Detection time constant

For each of the columns in table 7.2 the hold-up time (t0) can readily be calculated from eqn.(7.6) using k=0. The standard deviation in time units follows from t0 after division by vN (eqn.1.16). Eqns.(7.35) and (7.36) then provide the maximum allowable detection time constant (r), the required sample frequency for digital data handling (/) and the required number of datapoints (Ndat) for recording a chromatogram (0 < k< 4). All these characteristics are shown for the different columns in the bottom part of table 7.2. 

Table 7.3b shows the calculated maximum allowable detection time constants for the First three columns of table 7.1 for three different values of the capacity factor, using the values for N and t0 given in this table. 

In this section we have derived rules of thumb for the maximum allowable extra-column dispersion and detection time constant and for the minimum required sample frequency for digital data handling. 

Both in GC and in LC the detection time constant needs to be reduced. even for the application of conventional columns. A great reduction is required to follow modern developments in column technology and the use of digital data handling appears to be unavoidable. 

In addition to comparing the sum of squares, the experimental and simulated data should be compared by using complex plane and Bode plots. The phase-angle Bode plot is particularly sensitive in detecting time constants. Boukamp proposed to study the residual sum of squares after subtracting the assumed model values from the total impedance data. If the model is valid, the residuals should behave randomly. If they display regular tendencies, it may mean that the model is not correct and further elements should be added. However, the variations of the residuals should be statistically important. 

This technique may be further applied to the study of intramolecular motions of large molecules. If there is a change in optical anisotropy (in a laboratory-fixed system) associated with an intramolecular motion (see Pecora, 1968), the relaxation rate of the motion should affect the depolarized spectrum. Schmitz and Schurr (1973) have detected time constants for motions of this type in the depolarized spectra of DNAs in solution. < v... 

The goal of the investigations is to understand the microscopic properties of the electron transfer. The primary experimental result concerns the number n of intermediate states involved, which is equal to the number of detected time constants t.. This determination requires a very careful decomposition of the time dependence of AA(X, tj ) into exponentials ... 

When a toroidal ferromagnetic sample is subjected to shock loading, a pressure wave of pressure P moves through the sample with a velocity U and produces a change in magnetization AM. An N-turn detection coil with inductance L is wound around the sample and connected to a resistive circuit in which the L/R time constant is longer than the time required for the shock wave to traverse the sample thickness. The current i in the coil is then... 

Fiq. 20a. The pulsed Raman spectrum of Mn-doped ZnSe single crystal using a detection interval of 200 nsec. Broad band fluorescence superimposed on a large instrumental scattered light component was observed. Recordings taken with ratemeter time constants (TC) of 1 sec and 10 sec are shown (37). 

Temperature programmed desorption, TPD detection of backspillover species, 228 of oxygen, 228 Thermodynamics of adsorption, 306 of spillover, 104, 499 Three phase boundaries charge transfer at, 114 electrocatalysis at, 115 length, measurement of, 243 normalized length, 243 Time constants ofNEMCA analysis of, 198 and backspillover, 198 prediction of, 200... 

These can be solved by classical methods (i.e., eliminate Sout to obtain a second-order ODE in Cout), by Laplace transformation techniques, or by numerical integration. The initial conditions for the washout experiment are that the entire system is full of tracer at unit concentration, Cout = Sout = L Figure 15.7 shows the result of a numerical simulation. The difference between the model curve and that for a normal CSTR is subtle, and would not normally be detected by a washout experiment. The semilog plot in Figure 15.8 clearly shows the two time constants for the system, but the second one emerges at such low values of W t) that it would be missed using experiments of ordinary accuracy. 

Figure 3.3 The mechanics of obtaining a two-dimensional NMR spectrum. As the l value is varied, the magnetization vectors are caught during detection at their various positions on the x /-plane. The value of the detection time l-i is kept constant. The first set of Fourier transformations across is followed by transposition of the data, which aligns the peaks behind one another, and a second set of Fourier transformations across t then affords the 2D plot.

It is now possible to constmct a processor setup that combines good reproducibility and a low time constant with a theoretical sensitivity of 0.05mV for about a 0.5-mm air gap, changes in E equal to 0.5 may be detectable. Of course, it is easier for solid than for liquid surfaces. 

The current amplitude cannot be increased at free will, because the clamp voltage will usually not exceed + 100 mV. A simple calculation reveals that, given the limitations above, channels need to have a conductance of 10 pS, and time constants in the millisecond range to be detected. Any channel smaller or faster than this will escape detection in this analysis. 

In order to directly probe the dynamics of CT between Et and ZG, and to understand how the intervening DNA base stack regulates CT rate constants and efficiencies, we examined this reaction on the femtosecond time scale [96]. These investigations revealed not only the unique ability of the DNA n-stack to mediate CT, but also the remarkable capacity of dynamical motions to modulate CT efficiency. Ultrafast CT between tethered, intercalated Et and ZG was observed with two time constants, 5 and 75 ps, both of which were essentially independent of distance over the 10-17 A examined. Significantly, both time constants correspond to CT reactions, as these fast decay components were not detected in analogous duplexes where the ZG was re-... 

The first experimental data for a reaction involving proton transfer from a hydrogen-bonded acid to a series of bases which were chosen to give ApK-values each side of ApK=0 are given in Fig. 15 (Hibbert and Awwal, 1976, 1978 Hibbert, 1981). The results were obtained for proton transfer from 4-(3-nitrophenylazo)salicylate ion to a series of tertiary aliphatic amines in aqueous solution, as in (64) with R = 3-nitrophenylazo. Kinetic measurements were made using the temperature-jump technique with spectrophoto-metric detection to follow reactions with half-lives down to 5 x 10"6s. The reciprocal relaxation time (t ), which is the time constant of the exponential... 

The non-mono-exponentiality of the transverse relaxation in muscle and meat has most often been solved by decomposing the relaxation decay into two or three exponential components. In general, this has resulted in the detection of a major relaxation component characterised by a time constant around 35-50 ms, which corresponds to approximately 80-95% of the relaxation, and a slower relaxing component characterised by a time constant around 100-250 ms, which represents approximately 5-15% of the relaxation. In addition, a fast relaxing component with a time constant between 0 and 10 ms, which corresponds to about 5% of the relaxation, has been observed.9,11 The presence of three relaxation components in the... 

A pressure perturbation results in the shifting of the equilibrium the return of the system to the original equilibrium state (i.e., the relaxation) is related to the rates of all elementary reaction steps. The relaxation time constant associated with the relaxation can be used to evaluate the mechanism of the reaction. During the shift in equilibrium (due to pressure-jump and relaxation) the composition of the solution changes and this change can be monitored, for example by conductivity. A description of the pressure-jump apparatus with conductivity detection and the method of data evaluation is given by Hayes and Leckie (1986). 

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