Frequency domain spectroscopy, dielectric

The dielectric spectroscopy study of conductive samples is very complicated because of the need to take into account the effect of dc-conductivity. The dc-conductivity c>o contributes, in the frequency domain, to the imaginary part of the complex dielectric permittivity in the form of additional function a0/(so ). The presence of dc-conductivity makes it difficult to analyze relaxation processes especially when the contribution of the conductivity is much greater than the amplitude of the process. The correct calculation of the dc-conductivity is important in terms of the subsequent analysis of the dielectric data. Its evaluation... 

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. 

Practically, DMTA is limited to low frequencies (up to tens of hertz) and, consequently, provides information about relatively slow processes. Dielectric spectroscopy is a related approach in which an alternating electric field is applied to a sample and the complex permittivity is then obtained from phase and amplitude measurements of current and voltage again, it is possible to consider data in the frequency domain, the temperature domain, or even as frequency/temperature contour maps.2 ° 2 See Refs. 230 and 232 for a theoretical account of the underlying physics. The approach can provide information in the frequency range W -io" coupling the applied electric field... 

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]. 

One of the methods used to study emulsions has been the use of dielectric spectroscopy. The permittivity of the emulsion can be used to characterize an emulsion and assign a stability (1,42,48—54). The Sjoblom group has measured the dielectric spectra using time-domain spectroscopy (TDS) technique. A sample is placed at the end of a coaxial line to measure total reflection. Reflected pulses are observed in time windows of 20 ns, Fourier transformed in the frequency range from 50 MHz to 2 GHz, and the complex permittivity calculated. Water or air can be used as reference sample. The total complex permittivity at a frequency (co) is given by ... 

This paper is primarily concerned with the techniques usually described as time domain spectroscopy (TDS) or time domain reflectom-etry (TDR). These have been most commonly applied to studies of time or frequency dependent behavior of dielectrics with negligible ohmic or d.c. conductance, but can be used for substances with appreciable conductance and indeed for studies of any electrical properties which can be characterized by an effective admittance or impedance. 

Dielectric spectroscopy is routinely carried out in frequency rather than time domain. The dielectric constant is a frequency-dependent complex number, related to (t) by(3)... 

Figure 5 Ranges of some dielectric relaxation spectroscopy techniques (a) conventional transient methods (b) newer transient methods (c) low frequency impedance bridge (d) conventional impedance bridges and analyzers (e) high frequency impedance analyzers and time domain spectroscopy (f) microwave cavities, transmission lines ...

In most cases, the measurements are carried out isothermally in the frequency domain and the terms dielectric spectroscopy (DS) and dielectric relaxation spectroscopy (DRS) are then used. Other terms frequently used for DRS are impedance spectroscopy and admittance spectroscopy. Impedance spectroscopy is usually used in connection with electrolytes and electrochemical studies, whereas admittance spectroscopy often refers to semiconductors and devices. Isothermal measurements in the time domain are often used, either as a convenient tool for extending the range of measurements to low frequencies (slow time-domain spectroscopy, dc transient current method, isothermal charging-discharging current measurements) or for fast measurements corresponding to the frequency range of about 10 MHz - 10 GHz (time-domain spectroscopy or time-domain reflectometry). Finally, TSDC is a special dielectric technique in the temperature domain, which will be discussed in Section 2.2. 

Figure 1. Techniques and equipment for dielectric measurements. FRA means frequency response analyzer, TDS is time domain spectroscopy...

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. 

This chapter concentrates on the results of DS study of the structure, dynamics, and macroscopic behavior of complex materials. First, we present an introduction to the basic concepts of dielectric polarization in static and time-dependent fields, before the dielectric spectroscopy technique itself is reviewed for both frequency and time domains. This part has three sections, namely, broadband dielectric spectroscopy, time-domain dielectric spectroscopy, and a section where different aspects of data treatment and fitting routines are discussed in detail. Then, some examples of dielectric responses observed in various disordered materials are presented. Finally, we will consider the experimental evidence of non-Debye dielectric responses in several complex disordered systems such as microemulsions, porous glasses, porous silicon, H-bonding liquids, aqueous solutions of polymers, and composite materials. 

The FT technique has been applied in a multitude of different areas. Starting at low frequencies, FT methods have been used for dielectric response spectroscopy of solids (sometimes called time domain reflectometry). A short picosecond voltage pulse is applied to a dielectric and the current response is measured. Fourier transformation of the current gives the dielectric response function, s v), which is typically interpreted as the Debye relaxation of dipoles. 

In a similar manner to light, other types of radiation, e.g., electromagnetic waves in the X-ray domain, high-frequency electric fields, or acoustic waves, offer ways to monitor changes in composition and structure of suspensions. For instance, dielectric spectroscopy was used to investigate the moisture uptake and stability of cosmetic creams (Sutananta et al. 1996 Tamburic et al. 1996), and acoustic parameters (resonance frequency, attenuation, sound speed) were shown to correlate with sol-gel transition in suspensions of coUoidal silica (Senouci et al. 2001), as well as with the phase transition of renneted milk (Bakkali et al. 2001). 

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