Determining the Optimal Wait Between Scans

The net magnetization vector M, once tipped from its equilibrium position along the z-axis (Mg) and made to precess in the xy plane, will relax back toward its equilibrium position with a characteristic time constant. In the absence of any additional perturbations and starting with no z component of net magnetization—i.e., after applying a 90° pulse and completely tipping the M into the xy plane— the z component of the net magnetization vector (M ) will return to its equilibrium value as follows  

Because 1 —e is 0.993, a delay of five T/s is normally sufficient between the last RF pulse and the application of the next RF pulse (getting 99.3% of the original signal back is generally thought to be sufficient). We sometimes estimate the Tj value for the slowest relaxing resonance of interest and multiply this value by five to arrive at an appropriate relaxation delay for our sample. When waiting five 

Ernst angle. The optimal tip angle for repeated application of a 1-D pulse seguence based on the relaxation time of the spin being observed and the time required to execute the pulse sequence a single time. 

When we conduct a 2-D experiment or a 1-D experiment that requires a large number of scans, we rarely wait five times the longest Tj relaxation time between the pulse preceding NMR signal acquisition and start of the first pulse in the pulse sequence. 

If the collection of 1-D NMR data sets requires many thousands of repetitions of the pulse sequence (scans), the use of less than a 90° pulse is sometimes found to yield a higher S/N using the same amount of instrument time. For every relaxation delay and Tj value, there is an optimal tip angle (referred to as the Ernst angle) whose value can be determined by using relatively simple calculus. In practice, we rarely if ever know the Ti s of the resonances to which we have yet to devote many hours of instrument time. We are often left to guess at the T or we may simply elect to use a 30° or a 45° pulse along with a 2-3 s relaxation delay. 

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