# What is the main difference between "static dielectric constant" and "high frequency dielectric constant"?

What are the underlying properties of materials in general and conjugated polymers in particular, that affect the difference in values of the static and high frequency (optical domain ~10^15Hz) dielectric constant?

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Ralph H. Scheicher· Uppsala University## All Answers (8)

H. P. Huinink· Technische Universiteit EindhovenRalph H. Scheicher· Uppsala UniversityIoannis M. Kalogeras· National and Kapodistrian University of AthensThe difference (Δε) between the static dielectric constant (ε0, that is, the limiting value of the real part of complex permittivity obtained at an alternating field frequency approaching zero) and its high frequency analogue (εoo), is a measure of the overall polarizability of the dielectric material.

In polymers’ case, Δε incorporates contributions from a number of mechanisms: electronic/atomic polarizations (at the high-frequency end of the EM spectrum), orientational polarizations (from motions assigned to polar side-chains, chain segments, etc.) and more complex polarization/relaxation modes (e.g., translational motion of charges that are eventually trapped at interfaces, normal mode signals, complex transitions, which become significant at the low frequency end of the EM spectrum and at relatively high temperatures).

The relative strength of the above signals (and thus the magnitude of the static dielectric constant) is mostly relevant to properties and potential applications of polymeric materials related to dielectric devices and electrical insulation, but they could also be used as complementary information for several other applications of the system.

H. P. Huinink· Technische Universiteit EindhovenVolume 1 about statics:

http://www.amazon.com/Theory-Electric-Polarization-Vol-Dielectrics/dp/0444410198/ref=sr_1_1?s=books&ie=UTF8&qid=1377716434&sr=1-1

Volume 2 about dynamics:

http://www.amazon.com/Theory-Electric-Polarization-Vol-Time-Dependent/dp/0444415793

Finally a remark on polymers connecting to the answer of Ioannis. In my lab we have done some dielectric measurements on nylon-6 containing different amounts of water (equilibrated with RH). Extremely dry nylon-6 has a dielectric constant of about 3 and 4. That is the value that you expect on the basis of only induced polarizability that is limited to distances of atomic scale. The polymer is in the dry state glassy and permanent dipoles (amide part of the molecule) can not rotate and contribute to the polarization. At high humidities the dielectric constant reaches values around 10 and higher. This has two causes: water enters and that has a high dipole moment. However this cannot explain completely the rise. At higher water contents the polymer is plasticized and the permanent dipoles in the polymer can also rotate and contribute to the dielectric constant.

Vladimir Burtman· University of UtahSo you could not use the zero frequency dielectric constant in explanation/calculation of HF epsilon.

Charles Winthrop Clark· National Institute of Standards and Technologym d^2 r / dt^2 + k r = -e E sin (w t)

which has the driven solution

r(t) = E sin (w t) (-e/m) / ( w0^2 -w^2 ) where w0^2 = k/m. The time-dependent electric dipole moment is

-e r(t) = alpha(w) E sin (w t) where alpha(w) = (e^2 / m) / (w0^2 - w^2) is the frequency-dependent polarizability.

For w < w0, alpha is positive, and for w > w0, alpha is negative. One gets the same result in quantum mechanics using time-dependent perturbation theory. So you see, in the high-frequency limit the polarizability of this system is negative and is equal to the polarizability of a free electron.

I think this is also true for the ground states of real atoms and molecules: the static polarizability is always positive, and the high-frequency polarizability tends to -N e^2/( m w^2) where N is the total number of electrons (there is also a small correction due to finite masses of the nuclei).

Hiqmet Kamberaj· Research Institute of Science and Technology (RISAT), AlbaniaHowever, there is an interval of the frequencies (called also optical frequencies) for which we can still use the macroscopic of the electromagnetic field in the medium (i.e. use Maxwell equations) even though the dispersion effects are present.

To understand the optical frequency: think about the fact that in the electric and magnetic polarization the main role is played by the electronic mechanism. For wavelengths of the field (and so equivalently frequencies) that correspond to the characteristic time of relaxation of the electron we can still describe the field in the medium using macroscopic description (i.e. wavelength >> dimensions of atom).

For this high frequency, in the case of dispersion, we can write for electric filed in the medium

D = \epsilon_0 \epsilon(\omega) E

where \omega is the frequency of the field. \epsilon(omega) gives the law of dispersion of the dielectric constant, which now is a complex number.

For omega->0 we have that \epsilon(omega) --> static dielectric constant.

Some good references:

1) Classical electrodynamics, Jackson

2) Intr. Electrodynamics, Griffiths

3) Foundations of electrodynamics, H. Sykja

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