Composite dielectric constant

Thus, if the wavelength of the light is much greater than the grain size, the long wavelength approximation and effective medium theory can be applied to determine the effective value of the composite dielectric constant and, consequently, describe composites optical properties. However, if the size of the structure is of the order of tens and even units of nanometers, then the effective medium approach is not applicable. Indeed, within this approximation, the effective permittivity of a composite is determined as a function of the permittivity for each composite component and, in turn, the nanocomposite components are characterized by the same tensor of permittivity as those used for bulk media. ... 

Material Composition Dielectric constant Paraelectric (P) or Ferroelectric (F)... 

LTCC Suppliers Products (composition) Dielectric constant ) Resistivity (Jl cni) Thermal expansion co- cfHlcient ppm/°C) Thermal conduct- ivity (w/m K) Flexural strength (MPa)... 

Kofod G, Risse S, Stoyanov H et al (2011) Broad-spectrum enhancement of polymer composite dielectric constant at ultra-low doping caused by sihca-supported copper nanoparticles. Composites 5 1623-1629... 

Barium carbonate also reacts with titania to form barium titanate [12047-27-7] BaTiO, a ferroelectric material with a very high dielectric constant (see Ferroelectrics). Barium titanate is best manufactured as a single-phase composition by a soHd-state sintering technique. The asymmetrical perovskite stmcture of the titanate develops a potential difference when compressed in specific crystallographic directions, and vice versa. This material is most widely used for its strong piezoelectric characteristics in transducers for ultrasonic technical appHcations such as the emulsification of Hquids, mixing of powders and paints, and homogenization of milk, or in sonar devices (see Piezoelectrics Ultrasonics). 

Historically, materials based on doped barium titanate were used to achieve dielectric constants as high as 2,000 to 10,000. The high dielectric constants result from ionic polarization and the stress enhancement of k associated with the fine-grain size of the material. The specific dielectric properties are obtained through compositional modifications, ie, the inclusion of various additives at different doping levels. For example, additions of strontium titanate to barium titanate shift the Curie point, the temperature at which the ferroelectric to paraelectric phase transition occurs and the maximum dielectric constant is typically observed, to lower temperature as shown in Figure 1 (2). 

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

There is also growing iaterest ia thin-film dielectric capacitors. For example, through the use of processiag techniques such as sol—gel solution deposition, thin (--- 0.25 fim) ceramic layers having dielectric constants ranging from 500 to 2000 ia the PZT, Pb(Zr,Ti)03, and PMN—PT, Pb(Mn2 3Nb2 3)03-PbTi03, compositional families respectively, have been prepared (3). 

According to Eq. (13.52), saturation charge is directly proportional to the square of the particle diameter and the external electric field. Particle charging depends also on the composition of the particle, which is taken into account by the relative dielectric constant e,. It is worth noticing that the field charging model should not be applied for small particles (dp < 0.5 pm). 

The bulk properties of mixed solvents, especially of binary solvent mixtures of water and organic solvents, are often needed. Many dielectric constant measurements have been made on such binary mixtures. The surface tension of aqueous binary mixtures can be quantitatively related to composition. ... 

D2O and the tritium analogue T2O (p. 41). The high bp is notable (cf. H2S, etc.) as is the temperature of maximum density and its marked dependence on the isotopic composition of water. The high dielectric constant and measurable ionic dissociation equilibrium are also unusual and important properties. The ionic mobilities of [H30] and [OH] in water are abnormally high (350 X 10 " and 192 x 10 cms per V cm... 

Now, we should ask ourselves about the properties of water in this continuum of behavior mapped with temperature and pressure coordinates. First, let us look at temperature influence. The viscosity of the liquid water and its dielectric constant both drop when the temperature is raised (19). The balance between hydrogen bonding and other interactions changes. The diffusion rates increase with temperature. These dependencies on temperature provide uS with an opportunity to tune the solvation properties of the liquid and change the relative solubilities of dissolved solutes without invoking a chemical composition change on the water. 

Other methods for estimating the volume percentage of the interphases in a composition have been proposed, too, for example, measurements of density variations [76, 77], volume of compressed sample [78], the dielectric constant [77], etc. The important thing is that the interphase thickness determined in one way or another is an effective value dependent upon the conditions and type of the experiment by which it was determined [51]. 

When the silver nanocrystals are organized in a 2D superlattice, the plasmon peak is shifted toward an energy lower than that obtained in solution (Fig. 6). The covered support is washed with hexane, and the nanoparticles are dispersed again in the solvent. The absorption spectrum of the latter solution is similar to that used to cover the support (free particles in hexane). This clearly indicates that the shift in the absorption spectrum of nanosized silver particles is due to their self-organization on the support. The bandwidth of the plasmon peak (1.3 eV) obtained after deposition is larger than that in solution (0.9 eV). This can be attributed to a change in the dielectric constant of the composite medium. Similar behavior is observed for various nanocrystal sizes (from 3 to 8 nm). 

The addition of salts modifies the composition of the layer of charges at the micellar interface of ionic surfactants, reducing the static dielectric constant of the system [129,130]. Moreover, addition of an electrolyte (NaCl or CaCli) to water-containing AOT-reversed micelles leads to a marked decrease in the maximal solubihty of water, in the viscosity, and in the electrical birefringence relaxation time [131],... 

The possibility of realizing via percolated w/o microemulsion conductor/insulating composite materials with very large dielectric constant and exotic optical properties has been pointed out [284],... 

The dynamic viscoelasticity of particulate gels of silicone gel and lightly doped poly-p-phenylene (PPP) particles has been studied under ac excitation [55]. The influence of the dielectric constant of the PPP particles has been investigated in detail. It is well known that the dielectric constant varies with the frequency of the applied field, the content of doping, or the measured temperature. In Fig. 11 is displayed the relationship between an increase in shear modulus induced by ac excitation of 0.4kV/mm and the dielectric constant of PPP particles, which was varied by changing the frequency of the applied field. AG increases with s2 and then reaches a constant value. Although the composite gel of PPP particles has dc conductivity, the viscoelastic behavior of the gel in an electric field is qualitatively explained by the model in Sect. 4.2.1, in which the effect of dc conductivity is neglected. 

This thermal stability comes with a price, however, as low polarizability of the covalent matrix imparts a modest dielectric constant of 5 for A12P055 compositions (although substitution of 33 at% La can boost this value to 8.5). This suboptimal value can be somewhat mitigated by high breakdown fields... 

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