Frequency dependent conductivity

The conductivity increases at high frequency (>3 to 30 MHz, Debye-Falkenhagen effect). It takes approximately 0.1—1 ns to form an ionic atmosphere, and the time is dependent on the ion concentration. The literature is not clear as to the conductivity frequency dependence of electrolytes such as NaCl, but Cooper (1946) found no variations in the concentration range of 1—4 wt% and frequency range of 1—13 MHz. 

Figure Al.3.30. Theoretical frequency-dependent conductivity for GaAs and CdTe liquids from ab initio molecular dynamics simulations [42].

Fig. 109. Frequency dependence of conductivity (G) for single crystals of MsNbjOFis and KsNb3OF,g (electrodes were deposited onto the (001) faces). Reproduced from [443], A. I. Agulyansky, J. Ravez, R Von Der Mtihll, A. Simon, Ferroelectrics 158 (1994) 139, Copyright 1994, with permission of Taylor Francis, Inc., http //www.routledge-ny.com.

Microwave measurements are typically performed at frequencies between 8 and 40 Gc/s. The sensitivity with which photogenerated charge carriers can be detected in materials by microwave conductivity measurements depends on the conductivity of the materials, but it can be very high. It has been estimated that 109-1010 electronic charge carriers per cubic centimeter can be detected. Infrared radiation can, of course, also be used to detect and measure free electronic charge carriers. The sensitivity for such measurements, however, is several orders of magnitude less and has been estimated to be around 1015 electronic charge carriers per cubic centimeter.1 Microwave techniques, therefore, promise much more sensitive access to electrochemical mechanisms. 

Although the conductivity change Aa [relation (8)] of microwave conductivity measurements and the Ac of electrochemical measurements [relation (1)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemical and photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. 

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

Nelson I would like to return to what David Eisner mentioned about the plasma membrane determining the steady-state free Ca2+, and what Rick Paul said about sparks and long-conductance Ca2+-dependent K+ (BK) channels. We have looked at cerebral arteries from PLB knockout mice. The spark frequency and the associated transient BK current frequency are elevated by about a factor of three. SR load goes up, the membrane potential hyperpolarizes and the artery relaxes. It would be useful to measure membrane potential under all the conditions as well as determine the voltage dependence of tone, to make sure that your manipulations are not simply changing the membrane potential. 

Figure 30. Frequency dependence of AC conductivities of octa-alkyl Pc derivatives in the films.

Important electrical informations about OLEDs, such as charge transport, charge injection, carrier mobility, etc., can be obtained from bias-dependent impedance spectroscopy, which in turn provides insight into the operating mechanisms of the OLED [14,15,73,75 78]. Campbell et al. reported electrical measurements of a PLED with a 50-nm-thick emissive layer [75], Marai et al. studied electrical measurement of capacitance-voltage and impedance frequency of ITO/l,4-Mv-(9-anthrylvinyl)-benzene/Al OLED under different bias voltage conditions [76], They found that the current is space-charge limited with traps and the conductivity exhibits power-law frequency dependence. 

The type and magnitude of frequency dependence upon measured resistance depends upon the design of the conductance cell. Generally, measured resistance decreases with increasing frequency, although the opposite effect is observed in some cases with Erlenmeyer-type cells 21>2S>. Mysels et al. 2S> analyze this effect and extrapolate to zero frequency on a plot of resistance vs. f 2. 

Fig. 6.19 Frequency dependence of the conductivity at different temperatures for a micro PS film (5 U cm p-type, 30 mA cmf2, ethanoic HF). The transition from a frequency regime...

The intervalence transfer extinction coefficient, e, is proportional to a frequency-dependent conductivity, o, with a... 

Figure 3. Frequency-dependent conductivity [oM] for electron-transfer process.

Fig. 4.13 (a) Semilogarithmic plot of conductivity versus the nanotube content (wt%) in poly(phenylene vinylene-co-2,5-dioctoxy-m-phenylene vinylene) (PMPV) [2]. (b) Frequency dependent conductivity of carbon nanotubes at different wt% in PmPV (filled symbols) and polyvinyl alcohol (PVA) (unfilled symbols) based composites [250]. 

Fig. 6.8 (a) Calculated frequency-dependent conductivity for a simple dynamic percolation model. Lower line represents the diffusion coefficient without renewal, upper that with renewal. (f ) Frequency-dependent conductivity for pure PEO (bold) and PEO-NaSCN at 22 °C. Only ions are able to diffuse long distances, corresponding to renewal diffusion. 

Frequency-dependent measurements of the materials dielectric impedance as characterized by its equivalent capacitance, C, and conductance, G, are used to calculate the complex permitivity, e = d — id, where co = 2nf, f is the measurement frequency, and C0 is the equivalent air replacement capacitance of the sensor. 

From the hypothesis of a nonzero electrical conductivity in the vacuum and the corresponding dispersion relation [20,48, 50-52], the concepts of tired light and the observed cosmical redshift could be interpreted and associated with a nonzero photon mass of about 10 68 kg. The related frequency dependence can also become a measure of the mass. 

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