Dielectric coefficient

Impedance spectroscopy may provide quantitative information about the conductance, the dielectric coefficient, the static properties of a system at the interfaces, and its dynamic changes due to adsorption or charge-transfer phenomena. Since in this technique an alternating current with low amplitude is employed, a noninvasive observation of samples with no or low influence on the electrochemical state is possible. 

Clausius-Mossotti equation). In this expression, V designates the mole volume and Ae, Be, Cf,... are the first, second, third,... virial dielectric coefficients. A similar expansion exists for the refractive index, n, which is related to the (frequency dependent) dielectric constant as n2 = e (Lorentz-Lorenz equation, [87]). The second virial dielectric coefficient Be may be considered the sum of an orientational and a polarization term, Be = B0r + Bpo, arising from binary interactions, while the second virial refractive coefficient is given by just the polarization term, B = Bpo at high enough frequencies, the orientational component falls off to small values and the difference Be — B may be considered a measurement of the interaction-induced dipole moments [73],... 

In the case of a vacuum between the plates, the permittivity (eo) has a value of 8.854 x 10 12 F/m. When a dielectric material fills the space between the plates rather than a vacuum, the charge on the plate surface can be increased because of the nature of polarization of the dielectric as shown in Fig. 1.11. The ratio of e to eo is the relative permittivity or the dielectric coefficient of the dielectric. 

The class of ferroelectric materials have a lot of useful properties. High dielectric coefficients over a wide temperature and frequency range are used as dielectrics in integrated or in smd (surface mounted device) capacitors. The large piezoelectric effect is applied in a variety of electromechanical sensors, actuators and transducers. Infrared sensors need a high pyroelectric coefficient which is available with this class of materials. Tunable thermistor properties in semiconducting ferroelectrics are used in ptcr (positive temperature coefficient... 

Figure 1.17 (a) Schematic view of a core-shell structure and (b) Temperature behavior of the dielectric coefficient of BaTiC>3 doped with CdBi2Nb20g and hot-pressed fine-grained BaTiC>3 (grain size 0.5 gm)... 

In order to compare calculated and experimentally observed phase portraits it is necessary to know very exactly all the coefficients of the describing nonlinear differential Equation 14.3. Therefore, different methods of determination of the nonlinear coefficient in the Duffing equation have been compared. In the paraelectric phase the value of the nonlinear dielectric coefficient B is determined by measuring the shift of the resonance frequency in dependence on the amplitude of the excitation ( [1], [5]). In the ferroelectric phase three different methods are used in order to determine B. Firstly, the coefficient B is calculated in the framework of the Landau theory from the coefficient of the high temperature phase (e.g. [4]). This means B = const, and B has the same values above and below the phase transition. Secondly, the shift of the resonance frequency of the resonator in the ferroelectric phase as a function of the driving field is used in order to determine the coefficient B. The amplitude of the exciting field is smaller than the coercive field and does not produce polarization reversal during the measurements of the shift of the resonance frequency. In the third method the coefficient B was determined by the values of the spontaneous polarization... 

Thermodynamics is an experimental science based on a small number of principles that are generalisations made from experience. It is concerned only with macroscopic or large-scale properties of matter and it makes no hypotheses about the small-scale or microscopic structure of matter. From the principles of thermodynamics one can derived general relations between such quantities as coefficients of expansion, compressibility, heat capacities, heat of transformation, and magnetic and dielectric coefficients, especially as these are affected by temperature. The principles of thermodynamics also tell us which of these relations must be determined experimentally in order to completely specify all the properties of the system. 

Core-mantle grains. If particles consist of a core with dielectric coefficient e and radius r, and a mantle with dielectric coefficient 2 and thickness A, then... 

Inhomogeneous particles. For particles composed of a matrix and inclusions one approach for calculating optical properties is to assume an average dielectric coefficient (e) for the composed particle. A number of so-called mixing rules have been proposed a frequently used one is the Maxwell-Gamett mixing rule (cf. Bohren Huffman 1983). For a matrix with dielectric coefficient em, and a number of different kinds of inclusions with dielectric coefficients ej and volume fractions f) one uses... 

A full set of optical functions consists of reflectivity R and absorption coefficients, p, the imaginary 82 and real 81 parts of the dielectric function 8, the absorption and refraction indices k and n, the product of the integral joint density of states (DOS) function and the transition probability, equal within constant factor to the effective number of valence electrons n E) participating in the transitions to given energy level A the effective dielectric coefficient Sef, and the characteristic electron energy functions for volume (-Imc ) and surface (-Im(l+8) ) losses. 

The ferroelectric Pb(Mgy3Nb2/3)03 (PMN) ceramic has been the snbject of extensive investigations due to its high dielectric coefficient and high electrostrictive coefficient, which renders it suitable for use in capacitors and electrostrictive actuators. However, the successful exploitation of this material is limited by the difficulty of producing a single-phase material with the perovskite structnre. Conventional solid state synthesis techniques invariably resnlt in the formation of one or more pyrochlore phases, which exhibit poor dielectric properties. 

Empirical models for the induced trace have also been obtained from (nonspectroscopic) measurements of the second virial dielectric coefficient of the Clausius-Mosotti and Lorentz-Lorenz expansions [30]. Excellent surveys with numerous references to the historical as well as the modern dielectric research activities were given by Buckingham [27], Kielich [89], and Sutter [143] in 1972 see also a recent review with a somewhat more spectroscopic emphasis [11]. 

The Helmholtz capacitance may be described by Ch = e o/d, where e is the local value of the dielectric coefficient and d is the Stem layer thickness. Under conditions where e is independent of surface charge density, we can identify two domains of nearly constant capacitance under varying surface charge densities (i.e., pH). When Cq Ch (at high ionic strength), C == Ch when Cq Ch (lower ionic strength), C Cq. When the surface potential is small, for example, less than 25 mV, then Cq = eeox = 2.3 (25°C) (equation... 

Pack, G., G. Garrett, L. Wong and G. Lamm. (1993). The Effect of a Variable Dielectric Coefficient and Finite Ion Size on Poisson-boltzmann Calculations of Dna-electrolyte Systems. Biophysical Journal. 65 1363-1370. 

The dielectric coefficient g(>/, ) at the place of charge k appears in the denominator. This corresponds to a dielectric screening that is conventionally used in various descriptions of electrolytes where the solvent is interpreted as a dielectric continuum background (for instance, in the Debye-Hiickel theory, in the Gouy-Chapman theory, or in the RPM of electrolyte solutions). 

In the special case of sharp dielectric boundaries the dielectrics is separated into domains of uniform dielectric coefficients. The dielectric coefficient jumps from one value to another along a boundary. Let us denote the surface of the dielectric boundaries by B. Then the induced charge is a surface charge on the dielectric interfaces (if the induced charges around the source charges are not considered), and the volume integral in Eq. (15) becomes a surface integral over the surface B,... 

To solve Eq. (16) numerically, the surface B must be discretized specifically, each discrete surface element Ba of B is characterized by its center-of-mass sa, area aa, unit normal na = n(sa), value of the mean dielectric coefficient ea = e(sa), and value of the dielectric jump Aea = As(sn). Due to the assumption of the vanishingly small potential on S, the Green s function simply is,... 

In the planar geometry we consider a dielectric slab shown in Fig. 1. Two semi-infinite dielectrics of dielectric coefficients S and 3 are separated by a dielectric slab of thickness D and with a dielectric coefficient 2. The boundaries of the slab are flat, sharp, and parallel. This can be regarded as a simple model of a membrane. This case has been studied in our previous paper [58] where MC simulation results have been shown for the distribution of hard sphere ions around a slab. Nevertheless, in our previous work, we did not use the SC approximation. In the following, we will show that it is necessary only if the width of the slab is small compared to the width of the surface elements. 

Figure 2. The polarization energy Wi of a single charge of magnitude e as a function of the distance of the charge from the slab for different slab widths. The dielectric coefficients of the slab geometry are ei = 80 2 = 2 3 = 80. The polarization energy is normalized by kT where T = 300 K. The ICC curves as obtained from different approaches (PC/PC, SC/PC, and SC/SC the explanation of the abbreviations can be found in the main text) are compared to the analytical solution [66],...

A dielectric sphere of dielectric coefficient e embedded in an infinite dielectric of permittivity 82 is an important case from many points of view. The idea of a cavity formed in a dielectric is routinely used in the classical theories of the dielectric constant [67-69], Such cavities are used in the studies of solvation of molecules in the framework of PCM [1-7] although the shape of the cavities mimic that of the molecule and are usually not spherical. Dielectric spheres are important in models of colloid particles, electrorheological fluids, and macromolecules just to mention a few. Of course, the ICC method is not restricted to a spherical sample, but, for this study, the main advantage of this geometry lies just in its spherical symmetry. This is one of the simplest examples where the dielectric boundary is curved and an analytic solution is available for this geometry in the form of Legendre polynomials [60], In the previous subsection, we showed an example where the SC approximation is important while the boundaries are not curved. As mentioned before, using the SC approximation is especially important if we consider curved dielectric boundaries. The dielectric sphere is an excellent example to demonstrate the importance of curvature corrections . 

We will show results for the case where the dielectric coefficient is e = 80 inside, and 2 = 2 outside. For the reverse case, when the sourse charge is in the regime with the higher dielectric coefficient, we would obtain qualitatively similar, quantitatively even better converging results. Because of the... 

As mentioned before, the ions are modelled as point charges embedded in the center of a hard sphere where the sphere has the same dielectric coefficient as the surrounding medium. This approach replaces the polarization charges induced around the source charge from the surface of the sphere to the position of the source charge localized on it. The error made by this assumption was... 

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