Dielectric spectroscopy frequency response analysis

In order to actually cover 19 decades in frequency, dielectric spectroscopy makes use of different measurement techniques each working at its optimum in a particular frequency range. The techniques most commonly applied include time-domain spectroscopy, frequency response analysis, coaxial reflection and transmission methods, and at the highest frequencies quasi-optical and Fourier transform infrared spectroscopy (cf. Fig. 2). A detailed review of these techniques can be found in Kremer and Schonhals [37] and in Lunkenheimer [45], so that in the present context only a few aspects will be summarized. 

It is not a trivial problem to obtain a complete characterization of a material responding over many decades of time. The brute force method would be to carry out experiments over many decades of time. More efficient is to employ more than one instrument, and cover a time span that includes high frequencies. This is now possible with broad dielectric spectroscopy, with which the frequency reuige from 10 to 10 can be attained by using different techniques - time domain spectroscopy, frequency response analysis using AC-bridges, and coaxial line reflectrometry. Of course, each isothermal experiment has to be repeated at various temperatures in order to determine the temperature dependence. 

An innovative approach due to Haider et al. [113] may help to sidestep the challenges involved in explicit molecular dynamics simulation and obtain information on these slow dynamics. The authors use the results of dielectric reflectance spectroscopy to model the IL as a dielectric continuum, and study the solvation response of the IL in this framework. The calculated response is not a good description of the subpicosecond dynamics, a problem the authors ascribe to limited data on the high frequency dielectric response, but may be qualitatively correct at longer times. We have already expressed concern regarding the use of the dielectric continuum model for ILs in Section IV. A, but believe that if the wavelength dependence of the dielectric constant can be adequately modeled, this approach may be the most productive theoretical analysis of these slow dynamics. 

Alternatively, an equally powerful visualization of impedance data involves Bode analysis. In this case, the magnitude of the impedance and the phase shift are plotted separately as functions of the frequency of the perturbation. This approach was developed to analyze electric circuits in terms of critical resistive and capacitive elements. A similar approach is taken in impedance spectroscopy, and impedance responses of materials are interpreted in terms of equivalent electric circuits. The individual components of the equivalent circuit are further interpreted in terms of phemonenological responses such as ionic conductivity, dielectric behavior, relaxation times, mobility, and diffusion. 

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