Mixing Law Research Articles

Polarization and structural properties of high-energy electron irradiated poly(vinylidene fluoride-trifluoroethylene) copolymer films

The effect of high-energy electron irradiation on structural and polarization properties of 50/50 mol % copolymer of poly(vinylidene fluoride-trifluoroethylene) was investigated for both mechanically stretched and unstretched films. Although stretching can significantly enhance the polarization and dielectric responses in unirradiated films, it was observed that this enhancement was not significant in irradiated films. In addition, the polarization in both types of films after irradiation can be described quite well by a logarithmic mixing law of composites, which consist of crystallites embedded in an amorphous matrix with nearly the same fitting parameters. On the other hand, the enhancement of the mechanical properties from stretching persists after the irradiation, and the elastic modulus along the stretching direction remains high after irradiation in comparison with unstretched films. It was found that the dielectric dispersion in both types of films after irradiation fits well to the Vogel–Fulcher law. It was also observed that the crystallinity decreases and the crosslinking coefficient increases continuously with dose. However, there was no direct one to one type relationship between the crystallinity and the crosslinking coefficient. Although stretching can reduce the rate of crosslinking, the reduction of crystallinity with dose for stretched and unstretched films does not show a marked difference.

Microwave properties of carbon black-epoxy resin composites and their simulation by means of mixture laws

This article reports on a study of the dielectric properties of carbon black dispersions in an insulating epoxy matrix at microwave frequencies. Measurements showed that the complex permittivity of the composites depends strongly on the nature and concentrations of the conducting medium. The experimental values of the complex permittivity were compared to those obtained by using different mixing laws. We show that effective medium theories correctly account for the experimental results at low conducting particle concentrations. At concentrations higher than a few percent, these laws fail to interpret experimental results and all tentative results must take into account parameters such as the particle size, their distribution, and the existence of agglomerates. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 969–973, 1999

Dielectric properties of periodic heterostructures: A computational electrostatics approach

The dielectric properties of heterogeneous materials for various condensed-matter systems are important for several technologies, e.g. impregnated polymers for high-density capacitors, polymer carbon black mixtures for automotive tires and current limiters in circuit protection. These multiscale systems lead to challenging problems of connecting microstructural features (shape, spatial arrangement and size distribution of inclusions) to macroscopic materials response (permittivity, conductivity). In this paper, we briefly discuss an ab initio computational electrostatics approach, based either on the use of the field calculation package FLUX3D (or FLUX2D) and a conventional finite elements method, or the use of the field calculation package PHI3D and the resolution of boundary integral equations, for calculating the effective permittivity of two-component dielectric heterostructures. Numerical results concerning inclusions of permittivity e 1 with various geometrical shapes periodically arranged in a host matrix of permittivity e 2 are provided. Next we discuss these results in terms of phenomenological mixing laws, analytical theory and connectedness. During the pursuit of these activities, several interesting phenomena were discovered that will stimulate further investigation.

Dielectric permittivity of concrete between 50 Mhz and 1 Ghz and GPR measurements for building materials evaluation

A new dielectric measurement device has been designed and constructed for permittivity measurement of concrete consisting of aggregates of up to 30 mm in diameter. The permittivity is measured in the frequency range 50 Mhz–1 GHz. The samples can be removed from the measurement cell and stored in controlled conditions. The dielectric constant of 0–30 aggregate concrete is measured as a function of hydration level and chloride content. Different mixing laws were compared with the measurements. This comparison shows that volumetric laws such as the complex refraction index model cannot fit the frequency variation and that the Cole–Cole model is the only acceptable one. The influence of chloride content on the permittivity of the concrete is measured and can be used to develop special GPR data processing for the location of salt ingress in civil engineering structures.

Swelling of DGEBA/DDA epoxy resin during hygrothermal ageing

Understanding the swelling behaviour of polymers during hygrothermal ageing is potentially important for both composite materials and structural adhesives, since swelling may significantly influence the mechanical behaviour due to the increase of residual stresses at interfaces. In this article, the swelling of a DGEBA/DDA epoxy resin has been investigated. It has been found that the swelling of the polymer lags behind the behaviour predicted from the ideal mixing law. More importantly, our results show that swelling induced by hygrothermal ageing is not fully reversible, particularly at higher temperatures. Based on the assumption that water diffusion is governed by a classic diffusion controlled process and a swelling controlled process, a model is proposed to describe water uptake and swelling kinetics during hygrothermal ageing. The results show that the model is in good agreement with the experimental values.

Intrinsic Size Effects in a Barium Titanate Glass‐Ceramic

A series of glass ceramics have been synthesized to produce bulk materials with nanometer‐sized barium titanate (BaTiO3) crystals grown in a residue glass matrix. Structure‐property relations have been made to determine the size distribution and the dielectric temperature dependence of the ceramics. Through dielectric and density mixing laws, it has been inferred that depolarization fields limit the dielectric polarizability of the particles and influence the transition temperature. The transition temperature, dielectric anomaly broadening, and peak dielectric constant all scale systematically with the mean size of the BaTiO3 crystals, which is consistent with an intrinsic size effect. In addition, scaling the transition temperature with the Ishikawa relation predicts a critical size of 17 nm, for which BaTiO3 cannot support a ferroelectric transition. These results are discussed in relation to other size studies on ferroelectric materials.

Dielectric constant of water in a porous rock medium

The dielectric constant of water was measured for solid samples of sandstone in the frequency range from 5 Hz to 13 MHz with different water contents at room temperature. The two electrode technique was employed. The measurements were made on three samples with different cementation: loamy, loamy-carbonate and carbonate. For loamy-carbonate-cemented sandstone, two dielectric relaxation times were observed. The dielectric constant of water was estimated from the data by calculations based on the simple mixing law for partial saturation. The dielectric constant and the dielectric relaxation time of water are functions of water volume in a single pore space. The results are interpreted assuming dipole-dipole interactions, dipole-rock matrix interactions and taking into account Debye's theory.

Dielectric properties of dielectrophoretically assembled particulate-polymer composites

The dielectrophoretic effect is a phenomenon in which dipole-dipole interactions are induced between particles in a suspension by an electric field.1−5 This dipole interaction leads to the formation of chains or fibrils parallel to the applied electric field. Recently, the dielectrophoretic effect has been shown to be a possible composite assembly technique permitting property changes to be induced with the appropriate electric fields.6,7 The results presented in this paper show that the dielectrophoretic assembly process can be used to engineer anisotropy into composite materials. Various filler materials are aligned in a thermoset polyurethane matrix and the dielectric properties are measured. Comparisons are drawn between the dielectrophoretically assembled composites and those processed conventionally in the absence of an electric field. Dielectric properties are modeled with modified mixing laws and discussed in relation to the composite microstructure and the alpha relaxations of the polymer phase.

Elastoplastic Constitutive Law for Particle Dispersed Composite Material Accounting for Mesoscopic Inhomogeneity.

The prior theories about elastoplastic constitutive law for particle dispersed composite develop the relation between the average stress and the average strain in multiple phases. In our study, it is found that the local stress distribution in the mesoscale has a great effect on the global property of a composite that undergoes the plastic deformation. The present model considers the distributed stress in standard distribution function in each phase of the composite, where the distribution span is segmented. The macro-stress is linked with the distributed meso-stress by means of the proposed self-consistent compliance mixing law. On the other hand, a meso-mechanics analysis by FEM was conducted to investigate the interaction phenomena occurring in the composite. Also the result was used to provide a reference to the present constitutive model developed in this paper. The developed constitutive model shows an excellent correlation with the reference, thus demonstrates the effectiveness of the present model in both the elastic stage and the plastic stage.

Thickness and volume measurements of a Richtmyer–Meshkov instability-induced mixing zone in a square shock tube

A simultaneous three-directional laser absorption technique for the study of a shock-induced Richtmyer–Meshkov instability mixing zone is reported. It is an improvement of a CO2 laser absorption technique, using three detectors during the same run, through three different directions of the test section, for the simultaneous thickness measurement of the mixing zone near the corner, near the wall and at the centre of a square-cross-section shock tube. The three-dimensional mean front and rear shapes of the mixing zone, its thickness and volume are deduced from the experimental measurements. The cases when the shock wave passes from a heavy gas to a light one, from one gas to another of similar densities and from a light gas to a heavy one, are investigated before and after the mixing zone compression by the reflected shock, for different incident shock wave Mach numbers. It is shown that the mixing zone is strongly deformed by the wall boundary layer when it becomes turbulent. Consequently, the thickness of the mixing zone is not constant along the shock tube cross-section, and the measurement of the mean volume of the mixing zone appears to be more appropriate than its mean thickness at the centre of the shock tube. The influence of the incident shock wave Mach number is also studied. When the Atwood number tends to zero, we observe a limit-like regime and the thickness, or the volume, of the mixing zone no longer varies with the incident shock wave Mach number. Furthermore, a series of experiments undertaken with an Atwood number close to zero enabled us to define a membrane-induced minimum mixing thickness, L0, depending on the initial configuration of the experiments. From the experimental data, a hypothesis about the mixing zone thickness evolution law with time is deduced on the basis of L0. The results are found to follow two very different laws depending on whether they are considered before or after the establishment of the plenary turbulent regime. However, no general trend can be determined to describe the entire phenomenon, i.e. from the initial conditions until the turbulent stage.

Experimental Investigation on the Dielectric Constant of Rocks with Low Porosity and Permeability

Abstract Relation between the dielectric constant of rocks, sampled from the western exploring area of Daqing Oil Field, and water saturation, salinity is developed. Effect of shale and water distribution on the dielectric constant is discussed through experiments on artificial core samples and shale samples. The mixing law that describes the relation between dielectric constant and water saturation is revised and a new one characterized by the area is proposed.

Couple ε, µ Behaviour Study by the Electromagnetic Response of the Composite PVC/Fe3O4 by Time Domain Spectroscopy and Measurements at 10 GHz Versus the Applied Magnetic Field

Using the time domain spectroscopy (TDs) and a 10 GHz three waves reflecto - interferometer (TWRI) with an applied magnetic field, we have measured eμ as a function of the volumetric fraction of the composite material PVC-Fe 3 O 4 . The experimental results are compared to several mixing laws. Further, the moment expansion of the scattering matrix up to fifth order enables us to determine the size parameter as a function of the volumetric fraction.

Dielectric relaxations in liquid-impregnated porous solids

We have studied dielectric relaxation in liquid-impregnated porous solids. The samples were constructed from either glued sand grains or sintered polypropylene beads. We experimentally obtain two relaxations originating from the bulk of the sample. Electrode effects are seen at low frequencies, only for high liquid conductivities. The two bulk relaxations are interpreted as being due to diffusion in the electrochemical double layer surrounding the solid grains, and as a Maxwell–Wagner relaxation due to the heterogeneity of the samples, respectively. The experimental results can be qualitatively reproduced by calculations using the grain consolidation model, which was extended to take into account interfacial effects. The permittivity at high (megahertz) frequencies can be understood by using simple mixing laws. We also propose an equivalent circuit for the electrical properties of a liquid-impregnated porous solid.

A dielectric mixing law for porous ceramics based on fractal boundaries

The effect of porosity on the complex dielectric permittivity of microwave sintered zinc oxide at room temperature and 2.45 GHz is reported. The predictions of conventional Maxwell–Garnet theory and the effective medium approximation are in poor agreement with the experimental results. Various methods are employed to investigate the system in an effort to come up with new mixing laws, including combinations of these two analytic theories and finite difference electromagnetic simulations of representative microstructures. A model that assumes the existence of dielectrically inactive, fractal-geometry boundaries between ceramic grains provides an excellent description of the results with no free parameters. It gives physical insight into the experimentally observed mixing law.

The Dielectric Properties Of Porous Zinc Oxide Ceramics

AbstractMeasurements of the complex dielectric constant of microwave sintered, porous ZnO at 2.45 GHz are presented. The dielectric properties as a function of porosity do not obey the standard Maxwell-Garnet dielectric mixing law with the ceramic material as the major phase, but instead behave as if the ceramic grains always remain in relatively poor electrical contact even at very high densities. Electromagnetic simulations, carried out for a variety of microstructure geometries, are performed to explore this observation. A model which treats the ceramic as an array of grains and pores, with the grains separated from each other by nonor slightly-percolating, fractal-geometry surfaces, provides a good description of the experimental results.

Characterization of humidity-sensing NiONi(OH) 2 nanocomposites by impedance spectroscopy

Nanocomposites of NiO and Ni(OH) 2 prepared by compaction of powders synthesized by rapid thermal decomposition of precursors in solution (RTDS) were characterized by impedance spectroscopy at room temperature. The marked decrease of resistivity with increasing humidity was attributed to an increase of the water phase and ionic transport therein. Electrical behavior was modeled in terms standard electrocomposite mixing laws.

Frequency dispersion and temperature variation of complex permeability of Ni-Zn ferrite composite materials

Permeability spectra in Ni-Zn ferrite composite materials were studied at the volume loading of ferrite above 30% and at temperatures from 100 to 400 K. The permeability decreased with decreases in the volume loading of ferrite. This decrease was much larger than that expected from the empirical mixing law. This was attributed to the demagnetizing field, generated by the magnetic poles on the surface of the ferrite particles. Simultaneously, the demagnetizing field increased spin resonance frequency. For the sintered ferrite, the primary peak of the permeability was just below the Curie temperature. The peak becomes obscure and disappeared as the volume loading decreased. The temperature dependence of the spin resonance frequency was lower in the ferrite composite material than that in the sintered ferrite. These features were also discussed from the view point of the demagnetizing field.

The use of mixing laws for modelling the climatic ageing of dielectric materials

The prediction of the properties of polymers in contact with water is important for many applications. In this paper two kinds of materials are investigated: an epoxy resin and its glass fibre composite. The measured complex dielectric constant is analysed with different effective medium models, taking into account the variation of water uptake according to time. Since the mixing laws do not describe the experimental results accurately, three new models are proposed, based on the assumption of a time-varying dielectric constant of the matrix during water immersion. They all give a better agreement between measurement and theory. In order to check their validity, these models are also applied to other data sets, found in the literature, and good correlations are found. Finally, we discuss the conclusions that one may derive from this kind of modelling, since many factors can influence the permittivity. Nonetheless, the new models are able to predict the variation of the dielectric constant for water immersion ageing.

Rock/water interaction in dielectric properties: Experiments with hydrophobic sandstones

The dielectric constant of a partially saturated sandstone varies as a function of the level of water saturation. Experimental data indicate that rock/water interaction, at low saturations, has a large effect on the measured dielectric response. To theoretically predict the dielectric constant of the rock/water/air system, this rock/water interaction must be accounted for by including the effect of the water wetting the rock solid. Alternatively, if the rock/water interaction can be eliminated, a three‐component (dry rock, water, and air) mixing law can be used to model the dielectric behavior. In this laboratory study, a chemical treatment is used to change four water‐wet sandstones into hydrophobic sandstones. In three hydrophobic samples the rock/water interaction, seen in the data for the water‐wet samples, is eliminated and the dielectric constant of the partially saturated sandstones can be simply modeled as a dry rock/water/air system. This experimental study illustrates the importance of the chemical state of the rock surfaces in determining the dielectric behavior of sandstones.

Sensor for determining the water content of oil-in-water emulsion by specific admittance measurement

It is important to know the water content of oil-in-water emulsions for applications such as oil transportation. A new on-line sensor has been designed for this purpose. The real part of the specific admittance is used for the water-content determination. A simplified Van Beck mixing law and an appropriate frequency are applied to obtain the water content without polarization effects. Adaptive compensation is used in order to compensate temperature and salinity changes. On-line real-time parametric identification of conductivity versus temperature deviations observed in the water used in the emulsion is implemented. A microprocessor-based system with an open architecture and modular scheme allows the implementation of the electronic instrumentation and algorithms needed. Other features, such as auto-zero and auto-range, give the instrument a good performance and versatility for a wide range of salinities.