Electric field dielectric constant

Thus, dielectric constants(er) that determine the charge holding ability of the materials are characteristic for each substance and its state, and vary with temperature, voltage, and, finally, frequency of the electric field. Dielectric constants for some common materials are given in Table 1.1. 

The liquid-liquid interface is not only a boundary plane dividing two immiscible liquid phases, but also a nanoscaled, very thin liquid layer where properties such as cohesive energy, density, electrical potential, dielectric constant, and viscosity are drastically changed along with the axis from one phase to another. The interfacial region was anticipated to cause various specific chemical phenomena not found in bulk liquid phases. The chemical reactions at liquid-liquid interfaces have traditionally been less understood than those at liquid-solid or gas-liquid interfaces, much less than the bulk phases. These circumstances were mainly due to the lack of experimental methods which could measure the amount of adsorbed chemical species and the rate of chemical reaction at the interface [1,2]. Several experimental methods have recently been invented in the field of solvent extraction [3], which have made a significant breakthrough in the study of interfacial reactions. 

In the van der Waals attraction, the first important is the dielectric constant, s, dependent on the frequency at which alternating electric field varies. This is the name given to the factor by which the capacitance of a parallel plate condenser is increased on insertion of an insulating materials because net charges appears on the surface of the dielectric between the plates [59]. Under the electric field, dielectric molecules are polarized, so that an electric dipole moment can induce. These polarized charges are referred to the (total)... 

Electrical properties of polymers that are subject to low electric field strengths can be described by their electrical conductivity, dielectric constant, dissipation factor, and triboelectric behavior. Materials can be classified as a function of their conductivity (k) in (Q/cm)- as follows conductors, O-IO" dissipatives, and insulators, lO or lower. Plastics are considered nonconductive materials (if the newly developed conducting plastics are not included). The relative dielectric constant of insulating materials (s) is the ratio of the capacities of a parallel plate condenser with and without the material between the plates. A correlation between the dielectric constant and the solubility parameter (6) is given by 6 7.0s. There is also a relation between resistivity R (the inverse of conductivity) and the dielectric constant at 298 K log R = 23 - 2s. 

Electrical conductivity, dielectric constant, dissipation factor, and triboelectric behavior are electrical properties of polymers subject to low electric field strength. Materials can be classified as a function of their conductivity (K) in (Q/cm) as follows ... 

The dielectric constant (permittivity) tabulated is the relative dielectric constant, which is the ratio of the actual electric displacement to the electric field strength when an external field is applied to the substance, which is the ratio of the actual dielectric constant to the dielectric constant of a vacuum. The table gives the static dielectric constant e, measured in static fields or at relatively low frequencies where no relaxation effects occur. 

This result, called the Clausius-Mosotti equation, gives the relationship between the relative dielectric constant of a substance and its polarizability, and thus enables us to express the latter in terms of measurable quantities. The following additional comments will connect these ideas with the electric field associated with electromagnetic radiation ... 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

The magnitude of the induced dipole moment depends on the electric field strength in accord with the relationship = nT, where ]1 is the induced dipole moment, F is the electric field strength, and the constant a is caHed the polarizabHity of the molecule. The polarizabHity is related to the dielectric constant of the substance. Group-contribution methods (2) can be used to estimate the polarizabHity from knowledge of the number of each type of bond within the molecule, eg, the polarizabHity of an unsaturated bond is greater than that of a saturated bond. 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

A parameter used to characterize ER fluids is the Mason number, Af, which describes the ratio of viscous to electrical forces, and is given by equation 14, where S is the solvent dielectric constant T q, the solvent viscosity 7, the strain or shear rate P, the effective polarizabiUty of the particles and E, the electric field (117). 

At lower frequencies, orientational polarization may occur if the glass contains permanent ionic or molecular dipoles, such as H2O or an Si—OH group, that can rotate or oscillate in the presence of an appHed electric field. Another source of orientational polarization at even lower frequencies is the oscillatory movement of mobile ions such as Na". The higher the amount of alkaH oxide in the glass, the higher the dielectric constant. When the movement of mobile charge carriers is obstmcted by a barrier, the accumulation of carriers at the interface leads to interfacial polarization. Interfacial polarization can occur in phase-separated glasses if the phases have different dielectric constants. 

The observed dielectric constant M and the dielectric loss factor k = k tan S are defined by the charge displacement characteristics of the ceramic ie, the movement of charged species within the material in response to the appHed electric field. Discussion of polarization mechanisms is available (1). 

Heuristic Fxplanation As we can see from Fig. 22-31, the DEP response of real (as opposed to perfect insulator) particles with frequency can be rather complicated. We use a simple illustration to account for such a response. The force is proportional to the difference between the dielectric permittivities of the particle and the surrounding medium. Since a part of the polarization in real systems is thermally activated, there is a delayed response which shows as a phase lag between D, the dielectric displacement, and E, the electric-field intensity. To take this into account we may replace the simple (absolute) dielectric constant by the complex (absolute) dielectric... 

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