Conductivity at high frequency

The equation of motion for fhe electrons in an oscillating E-field can be written as 

Note that in the limit 0, the real part is just the DC conductivity and the imaginary part vanishes. 

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The dispersion of conductance at high frequencies was predicted by Debye and Falkenhagen, who developed the theory of the subject the phenomena were subsequently observed by Sack and others. The... 

For any method to be used prudently, it must be remembered that as a rule, the interphase consists of a resistor in series with a parallel combination of a capacitor and a resistor. If both resistances are high, one should try to conduct measurements at low frequencies. If both are low, the experiment should be conducted at high frequency. 

Solution The mechanical properties of polymers depend on time and temperature. The time dependence is usually expressed as a frequency dependence, which to a first approximation is related to time by 2jt 1) = 1/t where X> is the frequency. The combined dependence of molecular processes of viscoelastic materials on frequency and temperature can be described by an activation energy E, . Ej, is about 100 kcal/mol and 10 kcal/mol for primary and secondary transitions, respectively. This implies that the relaxation processes associated with the molecular motions shift to higher temperatures at higher frequencies however, the secondary transition shifts more than the primary transition. Therefore, if tests are conducted at high frequencies, the resolution between the energy absorption peaks for primary and secondary transitions that are close to each other is poor. Thus, in this case, the P and a peaks, which are relatively distinct at 0.1 Hz, merge at 50 Hz, and there is a shift in the peak to higher temperatures. 

It is seen that at high frequencies, the conductivity is determined by the majority carriers, i.e. carriers with a maximum partial conductivity (at high frequencies the bonds have not enough time to be polarized). At low frequencies the conductivity is determined by minority carriers, i.e. carriers with smallest partial conductivities which unblock the bonds. 

The treatment above refers to conductances under normal conditions of measurement. Conductance at high frequencies (q.v.) and conductance at high field strengths (q.v.) are discussed separately. 

See Refs. [7-12,386] for details. Note that conductivity means dc conductivity in our context. In the case of ac conductivity at high frequencies correlation effects have to be taken account of (see Section 6.6.1). 

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