Rotational Spin-Echo Experiment

The resulting carbon signal can be observed with magic-angle spinning for high resolution [6,7]. 

Matched spin-lock transfers were performed at 60 kHz.) 

Typical Spectra in the Chemical Shift and Dipolar Dimensions 

Comparison Between Experimental and Calculated Dipolar Sideband Patterns 

American ChemfcaF Society library 1155 16th Si. N. W. Washington, 0. C. 20038 

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The spin-echo experiment therefore leads to the refocusing not only of the individual nuclear resonances but also of the field inhomogeneity components lying in front or behind those resonances, a maximum negative amplitude being observed at time 2t after the initial 90° pulse. The frequency of rotation of each signal in the rotating frame will depend on its chemical shift and after the vector has been flipped by the 180° pulse, it... 

Figure 2.3 Spin-echo experiment. The behavior of nucleus X in an AX spin system is shown. (A) Application of the second 180° pulse to nucleus X in the AX hetero-nuclear system results in a spin-flip of the two X vectors across the x -axis. But the direction of rotation of the two X vectors does not change, and the two vectors therefore refocus along the —y axis. The spin-echo at the end of the t period along the -y axis results in a negative signal. (B) When the 180° pulse is applied to nucleus A in the AX heteronuclear system, the spin-flip of the X vectors...

Another study of the surface structure of CdSe NCs of 3.7 nm size used 31P MAS-NMR and 31P/77Se rotational-echo double-resonance (REDOR) to identify overlapping broad peaks from two surface species trioctylphosphine oxide (TOPO) at 29.3 ppm and trioctylphosphine selenide (TOPSe) at 22.2 ppm [343]. Both the isotropic chemical shift and CSA of the surface-bound TOPO were substantially different from those of the free ligand. Spin-echo experiments on 31P were stated to indicate an average P-P distance of 8-10 A at the surface, consistent with capping at alternate atomic sites (all Cd but not Se). 

The angles a and P define the orientation of the sample relative to the Bo-field cor denotes the rotation frequency. For the REDOR reference experiment, the rotor-synchronised spin-echo experiment for the S nuclei (cf. Figure lA), the dipolar Hamiltonian integrated over one rotor period Tr averages to zero... 

Figure 6. The Hahn spin echo experiment in the rotating frame, (a) Tipping of M into the x y plane by 90° pulse, (b) Decrease in M,. as spins dephase. (c) Application of a second (180°) pulse, (d) Increase in M. as spins refocus , (e) Complete refocusing, (f) Decay in M,. as spins dephase. From [2].

Figure 11 shows diagrammatically (Muller and Bloom, 1960) the arrangement of echoes and pulses which occur in a general type of three-pulse spin-echo experiment. In this diagram a pulse of duration 0 to t0 rotates the magnetization by the angle nj2. This pulse is followed by the free induction decay with time constant T determined by both extrinsic and intrinsic relaxation forces. At a time iq (iq > 11 t0) a pulse... 

Fig. 15. Pulse sequence for dipolar rotational spin-echo, SN NMR experiment...

The 2D ESE technique operates in a fashion fundamentally different from any of the techniques discussed above. In the discussion of motionally narrowed spectra we introduced the spin-spin relaxation time T2. This is a fundamental measure of relaxation in magnetic resonance that describes how spins dephase from random processes such as rotational diffusion. Time-domain EPR spectrometers use high power microwave pulses to measure directly free induction decays as well as various relaxation processes. The spin echo experiment uses a coherent two-pulse scheme to reveal T2. 

Powder as well as MAS studies are available for several r/ -bonded olefins. The spans of the chemical-shift tensors are reduced with respect to the free olefins, which is discussed in terms of the Dewar-Chatt-Duncanson model of fx-donation and tt- back-bonding." " " The bond lengths and the orientations of the shielding tensor elements are available from dipolar-chemical shift methods and 2-D spin-echo experiments on the doubly labelled oleflns." " 77 -cyclopentadienyl and 77 -benzene ligands of transition-metal complexes, but also some derivatives of alkali or main-group elements," exhibit single resonances and shielding tensors of axial symmetry at room temperature. Both observations point to relatively fast rotations around the respective 5- and 6-fold local rotor axis. ... 

The two-dimensional spin-echo experiment has found applications for static samples of compounds containing homonuclear spin pairs, where dipolar and chemical shift interactions could be separated allowing the determination of internuclear distances." " It was also shown that a considerable improvement in resolution could be obtained for samples rotated in the magic angle, thus allowing the determination of the magnitude of relatively smsdl homonuclear scalar coupling constants, e.g., P)ds in Wilkinson s-type rhodium complexes. ... 

A two-pulse spin echo experiment consists of a 90°-r-180°-r-echo pulse sequence (see Chapter 2.3, Section 2.3.2). The amplitude of the echo is monitored as a function of the time r between the echoes, and the decay time constant is denoted as Jin, the phase memory decay time. J is strongly dependent upon dynamic processes that result in echo dephasing on the time scale of the experiment. In Cu(dtc)2 the coupling of the unpaired electron to the spins of the protons of the ethyl groups is too small to be resolved in the CW spectra. However, when the rate of rotation of the... 

Example 24.17). In order to describe the COSY experiment we need to envision a Cartesian coordinate system that is rotating counterclockwise around the z axis at the reference frequency. The magnetic moment of an unshielded proton would be stationary in this rotating coordinate system. The vector sum of the proton magnetic moments of all protons is denoted by M, as before. Before the first pulse M is parallel to the z axis. The first 90° pulse rotates M onto the positive y axis, just as in the simple NMR experiment and the spin-echo experiment. 

Figure Bl.15.11. Fomiation of electron spin echoes. (A) Magnetization of spin packets i,j, /rand / during a two-pulse experiment (rotating frame representation). (B) The pulse sequence used to produce a stimulated echo. In addition to this echo, which appears at r after the third pulse, all possible pairs of the tluee pulses produce primary echoes. These occur at times 2x, 2(x+T) and (x+2T).

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