Bloch spin-lattice relaxation time

For direct polarization experiments (DPMAS), data were acquired from the Bloch decay following a single 13C pulse. Alternatively, FT spectra and spin-lattice relaxation times were measured in a high-resolution probe... 

Spin-Lattice Relaxation Time (7j), Spin-Spin Relaxation Time (T2), and the Bloch Equations... 

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). 

Misra SK. 2005. Microwave amplitude modulation technique to measure spin-lattice relaxation times solution of Bloch s equations by a matrix technique. Appl Magn Reson 28 55-67. 

Faced with a broad range of prospective spin-lattice relaxation times, the investigator needs two types of spectrometers, a situation that is further complicated if multi-frequency measmements are required. Furthermore, the phenomenological descriptions of measurements made by cw and transient spectrometers differ, as they correspond to separate solutions to Bloch s equations. This chapter describes refinements of both instrumental and theoretical/computational techniques that facilitate the measurement of spin-lattice relaxation times. 

The spectroscopic dynamics problem was examined mathematically for the case of the (two-level) magnetic resonance transition by Bloch, who described the temporal evolution of the magnetization in terms of a first-order differential equation analogous to dnidt = -k n—n, where n represents a time-dependent function that, in this case, represents a spin-state population difference. (In a two-level system and in the form written, n would represent the population difference between the ground and excited states and the solution of the differential equation would correspond to tire time course of the decay to the ground state.) The solution to this first-order differential equation is an exponential function in which a time constant is introduced and attributed to a characteristic relaxation time that is denoted by T]. In other words, k is proportional toTi. This time constant T is called the spin-lattice relaxation time, and is defined as the rate at which the electrons return to thermal equihbrium due to coupling with the lattice. 

High-resolution C spectra of solid polymers can principally be obtained by two ways from normal Bloch decays (SPE single-pulse excitation) of the carbon magnetisation, just as in 1-NMR, or from cross-polarisation. These techniques are complementary. Discriminating experiments may consist of comparing CP/MAS and SPE spectra (the latter obtained without cross-polarisation). Whereas the former depends on proton relaxation, the latter is affected only by carbon relaxation. Because of the great segmental mobility in elastomers, these systems have shorter spin-lattice relaxation times (in the order of seconds), which makes SPE feasible. 

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 ... 

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