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Monday, February 22, 2010

The Dephasing Power of Pulsed Field Gradients

Pulsed field gradients are used in many modern NMR measurements to select specific coherence pathways and eliminate (or at least minimize) the need for time consuming pulse and receiver phase cycles. The gradients are most often used in conjunction with spin echos such that unwanted coherences can be dephased and the desired coherences can be rephased. They are also used to measure diffusion constants or collect DOSY data. It is instructive to examine the magnetization vectors in the active volume of an NMR tube as a function of the gradient strength after the delivery of a 90° pulse. While a gradient is applied, the magnetization vectors precess at frequencies in the rotating frame which depend on their position in the NMR tube along the axis of the gradient. When the gradient is turned off, all of the magnetization vectors again precess at the same frequency however the phases of the vectors remain as they were at the end of the gradient. The top part of the first figure shows a series of 6 cases where z gradients of increasing strength are delivered after a 90°-x pulse. Each case shows 8 equally spaced slices of the NMR tube on the z axis (the center of the sample is between the 4th and 5th slices). The stronger the gradient the larger the dephasing angle between slices. In this figure, the receiver is assumed to be on the y axis. From left to right, the number of degrees of dephasing between slices are 0° (no gradient), 22.5°, 45°, 67.5°, 90° and 112.5°. The y components of all the vectors are added and the sum is shown in blue below. One can see the the y magnetization decreases and oscillates about zero as a function of the gradient strength. This is illustrated more clearly in the bottom part of the figure which shows a plot of y magnetization as a function of gradient strength for a numerical calculation done using 50 slices. The second figure demonstrates this experimentally. It shows the 500 MHz 1H NMR spectrum of HDO using the pulse sequence shown in the figure as a function of the % gradient strength (100% ~ 0.5 T/m). The gradient pulses were 1 msec in duration and rectangular in shape. One can see that the intensity profile matches closely to that predicted in the bottom of the first figure. The sample is almost entirely dephased using only 2% of the maximum gradient strength.

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