Dielectric constant frequency dependence

The observation of complex dielectric constant frequency dependence (e = s — ie") shows that, at low frequencies, the different polarisations contribute to a high permittivity c value, beyond that, each kind of polarisation will create one resonance or one relaxation process e decrease and a maximum appears for e . 

In a manner similar to the dielectric constant, frequency-dependent Cp co) is defined as a dynamic susceptibility. Under equilibrium conditions, the heat that the system can adsorb from its surroundings during a AT change isq = H = CpAT, that is, the change in enthalpy per volume H. If the system contains (t) relaxing degrees of freedom after a T change, H = H t). For a time-dependent T variation, AT t) in a time interval 0 < < t is... 

There is an important practical distinction between electronic and dipole polarisation whereas the former involves only movement of electrons the latter entails movement of part of or even the whole of the molecule. Molecular movements take a finite time and complete orientation as induced by an alternating current may or may not be possible depending on the frequency of the change of direction of the electric field. Thus at zero frequency the dielectric constant will be at a maximum and this will remain approximately constant until the dipole orientation time is of the same order as the reciprocal of the frequency. Dipole movement will now be limited and the dipole polarisation effect and the dielectric constant will be reduced. As the frequency further increases, the dipole polarisation effect will tend to zero and the dielectric constant will tend to be dependent only on the electronic polarisation Figure 6.3). Where there are two dipole species differing in ease of orientation there will be two points of inflection in the dielectric constant-frequency curve. 

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)... 

Generally, the literature shows that for pol)timides the dielectric constant decreases gradually with increasing frequency. This variation is attributed to the frequency dependence of the polarization mechanisms which include the dielectric constant. The magnitude of the dielectric constant is dependent on the ability of the polarizable emits in a polymer to orient fast enough to keep up with the oscillations of an alternating electric field. At optical frequencies (approx. 10 Hz), only the lowest mass species, the electrons, are efficiently polarized. At lower frequencies, the atomic polarization of nuclei, which move more slowly, also, contribute to the dielectric constant. Atomic polarization of induced... 

As shown above, the real and imaginary part of the complex dielectric constant are dependent on frequency, however, they are not independent of each other, e and s" can be correlated via the Kramers-Kronig relations [2,3], which describe the relation between the real and imaginary part of a certain class of complex-valued fiinctions in physics and mathematics. The real part of the complex dielectric constant can be expressed as in the form of dielectric loss [4]... 

A dipole cannot keep shifting orientation direction when the frequency of the applied electric field exceeds its relaxation frequency and, therefore, it will not make a contribution to the dielectric constant. The dependence of on the field frequency is represented schematically in Figure 18.34 for a dielectric medium that exhibits all three... 

The dielectric constant, e, depends on temperature only to the extent that the density changes with temperature, eg, a sharp change at the melting temperature, Tm. Except for the influence of ionic conductivity at low frequencies or temperatures above I m. the dissipation factor and the loss index, e", are essentially constant for an ideal, nonpolar polymer, such as PTFE, with some minor exceptions due to branching and other perturbations in the molecular structure. 

The quantity 1 + x is known as the dielectric constant, it is constant only in the sense of being independent of E, but is generally dependent on the frequency of E. Since x is generally complex so is the wavevector k. It is customary to write... 

Neumann M, Steinhauser O and Pawley G S 1984 Consistent calculation of the static and frequency-dependent dielectric constant in computer simulations Mol. Phys. 52 97-113... 

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

The simplest example is that of tire shallow P donor in Si. Four of its five valence electrons participate in tire covalent bonding to its four Si nearest neighbours at tire substitutional site. The energy of tire fiftli electron which, at 0 K, is in an energy level just below tire minimum of tire CB, is approximated by rrt /2wCplus tire screened Coulomb attraction to tire ion, e /sr, where is tire dielectric constant or the frequency-dependent dielectric function. The Sclirodinger equation for tliis electron reduces to tliat of tlie hydrogen atom, but m replaces tlie electronic mass and screens the Coulomb attraction. 

The same idea was actually exploited by Neumann in several papers on dielectric properties [52, 69, 70]. Using a tin-foil reaction field the relation between the (frequency-dependent) relative dielectric constant e(tj) and the autocorrelation function of the total dipole moment M t] becomes particularly simple ... 

Neumann, M., Steinhauser, O. On the calculation of the frequency-dependent dielectric constant in computer simulations. Chem. Phys. Lett. 102 (1983) 508-513. 

The attenuation of ultrasound (acoustic spectroscopy) or high frequency electrical current (dielectric spectroscopy) as it passes through a suspension is different for weU-dispersed individual particles than for floes of those particles because the floes adsorb energy by breakup and reformation as pressure or electrical waves josde them. The degree of attenuation varies with frequency in a manner related to floe breakup and reformation rate constants, which depend on the strength of the interparticle attraction, size, and density (inertia) of the particles, and viscosity of the Hquid. 

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. 

At low frequencies when power losses are low these values are also low but they increase when such frequencies are reached that the dipoles cannot keep in phase. After passing through a peak at some characteristic frequency they fall in value as the frequency further increases. This is because at such high frequencies there is no time for substantial dipole movement and so the power losses are reduced. Because of the dependence of the dipole movement on the internal viscosity, the power factor like the dielectric constant, is strongly dependent on temperature. 

With polar molecules the value of the dielectric constant is additionally dependent on dipole polarisation and commonly has values between 3.0 and 7.0. The extent of dipole polarisation will depend on frequency, an increase in frequency eventually leading to a reduction in dielectric constant. Power factor-frequency curves will go through a maximum. 

The insulating properties of polyethylene compare favourably with those of any other dielectric material. As it is a non-polar material, properties such as power factor and dielectric constant are almost independent of temperature and frequency. Dielectric constant is linearly dependent on density and a reduction of density on heating leads to a small reduction in dielectric constant. Some typical data are given in Table 10.6. 

Figure 21.12. Dependence of temperature (at 50Hz) and frequency (at 23°C) on the dielectric constant and power factor of polyhydantoin film...

The dielectric medium is normally taken to have a constant value of e, but may for some purposes also be taken to depend for example on the distance from M. For dynamical phenomena it can also be allowed to be frequency dependent i.e. the response of the solvent is different for a fast reaction, such as an electronic transition, and a slow reaction, such as a molecular reorientation. 

Clearly for titration purposes, it is low-dielectric constant conducting solutions which will be important, and addition of a suitable reagent to such a solution permits the plotting of a titration curve from which the end point can be deduced as described in Section 13.7. It should be noted that in view of the enhanced conductance in the high-frequency field, the maximum concentration of reagents is much smaller than with normal conductimetric titrations, and the maximum concentration will depend on the frequency chosen. It is found that... 

The fact that the dielectric constant depends on the frequency gives SPFM an interesting spectroscopic character. Local dielectric spectroscopy, i.e., the study of s(w), can be performed by varying the frequency of the applied bias. Application of this capability in the RF range has been pursued by Xiang et al. in the smdy of metal and superconductor films [39,40] and dielectric materials [41]. In these applications a metallic tip in contact with the surface was used. 

The dielectric constant of a polymer (K) (which we also refer to as relative electric permittivity or electric inductive capacity) is a measure of its interaction with an electrical field in which it is placed. It is inversely related to volume resistivity. The dielectric constant depends strongly on the polarizability of molecules tvithin the polymer. In polymers with negligible dipole moments, the dielectric constant is low and it is essentially independent of temperature and the frequency of an alternating electric field. Polymers with polar constituents have higher dielectric constants. When we place such polymers in an electrical field, their dipoles attempt... 

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