Frequency dependence ionic dispersion

In general, the study of transport processes in disordered media has its widest application to electronic materials, such as amorphous semiconductors, and very little attention has been given to its application to ionic conductors. The purpose of this section is to discuss briefly the effect of disorder on diffusion process and to point out the principles involved in some of the newly developing approaches. One of the important conclusions to be drawn is that frequency-dependent transport properties are predicted to be of the form exhibited by the CPE if certain statistical properties of the distribution functions associated with time or distance are fulfilled. If these functions exhibit anomalously long tails, such that certain moments are not finite, then power law freqnency dispersion of the transport properties is observed. However, if these moments are finite, then Gaussian diffusion, at least as limiting behavior, is inevitable. 

It should be noted, though that defective semiconductors - for instance oxide layers on metals - typically do not show an ideal capacitive behavior which often leads to a strong frequency-dependence of the capacitance. There are many possible reasons for non-ideal behavior such as ionic participation , a frequency-dependent dielectric constant, contributions from the Helmoltz-layer or from surface states, non-ideal structure or nonideal donor distribution, as well as inhomogeneous depth distribution in the composition or structure of the oxide layer. Independent of the origin of the non-ideal behavior, the frequency dispersion can partially be corrected by replacing the capacitance in impedance fits by a so-called constant phase element (CPE), which takes into consideration the non-ideal nature of a capacitance. While the introduction of CPE may eliminate the... 

When a low frequency AC electric field is imposed, the particle oscillates around its mean position and platy particles may become optimally aligned with the field. At high frequencies, neither particle shift nor alignment takes place. However, translational movement of dispersed particles can be attained in an asymmetric AC field (without a DC component). The observed drift is attributed to the velocity-dependent viscous drag force in relation to double layer polarization as sketched in Figure 2 for reference, bacteria swim at 0.02-1 mm/s. For more details see Palomino [2], The field frequency co must be low enough such that ionic concentrations and hydrodynamic fields may adjust to... 

The electromagnetic fields of the right- and left-propagating polaritons, respectively, follow the wave equations with the speeds and damping rates of the different frequency components dispersed according to the frequency- and wavevector-dependent complex refractive index n = v/e(k, oj). A typical example of the dispersion of these modes is shown in Fig. 1 for the case of a real permittivity e. The term Ao(r,t) represents the envelope of the wavepacket on the phonon-polariton coordinate A. Note that this phonon-polariton coordinate is a linear combination of ionic and electromagnetic displacements, which both contribute to the polarization... 

Conductive-system dispersion (CSD) usually involves thermally activated conduction extending to zero frequency plus an always-present bulk dielectric constant, usually taken to be frequency-independent in the experimental range. Dielectric-system dispersion (DSD) often involves dielectric-level response with only weak temperature dependence, and it may or may not involve a non-negligible frequency-independent leakage resistivity, pc = Pdc = po= 1/ob- There may be cases where separate processes lead to the simultaneous presence within an experimental frequency range of both types of dispersion, but this is rare for most solid electrolytes. Further complications are present when conduction involves both mobile ionic and electronic charges, neither of whose effects are negligible (Jamnik [2003]). Here only ionic, dipolar, and vibronic effects will be further considered, with the main emphasis on conductive rather than on dielectric dispersion. 

Effect of nano particles of Al Oj on conventional SPE films have been examined by FTIR, DSC and B-G spectroscopy. The dispersal of Al O nano particles to the SPEs shows dechnation in the glass transition and melting temperature as established from DSC analysis. The FUR spectra show possible interactions between Al O nano particles and host SPE films. The optimum room temperature ionic conductivity of the order of 7 x 10 S/cm having minimum activation energy (E 0.22eV) is observed for NCPE films. This shows one order increment in the conductivity over the conventional SPE films. The temperature dependent conductivity shows Arrhenius type thermally activated behavior before as well as after glass transition temperature. Maximum value of ion transference number is found to be 0.96 which is indicative of predominant ionic (protonic) transport in the SPE and NCPE thin films. It has been observed that dielectric constant for SPE and NCPEs increases with temperature while it decreases with frequency. 

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