Phase memory

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

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. 

In electron spin echo relaxation studies, the two-pulse echo amplitude, as a fiinction of tire pulse separation time T, gives a measure of the phase memory relaxation time from which can be extracted if Jj-effects are taken into consideration. Problems may arise from spectral diflfrision due to incomplete excitation of the EPR spectrum. In this case some of the transverse magnetization may leak into adjacent parts of the spectrum that have not been excited by the MW pulses. Spectral diflfrision effects can be suppressed by using the Carr-Purcell-Meiboom-Gill pulse sequence, which is also well known in NMR. The experiment involves using a sequence of n-pulses separated by 2r and can be denoted as [7i/2-(x-7i-T-echo) J. A series of echoes separated by lx is generated and the decay in their amplitudes is characterized by Ty. ... 

The main advantage of tlie tln-ee-pulse ESEEM experiment as compared to the two-pulse approach lies m the slow decay of the stimulated echo intensity detemiined by T, which is usually much longer than the phase memory time Ty that limits the observation of the two-pulse ESE. 

Burshtein A. I., Naberukhin Yu. I. Phase-memory effects in the theory of spectral line broadening in gases. Sov. Phys. JETP. 25, 799-805 (1967) [ZhETF, 52, 1202-11 (1967)]. 

Carotenoids incorporated in metal-substituted MCM-41 represent systems that contain a rapidly relaxing metal ion and a slowly relaxing organic radical. For distance determination, the effect of a rapidly relaxing framework Ti3+ ion on spin-lattice relaxation time,and phase memory time, Tu, of a slowly relaxing carotenoid radical was measured as a function of temperature in both siliceous and Ti-substituted MCM-41. It was found that the TM and 7) are shorter for carotenoids embedded in Ti-MCM-41 than those in siliceous MCM-41. 

The ID NOESY-TOCSY experiment [39] shown in fig. 1(c) is a straighffor-ward concatenation of ID NOESY and TOCSY experiments [34] (figs 1(a), (b)). Since the NOE transfer takes place along the z axis, and thus has no phase memory, no phase correction for the second selective pulse is needed to compensate for the change of the r.f. frequency during the tnoe interval. Nevertheless, any possible phase differences between the selective and consecutive nonselective pulses must be taken into account in both steps, by adjusting the phase of soft pulses. 

By spin-spin relaxation, the nuclei relax to equilibrium among themselves (i.e. precession occurs without phase coherence). The vectors dephase (Fig. 1.5 (b) - Fig. 1.5 (a)), and the components of transverse magnetization, Mx and My, decay to zero as a result (transverse relaxation). The spin-spin relaxation time T2 is thus also referred to as the phase memory time or the transverse relaxation time. 

The time constant tc is also called a phase-memory time, since it is related to the time for local fields to lose phase coherence (coupling) and decay to zero. 

The first result of this calculation is that the inertial motion causes almost no dephasing. This result is a direct contrast to models like the IBC theory, which attribute all the dephasing to collisional, i.e., inertial, dynamics. The difference between these theories lies in their assumptions about correlations in the solvent motion. The IBC explicitly assumes that the collisions are independent, i.e., the solvent motion has no correlations. As a result, the collisions are an effective sink for phase memory from the vibration. On the other hand, within the VE model the solvent motions appear as sound waves. Their effect on the vibrational frequency decays as they propagate away from the vibrator, but they remain fully coherent at all times. Because they remain coherent, they cannot destroy the phase... 

The electron spin echo of Ag°(B) has a very short phase memory time but relatively strong aluminum modulation can be identified. However, the phase memory time is too short to carry out a quantitative analysis of the modulation. This also precludes us from getting analyzable modulation from deuterated adsorbate molecules in a three pulse echo experiment. So the data is insufficient to locate Ag°(B) in the zeolite lattice without additional information. 

Eigure 12.5 presents TR ESR and ET ESR spectra obtained under photolysis of DAR (Scheme 12.1). One can observe a broadened signal of benzoyl radical in the ET ESR (or a signal of much lower apparent intensity). The intensity of the signals in CW TR ESR is determined by polarization, longitudinal (spin lattice) relaxation time Ti and by the rate of chemical disappearance of r. The intensity of signals in ET ESR is determined by polarization, and phase memory time Tm, which includes Ti, transverse (spin-spin) relaxation time T2, and a rate of chemical disappearance of r. Broad ESR components have short Tm, and they are difficult to observe. Broadening of components in spin adducts is ascribed to a hindered rotation around a Cp bond or cis-trans isomerization (Scheme 12.4). ... 

LPF - laser flash photolysis Tx-life-time of a triplet state Fm -phase memory... 

For a two-pulse (90° - t - 180°), or primary echo experiment, the integrated intensity of the spin echo, which occurs at time t after the 180° pulse, is measured as a fimction of increasing t from the probe s dead-time ( 100 ns) to a time where the echo amplitude has decayed to a few percent of its initial amplitude (2-8 ps for most powder samples). A two-pulse ESE decay envelope for the type-1 Cu(II) site of a multi-copper oxidase, Fet3p, is shown in Figure 1(a). The data show an overall decay characterized by a phase memory time, Tm or T, of < 1.0 ps. Superimposed on this decay are echo modulations that arise ft om hyperfine coupling to the N nuclei of two histidyl imidazole ligands and the protons of the snrronnding matrix. 

Some properties of the exciton dynamics of Mnp2 crystals have been elucidated through time-resolved studies of the emission at different parts of the exciton band after selective laser excitation jn some cases phase memory was found to be retained up to 1 /nsec but the details of the exciton dynamics require further knowledge of the exciton scattering mechanisms. 

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