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.     

The electrical properties of heterogeneous mixtures containing an oriented spheroidal dispersed phase

Theoretical equations for the permittivity and conductivity of a heterogeneous mixture containing an oriented dispersed phase of spheroidal shape are limited to low volume fractions of dispersed phase. Two new sets of equations have been derived here for such systems using approaches which have been shown previously to be applicable to higher concentrations. One set has generalised forms of equations given by Bruggeman and Hanai and includes simplifications applicable to oil in water (O/W) and water in oil (W/O) systems. The other set has generalised forms of an equation given by Looyenga. Tabulated mixture permittivityε and dielectric incrementΔε values are presented and, with the exception ofO 〈W systems containing prolate spheroids, the two types of equation show significant differences in bothε andΔε. For both typesΔε is strongly dependent on the ratio of the conductivities of the two media of aW/O system. The relevance of the mixture equations to the electrical behaviour of micellar, microemulsion and liquid crystalline systems is considered.     

Dielectric properties of solutions of tetra-iso-pentylammonium nitrate in dioxane-water mixtures

Dielectric properties of solutions of tetra-iso-pentylammonium nitrate, i-Pen ₄ NNO ₃ . in various dioxane-water mixtures have been studied using dielectric time domain spectroscopy (TDS). The static permittivity of the solutions _s increases for low concentrations of solute but levels off to asymptotic values at higher concentrations. The limiting sloped_s dc, and the asymptotic value depend on the static permittivity of the solvent mixture. The relaxation time due to the solute varies with solute concentration and depends on the solvent mixture. In the solvent mixtures of lowest permittivity the plots of relaxation time vs. concentration go through a maximum, while in the mixtures of highest permittivity the relaxation time initially decreases and then levels off to an asymptotic value. The concentration dependence of the dielectric parameters is discussed in relation to ion association.     

Role of electrostatic interaction in the processes of complex formation

Aspects of the theory of associate mixtures formed as a result of electrostatic interaction between their components are discussed. We obtained equations, convenient for comparison with the experiment, that elucidate the dependence of the association constant on the dielectric susceptibility of the solvent. The experimental results of the associates studied, which were composed of a diazo-salt cation and an anion of a xanthene dye, are described satisfactorily by the theoretical dependences, but with a smaller equilibrium distance between the associate component. We have shown that the smaller equilibrium distances are due to the fact that the dependence of the dielectric susceptibility of the solvent on the distance (r) for small distances between the interacting ions is not taken into account in the qualitative theory.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 5, pp. 591–596, September–October, 1986.     

Etude de phases quaternaires Winsor IV. Diagrammes de phases et propriétés electriques

A comparative study of phase diagram features and electrical properties of Winsor IV phases (so-called microemulsions) led to define two types of quaternary systems involving water, a hydrocarbon, and an ionic surfactant/alcohol combination defined byk, the surfactant/alcohol mass ratio. Systems of the first type exhibit a Winsor IV domain consisting of two disjointed areas corresponding to water-in-oil (w/o) and oil-in-water (o/w) monophasic fluid transparent isotropic media. The w/o and o/w areas are separated by a composition zone over which exist viscous turbid long-range organized structures related to the o/w w/o phase inversion mechanism. In that case, over the w/o area, the low frequency electrical conductivity and permittivity undergo non-monotonous changes as the composition varies. From conductivity maxima and minima, it is possible to define in the general case two lines ₁ and ₂ separating three adjacent sub-areas to which can be assigned compositions representing pre-micellar entities, inverted swollen spherical micelles and micelles clusters. For systems of the second type, the w/o and o/w sub-areas merge so as to form a unique monophasic area, which implies that the w/o o/w phase inversion occurs through a progressive diffuse mechanism. In that case the conductivity exhibits much higher values than in the preceding situation, and its variations with composition allow to define two linesC _d andC _m partitioning the Winsor IV domain into three adjacent areas. AboveC _d , that is for low and medium water contents, the conductivity variations with water content follow equations derived from the Percolation and Effective Medium theories, which indicates that the w/o swollen spherical micelles are submitted to attractive interactions. Below C_m, i. e. in the water rich region, the conductivity decrease with water content results from the progressive dilution of the external aqueous phase of the o/w Winsor IV media. BetweenC _d andC _m , the Winsor IV media exhibit an anomalous conductive behaviour which suggests that they are neither w/o nor o/w systems. This region can be considered as the diffuse phase inversion zone over which the systems are in a hybrid state that could be depicted tentatively as resulting from the formation of equilibrium bicontinuous structures.

     

Computer simulation of interfacial polarization in stratified dielectric systems

Time and frequency dependent dielectric properties of bilayer dielectrics are treated with components showing dielectric relaxation. The time dependent behaviour can be calculated using the Boltzmann superposition principle. The exact integro-differential equations are derived, and the boundary conditions discussed. The analytical formulae resulting for the frequency domain are an extension of those published for bilayer dielectrics with nonrelaxing components. For the time domain the numerical solution is preferred because the analytical solution is very complicated. After a short discussion of the numerical method some examples are presented, and the effect of various component parameters on the dielectric properties is studied.The main conclusion is that two types of interfacial polarization mechanisms must be distinguished: the classical ohmic, and the dielectric. The latter is the consequence of the polarizational surface charge density, and influences strongly the observed relaxation strengths of the components.Presented at the 20. Jahrestagung Organische Festkörper, July 1983, Brandenburg, German Democratic Republic     

The Goldstone mode in mixtures containing ferroelectric liquid crystals

Measurements of complex electric permittivity of room temperature ferroelectric liquid crystal mixtures have been made on aligned samples with the electric measuring field being parallel to the layer planes. The spontaneous polarization, the tilt angles and pitch have been measured in these mixtures. By theoretical fitting of the experimental points of electric permittivity for the Cole-Cole modification of the Debye equation dielectric parameters, the dielectric strength, relaxation frequency, and distribution parameter for the Goldstone mode have been computed. The dielectrically observed Goldstone mode in our mixtures is shown to have both DC bias field and AC field dependences.     

Dielectric properties near the isotropic-smectic-C* phase transition

The dielectric properties in the vicinity of the isotropic-smectic-C* phase transition in ferroelectric liquid crystals are discussed. The temperature and frequency dependence of the complex dielectric permittivity in both the phases of the transition are calculated. The theoretical phase diagram of the dielectric permittivity is studied.     

Dielectric properties for the binary mixture of dimethylsuphoxide and dimethylacetamide with 2-nitrotoluene at microwave frequencies

The dielectric properties of various organic solvents and binary solvent mixtures at different temperatures over the frequency range of 10 MHz–20 GHz, are investigated using the time domain reflectometry technique, at various temperatures from 15 to 45 °C. These solvent mixtures—dimethylacetamide–2-nitrotoluene and dimethylsulphoxide–2-nitrotoluene as well as pure solvents display a Debye type dispersion. Their frequency-dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters, for these solvent systems at various temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The static permittivity increases with increase in volume percentage of 2-nitrotoluene in dimethylacetamide as well as dimethylsulphoxide whereas the relaxation time decreases for both the systems.     

Dielectric Relaxation and Thermodynamic Studies of Binary Mixtures of 2-Nitrotoluene with Primary and Secondary Alcohols at Different Temperatures

The dielectric complex spectra of 2-nitrotoluene with primary or secondary alcohol binary mixtures were studied over the frequency range of 10 MHz to 20 GHz for the whole solute mole fraction range at four different temperatures. An unusual suppression phenomenon was observed in the real and imaginary parts of the mixture complex spectrum, which are smaller than those for the pure alcohols, at low solute concentrations. The dielectric constant and dielectric relaxation time values were obtained by fitting the complex dielectric spectrum data to the single Debye model using a non-linear least squares method. The dielectric constant of mixtures decrease with the increasing mole fraction of 2NT in both the primary alcohols and secondary alcohols; the dielectric relaxation time decreases for all the five binary systems. Using the dielectric data, derived dielectric parameters, namely: the excess dielectric constant, excess inverse relaxation time, effective Kirkwood correlation factor, molar activation enthalpy and molar activation entropy, were calculated. The non-linear variation of permittivity (?₀) reveals the change in size and shape of hetero-molecular complex due to intermolecular H-bond interaction. The negative variation of the excess permittivity constant confirms that the dipoles form multimer structures with anti-parallel ordering of unlike dipoles. The molar activation enthalpy was found to be higher at 0.2 mol fraction of 2NT for primary alcohol binary system. To confirm the molecular function group interaction, a FT-IR spectroscopy study was carried out at 298 K. The FT-IR analysis confirmed the formation of hydrogen bonds between the hydrogen atom of hydroxyl groups of the alcohols and the oxygen atom of nitro groups of 2NT in the binary mixtures.     

The Goldstone mode in mixtures containing ferroelectric liquid crystals

Abstract

Measurements of complex electric permittivity of room temperature ferroelectric liquid crystal mixtures have been made on aligned samples with the electric measuring field being parallel to the layer planes. The spontaneous polarization, the tilt angles and pitch have been measured in these mixtures. By theoretical fitting of the experimental points of electric permittivity for the Cole–Cole modification of the Debye equation dielectric parameters, the dielectric strength, relaxation frequency, and distribution parameter for the Goldstone mode have been computed. The dielectrically observed Goldstone mode in our mixtures is shown to have both DC bias field and AC field dependences.     

Solution properties of octyl β-D glucoside. Part 1: Aggregate size. shape and hydration

Aqueous solutions of octyl--D-glucoside have been examined in a wide concentration range. By combining information from density, viscosity and dielectric permittivity, the transition from molecular to micellar state has been evidentiated. Classical equations for the viscosity colloidal dispersions have been reexamined and applied to get information on micelle shape. A combined analysis of dielectric and viscosity findings indicates a slight and continuous dependence of micellar shape on surfactant content. The role of hydration on micellar stability is significant.     

A boundary element method for molecular electrostatics with electrolyte effects

A boundary element method is developed to compute the electrostatic potential inside and around molecules in an electrolyte solution. A set of boundary integral equations are derived based on the integral formulations of the Poisson equation and the linearized Poisson-Boltzmann equation. The boundary integral equations are then solved numerically after discretizing the molecular surface into a number of flat triangular elements. The method is applied to a spherical molecule for which analytical solutions are available. Use is made of both constant and linearly varying unknowns over the boundary elements, and the method is tested for various values of parameters such as the dielectric constant of the molecule, ionic strength, and the location of the interior point charge. The use of the boundary integral method incorporating the nonlinear Poisson-Boltzmann equation is also briefly discussed.     

Dielectric relaxation and hydrogen bonding studies of chlorobutane-dioxane mixtures using a time domain technique

Complex permittivity spectra have been computed for the binary mixtures of Chlorobutane (CLB) with 1, 4-Dioxane (DX) using Time Domain Reflectometry (TDR) for different concentrations and temperatures in the frequency range from 10 MHz to 30 GHz. The static dielectric permittivity and relaxation time have been obtained by fitting complex permittivity spectra to the Debye relaxation using least squares fit method. The Kirkwood correlation factor have been determined at various concentrations of 1, 4-dioxane. The Bruggeman model for the non-linear case has been fitted to the dielectric data for the mixtures.     

Structural,electrostatic, and thermodynamic properties of the surface of spherical micelles in solutions of sodium <Emphasis Type="Italic">n</Emphasis>-alkyl sulfate homologues. II. Electrostatic and thermodynamic characteristics

The structural characteristics of micelles from our previous work (Part I) are used to calculate the electrostatic energy of ions in the electric double layer on the surface of spherical ionic micelles in solutions of sodium n-alkyl sulfate homologues with the following number of carbon atoms in the molecule: n _C = 8, 10, 12, and 14. This energy is found to depend on the thickness of the electric double layer and its average radius on the surface of a micelle, the aggregation number, the degree of binding of counterions, and the dielectric constant. The developed semi-empirical method is used to calculate interfacial tensions in spherical micelles for the said homologues in solutions at their critical micellar concentrations and T = 303 K. These values are split into the contributions from the hydrophobic and electrostatic components. The electrostatic component of the interfacial tension in spherical micelles is compared with the expression for the ion–ion repulsion energy to obtain the values of static permittivity (dielectric constant) in the surface layer of micelles.     

Identification of dielectric and structural relaxations in glass-forming secondary amides

Dielectric relaxation dynamics of secondary amides is explored in their supercooled state near the glass transition temperature Tg by investigating N-ethylacetamide and its mixtures with N-methylformamide. All the samples are found to exhibit giant dielectric permittivities, reaching over 500 in N-methylformamide-rich mixtures around Tg. For both the neat and binary systems, the predominant relaxation peak is of the Debye-type throughout the viscous regime, which is an unexpected feature for a glass former with intermediate fragility. The present results combined with the earlier reported high-temperature data reveal that the dielectric strength delta epsilon(D) of the Debye relaxation extrapolates to zero at frequencies of 10(10)-10(11) Hz, which is about two orders of magnitude lower than the phonon frequency limit typical of the structural relaxation. This Debye process is remarkably similar to the dielectric behavior of many monohydroxy alcohols, which implies a common nature of purely exponential relaxation dynamics in these liquids. Based on the dielectric properties, we conclude that the Debye relaxation in the secondary amides is not a direct signature of the primary or alpha-relaxation, the latter being obscured at low temperatures due to the relatively low permittivity and close spectral proximity to the Debye peak. As in the case of monohydroxy alcohols, dielectric polarization and structure fluctuate on different time scales in secondary amides. The Kirkwood-Fr?hlich correlation factors for Debye-type liquids are also discussed.     

Analysis of dielectric relaxations of w/o emulsions in the light of theories of interfacial polarization

An attempt is made to apply dielectric theories of interfacial polarization to observations of dielectric relaxations for W/O emulsions. Approximate formulas for disperse systems in a W/O type were derived from the two theories: one proposed by Maxwell and Wagner for dilute disperse systems of spherical particles, and the other developed by Hanai for concentrated disperse systems. Dielectric measurements were carried out on concentrated W/O emulsions prepared from kerosene and distilled water or KCl aqueous solutions by minimal use of emulsifiers. Marked dielectric relaxations were observed with the emulsions, the dielectric parameters having been determined to characterize the relaxation data. Phase parameters such as relative permittivity, electric conductivity and volume fraction of the disperse phase were evaluated from the dielectric parameters by use of the approximate formulas of the respective theories. The phase parameters evaluated and the frequency dependence of complex permittivity of the W/O emulsions deduced from the theory for concentrated disperse systems are in excellent agreement with the observed data in comparison to that for dilute disperse systems. It is concluded that the dielectric relaxations due to the interfacial polarization of disperse systems of spheres are explained satisfactorily by the theory for concentrated disperse systems.     

Dielectric imaging of biological cells

A dielectric technique that can image local permittivity and conductivity has been applied to living biological cells in an aqueous environment. The local permittivity and conductivity were measured between 10 kHz and 10 MHz with a fine probe electrode, which was laterally scanned over cells on a plate electrode. The dielectric images of the cells depended on frequency, indicating dielectric relaxation that is due to interfacial polarization. The low-frequency image (at 10 KHz) in which the cells have high permittivity and low conductivity compared with the medium results from the presence of the plasma membrane with high resistivity. The dielectric image of the cell interior is obtainable at high frequencies (10 MHz), where the plasma membrane is short-circuited.     

Modelling of surface exchange reactions and diffusion in composites and polycrystalline materials

Abstract  Surface exchange reactions and chemical diffusion in composites, consisting of a dilute distribution of inclusions in a matrix, and polycrystalline materials have been modelled by application of both a square grain and a spherical grain model. The diffusion equations have been solved numerically by employing a finite element approach in the case of the square grain model and the Laplace transform method involving numerical Laplace inversion with respect to the spherical grain model. The boundary conditions refer to oxygen exchange reactions between a gas phase and a mixed ionically–electronically conducting ceramic sample within the linear response regime, i.e. small variations of the oxygen partial pressure. Diffusion profiles as well as the time dependence of the total amount of exchanged oxygen (relaxation curves) have been calculated. A necessary requirement for effective medium diffusion is proposed, and appropriate relations for the effective chemical surface exchange coefficient and the effective chemical diffusion coefficient are derived. On the contrary, when the time constant for diffusion from the matrix into the inclusions of a composite exceeds considerably the relaxation time for effective medium diffusion, relaxation curves with two separate time constants are observed. Analogously, in the case of polycrystalline materials the overall transport process is determined by slow (rate-limiting) bulk diffusion from the grain boundaries into the grains. Adequate formulae for the relaxation times are given based on analytical approximations of the solution functions to the diffusion equations. In addition, the spherical grain model is applied to interpret the re-oxidation kinetics of the positive temperature coefficient of resistivity (PTC) ceramics based on conductivity relaxation experiments. Graphical abstract        

Temperature Dependent Dielectric Relaxation in Solvent Mixtures at Microwave Frequencies

By the use of time domain reflectometry method, dielectric measurements were carried out on dimethylformamide‐2‐nitrotoluene solvent mixtures in the frequency range 10 MHz‐20 GHz, at various temperatures from 15 °C to 45 °C. These solvent mixtures as well as pure solvents display a Debye type dispersion. Their frequency dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters for these solvent mixtures at various concentrations and temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The excess permittivity is found to be positive for all concentrations and temperatures whereas the excess inverse relaxation time is negative.