Dielectric spectroscopy time-domain analysis

T. Sun, S. Gawad, N. G. Green and H. Morgan, Dielectric spectroscopy of single cells time domain analysis using Maxwell s mixture equation, J. Phys. D. Appl Phys., 40, 1-8 (2007). 

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. 

Time Domain Spectroscopy (T.D.S.).—Transient dielectric methods for the study of molecular motions occurring in less than 10 s are a relatively recent addition to the chemist s armoury. The availability of tunnd diode pulse-geam ators and wide-band sampling oscilloscopes led to the devdop-ment in the 1960 s of pulse reflection techniques known as time domain reilectometry (Ld.r.). The value of these methods was soon recognized in the fields of electronic and communication engineering for the qualitative analysis of transmission line systems and by 1965 had been used for... 

Fordedal H, Midttun O, Sjoblom J, Kvalheim OM, Schildberg Y, Voile JL. A multivariate screening analysis of W/O emulsions in high external electric fields as studied by means of dielectric time domain spectroscopy. II. Model emulsions stabilized by interfacially active fractions from crude oils. J. Colloid Interface Sci 1996 182 117-125. 

These authors noted that the intermediate power law (i.e., t l+y, with a small positive 7) of the OKE data was formally equivalent to the excess wing in the frequency-dependent susceptibility, the latter discussed in the dielectric literature since 1951. Brodin and Rossler argued that the intermediate power law observed in the OKE data was in essence a manifestation of the excess wing of the corresponding frequency-domain data, known long since from broadband dielectric spectroscopy and anticipated from DLS studies of supercooled liquids [83]. More recently, these authors showed that the excess wing was an equally common feature of the DLS data and discussed the merits of the Mode coupling theory analysis of the time and frequency-domain data [84]. 

Dielectric spectroscopy also allows monitoring the structural relaxation time and, eventually, its slowdown as expected in the case of higher fractions of MROs. Furthermore, investigation of the form of the relaxation peaks in the frequency domain permitted us to characterize the dynamic heterogeneity of our films. For this purpose, a quantitative analysis was achieved via fits of the experimental data to the Havrialiak-Negami equation... 

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. 

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