Single quantum relaxation time

A single-quantum transition involves one spin only, whereas the zero- and doublequantum transitions involve two spins at the same time. The zero- and double-quantum transitions give rise to cross-relaxation pathways, which provide an efficient mechanism for dipole-dipole relaxation. 

Finally, the double quantum (DQ) spin spin relaxation time T2d can be determined using the pulse sequence 90° — x — 45° — 90° —t — 45°.51 The first three pulses create the DQ coherence, and the last read pulse converts the DQ to a single quantum coherence for detection. 

N single quantum coherence. The chemical shift of 15N is recorded in a (semi-)constant-time manner during t2 and ultimately the 15N-1Hn PEP-TROSY element selects the most slowly relaxing 15N Hn multiplet component prior the acquisition. The coherence flow can thus be described as... 

Now let s look at the more interesting situation where the cross-relaxation pathways (single quantum and double quantum) are available. Spins in the pfi state can relax by any of three pathways they can drop down to the aft state (rate Wf), drop down to the Pa state (rate W ), or follow the double-quantum pathway down to the aa state (rate Wi)- All of these pathways will contribute to the change in population of the pp state as a function of time (Fig. 10.3). Considering all three pathways leading away from the pp state, we can... 

Except for being unobservable, these coherences (and antiphase coherences, as well) behave much like magnetizations in that they have relaxation times, which are different from those of single quantum coherences. Multiple quantum coherences can be further manipulated to produce observable magnetization, as we shall see in Chapter 12. 

When the H- H dipole-dipole interaction can be measured for a specific pair of H nuclei, studies of the temperature dependence of both the H NMR line-shape and the H NMR relaxation provide a powerful way of probing the molecular dynamics, even in very low temperature regimes at which the dynamics often exhibit quantum tunnelling behaviour. In such cases, H NMR can be superior to quasielastic neutron scattering experiments in terms of both practicality and resolution. The experimental analysis can be made even more informative by carrying out H NMR measurements on single crystal samples. In principle, studies of both the H NMR lineshape and relaxation properties can be used to derive correlation times (rc) for the motion in practice, however, spin-lattice relaxation time (T measurements are more often used to measure rc as they are sensitive to the effects of motion over considerably wider temperature ranges. 

For the partially deuterated benzoic acid (C6D5COOH), the solid state H NMR spectrum is dominated by the intra-dimer H- H dipole-dipole interaction. In a single crystal, both tautomers A and B are characterised by a well-defined interproton vector with respect to the direction of the magnetic field (Fig. 1). Proton motion modulates the H- H dipole-dipole interactions, which in turn affects the H NMR lineshape and the spin-lattice relaxation time. It has been shown that spin-lattice relaxation times are sensitive to the proton dynamics over the temperature range from 10 K to 300 K, and at low temperatures incoherent quantum tunnelling characterises the proton dynamics. A dipolar splitting of about 16 kHz is observed at 20 K. From the orientation dependence of the dipolar splitting, the... 

The overall experiment thus becomes BIRD-t-HMQC-DT, in which t is chosen to null the single quantum coherences and DT is the normal delay time between pulse repetitions, which includes the time taken to acquire the signal, as well as a recycle time during which the signal is regenerated through relaxation. The details of the experiment require... 

Figure 3.17 Time evolution of the ISe ISh exciton population as a function of the relaxation times and Coulomb coupling for the single and biexcitons. The rise time of the biexciton (formation time) and the presence of strong or damped quantum beating depends upon the relative values of the Wc, yi, and j2 as shown above. Source Shabaev et al. (2006).

Time-resolved measurements of electron transfer times for quantum well photoelectrodes which can be compared with hot electron relaxation times, have not yet been reported. Only some excitation spectra, i.e. photocurrent vs. photon energy for MQWs and single quantum wells (SQWs), have been published so far [2]. In both cases, the photocurrent spectra show distinct structures corresponding to transitions between the hole and electron wells as shown for SQW electrodes in Fig. 9.32. The... 

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