Molecular Tumbling and NMR Relaxation

What is the mechanism of spins dropping down from the state to the a state and fanning out around the two cones, and what determines the rates (R = HT and/ 2 = 1/72) of NMR relaxation These processes are intimately tied to the motion of molecules as they tumble ( reorient ) in solution in their rapid Brownian motion, and measurement of the NMR relaxation parameters T and T2 can even give us detailed information about molecular dynamics (motion) from the point of view of each spin in the molecule. A simplified model 

Consider a nucleus such as a 13C nucleus within a molecule. If the carbon in question is a methine (CH) carbon, then it has a hydrogen atom (1H) rigidly attached to it at a distance of 

Although Ti increases with molecular size for large molecules, note that the spin-spin or transverse relaxation rate 74 continues to decrease as molecular size increases (Fig. 5.14). This is harder to explain, but we can rationalize this effect by considering that the fanning 

Notice how we diagram a multiple-pulse NMR experiment the horizontal axis represents time and the vertical axis represents RF amplitude for pulses. The times and amplitudes are not drawn to scale—they are just cartoon representations. 90° pulses are shown as half the width of 180° pulses, and recording of the FID is shown as a decaying signal. Each RF channel is labeled according to the nucleus being irradiated (pulses) and/or observed (FID). 

The magnitude of the FID signal that results from this x-y magnetization (and the peak height in the spectrum) should be directly proportional to the sample s z magnetization just before the 90° pulse. By repeating the experiment with different time delays after the 180° pulse, we can monitor this return of z magnetization to equilibrium and determine the value 

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