plate capacitor connected to an Impedance Analyzer (HP 4194A). As a basis for the dielectric prediction model, statistical equations were developed from measurements of the solid density and the solid dielectric properties of flour-water mixtures at various moistures between 2% and 100% moisture. A square root dielectric mixture equation was selected and combined with the regression equations to give modified prediction equations for the dielectric properties of baked dough as functions of moisture content and bulk density at room temperature. These prediction models were further developed by introducing temperature correction terms. These developed models successfully predicted the dielectric properties ofbaked dough at different moisture content, density and high temperature.