Slow time-domain measurements

Figure 6.12. Schematic of the apparatus used for thermally stimulated current (TSC) studies. The basic concept apphes also for slow time-domain spectroscopy measurements.

In practice, time-domain measurements can be done using time correlated single photon counting (TCSPC) whereby the arrival time of the first photon after each pulse is monitored at very high time resolution [ 17]. By recording the arrival times of a large number of photons, a representation of the decay curve is obtained. In order for this approach to work, the chance of detection of a photon after a pulse should be low. If this is not the case, the distribution will be biased toward shorter lifetimes. It has been estimated that, for TCSPC to work for lifetime measurements, the detection efficiency should be 1% or lower [15]. This means that TCSPC always is relatively slow. Advantage is that the actual decay curve is measured directly. 

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. 

In frequency-domain FLIM, the optics and detection system (MCP image intensifier and slow scan CCD camera) are similar to that of time-domain FLIM, except for the light source, which consists of a CW laser and an acousto-optical modulator instead of a pulsed laser. The principle of lifetime measurement is the same as that described in Chapter 6 (Section 6.2.3.1). The phase shift and modulation depth are measured relative to a known fluorescence standard or to scattering of the excitation light. There are two possible modes of detection heterodyne and homodyne detection. 

In order to implement frequency domain based sensing systems capable of monitoring the temporal luminescence of sensors, in few seconds, data must be collected at multiple frequencies simultaneously. Single-frequency techniques have been used to make frequency domain measurements of luminescent decays. 14, 23 28) This approach is unsuitable for real-time applications since data must be acquired at several frequencies in order to precisely and accurately determine the temporal variables of luminescent systems. 1 Each frequency requires a separate measurement, which makes the single frequency approach too slow to monitor the evolution... 

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. ... 

The photoreduction of 9,10-anthraquinone-1,5-disulfonate by 2,2,6,6-tetramethyl piperidine in aqueous media has been studied in the nanosecond and microsecond time domains by use of time-resolved optical and ESR measurements [171]. Electron transfer from the amine to the excited state of the anthraquinone derivative occurs with a rate constant of 5.7 x 10 m s . The aminyl radicals formed via deprotonation of the aminium radicals are long-lived (ca 0.5 ms), because the steric hindrance of these radicals slows down recombination reactions. The aminyl radicals formed in these systems have been characterized by ESR. 

In time-domain interferometry the two pulses are sent collinearly to a square law detector which responds equally to all the frequencies in the pulses. The current in the slow detector circuit S x) is measured as a function of the delay, x, between the two pulses. A common but not necessary situation in heterodyning is that one field, El (f ) is very weak so that its square can be neglected while the other, the local oscillator field, E2 t — t) is much larger. The signal is time integrated by the slow detector ... 

As an experimental approach to investigate the temperature behavior of extremely slow structural glass relaxation processes (a-relaxation) we resently presented measurements with time domain Brillouin spectroscopy (TDBS) performed... 

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