Echo decay time

ESE-detected EPR spectroscopy has been used advantageously for the separation of spectra arising from different paramagnetic species according to their different echo decay times. Furthemiore, field-swept ESE... 

The vibrational echo experiments yielded exponential decays at all temperatures. The Fourier-transfonn of the echo decay gives the homogeneous lineshape, in this case Lorentzian. The echo decay time constant is AT, where is... 

Morrow et al. measured the spin-lattice relaxation time Ti and quadrupole echo decay times T ) of headgroup deuterated d4-DMPC as a function of temperature and pressure to yield additional information about changes in the headgroup dynamics. Generally, motions in a LC phospholipid bilayer can... 

The excellent resolution of the 0-tensor components at W band has been used to measure the relaxation properties of QA in the Zn-substituted bRC of R. sphaeroides.m The experiment showed, in contrast to the respective ubiquinone radical in organic solution, an anisotropic relaxation behavior in the pulse high field ESE experiments. From the analysis of the T2 experiments a motional anisotropy of Q% in the protein pocket was deduced with a preferred libration about the C-O symmetry axis. Recently, similar experiments were also performed on Qb- in ZnbRCs. Compared to QA different echo decay time constants were found. A model was proposed in which the relaxation is related to reorientational fluctuations around the quinones specific H-bonds to the protein.142... 

Physical parameters Molecular 0.1-1 nm Dipole-dipole interaction Second moment, fourth moment of lineshape Incoherent magnetization transfer characteristic times for cross-polarization and exchange Mesoscopic lnm-0.1 p,m Longitudinal relaxation time Ti Transverse relaxation time T2 Relaxation time Tip in the rotating frame Solid-echo decay time T2e Spin-diffusion constant Microscopic 0.1-lOp.m Molecular self-diffusion constant D Macroscopic 10 p,m and larger Spin density... 

Fig. 11. Plot of Tj vs 1/r for the origin of the Si -Sq absorption of Zn-porphin in n-octane as measured in a picosecond photon echo experiment. Note that the echo decay time is jT2, where 1/72 = 1/7 + 1/27 ,.

In Fig. 18 we exhibit the results of both a two-pulse and a three-pulse echo measurement at low temperature on pentacene in p-terphenyl. The important point to note is that the echo decay times are identical but shorter than the fluorescence lifetime for this more concentrated crystal. The implication is that at higher concentration, optical dephasing is also caused by energy-transfer processes in this system and that the process is irreversible (7 ,-type). 

Fig. 25. Plot of the measured relaxation times as a function of temperature. Note that the echo decay time is Typical uncertainty in the temperature is 0.1 K. (After Ref. 60.)...

At higher guest concentrations they observe a shortening of the echo decay time, which they attribute to a photon induced modulation of the guest-guest dipole-dipole interaction. 

Echo decay times must be sufficiently long to obtain a satisfactory spectrum. Low temperatures are often required to increase the decay time. Rapid echo decay is still often a problem with the two-pulse method. 

Figure 20. Histogram of the Hahn echo decay times T2 for 9 different molecules. The width of the boxes is given by the error in the determination of T2. The two arrows in the diagram represent the calculated variation AT2 of the phase memory time when a variation in the lattice constant of 10% is assumed (see text).

To measure the longitudinal relaxation time Ti, an inversion or saturation pulse is applied, followed, after a variable time T, by a two-pulse echo experiment for detection (Fig. 5b). The inversion or saturation pulse induces a large change of the echo amplitude for T < T. With increasing T, the echo amphtude recovers to its equilibriiun value with time constant Ti. The echo amphtude of the stimulated echo (Fig. 5c) decays with time constant T2 when the interpulse delay T is incremented, and with the stimulated-echo decay time constant Tse < T1 when the interpulse delay T is incremented. A faster decay, compared to inversion or saturation recovery experiments, can arise from spectral diffusion, because of a change of the resonance frequency for the observed spins, of the order of Av = 1/t on the time scale of T. Quantitative analysis of spectral diffusion can provide information on the reorientation dynamics of the paramagnetic centers. 

A Se NMR was observed at 56.82 MHz at 1.46 Kina zero field with polycrystalline EuSe. This was attributed to nuclei on the Se sites located between two neighboring N planes in the ferrimagnetic NNS structure. As the temperature increased, the NMR intensity became weak near 2.6 K and the signal was not observed above 2.9 K. The frequencies obtained followed a V dependence below 2.2 K and extrapolated for T- 0 v = 58.7 MHz, Suzuki et al. [10]. A symmetric line was found by Budnick et al. [5] at v = 57.50 MHz at 1.3 K and was still detected at 3.325 K. Fig. 95 shows the variation of the Se NMR with an applied field. An asymmetry developed as an external field was applied for temperatures below 1.6 K and above 2.2 K. Finally, two lines were observed in a limited range of field. At 1.3 K, the new line with shorter spin echo decay time Tg appeared on the high frequency side of the original line. At 2.26 K, the new line was on the low frequency side. At 1.3 K above 7 kOe, the high frequency line shifted to lower... 

The characteristic time of the tliree-pulse echo decay as a fimction of the waiting time T is much longer than the phase memory time T- (which governs the decay of a two-pulse echo as a function of x), since tlie phase infomiation is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

Resolvable modulation is detected on a three-pulse echo decay spectrum of predeuterated 3-carotene radical (Gao et al. 2005) as a function of delay time, T. The resulting modulation is known as ESEEM. Resolvable modulation will not be detected for nondeuterated P-carotene radical since the proton frequency is six times larger. The modulation signal intensity is proportional to the square root of phase sensitive detection and interfering two-pulse echoes and suppressed by phase-cycling technique (Gao et al. 2005). Analysis of the ESEEM spectrum yields the distance from the radical to the D nucleus, a the deuterium coupling constant, and the number of equivalent interacting nuclei (D). The details related to the analysis of the ESEEM spectrum are presented in Gao et al. 2005. 

Three-pulse ESEEM spectrum of perdeuterated P-carotene imbedded in Cu-MCM-41 exhibits an echo decay with an echo modulation due to deuterons. The three-pulse ESEEM is plotted as a function of time, and curves are drawn through the maximum and minima. From ratio analysis of these curves, a best nonlinear least-squares lit determines the number of interacting deuterons, the distance (3.3 0.2A), and the isotopic coupling (0.06 0.2MHz). This analysis made it possible to explain the observed reversible forward and backward electron transfer between the carotenoid and Cu2+ as the temperature was cycled (77-300 K). 

Shortly thereafter came reports of integrated three-pulse photon echoes, especially using the echo peak shift to provide information about spectral diffusion [21, 23]. In one experiment [10, 23] the peak shift shows an intriguing oscillation at short times with a period of about 180 fs, followed by a slower relaxation with a decay time of 1.4 ps. The three-pulse echo amplitude can also be heterodyned, leading to 2DIR experiments [24 26]. The latter experiments provide a wealth of information, and there are several ways to extract the desired spectral diffusion dynamics [149]. 

Fig. 3 Temperature dependence of the transverse relaxation time Ti for D-RADP-20 as obtained from a bi-exponential fit to the Rb spin echo decay. The fact that T2 changes discontinuously at the phase transition clearly indicates the first order character of the transition...

Fig. 5 Stacked Fourier transforms of the NMR spin echoes in D-RADP-20 versus echo delay time for various temperatures. This sequence of 2D plots corresponds to Fig. 2. It is evident that the PE rim decays much faster than the FE rim...

The spectrum obtained by FT of the whole train of decaying echoes consisfs of a series of spikelets separated by the frequency vcpMG = l/ra. The envelope of these sidebands is defined by the second-order quadrupolar CT lineshape under MAS. The linewidth of each spikelet is determined by the true transverse relaxation time (T2) of the material, which is a measure of the decay time of the amplitude of the echoes in the... 

The late reverberation is characterized by a dense collection of echoes traveling in all directions, in other words a diffuse sound field. The time decay of the diffuse reverberation can be broadly described in terms of the mid frequency reverberation time. A more accurate description considers the energy decay relief of the room. This yields the frequency response envelope and the reverberation decay time, both functions of frequency. The modal approach reveals that reverberation can be described statistically for sufficiently high frequencies. Thus, certain statistical properties of rooms, such as the mean spacing and height of frequency maxima, are independent of the shape of the room. 

Adjust the t-axis of the experiment until the actual time point zero is at the maximum amplitude of the echo decay function. The now negative time part is usually disregarded. With mathematical procedures it is also possible to correct the phase of the time trace using the real and imaginary part of the data. In DeerAnalysis2008 both steps are done automatically but can also be adjusted. 

Figure 7.8 The shape of the Hahn-echo decay in cross-linked elastomers is given by the line of diamonds. In the short-time limit the curve can be approximated by a Gaussian (broken line) and in the long time limit it follows an exponential (solid line) [30]...

Figure 10.15 The decay of the transverse magnetisation (points) for ethylene-octene copolymer at different temperatures [136]. The decay was measured using the solid-echo pulse sequence. The solid lines represent the result of a least-squares adjustment of the decay using a linear combination of Weibull and exponential functions. The dotted lines represent the relaxation component with a long decay time. In the experiments the sample was heated from room temperature to 343 K (70 °C)...

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