Two New Twitter Feeds to Follow

Two new and very useful Twitter feeds have recently appeared online. The first is by Luke O'Dell called solidstateNMR. It posts links to publications related to solid state NMR as soon as they appear online. The second is by Victor Terskikh called nmr900 which posts news and information from Canada's showpiece high field solids NMR facility, The National Ultrahigh-Field NMR Facility for Solids.

Stay up-to-date and check them out!

Excitation Profiles for Shaped Pulses

Shaped pulses are very commonly used for selective excitation and nonselective inversion in a large number of NMR pulse sequences. The frequency domain excitation profile of a radio frequency pulse is the Fourier transform of the time dependent pulse shape and determines the width, uniformity and phase of the frequency spectrum excited. Since time and frequency are reciprocals of one another, short rf pulses have very wide excitation profiles and long rf pulses have very narrow selective excitation profiles. In a previous BLOG post the excitation profiles of rectangular pulses of varying duration were determined experimentally. The Fourier transform of a rectangular pulse is a sinc function which is observed to be the experimentally determined excitation profile. Short high power rectangular pulses are very desirable for uniform excitation over wide frequency ranges as the entire NMR spectrum of interest usually occupies only a very small central portion of the central lobe of the sinc shaped excitation profile which, to a first approximation, is flat over the observed spectral width. Rectangular pulses are often not desirable when narrow excitation profiles are required as the excitation is not uniform over the desired region and the ripples of the sinc excitation profile cause nodes of excitation and negative peaks.

The Fourier transform of a sinc function is a box function, so if a long low power sinc shaped rf pulse is used one obtains a narrow flat box shaped excitation profile. This is indeed the case as can be seen in the bottom trace of the figure below. The trace is composed of a series of ¹H NMR spectra of H₂O/D₂O where a truncated, 200 msec, 10 cycle sinc shaped monochromatic rf pulse was applied with varying rf frequency offsets. One can see that the excitation profile is, to a good approximation, a narrow flat box function. The deviation from a flat box function is the result of the truncation of the sinc pulse. It should be noted that the phase of the resonances is not constant across the excitation profile. Sinc pulses are not frequently used for selective excitation because of the phase problem and the fact that very long, minimally truncated pulses must be used. A frequently used alternative to the sinc pulse for selective excitation is the Gaussian shaped pulse. The Fourier transform of a Gaussian is a Gaussian and one therefore will obtain a narrow Gaussian shaped excitation profile when a long low power Gaussian shaped pulse is used. This is shown in the top trace of the figure below. This trace is similar to the bottom trace except a 20 msec Gaussian shaped pulse (with truncation at 1 % of the total height) was used rather than a 200 msec sinc pulse. Although the excitation is not flat, the phase is constant across the excitation profile and the total duration of the pulse is 10 times shorter than the sinc pulse.

First-Order Phase Errors

The phase of a signal in an NMR spectrum is described here and is determined by the axis on which the magnetization vector resides after the observe pulse relative to the receiver. The phase of the spectrum is typically corrected such that the peak in the real spectrum is entirely in absorption mode while that in the imaginary spectrum is entirely in dispersion mode. The correction in phase is referred to as the zero-order phase correction. A zero-order phase correction applies to all peaks in the spectrum regardless of their offset, Ω, from resonance. There are also first-order phase errors where the phase error for a resonance is linearly dependant on Ω and the duration of the pulse, t_p. The further a peak is away from the center of the spectrum for a given pulse duration, the larger the first-order phase error. Similarly, the longer the duration of the pulse for a peak of given offset, the larger the first-order phase error. These errors arise from the fact that a 90° pulse of fixed duration is only a true 90° pulse for a peak on-resonance. For off-resonance peaks, the pulse will not only be slightly less than 90° but also produce a small amount of magnetization along the axis of the pulse. For example, a 90°_x pulse applied to an equilibrium magnetization vector will produce only –y magnetization for an on-resonance signal but for an off-resonance signal, it will also leave a small amount of residual z magnetization as well as produce some x magnetization. It is the x magnetization that gives rise to the first order phase error. The effect of the pulse duration for a peak of given offset frequency is demonstrated in the figure below. The sample was a mixture of chloroform and acetone. The transmitter was set such that the chloroform signal was on-resonance. Six 90° pulses were calibrated at different power levels based on the on-resonance chloroform signal, ranging from 10 µsec in the lower trace to 320 µsec in the upper trace. For all spectra, the same zero-order phase correction was applied such that the chloroform signal was in-phase. No first-order phase correction was applied. One can see that the phase error in the off-resonance acetone signal increases as a function of the pulse duration. It should also be noted that the overall intensity of the acetone signal decreases with respect to the chloroform signal as a function of the pulse duration due to the width of the excitation profile decreasing as a function of the pulse duration.

Agilent's MR BLOG - SPINSIGHTS

Recently Agilent Technologies has started a MR BLOG called "SPINSIGHTS". The posts to this BLOG are written by Agilent employees and discuss the advances of Agilent's MR products as well as educational posts on both MRI and NMR spectroscopy. It is a very interesting read and promises to be a very useful resource. Thanks Agilent - keep it up!

"The MRI Photocopier"

A very interesting note* has recently been published in Concepts in Magnetic Resonance Part A by Joseph Hornak (generous provider of the two excellent free online text books, The Basics of NMR and The Basics of MRI ). In this work, it is demonstrated that an MRI scanner can be used to reproduce an image of printed text. The technique is based on the fact that the toner used to print text contains ferromagnetic particles and when placed in the uniform magnetic field of an MRI magnet, the magnetic field near the ferromagnetic toner is distorted. The "sample" is prepared by placing the printed page face up on a polycarbonate plate and covering it with a very thin sheet of polyethylene. The polyethylene is covered with water (doped with CuSO4 as a relaxation agent). The "sample" is placed in the magnet such that the plane of the page is perpendicular to the magnetic field. The text is "scanned" by taking a 2D proton MR image of a slice of the water near the surface of the polyethylene. The distortion in the magnetic field due to the ferromagnetic toner renders the text visible in the 2D magnetic resonance image. This is demonstrated in the figure below (from the reference) where a 2.5 mm thick slice above the polyethylene was imaged. The text was printed in #36 Arial font. The author speculates that this technique may be applied to the analysis of paintings.
* Joseph P. Hornak, "Magnetic Resonance Imaging of Printed Text", Concepts in Magnetic Resonance Part A. 36A, 347 (2010).

Sample Slice Selection in NMR Spectroscopy

In MRI, field gradients are used routinely for slice selection while imaging a sample. Gradients are also finding applications in high resolution NMR spectroscopy employing fast data collection techniques using parallel data acquisition for multiple slices of the same sample. A good example of this can be found in Carlos' BLOG (and the references therein). The slice selection is accomplished by turning on a linear field gradient across the sample while applying an excitation pulse. While the gradient is on, the frequencies of each of the NMR resonances is spread out according to length of the sample and the strength of the field gradient across the sample. A particular individual slice of the sample can be selected by either modifying the strength of the gradient while using a semi-selective pulse of a given excitation frequency or by modifying the offset frequency of the semi-selective pulse for a constant gradient strength. Both the gradient strength and the excitation profile of the pulse determine the thickness of the slice selected. When the gradient is turned off and the receiver turned on, the FID representing only the spectrum of the selected slice of the sample is collected. An educational example is shown in the figure below. A sample of toluene and H₂O/D₂O was prepared. As these two liquids are immiscible, the sample is layered with the less dense toluene on top and the more dense water on the bottom. The bottom trace in the figure shows a conventional ¹H NMR spectrum. Since the pulse used to collect the spectrum was a hard 90° pulse with a wide excitation profile, one can see both the toluene and the water in the spectrum. For the middle and upper traces, a field gradient of 48 G/cm was turned on while a 100 µs 90° Gaussian excitation pulse was applied. The only difference between the middle and upper traces is the offset frequency used in the excitation pulse. The middle trace represents the spectrum of a slice of the water in the bottom layer of the sample and the upper trace represents the spectrum of a slice of the toluene in the top layer of the sample.