Time Domain Measurement

Very Fast Kinetics. One nanosecond is by no means the limit for kinetic measurements. The state-of-the-art for direct, time-domain measurements Hes close to s (10 fs). At times shorter than a few nanoseconds, however, there is usually not a weU-stinred solution. Even usiag a... 

An intuitive way to measure the rate constant, k, is to prepare some number of molecules in the excited state, perhaps with a pulse of light, and observe the amount of light given off per unit of time after the pulse. A logarithmic plot of intensity with time will give a straight-line graph with a slope of -k. This approach is the basis of time domain measurements. 

Bond et al. [791 ] studied strategies for trace metal determination in seawater by ASV using a computerised multi-time domain measurement method. A microcomputer-based system allowed the reliability of the determination of trace amounts of metals to be estimated. Peak height, width, and potential were measured as a function of time and concentration to construct the database. Measurements were made with a potentiostat polarographic analyser connected to the microcomputer and a hanging drop mercury electrode. The presence of surfactants, which presented a matrix problem, was detected via time domain dependent results and nonlinearity of the calibration. A decision to pretreat the samples could then be made. In the presence of surfactants, neither a direct calibration mode nor a linear standard addition method yielded precise data. Alternative ways to eliminate the interferences based either on theoretical considerations or destruction of the matrix needed to be considered. 

The dyes with long-lived luminescence are particularly attractive since background fluorescence can easily be discarded in time domain measurements. Crosssensitivity to oxygen may be problematic but it can be minimized by utilizing gas-blocking polymers. For example, Kuemer et al. [15] used the precipitation technique to prepare polyacrylonitrile-based beads doped with a ruthenium(II) complex which showed virtually no cross-sensitivity to oxygen. Copolymers of polyacrylonitrile and polyacrylic acid were used to provide the beads with... 

This comparison between time and frequency domain measurements is performed at submegahertz frequencies in order to avoid the issue of deconvolution of time domain signals. At megahertz frequencies time domain measurements encounter an additional limitation, these signals must be deconvoluted to isolate the sensor response from the instrument response. The need for deconvolutions adds extra software and computation time, which limits the versatility of time domain techniques for real-time applications. No deconvolutions are necessary in the frequency domain as shown below. 

In phase-modulation fluorometry, the pulsed light source typical of time-domain measurements is replaced with an intensity-modulated source (Figure 10.5). Because of the time lag between absorption and emission, the emission is delayed in time relative to the modulated excitation. At each modulation frequency (to = 2nf) this delay is described as the phase shift (0, ), which increases from 0 to 90° with increasing modulation frequency. The finite time response of the sample also results in demodulation to the emission by a factor m which decreases from 1.0 to 0.0 with increasing modulation frequency. The phase angle (Ow) and the modulation (m, ) are separate... 

Zhong Z, Gabor NM, Sharping JE et al (2008) Terahertz time-domain measurement of ballistic electron resonance in a single-walled carbon nanotube. Nat Nanotechnol 3 201-205... 

More complex chemical species have been determined using different cappings on the QDs surfaces. Shi et al. have recently demonstrated that QDs coated with oleic acid were efficiently quenched by a diversity of nitroaromatic explosives, such as 2,4,6-trinitrotoluene (TNT) or nitrobenzene.49 Different quenching behaviors were observed for the different molecules. Nevertheless, modified Stern-Volmer equations could be used, in most cases, to provide linear calibration curves. Time domain measurements showed that static quenching was the dominant process as no change in luminescence lifetime was observed in the presence of the analyte. 

Lastly it should be noted that the time or scan rate issue equally plagues time as well as frequency domain methods for obtaining Rf, since in the time domain measurement, the triangle waveform is simply the Fourier synthesis of a series of sinusoidal signal functions. However, voltage sweep, potential step, and impedance methods should all yield the same value of Rf when all the scan... 

Husimi Y, Wada A (1976) Time-domain measurement of dielectric dispersion as a response to pseudorandom noise. Rev Sci Instrum 47 213-19... 

Several comprehensive reviews on the BDS measurement technique and its application have been published recently [3,4,95,98], and the details of experimental tools, sample holders for solids, powders, thin films, and liquids were described there. Note that in the frequency range 10 6-3 x 1010 Hz the complex dielectric permittivity e (co) can be also evaluated from time-domain measurements of the dielectric relaxation function (t) which is related to ( ) by (14). In the frequency range 10-6-105 Hz the experimental approach is simple and less time-consuming than measurement in the frequency domain [3,99-102], However, the evaluation of complex dielectric permittivity in the frequency domain requires the Fourier transform. The details of this technique and different approaches including electrical modulus M oo) = 1/ ( ) measurements in the low-frequency range were presented recently in a very detailed review [3]. Here we will concentrate more on the time-domain measurements in the high-frequency range 105—3 x 1010, usually called time-domain reflectometry (TDR) methods. These will still be called TDS methods. 

Time Domain Measurements in Electromagnatics, E. K. Miller, ed., Van Nostrand Reinhold, New York, 1986. 

As an alternative to methods that use an applied sinusoidal voltage, called frequency-domain measurements, a step change in voltage across a specimen may be made and the ensuing current transient observed. Such time-domain measurements may be translated into frequency-domain terms by Fourierj integral transformations. 

Fast-response time-domain measurements suffer from error sources which in general are more commonly associated with spectroscopic techniques (e.g. n.m.r.) than with other dielectric methods. The existence of these sources of error must be recognized, particularly when selecting the most appropriate method for the collection and handling of exp -mental data. It is convenient to separate error sources into foru major categories ... 

Non-linear least-squares fitting by the Marquardt method [19,20] appears to be the most commonly used technique for hiexponential fluorescence decay analysis, at least for a time-domain measurement such as used here [21,22]. Fitting by this method requires evaluation of the derivatives of the model equation (Equation... 

Llnewldths and Unlmolecular Decay Rates. Now let us consider the questions posed In the Introduction, In the light cast by these data. The first two questions, having to do with the Interpretation of the lifetimes x and the dynamics of unlmolecular decay, are closely related. One possible Interpretation is that t is.the predissociation lifetime of the vdU molecule. It is Important to realize that a direct measurement of the excited vdU molecule population as a function of time following excitation has not been made in any of the cases cited. These are all frequency-domain experiments. A time-domain measurement is certainly possible in principle, and will probably be done in the near future. In the meantime, we must make do with circumstantial evidence. 

HRV assesses the modulation of autonomic tone on the sinus node, or simply put, the irregularity of sinus rhythm. Methods of measuring HRV fall under broad categories of being either time domain or frequency domain analyses. Time domain measurements involve statistical analyses of the variability in the R-R interval, while frequency domain measurements use spectral analysis of a series of R-R intervals to classify HRV into ultra-low frequency, very low frequency, low frequency, high frequency, and total power. One method is not better than another as there is no gold standard (65). 

The utility of low HRV in predicting SCD outcomes is not certain (65). In 900 patients without coronary heart disease (CHD), time domain measures of HRV were determined for all subjects with incident CHD and for all deaths that occurred (66). The study found that low HRV portended an elevated risk of CHD and death. In another study of 202 patients with moderate to severe HF (mean LVEF 24 7%... 

Time Domain Measurements and Fourier Transform Analysis... 

In time domain measurements, the electrochemical system is subjected to a potential variation that is the resultant of many frequencies, like a pulse or white noise signal, and the time-dependent current from the cell is recorded. The stimulus and the response can be converted via Fourier transform methods to spectral representations of amplitude and phase angle frequency, from which the desired impedance can be computed as a function of frequency. 

The autocorrelation function (ACT) reveals how the correlation between any two values of the signal changes as their separation changes [16]. It is a time domain measure of the stochastic process memory, and does not reveal any information about the frequency content of the process. Generally, for an error signal, e, the ACT is defined as. 

A. Liebert, H. Wabnitz, D. Grosenick, R. Macdonald, Fiber dispersion in time domain measurements compromising the accuracy of determination of optical properties of strongly scattering media, J. Biomed. Opt. 8, 512-516 (2003). 

We should note that, given the difference in quantum yield between the free and bound probe, the fractional intensities utilized in Fig. 7 actually represent small percentages of bound probe on a molar basis. In fact, considering the accuracy of the differential phase measurement (better than O.r) one can detect, in this system, on the order of 0.1% bound probe. This phenomenon also occurs in time-domain measurements. Specifically, if one monitors the anisotropy decay of a system which displays multiple lifetimes associated with multiple rotational diffusion rates then one may observe a decline at short times of the anisotropy followed by a rise at latter times and subsequent decrease. This dip and rise effect has been observed by Millar and co-workers in studies on protein-DNA interactions, specifically in the case of the interaction of a fluorescent DNA duplex with the Klenow fragment of DNA polymerase. 

---