Decay curves

Computations done in imaginary time can yield an excited-state energy by a transformation of the energy decay curve. If an accurate description of the ground state is already available, an excited-state description can be obtained by forcing the wave function to be orthogonal to the ground-state wave function. 

A rotational viscometer connected to a recorder is used. After the sample is loaded and allowed to come to mechanical and thermal equiUbtium, the viscometer is turned on and the rotational speed is increased in steps, starting from the lowest speed. The resultant shear stress is recorded with time. On each speed change the shear stress reaches a maximum value and then decreases exponentially toward an equiUbrium level. The peak shear stress, which is obtained by extrapolating the curve to zero time, and the equiUbrium shear stress are indicative of the viscosity—shear behavior of unsheared and sheared material, respectively. The stress-decay curves are indicative of the time-dependent behavior. A rate constant for the relaxation process can be deterrnined at each shear rate. In addition, zero-time and equiUbrium shear stress values can be used to constmct a hysteresis loop that is similar to that shown in Figure 5, but unlike that plot, is independent of acceleration and time of shear. 

Let us define n = tlti/, so that n is the number of half-lives elapsed. Combining this definition with Eqs. (2-8) and (2-9) gives (2-10), which is a generalized form of the first-order decay curve. 

Starting from the assumption that the geometry relaxation after excitation is of primary importance with respect to the luminescence response, we decided to employ a solid polymer matrix to suppress conformational changes of the oligomers. For the measurements, dilute blends with polysulfone as the transparent host matrix were prepared. In Figure 16-13, the PL decay curves for the two cyano compounds in both chloroform and polysulfone are presented, as are the PL spectra of Ooct-OPV5-CN in chloroform and polysulfone [69J. 

Figure 16-26. Normalized phololumincsccncc spectra of (I) Oocl-OPV5, (2) Oocl-OPV5-CN and (3) Ooct-OPV5-CN" single crystals. Inset corresponding PL-decay curves (semi log plol).

Figure 16-13. PL decay curves of cyanu-subslilulcd OPVs (I) system response (2) Ooel-OPV5-CN in CHCh (3) Ooct-OPV.S-CN" in CHCl.i (4) Ooel-OPVS-C N" in polysulldne (5) Ooel-OPV5-CN in polysiilldiie. Inset Pi. spectra of Ooet-OPV5-CN in cliloroldini (--) and polysulfoiie (.).

Fig. 11a and b. Decay of the alignment echo height as a function of the mixing time x2 for different motional mechanisms, a Tetrahedral jumps as a model for conformational changes b Diffusive motion, the solid lines correspond to unrestricted rotational diffusion, the dashed lines to diffusion restricted to an angular region of 8°. Note the strong dependence of the decay curves on the evolution time t, in case of diffusive motion... 

Fig. 19. Experimental spin alignment decay curves of chain deuterated PS-d3 at temperatures above and below the glass transition for various evolution times t,. Note the different timescales of t2 at the different temperatures. The straight lines indicate the decays of the plateau values on the timescale of the spin-lattice relaxation time T,. Sample characterization Mw = 141000, Mw/Mn = 1.13, atactic...

Fig. 20. Experimental spin alignment spectra of chain deuterated PS-d3 above and below Tg corresponding to the decay curves shown in Fig. 19...

The "add-to-memory" signal averaging method currently available to us distorts fluorescence intensity versus time plots when the fluorescence intensity is a non-linear function of incident laser energy and the laser energy varies from shot to shot. For this reason we have not attempted detailed kinetic modelling of the observed fluorescence intensity decay curves recorded at high 532 nm laser fluence. 

Typical decay curves for various ionic masses are shown in Figure 3b, where the effect of differing thermal velocity is clearly evident. Neglect of such decay characteristics can lead to serious discrimination effects. Note that all the experimental curves have the sigmoid shape... 

Figure 8. Observed decay curves for TCP0-H202"DPA chemiluminescence. TEA, triethylamine a.u., arbitrary units. (Reproduced from Ref. 24.Copyright 1986 American Chemical Society.)...

In principle, pulsed excitation measurements can provide direct observation of time-resolved polarization decays and permit the single-exponential or multiexponential nature of the decay curves to be measured. In practice, however, accurate quantification of a multiexponential curve often requires that the emission decay be measured down to low intensity values, where obtaining a satisfactory signal -to-noise ratio can be a time-consuming process. In addition, the accuracy of rotational rate measurements close to a nanosecond or less are severely limited by tbe pulse width of the flash lamps. As a result, pulsed-excitation polarization measurements are not commonly used for short rotational periods or for careful measurements of rotational anisotropy. 

Agarwal et al. 1978), the quantification of these specific enzymes may indicate that exposure to endosulfan has occurred. Blood tests, such as decay curves for aminopyrine in plasma, which are semiquantitative indices of liver enzyme induction, have been used successfully in the past to demonstrate enzyme induction in pesticide-exposed workers. Because numerous chemicals found at hazardous waste sites also induce these hepatic enzymes, these measurements are not specific for endosulfan exposure. However, measurements of enzyme activity, together with the detection of the parent compound or its metabolites in tissue or excreta, can be useful indicators of exposure. All of these potential biomarkers require further verification in epidemiological studies. Further studies with focus on the development of methods to separate and measure the estrogenicity of endosulfan in in vitro assays would be valuable since these assays are more sensitive and discriminative than other conventional biomarkers. Preliminary results have been presented by Sonnenschein et al. (1995). 

Figure 21.23 exhibits the room-temperature fluorescence decay profiles of Ba3BP30i2 Eu powders. The experimental decay curve can be fitted by an equation with two exponential terms corresponding to two decay times of 20 ns (98.97%) and 522 ns (1.03%), respectively. 

There are several correlations for estimating the film mass transfer coefficient, kf, in a batch system. In this work, we estimated kf from the initial concentration decay curve when the diffusion resistance does not prevail [3]. The value of kf obtained firom the initial concentration decay curve is given in Table 2. In this study, the pore diffusion coefficient. Dp, and surface diffusion coefficient, are estimated by pore diffusion model (PDM) and surface diffusion model (SDM) [4], The estimated values of kf. Dp, and A for the phenoxyacetic acids are listed in Table 2. 

We can see when analyzing this equation that the right-hand side is smaller than unity and increases with increasing X. For A, > 5 it tends toward unity (i.e., the reaction is practically reversible under the given conditions). Therefore, the kinetic reaction parameters (X, and hence h) can be determined from the current decay curve only when X<5 (i.e., when Parameters of reactions for which... 

A version of the galvanostatic method is that where the current is turned off (or a current f = 0 is applied ) and the polarization decay curve is measured. Consider an electrode which up to the time t = 0, when the current was turned off, had the potentiaf F at the net current density When the current is turned off, the ohmic voftage drop in the electrolyte gap between the electrode and the tip of the Luggin capillary vanishes, so that the potential instantaneously shifts to the value F (Fig. 12.11). After that the electrode potential returns (falls) relatively slowly to its open-circuit value, for which a certain nonfaradaic charging current is required. Since ip + =... 

FIGURE 12.11 Potential decay curves recorded after switching off the current (a) at short times (b) at long times. 

Integrating this equation between the limits of f = 0 and t, taking into account that at f = 0 the potential E = E, and performing simple transformations, we obtain an equation for the potential decay curve ... 

Figure 4.7 Fluorescence anisotropy decay curves for the PMMA brush swollen in benzene (filled circles) and the free PMMA chain in benzene solution at concentrations of 0.33 (triangles) and 2.9 X 10 g (open circles). The graft density of the brush is 0.46 chains nm . The solid curve indicates the instrument response function. Reproduced with permission from the American Chemical Society.

Figure 4.8 shows the fluorescence anisotropy decay curves for PMMA brushes with various graft densities swollen in benzene and acetonitrile. Benzene and acetonitrile are good and 0 solvents for PMMA. As clearly shown in this figure. 

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