Decay rate time constant

Transient absorption measurements on the Dll mutant of Rb. capsulatus in the region of the bacteriopheophytins at (520-560)nm show a broad structureless feature similar to the one observed for R. viridis RCs in the state PH Qa- Neither bleaching in the region of Ha nor in the one of H3 is observed. The positive difference absorption decays with time constants of (300 100)ps and (500 100)ps at 280K and 80K, respectively (Fig.3a). These values are very well compatible with the results from the time-resolved fluorescence measurements. The temperature dependence of the decay rate is the same as in the doubly reduced RCs of R. viridis in both cases the rate increases slowly with increasing temperature. 

The anisotropy of the g and hyperfine tensor leads to a dependence of the spectral line shape of nitroxides on the reorientation rate in soft matter or liquid solution. In the simplest case, nitroxide motion can be considered as isotropic Brownian rotational diffusion and can then be characterized by a single rotational correlation time Zr. To understand Zr, one can consider the reorientation of the molecular z axis caused by stochastic molecular motion. With the angle 0 between the orientation of this axis at zero time and the orientation at time t, the correlation fimction (cos0) exhibits exponential decay with time constant (the brackets () denote the average over a large ensemble of nitroxide molecules). Starting from the rigid limit, exemplified by a solid sample at very low... 

The first detailed investigation of the reaction kinetics was reported in 1984 (68). The reaction of bis(pentachlorophenyl) oxalate [1173-75-7] (PCPO) and hydrogen peroxide cataly2ed by sodium saUcylate in chlorobenzene produced chemiluminescence from diphenylamine (DPA) as a simple time—intensity profile from which a chemiluminescence decay rate constant could be determined. These studies demonstrated a first-order dependence for both PCPO and hydrogen peroxide and a zero-order dependence on the fluorescer in accord with an earher study (9). Furthermore, the chemiluminescence quantum efficiencies Qc) are dependent on the ease of oxidation of the fluorescer, an unstable, short-hved intermediate (r = 0.5 /is) serves as the chemical activator, and such a short-hved species "is not consistent with attempts to identify a relatively stable dioxetane as the intermediate" (68). 

Ohmic charge decay processes obey a first order rate law from which the charge Q remaining at any time t can be expressed in terms of the initial charge Qq and relaxation time constant r. Using Eqs. (2-3.4) through (2-3.5) the time constant r can alternatively be expressed as... 

One example of this occurs with stress relaxation. If a polymer is deformed to a fixed strain at constant temperature the force required to maintain that strain will decay with time owing to viscous slippage of the molecules. One measure of this rate of decay or stress relaxation is the relaxation time 0, i.e. the time taken for the material to relax to 1/e of its stress on initial application of strain. 

Figure 13, indicates that the first mole of phenol is released in <30 s, the same elapsed time for the chemiluminescence to reach a maximum intensity. In fact, the measured rate constant r, for the rise in the chemiluminescence emission, is identical to the rate of the first phenol s release from the oxalate ester. Furthermore, the slower rate of release of the second phenol ligand has a rate constant that is identical to the chemiluminescence decay rate f. Thus, the model allows a quantitative analysis of the reaction mechanism, heretofore not available to us. We intend to continue this avenue of investigation in order to optimize the chemiluminescence efficiencies under HPLC conditions and to delineate further the mechanism for peroxy-oxalate chemiluminescence. 

Equation (75) shows that (u(t) is an exponentially decaying function for long times with a decay constant /p. For very massive B particles M N mN with M/mN = q = const, the decay rate should vary as 1 /N since p = mNq/ (q + 1). The time-dependent friction coefficient (u(t) for a B particle interacting with the mesoscopic solvent molecules through repulsive LJ potentials... 

In this system, the rate of decay might be expressed as a change in concentration per unit time, AC/At, which corresponds to the slope of the line. But the line in Fig. 1 is curved, which means that the rate is constantly changing and therefore cannot be expressed in terms of a finite time interval. By resorting to differential calculus, it is possible to express the rate of decay in terms of an infinitesimally small change in concentration (dC) over an infinitesimally small time interval (dt). The resulting function, dC/dt, is the slope of the line, and it is this function that is proportional to concentration in a first-order process. Thus,... 

When [El] has been reduced to the point that it is equal in concentration to [EI Je, the natural logarithm of the ratio /f/, /[ 7]0 would be ln(l/< ) = -1.0. The length of time required for [EI to decay by this amount can be obtained from the semilog plot shown in Figure A1.4B. This time interval is referred to as the relaxation time or the time constant and is given the symbol x. The relaxation time is the reciprocal of the rate constant ... 

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-... 

In (8), the solvent-independent constants kr, kQnr, and Ax can be combined into a common dye-dependent constant C, which leads directly to (5). The radiative decay rate xr can be determined when rotational reorientation is almost completely inhibited, that is, by embedding the molecular rotor molecules in a glass-like polymer and performing time-resolved spectroscopy measurements at 77 K. In one study [33], the radiative decay rate was found to be kr = 2.78 x 108 s-1, which leads to the natural lifetime t0 = 3.6 ns. Two related studies where similar fluorophores were examined yielded values of t0 = 3.3 ns [25] and t0 = 3.6 ns [29]. It is likely that values between 3 and 4 ns for t0 are typical for molecular rotors. 

Figure 5. The areal exhalation rate from the porous sample in Figure 2, enclosed in three different exhalation cans. Two of them ( a1 and 0 ) are completely radon-tight and the third Cb1) has a radon leak rate constant v, numerically equal to the radon decay rate constant (v=A= 2.1 10" s" ). The cans are closed at time zero. The radon exhalation evolution as a function of time is discussed in the text (theory).

The fluorescence decay time is one of the most important characteristics of a fluorescent molecule because it defines the time window of observation of dynamic phenomena. As illustrated in Figure 3.2, no accurate information on the rate of phenomena occurring at time-scales shorter than about t/100 ( private life of the molecule) or longer than about 10t ( death of the molecule) can be obtained, whereas at intermediate times ( public life of the molecule) the time evolution of phenomena can be followed. It is interesting to note that a similar situation is found in the use of radioisotopes for dating the period (i.e. the time constant of the exponential radioactive decay) must be of the same order of magnitude as the age of the object to be dated (Figure 3.2). 

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