Relaxation longitudinal, transverse

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. 

The restoration process of the spin magnetization toward the thermal equilibrium is called paramagnetic relaxation. It can be divided into two categories longitudinal relaxation and transverse relaxation. The z-component of the total magnetization is restored by the former relaxation, while the coherence in precessing on the xy-plane is destroyed by the latter relaxation. 

Electron spin quantum component Electron spin quantum number Hyperhne coupling constant Larmor angular frequency Larmor frequency Magnetogyric ratio Nuclear magneton Nuclear spin quantum component Nuclear spin quantum number Orbital quantum number Orbital quantum number component Principal quantum number Quadrupole moment Relaxation time longitudinal transverse Shielding constant... 

Some 205T1 n.m.r. spectra have been reported for Tl1 ions in aqueous solutions.592 The relaxation (longitudinal and transverse) of the Tl ions is independent of the resonance frequency, isotopic substitution of the solvent, salt concentration, or nature of the anions. It is very sensitive to... 

Similar to transverse relaxation longitudinal relaxation in the rotating frame is also sensitive to slow molecular motion (cf. Fig. 7.1.3) and is thus a good probe for elastomer... 

NMR parameter images can be translated to material property images by calibration or relationships known from theory. For example, cross-link density can be linked to the transverse relaxation decay [101-103] and the longitudinal relaxation decay in the rotating frame [104, 105]. Relaxation of transverse magnetization in cross-linked elastomers is nonexponential (Fig. 

The length of time the nucleus spends in the excited state is At. This lifetime is controlled by the rate at which the excited nucleus loses its energy of excitation and returns to the unexcited state. The process of losing energy is called relaxation, and the time spent in the excited state is the relaxation time. There are two principal modes of relaxation longitudinal and transverse. Longitudinal relaxation is also called spin-lattice relaxation transverse relaxation is called spin-spin relaxation. 

Larmor circular frequency Larmor frequency longitudinal relaxation time transverse relaxation time electric dipole moment of a molecule quadrupole moment of a molecule quadrupole moment of a nucleus electric field gradient tensor... 

Figure 9.19 Relaxation times, a) Longitudinal relaxation h) transverse relaxation.

DTPA = diethylenetriaminepentaacetic acid DOTA = l,4,7,10-tetraazacyclododecane-l,4,7,10-tetraacetic acid MRI = magnetic resonance imaging NMR = nuclear magnetic resonance T = longitudinal or spin lattice relaxation time Ti = transverse or spin-spin relaxation time r = longitudinal relaxivity V2 = transverse relaxivity. 

There are two main types of relaxation processes by which nuclei in upper energy states can relax to lower energy states. These are spin-lattice relaxation (or longitudinal relaxation), T, and spin-spin relaxation (or transverse relaxation), T2. 

In polymers one will often particularly be interested in very slow dynamic processes. The solid echo technique just described is still limited by the transverse relaxation time T being of the order of a few ps at most. The ultimate limitation in every NMR experiment however, is not T but the longitudinal relaxation time T, which for 2H in solid polymers typically is much longer, being in the range 10 ms to 10 s. The spin alignment technique (20) circumvents transverse relaxation and is limited by Tx only, thus ultraslow motions become accessible of experiment. 

In NMR theory the analogue of the relation (1.57) connects the times of longitudinal (Ti) and transverse (T2) relaxation [39]. In the case of weak non-adiabatic interaction with a medium it turns out that T = Ti/2. This also happens in a harmonic oscillator [40, 41] and in any two-level system. However, if the system is perturbed by strong collisions then Ti = T2 as for y=0 [42], Thus in non-adiabatic theory these times differ by not more than a factor 2 regardless of the type of system, or the type of perturbation, which may be either impact or a continuous process. 

To extract information about xj from NMR data, the transverse relaxation time Tj may be used as well as the longitudinal time T. For gaseous nitrogen it was done first with Ti in [81] and confirmed later [82] when T was measured and used for the same goal. The NMR linewidth of 15N2 is the inverse of T2, and the theory, relating to Ti to x.1, is well known [39, 83]. For the case of diatomic and linear molecules the formula is... 

Moreover, precession under selective irradiation occurs in the longitudinal plane of the rotating frame, instead of rotation in the transverse plane, which occurs during the evolution of the FID. The magnitude of the vector undergoing precession about the axis of irradiation decreases due to relaxation and field inhomogeneity effects. 

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