Spectral relaxation continuous

The time-dependentspectral half-width AV(f) (cm" )can be used to reveal whetiter the spectral relax on is best described by a continuous or a two-step model. This halfwidth can be defined in various ways. One method is lo use a function comparable to a standard deviation. In this case AP(f) can be defined as... 

Relaxation dynamics, 212-233 continuous and twostate spectral relaxation, 212-213... 

Cole and Davidson s continuous distribution of correlation times [9] has found broad application in the interpretation of relaxation data of viscous liquids and glassy solids. The corresponding spectral density is ... 

Simulations of the experimental signal were performed using Equation 1 without adjustable parameters. The spectrum of the pulse and the absorption spectrum of HPTS were measured experimentally. An examination of the molecular structure of HPTS shows that it has no center of symmetry. Since parity restrictions may be relaxed in this case, the similarity between one-photon and two-photon absorption spectra is expected. The spectral phase

phase mask was the same used for the simulations. Both experimental and theoretical data were normalized such that the signal intensity is unity and the background observed is zero. The experimental data (dots) generally agree with the calculated response (continuous line) of the dyes in all pH environments (see Fig. 2). 

When Z is sufficiently large, it is convenient to replace the sums involved in the above expressions by integrals and define continuous distributions of relaxation and retardation times. These spectral functions are usually defined on log time scales through the relations (9) ... 

Continuous-flow 19F LC-NMR spectra were acquired for 16 transients using 60° pulses into 8192 data points over a spectral width of 11 364 Hz, giving an acquisition time of 0.36 s. A relaxation delay of 0.64 s was added to give a total acquisition time for each spectrum of 16 s. The data were multiplied by a line-broadening function of 3 Hz to improve the signal-to-noise ratio and zero-filled by a factor of two before Fourier transformation. The results are presented as a contour plot with 19F NMR chemical shift on the horizontal axis and chromatographic retention time on the vertical axis. 

For the continuous-flow measurements, the pseudo-2D spectrum was recorded with a spectral width of 9616 Hz and 64 transients with 8K complex data points, thus resulting in an acquisition time of 0.42 s/transient along the 128 t increments. A relaxation delay of 1.2 s was used and the time resolution... 

Goulet T, Pepin C, Houde D, Jay-Gerin J-P. (1999) On the relaxation kinetics following the absorption of light by solvated electrons in polar liquids Roles of the continuous spectral shifts and of the stepwise transition. Radiat Phys Chem 54 441 48. 

The power satnration occurs when the rate of absorption of microwave exceeds the rate at which the system returns to eqnilibrinm. A spectral parameter, R1/2, is used to describe quantitatively the microwave power saturation profile. In the RNR tyrosyl radical case, the R1/2 values at four representative temperatnres are given in Table 3. The most straightforward interpretation for the easily saturated radical spectra with very small P j2 values, as seen in M. tuberculosis R2, is that the tyrosyl radical is minimally influenced in its relaxation by the di-ferric clnster. This finding is reverse in mouse and yeast R2 proteins. To obtain the precise distance information in a biological system, advanced techniques such as ESSEM would be more pertinent than the continuous-wave EPR spectroscopy. 

Figure 2 shows the spectral response functions (5,(r), Eq. 1) derived firom the spectra of Fig. 1. In order to adequately display data for these varied solvents, whose dynamics occur on very different time scales, we employ a logarithmic time axis. Such a representation is also useful because a number of solvents, especially the alcohols, show highly dispersive response functions. For example, one observes in methanol significant relaxation taking place over 3-4 decades in time. (Mdtiexponential fits to the methanol data yield roughly equal contributions from components with time constants of 0.2, 2, and 12 ps). Even in sinqrle, non-associated solvents such as acetonitrile, one seldom observes 5,(r) functions that decay exponentially in time. Most often, biexponential fits are required to describe the observed relaxation. This biexponential behavior does not reflect any clear separation between fast inertial dynamics and slower diffusive dynamics in most solvents. Rather, the observed spectral shift usually appears to sirrply be a continuous non-exponential process. That is not to say that ultrafast inertial relaxation does not occur in many solvents, just that there is no clear time scale separation observed. Of the 18 polar solvents observed to date, a number of them do show prominent fast components that are probably inertial in origin. For example, in the solvents water [16], formamide, acetoniuile, acetone, dimethylformamide, dimethylsulfoxide, and nitromethane [8], we find that more than half of the solvation response involves components with time constants of 00 fs.

A characteristic feature of phytochrome photochemistry is the formation of intermediates between Pr and Pfr- The initial photochemical reaction is followed by a series of dark relaxation processes in both directions. Intermediates in the forward reaction seem to be different from those of the backward reaction. There have been four experimental approaches to these intermediates (1) determination of rapid kinetics after flash irradiation (2) low temperature studies (3) dehydration of phytochrome and (4) investigation of spectral changes after continuous irradiation. 

However, the fact that the time-evolution ofthe absorption spectrum ofthe solvated electron can be accurately described by the temperature-dependent absorption spectrum ofthe ground state solvated electron (Fig. 11) suggests that the spectral blue shift would be mostly caused by a continuous relaxation, or"cooling"of the electron trapped in a solvent cavity.To conclude, this analysis clearly indicates that it is not obvious to select a unique model to describe the solvation dynamics of electron in ethane-1,2-diol, and in other solvents. 

On approaching the transition point of a continuous-phase transition, a critical slowing down of the fluctuations occurs (t [a(T—Tc) + Dq2] x) and the amplitudes of the fluctuations increase (< q y [a(T— Tc) + Dq2] x) at wave vector q (Fig. 7a). It can be proved that apparent pseudodivergences of the relaxation rate (]/Tr)c (T Tc) 7 (with y = 1/2 in mean field theories) can be observed near a phase transition if Tqm <3 1 where cop is the probing frequency. In that case, the associated spectral density... 

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