Relative dielectric permittivity

Relaxor Ferroelectrics. The general characteristics distinguishing relaxor ferroelectrics, eg, the PbMg 2N b2 302 family, from normal ferroelectrics such as BaTiO, are summari2ed in Table 2 (97). The dielectric response in the paraelectric-ferroelectric transition region is significantly more diffuse for the former. Maximum relative dielectric permittivities, referred to as are greater than 20,000. The temperature dependence of the dielectric... 

The fourth term is a polarisation term. Here E(z) = di/z/dz is the electric field at position z. In previously published SCF results for charged bilayers, this last term is typically absent. It can be shown that the polarisation term is necessary to obtain accurate thermodynamic data. We note that all qualitative results of previous calculations remain valid and that, for example, properties such as the equilibrium membrane thickness are not affected significantly. The polarisation term represents relatively straightforward physics. If a (united) atom with a finite polarisability of erA is introduced from the bulk where the potential is zero to the coordinate z where a finite electric field exists, it will be polarised. The dipole that forms is proportional to the electric field and the relative dielectric permittivity of the (united) atom. The energy gain due to this is also proportional to the electric field, hence this term is proportional to the square of the electric field. The polarisation of the molecule also has an entropic consequence. It can be shown that the free energy effect for the polarisation, which should be included in the segment potential, is just half this value... 

Not to be forgotten is the assumption that neither the presence of the electrolyte nor the interface itself changes the dielectric medium properties of the aqueous phase. It is assumed to behave as a dielectric continuum with a constant relative dielectric permittivity equal to the value of the bulk phase. The electrolyte is presumed to be made up of point charges, i.e. ions with no size, and responds to the presence of the charged interface in a competitive way described by statistical mechanics. Counterions are drawn to the surface by electrostatic attraction while thermal fluctuations tend to disperse them into solution, surface co-ions are repelled electrostatically and also tend to be dispersed by thermal motion, but are attracted to the accumulated cluster of counterions found near the surface. The end result of this electrical-thermodynamic conflict is an ion distribution which can be represented (approximately) by a Boltzmann distribution dependent on the average electrostatic potential at an arbitrary point multiplied by the valency of individual species, v/. 

The charge is assumed to be uniformly distributed on the surface of the sphere. Such an ion is transferred from vacuum, with a relative dielectric permittivity equal to 1, to the solvent, which is considered to be a structureless dielectric continuum characterized by the static dielectric permittivity, This transfer may be divided into two processes the transfer of a noncharged sphere from vacuum to continuum and the charging (to ne) of the transferred sphere. 

In sec. 1.7.10b static adsorbates were considered and interpreted as equivalent to thin layers with different refractive indices and/or dielectric permittivities. For such layers one usually introduces the coefficient of ellipticity p, which is the Imaginary part of / f at the Brewster angle, where the real part of this quotient is zero. For a thin homogeneous layer of thickness h of a material with relative dielectric permittivity e between a substrate 2 and a gas or liquid 1 with permittivities and, respectively ... 

Incomplete dissociation would also reduce the screening power of electrolytes. Ions of higher valency could, as a result of Ion association, become entitles of lower vzdency this has substantial consequences because the valency occurs In the exponentials, see for instance sec. 3.5c. For otherwise strong electrolytes this complication starts when the relative dielectric permittivity Is low. say < 30. 

Ionic double layers and double layers caused by interfacied poleirlzation occur together but are not Independent. Changing the surface charge will affect the polarization of adjacent solvent, so that x Is generally a function of a°. Specific adsorption of ions in the Stern layer is intimately coupled to the solvent structure and conversely. The inner layer capacitances Kj, K, C and are also coupled to the interfacial polarization via the local relative dielectric permittivities ej and e. ... 

The overall conclusion that, with respect to all water-shunning or hydro-phobic phases studied so far, water turns its oxygen away from the water phase must mean that this is mainly a property of the water and not of water-adjacent phase interaction. For hydrophilic surfaces, containing donors actively promoting the formation of hydrogen bridges, this may be different. Information from inner layer capacitances, suggesting that the relative dielectric permittivity of water adjacent to silver iodide and mercury is much lower than It is for oxides, may be in line with this. 

The relative dielectric permittivity of open porous materials (e.g. aerogels) especially its variation with ambient conditions is very important for materials application. A precise measurement has to be assured because of highly porous materials has a value close to unity in the limit of 100 % porosity. Also the variation of due to changes in the environmental parameters (humidity etc.) might be small on a absolute scale, but large on a relative one. This had been the case in previous studies who focused on the relationship between the adsorption of water and/or chemical compounds and of porous systems, e.g. zeolithes[l] and Si02 aerogels [2]. To avoid misinterpretation of the data the measurement has to be checked for the influence of cables and of the electronic devices etc. 

Electrostatic interactions are more important in organic semiconductors (partly because the relative dielectric permittivity is small, at typically 2-4) ... 

Many examples exist of interfaces formed between two immiscible liquids. A well-known one is the interface between a long-chain hydrocarbon, for example, dodecane, and water, which is commonly known as the oil water interface. Dodecane and water are immiscible because the hydrocarbon phase is nonpolar. Liquid liquid interfaces are also formed between water and organic liquids with polar groups such as octanol and heptanoic acid, which also have rather long hydrocarbon chains. The polar liquid nitrobenzene, which has a relative permittivity of 35, is also immiscible with water. Another well-known system is the mercury polar liquid interface. This has been studied extensively, especially for aqueous electrolyte solutions. However, the mercury polar liquid interface is also an example of a metal solution interface which was considered in the previous section. The discussion here is limited to liquids with relative dielectric permittivities falling in the range 1-200, and systems which have poor conductivities as pure liquids. 

The simplest quantitative treatment of the solvent relaxation assumes that the fluorophore is placed in the cavity of radius a in the medium characterized by the relative dielectric permittivity e and the refractive index n. It yields the Lippert equation [42] for the wavenumber shift between absorption and emission maxima of the fully relaxed host system ... 

The stability of an emulsion depends not only on the surfactant type, but also on die nature of the organic phase. To characterize die oil phase, the concept of a necessary (required) HLB number is used. This number is taken to be equal to die HLB number of die surfactant which ensures the best possible emulsification of the oil. Tables of necessary HLB numbers for various oils were published in Ref 258. For example, with respect to oil-in-water emulsions, the necessary HLB number is 17 for oleic acid, 15 for toluene, 14 for xylene and cetyl alcohol, 10.5 to 12 for mineral oils, 7.5 to 8 for vegetable oils, 5 to 7 for vaseline, and 4 for paraffin. In Refs 263 and 264 the necessary HLB numbers for various oils are compared with the relative dielectric permittivity of the oil e. In the series of saturated hydrocarbons, a weak inverse dependence between the necessary HLB number and e was observed (264) e.g., e =... 

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