Slow time-domain dielectric

Besides the abovementioned commercial systems, it is also possible to build homemade systems for TSC and slow time-domain dielectric experiments by constructing a simple electric circuit that includes the sample capacitor and either a typical voltage source for the polarization step (e.g., a Keithley 450 source) or an electrometer for the depolarization step (e.g., a Keithley 617 or 642 electrometer). A suitable sample cell (e.g., a parallel-plate capacitor placed within a homemade or a commercial cryostat with controlled inert gas flow) and a compatible temperature control system are also required. The creative minds of the technicians working in the laboratory and the use of the technical information and diagrams available in several journal publications, books, or... 

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. 

In slow time domain spectroscopy, a voltage step is applied to the sample and the polarization or depolarization current /(t) is measured as a function of time. The time-dependent dielectric permittivity e(t) is then given by... 

The observation of slow, confined water motion in AOT reverse micelles is also supported by measured dielectric relaxation of the water pool. Using terahertz time-domain spectroscopy, the dielectric properties of water in the reverse micelles have been investigated by Mittleman et al. [36]. They found that both the time scale and amplitude of the relaxation was smaller than those of bulk water. They attributed these results to the reduction of long-range collective motion due to the confinement of the water in the nanometer-sized micelles. These results suggested that free water motion in the reverse micelles are not equivalent to bulk solvation dynamics. 

Direct numerical Fourier transformation when a wide range of frequencies is involved requires the storage of a very large number of data samples [i (0] d extendve computation. The usual practice in slow-response time-domain methods has consequently been to employ more approximate transformation methods, such as the Hamon approximation. This relates the current per unit voltage at time t, i(/), to the dielectric loss e at the frequency v = 1/10/ by... 

Application to Polymeric Materials.—There have been several notable examples of the application of slow-response time-domain methods to dielectric measurements of polymers. - Williams used a step-up and step-down method and calculated e"(to), via the Hamon approximation, from the average of the transient charging and discharging currents. Later usage has led to improved precision. ... 

Figure 6.4.7 compares C(f) of two polymer dielectrics that manifest slow polarizability with a dielectric that does not. At very low frequencies (below 100 mHz), the capacitances of the dielectrics with absorbed water increase significantly. In the time domain, this leads to memory effects in which voltages applied in the past affect how the OTFT responds to applied signals in the present. 

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