Dispersion Time

There are a number of observations to be drawn from the above fomuila the relative uncertainty can be reduced to an arbitrarily small value by increasing T, but because the relative uncertainty is proportional to /s/f, a reduction in relative uncertainty by a factor of two requires a factor of four increase in collection time. The relative uncertainty can also be reduced by reducing At. Flere, it is understood that At is the smallest time window that just includes all of the signal. At can be decreased by using the fastest possible detectors, preamplifiers and discriminators and minimizing time dispersion in the section of the experiment ahead of the detectors. 

Stephens, W. E. A pulsed mass spectrometer with time dispersion. (Proc. Am. Phys. Soc.) Phys. Rev. 1946, 69, 691. 

At one time disperse-type FBAs, such as pyrazoline, coumarin or naphthalimide derivatives, were commonly used to brighten acrylic fibres. Today all the important brighteners for these fibres are cationic in character and can be divided into two main categories ... 

W. E. Stephens. A Pulsed Mass Spectrometer with Time Dispersion. Phys. Rev., 69(1946) 691. 

Low transit-time dispersion with photon wavelength, i.e., < 0.5 psec/nm. This minimizes the effect on convolution of the difference between the excitation and fluorescence wavelengths. Both side-window and linear focused photomultipliers satisfy this. 

Low transit-time dispersion with point of illumination on the photocathode, i.e., < 20 psec/mm. Linear focused photomultipliers satisfy this criterion, but side-window devices do not. This again is relevant to successful data analysis. 

Figure 3.20 shows the effect of the transit time dispersion on the measurement of an ideal light pulse. Since photoelectrons spend some time traveling from the photocathode to the anode (transit time), the photomultiplier signal is delayed in time with respect to the incident pulse. Furthermore, due to the transit time dispersion, the... 

Time-of-flight TOP Time dispersion of a pulsed ion beam separation by time-of-flight... 

Wolff, M.M. Stephens, W.E. A Pulsed Mass Spectrometer With Time Dispersion. Rev. Sci. Instrum. 1953, 24, 616-617. 

Fig. 6 Zero field hole mobility of the bis-fluorene dendrimer of Fig. 5 as a function of lAT. The deviation of the ln t(F )cxl/r dependence below 215 K is a signature of the onset of transit time dispersion. From [49] with permission. Copyright (2008) by Elsevier...

Scher H, Montroll EW (1975) Anomalous transit-time dispersion in amorphous solids. Phys Rev B 12 2455... 

The study of the dispersion of photoinjected charge-carrier packets in conventional TOP measurements can provide important information about the electronic and ionic charge transport mechanism in disordered semiconductors [5]. In several materials—among which polysilicon, a-Si H, and amorphous Se films are typical examples—it has been observed that following photoexcitation, the TOP photocurrent reaches the plateau region, within which the photocurrent is constant, and then exhibits considerable spread around the transit time. Because the photocurrent remains constant at times shorter than the transit time and, further, because the drift mobility determined from tt does not depend on the applied electric field, the sample thickness carrier thermalization effects cannot be responsible for the transit time dispersion observed in these experiments. 

There are several mechanisms that can lead to the carrier packet and transit time dispersion under quasi-equilibrium transport conditions [11]. Pirst, the propagating carrier packet experiences dispersion arising from the mutual Coulombic repulsion of the carriers. This Coulombic spatial dispersion increases linearly with time and with the amount of injected charge Qo as... 

The preceding equation shows that the transit time dispersion under weak field conditions is controlled by conventional diffusion, whereas at strong fields, the main contribution to Ate arises from the field-assisted diffusion term. A crossover from Atj to Atj occurs in the field dependence of the transit time dispersion that corresponds to the crossover from Atj E to Atj E in the dependence of the transit time dispersion on the transit time. It is worth noting that all parameters describing the contribution of the preceding equation are defined by independent measurements, while the contribution of the field-induced diffusion depends on the value of the effective release time, which is poorly known and can be very different in different disordered materials. 

All the preceding mechanisms of the carrier packet spread and transit time dispersion imply that charge transport is controlled by traps randomly distributed in both energy and space. This traditional approach completely disregards the occurrence of long-range potential fluctuations. The concept of random potential landscape was used by Tauc [15] and Fritzsche [16] in their models of optical absorption in amorphous semiconductors. The suppressed rate of bimolecular recombination, which is typical for many amorphous materials, can also be explained by a fluctuating potential landscape. 

The effect of Sb on electron transport is not so drastic. Although Sb alloying increases the transit time dispersion, the transit time shown contains a clearly identifi-ably break in the waveform. The electron drift mobihty in a-Sb Sci alloys exhibits Arrhenius behavior. The experimentally observed activation energy of a-Se—namely,... 

Fixation is performed by steaming under various conditions, depending on the fibers and dyes involved. Generally, saturated steam at ca. 100°C is applied. Pressure steamers permit a reduction of the steaming time. Disperse dyes are fixed in polyester fibers by the Thermosol process the fabric is heated in a infrared unit by radiation, by hot air, or with contact heat to 210-220°C for 30-60 s. Superheated steam facilitates rapid fixation at lower temperatures. 

The relationship for the interpretation of data measured for RTD can be easily derived with Laplace transformation [54]. However, the equations so obtained are not convenient for time-dispersed measurement because they still need Laplace transformation to deal with the data. In the following, another relationship will be derived. 

Choosing between these three approaches is not always easy. Diffusion problems normally give a concentration profile as a function of position and time. Dispersion can do the same, but dispersion tends to be dependent solely on the physics, and not be affected by chemistry. Mass transfer coefficients, on the other hand, tend to describe concentrations as a function of position or time, rather than both variables at once. 

Diffusion, dispersion, and mass transfer are three ways to describe molecular mixing. Diffusion, the result of molecular motions, is the most fundemental, and leads to predictions of concentration as a function of position and time. Dispersion can follow the same mathematics used for diffusion, but it is due not to molecular motion but to flow. Mass transfer, the description of greatest value to the chemical industry, commonly involves solutes moving across interfaces, most commonly, fluid-fluid interfaces. Together, these three methods of analysis are important tools for chemical engineering. 

IRS and OHD-RIKES are less effected by the background interference, but the signal levels tend to be low, and they are subject to noise in the broad-band dye laser probe. Attempts to eliminate the remaining noise by time dispersal of the Raman signal and local oscillator by means of a streak camera (9) or a smoothing of the dye probe mode structure by intracavity phase shifting of the dye radiation are under consideration. 

Enokida et al. (1991) measured hole mdbilities of PMPS before and after ultraviolet exposures. The exposures were of the order of 1 erg/s-cm2. Prior to the exposures, the mobilities were approximately 10-4 cm2/Vs and weakly field dependent. Following the exposures, a decrease in the mobility was observed. Under vacuum exposure conditions, a decrease of approximately 40% was observed for a 1 h exposure. Under atmospheric conditions, however, the decrease was approximately a factor of 4. Enokida et al. attributed the decrease in mobility to the formation of Si-O-Si bonds in the Si backbone chain. A similar study of PMPS was described by Naito et al. (1991). While the field and temperature dependencies of the mobility were not affected by the ultraviolet exposures, the dispersion in transit times increased significantly. The change in dispersion could be removed by subsequent annealing. The authors attributed the increase in transit time dispersion to a reduction in the hole lifetime, induced by Si dangling bonds created by the ultraviolet radiation. 

Saltbones J, Eoss A, Bartnicki J (1995) Severe nuclear accident program (SNAP) - a real time dispersion model. In Gryning SE, Schiermeier FA (eds) Proceedings of the 21st NATO/ CCMS Meeting on air pollution modelling and its application, November 1995, Baltimore, USA, pp 333-340... 

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