Bloch transverse relaxation time

By the usual convention, the component Bz = B0, the static field, while Bx and By represent the rotating rf field, as expressed in Eq. 2.41, when it is applied, and are normally zero otherwise. To account for relaxation, Bloch assumed that Mz would decay to its equilibrium value of M0 by a first-order process characterized by a time T, (called the longitudinal relaxation time, because it covers relaxation along the static field), while Mx and AT, would decay to their equilibrium value of zero with a first-order time constant T2 (the transverse relaxation time). Overall, then the Bloch equations become... 

Several formalisms have been applied to relaxation in exchanging radicals. Principal among these are modifications of the classical Bloch equations (8, l ) and the more rigorous quantum mechanical theory of Redfield al. (8 - IJ ). When applied in their simplest form, as in the present case for K3, both approaches lead to the same result. Since the theory has been elegantly described by many authors (8 - 12 ), only those details which pertain to the particular example of K3 will be presented here. Secular terms contribute to the ESR linewidth (r) and transverse relaxation time (T ) by an amount... 

So far, we have considered only experiments with continuous-wave lasers under steady state conditions. With time-resolved experiments, on the other hand, energy transfer rates and transition probabilities can be obtained. Such measurements were carried out by mechanically chopping the laser beam directed into an external absorption cell together with the microwave radiation. Later, Levy et at reported time-resolved infrared-microwave experiments with an N2O laser Q-switched with a rotating mirror to produce pulses less than 1 /tsec in duration. They observed a transient nutation of the inversion levels of the molecule following the infrared laser pulse. Based on the Bloch equations, the observed phenomena could be explained quantitatively. From the decay envelope of the oscillations a value for the transverse relaxation time T2 was determined. Similar effects were produced by rapidly switching a Stark field which brings the molecules into resonance with the cw microwave radiation. 

Fig. 45a, b. Frequency dependence of the deuteron spin-lattice relaxation time of perdeuterated PEG confined in 10-nm pores of solid PHEMA at 80 °C (a) and in bulk melts (b) [95, 185]. The dispersion of the confined polymers verifies the law Ti (X M° ft)° at high frequencies as predicted for limit (II)de of the tube/reptation model (see Table 1). The low-frequency plateau observed with the confined polymers indicates that the correlation function implies components decaying more slowly than the magnetization relaxation curves, so that the Bloch/Wangsness/Redfield relaxation theory [2] is no longer valid in this regime. The plateau value corresponds to the transverse relaxation time, T2, for deuterons extrapolated from the high-field value measured at 9.4 T... 

Longitudinal and transverse relaxations have been assumed by Bloch et al. [6] to be first-order rate processes. Following this assumption, the increase of Mz to M0 and the decay of Mx and My to zero may be expressed in terms of spin-lattice and spin-spin relaxation times, T, and T2 ... 

The spin-lattice relaxation time is found by several techniques, which consist basically of applying an oscillating field, Hx, perpendicular to the static field H0 with a duration shorter than 7, to obtain a maximum signal amplitude. The measurement is made by preparing the system in a state Mx = My = 0, Mz Mq at a time t = 0 and measuring the decay to the equilibrium state M0. According to the Bloch equations the transverse magnetization stays zero and Mz decays exponentially as Mz(t) = M0( 1 — e t/Tl). 

The interaction of the particle with its surroundings causes a random shift of the phase of the particle s wave function in each of its steady states, which is not necessarily accompanied by the decay of the particle to the lower level. The mean time of such a phase relaxation is denoted by T2, and the relaxation itself is frequently referred to as transverse relaxation (Bloch 1946). The phase relaxation has no effect on the relaxation of the population of levels, but it broadens the spectral line of the 1 —> 2 transition. The homogeneous half-width F of the Lorentzian in eqn (2.47) is related to the time T2 by a simple relation at Ti T2 ... 

In equilibrium, there is no transverse magnetization, consequently the internal fields must act to reduce any Mj, and My that may be present. Bloch proposed quantifying this process by using a second relaxation time T2 ... 

The signal intensities A correspond to the transverse magnetization after the 180°, t, 90° sequence. The transverse magnetization, in turn, arises from the partially relaxed longitudinal magnetization, given by integration of the Bloch equation (1.17 a) between AT, = — Mq at time t = 0 and Mz = Mz at t = v. 

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