An interlayer model for the complex dielectric constant of composites: An extension to ellipsoidally shaped particles

A theoretical interlayer model (IL) has been developed for the complex dielectric constant of a composite in which the filler particles are enveloped with a layer of interfacial material. The filler particles can be of any ellipsoidal shape. Special cases such as spherical particles, needles, and fabrics are shown to be covered by the model.The analytical formula as derived describes the composite properties as a function of the volume fractions of the filler, the layer and the matrix material, their dielectric properties and the filler particle shape factor.In the case of a two-phase composite the model reduces to the well-known Sillars relation for the complex dielectric constant of composite which contains filler particles of ellipsoidal shape.The effect of an interfacial layer on the static dielectric constant of the composite is discussed using the model. Next, the special case of a conductive interfacial layer in an otherwise non-conductive composite is discussed; it illustrates the effect of interfacially adsorbed water on the electrical properties of composites. Some practical examples are shown.     

Numerical analysis of complex dielectric mixture formulae

As a continuation of our earlier work (Ref. [9]) the complex (frequency dependent) dielectric behaviour of some mixture formulae are studied numerically. These include matrix-inclusion type formulae (as the Wagner-Sillars or the Bruggeman-Boyle equations), mean-field statistical mixture formulae (as the Böttcher-Hsu equation) and symmetrical integral formulae (as the Looyenga equation). The frequency dependent dielectric properties are first calculated for a model system at various particle shapes, field orientations and volume fractions. After this, the validity of these equations is checked on typical sets of experimental data. For low loss powders, the Böttcher and Looyenga equations are suggested; for emulsions, suspensions and filled polymers, the matrix-inclusion type formulae give acceptable results in most cases, while for metal-insulator composites mean-field statistical mixture formulae have to be used, as they are capable of describing the percolation phenomenon.     

DC dielectric study of polyethylene/CaCO3 composites

The dielectric properties of composite samples prepared by polymerizing ethylene on the surface of filler are compared to those of mechanical mixtures consisting of CaCO₃ and ultra high molecular weight polyethylene. After presenting the normalized master curves of AC dispersion and loss measured at different relative humidities, the field strength dependence of the 50 Hz AC and DC responses were studied. With one exception, the effect is small. Thermally stimulated polarization (TSP) and depolarization (TSD) curves are presented; the peak appearing on the TSP curves of the samples stored under ambient conditions is interpreted as a result of water desorption. The high temperature DC conductivity and the depolarization current density are higher in the composites and mechanical mixtures than in the matrix. The dielectric properties of the wet filler particles were calculated from the measured composite and matrix data using various mixture formulae. The results can be understood and interpreted if the dielectric properties of adsorbed water are described by the cluster theory of dielectric relaxation.     

Interfacial polarization in composite materials with spherical fillers: characteristic frequencies and scaling laws

The dielectric properties of composite materials consisting of a host matrix filled with spherical particles are investigated as a function of frequency by means of numerical calculations. Two different cases are analyzed: (a) composites with a conductive matrix and insulating fillers and (b) composites with an insulating matrix and conductive fillers. In both situations, dielectric dispersions due to interfacial polarization effects are observed in the dielectric spectra. In the present contribution, the characteristic frequencies of interfacial polarization effects are systematically analyzed in dependence on the volume fraction of the spherical fillers and on the conductivity values of the composite phases. The resulting scaling laws are discussed in detail.     

Viscoelastic properties of polyacrylonitrile particles stabilised by a poly-2-vinylpyridine/polytert butylstyrene block copolymer

The viscoelastic properties of a dispersion of polyacrylonitrile particles stabilised by a block copolymer poly-2-vinylpyridine/polytert butylstyrene dispersed in solvesso have been measured as a function of particle concentration and frequency at ambient temperatures. At low volume fraction of particles it was found that the loss modulus of the dispersions was larger than the storage modulus, whilst at volume fractions > 0.40 the storage modulus dominates the rheology. This is attributable to there being a steric repulsion between the particles as a result of an increasing concentration of particles and the resultant reduction in interparticle separation in the dispersion. In addition the observed exponential increase of the storage modulus with increasing particle volume fraction mirrors the exponential increase in force with decreasing surface separation of the same type of polymers adsorbed to mica.     

Double percolation effect on the electrical conductivity of conductive particles filled polymer blends

Electrical conductivity of carbon black (CB) filled polymer blends which are incompatible with each other was studied as a function of the polymer's blend ratio. Transmission electron microscope (TEM) analysis shows that CB distributes unevenly in each component of a polymer blend. TEM photographs of phase structure of solvent extracted HDPE/PMMA blend and solvent extraction experiments of PMMA/PP blend detect the blend ratio at which the structural continuity of filler rich phase is formed. The electrical conductivity of polymer blends is found to be determined by two factors. One is the concentration of CB in the filler rich phase and the other is the structural continuity of this phase. This double percolation affects the conductivity of conductive particle filled polymer blends.     

Investigations of the influence on the phase morphology of PP-EPDM-blends on their mechanical properties

This work covers the dependence of the mechanical properties of polymer blends on their composition and their phase morphology. Blends of EPDM-elastomers and polypropylene were prepared covering the whole concentration range. The phase morphology was varied strongly by employing different mixing techniques and its morphology was characterized by means of electron microscopy and light microscopy, as well as by x-ray scattering and calorimetry.Mechanical properties such as the complex shear modulus, the tensile modulus as well as the stress strain behavior were investigated as a function of the composition of the blends and their phase morphology. The experimental finding is that the complex modulus, the tensile modulus, the yield stress, and the ultimate stress are rather insensitive with respect to the phase morphology and vary continuosly with the composition. The elongation at break, on the other hand, as well as the impact strength were found to depend on the phase morphology and to vary discontinously with the composition. One conclusion to be drawn is that one is not always forced to control the phase morphology tightly during processing in order to obtain materials with sufficiently good mechanical properties. Rather, simple theoretical approaches, neglecting details of the phase morphology are frequently able to satisfactorily predict mechanical properties of multiphase blends.     

The exact shear modulus of particulates based on the concept of mesophase

An accurate relationship for the shear modulus of particulates is derived based on the Kerner model, but not using its approximate relations. Furthermore, the model takes into account the existence of the mesophase layer between the inclusions and the matrix, which acts as a smooth transition boundary layer between constituent materials. By applying Christensen's field to the Kerner model, modified by introducing the mesophase, the new model is liberated from any inconsistencies. Experimental evidence and application to a glass particle-epoxy resin-matrix composite indicated the superiority of the model over previous ones.     

The effect of coating on the stiffness and toughness of encapsulated fiber composites

The effect of the coating of the fiber on the stiffness and toughness of composite materials is presented in this paper. The type of composite material considered is of a macroscopically isotropic composite medium containing coated fibers. The models used to simulate such materials consists of: the cylindrical fiber, a cylindrical annulus of the coating, an annulus of the matrix enveloped by an infinite region of an equivalent composite consisting of a transversely isotropic material and representing the real composite with dispersed coated fibers. Solutions for the longitudinal, transverse and shear elastic moduli in the four-phase model were established assuming linear elastic conditions. The results were found to depend on the extent and the mechanical properties of the coating. The stiffness and toughness of the composite were evaluated in models representing plane-stress equatorial sections of the representative volume element of the real material according to the Hashin-Rosen model. The stiffness of the fiber composites was studied by varying the rigidity and the extent of the fiber-coating in the model and evaluating its influence on the overall mechanical behavior of the model. On the other hand, the toughness of the composite was evaluated by the method of caustics in models made of composite PMMA plates with PMMA inclusions coated with a ductile annulus. Interesting results were derived concerning the influence of the soft annulus on the mechanical behavior of the composite.     

Relationship between electrical resistivity and particle dispersion state for carbon black filled poly (ethylene-<Emphasis Type="Italic">co</Emphasis>-vinyl acetate)/poly (<Emphasis Type="SmallCaps">L</Emphasis>-lactic acid) blend

It is known that the electrical volume resistivity of insulating polymers filled with conductive fillers suddenly decreases at a certain content of filler. This phenomenon is called percolation. Therefore, it is known that controlling resistivity in the semi-conductive region for carbon black (CB) filled composites is very difficult. When poly (ethylene-co-vinyl acetate) (EVA) is used as a matrix, the percolation curve becomes gradual because CB particles disperse well in EVA. In this study, the relationship between the dispersion state of CB particles and electrical resistivity for EVA/poly (L-lactic acid) (PLLA) filled with CB composite was investigated. The apparent phase separation was seen in the SEM photograph. It was predicted that the CB particles located into the EVA phase in the light of thermodynamical consideration, which was estimated from the wetting coefficient between polymer matrix and CB particles. The total surface area per unit mass of dispersed CB particles in the polymer blend matrix was estimated from small-angle X-ray scattering and the volume resistivity decreased with increasing CB content. The values of the surface area of CB particles in CB filled EVA/PLLA (25/75 wt%) and EVA/PLLA (50/50 wt%) polymer blends showed a value similar to that of the CB filled EVA single polymer matrix. In electrical volume resistivity measurement, moreover, the slopes of percolation curves of EVA/PLLA (25/75 wt%) and EVA/PLLA (50/50 wt%) filled with CB composite are similar to that of EVA single polymer filled with CB composite. As a result, it was found that CB particles selectively locate in the EVA phase, and then the particle forms conductive networks similar to the networks in the case of EVA single polymer used as a matrix.     

Dynamics of hydrogen bond complexes in polymer melts

The dynamics of hydrogen bond complex formation between functional groups which are attached to a polymer chain, is studied in the molten state. The concentration of complexes in the thermodynamic equilibrium is distorted by the application of a large oscillatory strain in the nonlinear viscoelastic regime. The relaxation back to the thermodynamic equilibrium is studied as a function of the temperature in the linear viscoelastic regime. From the mechanical response the kinetic analysis can be performed using a modified Doi-Edwards theory. Using the equilibrium constants obtained from IR-spectroscopy, the rate constants for complex formation and decomplexation are obtained. The temperature dependence is equivalent to the temperature dependence of the zero shear viscosity which implies that complex formation is a diffusion-controlled process.     

Study of the polymer latex coalescence by dielectric measurements at microwave frequency—feasibility of the method

The measurement of the complex dielectric constant ( ^*=–j) in the dipolar absorption domain of the free water molecule (microwave region) permits us to follow quasi-specifically and precisely the water circulation during the coalescence process of a latex. Weight losses and dielectric constants variations have been simultaneously recorded upon latex drying, in a resonant cavity at 5 and 9 GHz and under controlled atmosphere and temperature. Two different latexes were studied (polybutylacrylate (PBuA) and polystyrene (PS)) from which the glass transition temperature effect was investigated. It is found that the harder the polymer particles, the more clearly evidenced the flocculation and packing points are. This method appears to be quite reliable for discriminating the various steps in the film formation process of latexes.     

Ag负载KTa1-xNbxO3-BaTiO3颗粒掺杂P(VDF-TrFE-CTFE)复合材料的制备及介电性能

通过光照还原法制备了银颗粒负载的铌钽酸钾-钛酸钡复合粉体（Ag/KTN-BT）,并将其与聚偏氟乙烯-三氟乙烯-三氟氯乙烯（P（VDF-TrFE-CTFE））聚合物复合,获得Ag/KTN-BT聚合物基复合材料。研究发现,Ag/KTN-BT填料颗粒在聚合物基体中分散均匀,复合材料结构致密,无明显气孔和裂纹,且具有较好的柔韧性。银纳米颗粒的负载,一方面在复合材料中引入了额外的界面,导致界面极化作用增强,明显提高复合材料的介电常数;另一方面银纳米颗粒的量子尺寸效应和库伦阻塞效应使得复合材料保持较低的介电损耗。当填充体积分数为20%的Ag/KTN-BT颗粒时,聚合物基复合材料的介电常数大幅提升,从聚合物的37提升到125（100 Hz）,介电损耗仅为0.12。与KTN-BT基复合材料对比,Ag/KTN-BT基复合材料也显示出较好的介电性能。     

Electrical properties of carbon black‐filled polymer composites

This work deals with the dielectric properties of conductive composite materials, which consist of thermoplastic polypropylene (PP) matrix filled with carbon black (CB). The CB concentration was systematically varied in a wide range. Our main interest is focused on the investigation of electrical conductivity mechanism and related percolation phenomena in these materials. To study the electrical and dielectric properties of composites we used broadband ac dielectric relaxation spectroscopy (DRS) techniques in a wide temperature range. By measurements of complex dielectric permittivity, ϵ*, the dependence of ac conductivity, σ_ac, and dc conductivity, σ_dc, on the frequency, the temperature and the concentration of the conductive filler was investigated. The behavior of this system is described by means of percolation theory. The percolation threshold, P_C, value was calculated to be 6.2 wt.% CB. Both, dielectric constant and dc conductivity follow power‐law behavior, yielding values for the critical exponents, which are in good agreement with the theoretical ones. Indications for tunneling effect in the charge carriers transport through the composites are presented. The temperature dependence of dc conductivity gives evidence for the presence of positive temperature coefficient (PTC) effect.     

On the observation of micellar structures by dielectric spectroscopy

Many cationic surfactants form, in the presence of certain organic acids, large supramolecular micellar structures in water. The dielectric response of one such system (cetyl trimethyl ammonium bromide-salicylic acid, CTMAS) has been studied as a function of frequency, concentration and temperature. The results are compared with dynamic mechanical data on the same system, which has been published in the literature.The dielectric response shows that the micelles form a rigid, open network structure, which does not impede ionic transport in the bulk liquid. However, the response also shows the presence of a frequency dispersive barrier capacitance. From the variation of the properties of this capacitance with CTMAS concentration and applied voltage over a range of frequencies, it is deduced that the barrier originates in an ordered micelle structure at each electrode.     

Dielectric Properties of Polymer Composites Filled with Different Metals

Electrically conductive composite systems based on polyvinyl chloride (PVC) and polymethyl methacrylate (PMMA) filled with metal powders of Al and Cu have been studied. The composite preparation conditions allow the formation of a random distribution of metallic particles in the polymer matrix. Dependence of the dielectric and conductivity properties of the PVC and PMMA/fillers was studied over a broad range of frequency and volume fraction of metal fillers. The experimental results could be explained by means of the conductivity of fillers and the interface polarization between polymers and fillers. Percolation was also seen in this study when the volume fraction of conducting fillers was close to critical value, in which the composites undergo an insulator‐conductor transition. The relation among the dielectric property and the fillers with different conductivity was proposed.     

Relation between syneresis and rheological properties of particle gels

The relation between the tendency to exhibit syneresis of rennet (pH 6.65) and acid (pH 4.6) skim-milk gels and the rheological properties of these gels is discussed. Based on the syneresis model for milk gels of Van Dijk and Walstra [1, 4, 14, 19] it is reasoned that the average lifetime of the protein-protein bonds in the casein strands forming the gel network, the fracture force of these strands, and their flexibility are the main mechanical properties of importance. It is argued that the ratio of the loss modulus to the storage modulus (tan δ) as a function of the time scale of the measurement in dynamic experiments is a good measure of the first property. Results are given for rennet skim-milk gels at 25, 30, and 40°C and for an acid skim-milk gel at 30°C. Moreover, the stress strain relation and fracture behavior of both gels were assessed in creep measurements as a function of the duration of the applied stress. Rennet skim-milk gels have a lower fracture stress σ _f and therefore probably a lower fracture force per strand and a higher tan δ over long time periods than acid gels, while tan δ increases with temperature. As predicted, low fracture stresses and high tan δ correlated with an increased tendency to exhibit syneresis.     

Effect of intercalation of metal ions on the colloidal and solid properties of vanadium pentaoxide hydrate,V2O5 nH2O

The colloidal stability of V₂O₅ nH₂O was studied on the basis of the measurements of critical flocculation concentration (CFC) by metal ions, amount of ions exchanged (or intercalated), and -potential. In total, the CFC values obeyed the Schulze Hardy law and strong Hofmeister's series was found in the systems including alkaline ions. The sequence of colloidal stability of V₂O₅ nH₂O in the electrolyte solutions was related to the intercalation of metal ions in the interlayer spaces of the solid. The largest CFC value for Li⁺ (87 mmol dm^–3) was explained by smaller affinity of Li⁺ to be intercalated in V₂O₅ nH₂O as well as smaller Hamaker constant of the intercalated solid compared to the other systems.Effect of intercalation of metal ions on the crystalline properties of the materials was measured by use of XRD and electron microscope. Under highly dehydrated condition the ions whose radii are smaller than 0.1 nm are captured in the structure of V₂O₅ nH₂O without changing interlayer distances, while those larger than 0.1 nm increase the interlayer distance. In a saturated H₂O vapor interlayer distances increased with increasing charge of intercalated ions. However, when intercalated with ions carrying the same valency the interlayer distances of the sample decreased with decrease in the hydration property of ions. Hydrolyzable Cr³⁺ gave exceptionally larger interlayer distances, both in a vacuum and in H₂O vapor.     

Dielectric properties of moist CaCO3 filled polyethylene composites

The capacitance and the dielectric loss tangents of CaCO₃ filled polyethylene composites were studied. Composite samples, prepared by polymerizing ethylene on the surfaces of fillers, pre-treated by polymerization catalysts, were compared to normal mechanical mixtures. Dielectric dispersion,, and loss, , proved to be sensitive to heating or vacuum treatment. Investigation of samples under conditions of different relative humidities showed that the dielectric dispersion is due to adsorbed water. Both and increased with decreasing frequency and the ratio of loss and dispersion was nearly constant. Dielectric data measured at different relative humidities could be represented by a single Cole-Cole plot. Samples soaked in water for different periods yielded qualitatively similar but quantitatively different Cole-Cole plots. Composite samples showed higher losses at similar humidities.Possible interpretations in terms of a molecular relaxation model, an interfacial relaxation model, including a charged double layer mechanism, percolation theory and the universal response theory were examined, but none was able to fully explain the observed phenomena.     

Studies of thermally stimulated current in polypropylene/calcium carbonate/surfactant systems

Thermally stimulated polarization (TSP) and depolarization (TSD) experiments have been performed with two grades of polypropylene and some respective CaCO₃-filled composites containing small amounts of nonionic surfactant (0–2 wt%). The effects of electrode blocking, electrode materials on the thermally stimulated currents, and reproducibility of the measurements have been studied. The effect of water vapor adsorbed from the ambient air on the AC dielectric properties and on the thermally stimulated polarization behavior has been determined.The addition of either CaCO₃ or surfactant to PP decreases the intensity of the _c depolarization current peak in the pre-melting region, while the presence of both components increases the current. Partial discharges are present in poly propylene/CaCO₃ composites under high voltages if neither water vapor nor a coherent surfactant layer is present at the matrix/filler interface.A short literature survey is presented on the TSC studies of polyolefins and their composites, and various mechanisms responsible for the observed changes are discussed, including interfacial polarization, trap redistribution through nucleation, and oriented adsorption.