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.

iPods and Fourier Transforms

The way people collect and listen to music has changed drastically over the last several years. One's entire music collection, which once occupied several shelves in the living room, can now fit in the palm of one's hand and can be listened to virtually anywhere. The iPod / mp3 technology is also being used to change the way we can learn. Many, if not all of us, have spent tens of thousands of dollars to educate ourselves. If you are like me, there were courses in university you would have liked to take but did not have the time. Now, many universities have made their courses available free of charge online through iTunes University. Now, one can audit all of those expensive university courses for free through their iPod Touch or iPhone on the bus or train on the way to work. One excellent course I have been auditing is one called The Fourier Transform and its Applications, given by Brad Osgood of Stanford University's School of Engineering. As NMR spectroscopists, we use the Fourier Transform daily. This course covers many of the mathematical details not learned in NMR courses and explores many applications (other than NMR spectroscopy) where Fourier Transforms are useful. I highly recommend it and I hope that many more universities make their course material public.I regret to say that Bob Dylan is temporarily taking a back seat on my daily commute to work. Sorry Bob!

Presaturation

One of the simplest and widely used ways to eliminate a strong water signal is to use presaturation. In this technique, the transmitter is set to the water resonance. a very long (seconds) low power (mW) pulse is given. The excitation profile of this pulse is very narrow due to its length and it saturates the water resonance at the transmitter frequency. A non-selective hard 90° pulse (with a wide excitation profile) is then given to place all remaining spins in the transverse plane for detection. An example of this is shown in the figure below. The top trace is a standard 500 MHz ¹H NMR spectrum of phenylalanine in 90% H₂O / 10% D₂O. The resonance due to the water is huge and off-scale in the figure. The bottom trace is the same sample run with presatutation.

WATERGATE

WATER suppression by GrAdient Tailored Excitation (WATERGATE) is a clever technique used to suppress the water signal in an aqueous sample. It is widely used in many complicated pulse sequences. Unlike presaturation which irradiates the water resonance with a long low power pulse, this method is based on the gradient spin echo technique used also to measure diffusion constants and DOSY spectra. The pulse sequence is shown here:The transmitter frequency is set on the water resonance. A non-selective hard 90° pulse is applied followed by a 1 -2 msec gradient pulse. The gradient pulse dephases all of the resonances. A composite pulse (consisting of 6 hard pulses seperated by a delay, τ) is then applied which acts as a 180° pulse for everything except peaks on resonance (i.e. water) and any peaks at frequencies n/τ away from the transmitter, where n is an integer. τ is chosen such that 1/τ lies outside of the spectral width (typically several hundred µsec). The second gradient pulse (equal in magnitude, duration and sign, to the first) further dephases the water resonance at the center of the spectrum which was unaffected by the composite pulse but rephases everything else which was inverted by the composite pulse. The gradients and composite pulse act as a gradient spin echo for all but the water. The FID is then collected with the water resonance suppressed by the two dephasing gradients. An example of the application of WATERGATE is shown in the figure below. The top trace shows a standard 500 MHz ¹H NMR spectrum of phenylalanine in H₂O / D₂O scaled to the water peak. The resonances of the phenylalanine are not visible on this scale. The middle trace is the same spectrum as the top trace with the phenylalanine resonances on scale. The huge water resonance is truncated. The bottom trace shows the WATERGATE spectrum. The water signal is greatly suppressed.

CPMG to Enhance Sharp Lines

The Carr - Purcell - Meiboom - Gill (CPMG) sequence is used to measure T₂ relaxation times and more recently has made an impact in measuring the line shapes of very broad solid lines by breaking them up into spikelet patterns which mimic the static line shape. The very simple pulse sequence is shown here:During the (D2 - π -D2)_n period the intensity of lines with short T₂ (broad lines) diminishes much more quickly than that for lines with long T₂ (sharp lines). The CPMG sequence is therefore useful for enhancing the sharp features in a spectrum by suppressing the broad features. This is demonstrated in the figure below. The top panel of the figure shows a portion of a conventional 500 MHz ¹H NMR spectrum of a polymer sample contaminated with small amounts of smaller molecules. The broad lines (truncated in the figure) are due to the polymer whereas the much smaller sharp lines are due to the impurities. The bottom panel of the figure shows the CPMG spectrum of the same sample with D2 = 4 msec and n = 32. One can see that the broad polymer lines are greatly suppressed and the smaller sharp lines are much more obvious.