Dielectric constant zero-frequency

High Frequency Dielectric Strength. Dielectric strength at high frequency is important in microwave power uses such as radar (see Microwave technology). Because SF has zero dipole moment, its dielectric strength is substantially constant as frequency increases. At 1.2 MHz, SF has... 

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. 

Treating the free electrons in a metal as a collection of zero-frequency oscillators gives rise51 to a complex frequency-dependent dielectric constant of 1 - a>2/(co2 - ia>/r), with (op = (47me2/m)l/2 the plasma frequency and r a collision time. For metals like Ag and Au, and with frequencies (o corresponding to visible or ultraviolet light, this simplifies to give a real part... 

In Eq. (154), we assume indeed that only the ions (Z 0) interact with each other and that the resulting interaction is simply the Coulomb potential modified by the zero-frequency dielectric constant e of the solvent. Of course, in an exact theory, we would have to take explicitly into account the interactions with the solvent, and the dielectric constant itself should come out of the calculation. The proper way of attacking this problem is based on the theory of the potential of average forces and is carefully analyzed in H. L. Friedman s monograph.11 However, the explicit calculations always become exceedingly complicated and, in one way or another, one always has to have recourse to an approximation of the type (154). It amounts to assuming ... 

Thus the time constant t may also be estimated from (e )J h, the value of (e )ch extrapolated to zero frequency, and (co< ")SU the value of (coc")ch extrapolated to infinite frequency. For a chemically induced dielectric dispersion to be observable experimentally, the time constant t ought to be much shorter than the mean rotational relaxation time of the solute molecule, yet still in the range accessible to available experimental techniques. 

The high-frequency dielectric constant is determined by the effects of electronic polarization. An accurate estimate of this property lends confidence to the modeling of the electronic polarization contribution in the piezoelectric and pyroelectric responses. The constant strain dielectric constants (k, dimensionless) are computed from the normal modes of the crystal (see Table 11.1). Comparison of the zero- and high-frequency dielectric constants indicates that electronic polarization accounts for 94% of the total dielectric response. Our calculated value for k (experimental value of 1.85 estimated from the index of refraction of the P-phase of PVDF. ... 

Microwaves. Among the lowest frequencies of interest in collisional absorption are radio- and microwaves. As will be seen below, the absorption coefficient a is extremely small at low frequencies because absorption falls off to zero frequency as of2 see Chapter 5 for details. As a consequence, it has generally been necessary to use sensitive resonator techniques for the measurement of the loss tangent, tan <5 = s"/s, where s and s" are the real and imaginary part of the dielectric constant. The loss tangent is obtained by determination of the quality factors Qa, Qo, of the cavity with and without the gas filling, as (Dagg 1985)... 

The dielectric constant e is measured with static fields, i.e., at zero frequency. At optical frequencies, the refractive index n is of interest, which can be represented by a similar expression,... 

At low frequencies of the alternating field, the dielectric loss is normally zero and e is indistinguishable from the dielectric constant edc measured with a static field. Debye has shown that... 

In Equation (I). i2 ikT is the average component in the direction of the field of the permanent dipole moment of the molecule. In order that this average contribution should exist, the molecules must be able to rotate into equilibrium with the field. When the frequency of the alternating electric field used in the measurement is so high that dipolar molecules cannot respond to it, the second term on the right of the above equation decreases to zero, and we have what may he termed the optical dielectric constant f,.t defined by the expression... 

Thcse equations require that the dielectric constant decrease from the static to the optical dielectric constant with increasing frequency, while the dielectric loss changes from zero to a maximum value f" and back to zero. These changes are the phenomenon of anomalous dielectric dispersion. From the above equations, it follows that... 

For instance, for a nematic polymer with positive anisotropy of dielectric constant (Ae > 0) orientation of mesogenic groups along the applied field takes place (homeo-tropic orientation). The fact of orientation is illustrated in Fig. 25, which shows that under crossed polarizers the optical transmittance I of a film of nematic polymer with optically anisotropic texture (taken for 100%) falls practically to zero when a low-frequency field is switched on. 

The first term, which contains the the static dielectric permittivities of the three media , 2, and 3, represents the Keesom plus the Debye energy. It plays an important role for forces in water since water molecules have a strong dipole moment. Usually, however, the second term dominates in Eq. (6.23). The dielectric permittivity is not a constant but it depends on the frequency of the electric field. The static dielectric permittivities are the values of this dielectric function at zero frequency. 1 iv), 2 iv), and 3(iv) are the dielectric permittivities at imaginary frequencies iv, and v = 2 KksT/h = 3.9 x 1013 Hz at 25°C. This corresponds to a wavelength of 760 nm, which is the optical regime of the spectrum. The energy is in the order of electronic states of the outer electrons. 

X2 [3X2-(9lmaX)2]r0/3[ i2-( imax)2] Zero frequency local field factor for poling field f0=er(n2+2)/[2er+n2] where 8r is the relative dielectric constant... 

Because the dielectric constant of water at low frequency is ew(0) = 80, the coefficient of z-6 in the zero-frequency term is (in kTI0om units)... 

Relative isotropic dielectric, magnetic permittivity or permeability at zero frequency s(0) is the dielectric constant. 

For ionic-fluctuation forces, the e s are now the dielectric constants in the limit of zero frequency (f = 0). The integration over wave vectors u, v can be converted to a p, ir integration ... 

P. J. W. Debye, Polar Molecules (Dover, New York, reprint of 1929 edition) presents the fundamental theory with stunning clarity. See also, e.g., H. Frohlich, "Theory of dielectrics Dielectric constant and dielectric loss," in Monographs on the Physics and Chemistry of Materials Series, 2nd ed. (Clarendon, Oxford University Press, Oxford, June 1987). Here I have taken the zero-frequency response and multiplied it by the frequency dependence of the simplest dipolar relaxation. I have also put a> = if and taken the sign to follow the convention for poles consistent with the form of derivation of the general Lifshitz formula. This last detail is of no practical importance because in the summation Jf over frequencies fn only the first, n = 0, term counts. The relaxation time r is such that permanent-dipole response is dead by fi anyway. The permanent-dipole response is derived in many standard texts. 

Equation (8.1.24) implies that the dielectric constant e(co) becomes zero at co = cQp/ is real but negative for coelectromagnetic waves with frequencies smaller than the plasma frequency will be attenuated or absorbed by the solid), and is positive definite for co>cop... 

The oscillator strength of this mode can be derived using the frequency dependence of the dielectric constant of a damped oscillator at zero frequency, which reads... 

The dielectric constants of an aligned nematic phase are dependent upon both the temperature and the frequency of the applied field at temperatures below the clearing point. The dielectric permitivity, j, measured parallel to all three axes above the clearing point in the isotropic liquid is the same. Therefore, the dielectric anisotropy of the same compound in the liquid state is zero, see Figure 2.10. The sign and magnitude of the dielectric constants and, therefore, the dielectric anisotropy are dependent upon the anisotropy of the induced molecular polarisability, Aa, as well as the anisotropy and direction of the resultant permanent molecular polarisation determined by permanent dipole moments. 

Many of the different susceptibilities in (18)-(21) correspond to important experiments in linear and non-linear optics. The argument in parentheses again describes the kind of interacting waves. TWo waves interact in a first-order process as described above in (9), three waves in a second-order process, and four in a third-order process. x ° describes a possible zeroth-order (permanent) polarization of the medium t- (0 0) is the first-order static susceptibility which is related to the relative permittivity (dielectric constant) at zero frequency, e,.(0), by (22). 

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