Relaxation times radiofrequency pulses measure

Radiofrequency pulses are also utilized to measure relaxation times. Three relaxation times have been measured in TPEs, and each is sensitive to different phenomena. Ti, the spin-lattice relaxation time in the laboratory frame, is the relaxation from the nonequilibrium population distribution created by the pulse to the equilibrium Boltzmann distribution. Ti is sensitive to molecular motions that rate in the range of 10 -10 Hz. T2, the spin-spin relaxation time, is the relaxation caused by the establishment of equilibrium between nuclear spins within the system. Spin-spin relaxation measurements also probe motions with rates in the range of 10M0 Hz however, low frequency motions (lOMtPHz) also affect T2. Generally,T2 is one to three orders of magnitude smaller than Ti in solid polymers. Tip, the spin-lattice relaxation time in the rotating frame, probes motions with rates on the order of lO -KfHz. Cross polarization is usually used in Tip measurements. 

The technique for measurement which is most easily interpreted is the inversion-recovery method, in which the distribution of the nuclear spins among the energy levels is inverted by means of a suitable 180° radiofrequency pulse A negative signal is observed at first, which becomes increasingly positive with time (and hence also with increasing spin-lattice relaxation) and which... 

Pulsed ENDOR. In both the inversion recovery (Fig. 5b) and stimulated echo experiment (Fig. 5c), the echo amplitude is influenced by a radiofrequency pulse applied during the interpulse delay of length T, if this pulse is on-resonance with a nuclear transition. In the former experiment, such a pulse exchanges magnetization between inverted and noninverted transitions, so that echo recovery is enhanced (Davies ENDOR) (32). In the latter experiment the on-resonance radiofrequency pulse induces artificial spectral diffusion, so that the echo amplitude decreases (Mims ENDOR) (33). These pulsed ENDOR experiments exhibit less baseline artifacts and are easier to set up compared with CW ENDOR experiments, as the required mean radiofrequency power is smaller and the ENDOR effect does not depend on a certain balance of relaxation times. Davies ENDOR is better suited for couplings exceeding 1-2 MHz, while Mims ENDOR is better suited for small couplings, for instance matrix ENDOR measurements. 

When the irradiation of the perturbed proton(s) is maintained for a long time, the populations of the neighbor spins reach a nonequilibrium steady-state value that can be measured by the signal produced after a radiofrequency pulse. The intensity of the signal reflects the population and is compared with the value measured from an equilibrium sample to determine the steady-state NOE value. Steady-state NOE experiments may be difficult to interpret since the relative intensities depend in a molecule-specific way on the number and relative distances of all protons in the molecule and their existence of alternative relaxation mechanisms for each of them. 

In solid state systems the perturbation from the ideal radiofrequency (rf) pulses often causes random fluctuations of dipole-dipole interactions that hinder accurate measurements of the relaxation time. Undertaking measurements in a rotating frame, achieved by a spin-locking process, an unperturbed value of the relaxation time of Tip is obtained. Another benefit is that Tip is sensitive to motions on a somewhat longer timescale than Ti. In contrast to the other relaxation processes Tip magnetization decay is often non-exponential, owing to complex interactions or a multitude of phases within the solid samples. 

In the presence of radiofrequency irradiation, relaxation of magnetization aligned with the effective magnetic field is characterized by the time constant Tip. On the other hand, the time constant T2p. characterizes the relaxation of magnetization that is perpendicular to the effective field. Michael et showed that T2p can be measured directly with Carr Purcell sequences composed of a train of adiabatic full-passage (AFP) pulses. During adiabatic rotation T2p characterizes the relaxation of the magnetization, which under adiabatic conditions remains approximately perpendicular to the time-dependent effective field. Theory is derived to describe the influence of chemical... 

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