Retrieving Empty Spinners From Magnets

Despite my best efforts in teaching students how to properly use NMR spectrometers, invariably a new user will, on occasion, drop a sample spinner into a magnet without a sample. This is usually done in our undergraduate laboratory by inexperienced students who have finished collecting their data and feel a need to return the empty spinner to the magnet. The problem is that ejecting the empty spinner with the eject air is not possible as the air passes through the spinner. In the past I have removed empty rotors from magnets on Varian spectrometers by removing the upper barrel of the magnet. On Bruker spectrometers, I have removed the probe and inserted a semi-rigid NONMAGNETIC plastic hose in the bottom of the magnet and pushed the spinner to the top of the upper barrel where it can be removed by a helper. In either case, the entire operation took between 5 minutes (Varian) and 30 minutes (Bruker) depending on how much reshimming was required. To avoid this tedious chore, I had our machine shop make a plastic tool for empty rotor removal shown below.

This tool consists of a pole with a diameter slightly less than that of the spinner. On the end of the pole is a tapered prong with a diameter of 4 mm at the tip and 6 mm at the base. This tool is inserted in the top of the magnet and gently lowered until the prong gets wedged into the empty spinner. The spinner is removed with the tool. The entire operation takes less than 10 seconds and no reshimming is required.

Gradient Spin Echoes for Selective Excitation

Shaped excitation pulses can replace the non-selective hard pulses typically used in a one-pulse measurement to achieve selective excitation. Another method of achieving selective excitation is the gradient spin echo using a selective 180° pulse. This technique is demonstrated in the figure below. A non-selective hard 90°_x pulse is first given followed by a pair of identical pulsed field gradients sandwiching a soft selective 180° pulse about the y axis. The hard 90° pulse rotates all spin vectors onto the -y axis. During the first gradient pulse the spin vectors dephase and evolve according to their offset frequencies. The soft 180°_y pulse flips a single resonance 180° about the y axis leaving all other resonances untouched. During the second gradient pulse, the "selected" resonance is rephased and its offset frequency evolution is refocused. The unselected resonances dephase more and continue to evolve according to their offset frequencies. The receiver is then turned on to collect the FID of the "selected" resonance, all others are dephased and therefore suppressed. This is demonstrated in the figure below which shows ¹H NMR spectra for a mixture of methylence chloride and acetone. The bottom trace shows a standard one-pulse measurement. The middle and top traces show results from a selective gradient spin echo measurement with the selective 180° pulse set for methylene chloride and acetone, respectively.

Background Suppression in Liquids

High resolution NMR probes for liquids may contain parts near the coil consiting of the nuclei being observed. The parts give rise to background signals which can severely affect the NMR data. When observing¹¹B, there is a background signal from boron containing parts near the coil and also the borosilicate glass in the NMR tube containing the sample.

Cory and Ritchey* introduced a very simple, clever method to suppress background signals in 1988. Their method uses a composite pulse, consisting of a 90° and two 180° pulses with appropriate phase cycling, in place of a conventional 90° pulse. The phase cycled composite pulse is essentially a 90° pulse for all spins inside the coil and 0° for all spins outside of the coil. An example of its implementation is shown in the figure below. The bottom traces show the ¹¹B [¹H] NMR spectra for a dilute sample of NaBH₄ and a "real" synthetic sample on the left and right, respectively. One can see an enormous background signal from both the NMR probe and the NMR tube. In the case of the "real" synthetic sample, the information from the spectrum is difficult or impossible to recover. The top traces show similar spectra acquired using the composite pulse. The only background signal remaining is that from the portion of the NMR tube inside the coil. This pulse sequence (without proton decoupling) is in the Bruker pulse program library called "zgbs". It is not exclusive to ¹¹B.

D.G. Cory and W.M. Ritchey. Journal of Magnetic Resonance, 80, 128 (1988).

Hahn Echo for 11B Background Suppression in Solids

Solids NMR probes often contain boron rich parts near the coil in which the sample resides. Boron nitride, in particular, is a material very commonly used. This can be very problematic if one wishes to collect ¹¹B NMR data, in that a strong background signal may be observed. Even though these parts are not directly inside the coil with the sample, they do experience a small amount of rf from the coil and the coil does detect a ¹¹B NMR signal from them. One simple way to avoid this problem is to use a Hahn echo to observe the ¹¹B spectrum. Unlike the sample inside the coil, which experiences the 90° and 180° pulses required for the Hahn echo, the boron rich parts outside of the coil experience pulses of much smaller flip angles and therefore the echo signal from them is much reduced. This is illustrated in the figure below, which shows ¹¹B NMR spectra collected in a 4 mm MAS probe without magic angle spinning. In the lower trace a simple one-pulse measurement was made with high power ¹H decoupling. The spectrum contains a very large background signal and it is very difficult to extract any useful information from the data. The spectrum in the upper trace was collected with a Hahn echo with high power ¹H decoupling during the acquisition. The background signal is completely removed revealing a beautiful, information-rich line shape for the central transition resulting from the second order quadrupolar and chemical shielding anisotropy interactions.

Thank you to Joseph Weiss of David Bryce's laboratory for providing the sample and collecting the data. See more of Joseph's beautiful ¹¹B spectra here:

Joseph W.E. Weiss and David L. Bryce J. Phys. Chem. 114 (2010) ASAP.
http://dx.doi.org/10.1021/jp101416k

Dummy Scans

Dummy scans (DS, Bruker) or steady state scans (SS, Varian) are scans taken in an NMR acquisition before the receiver is turned on and data are collected. Each dummy scan contains all of the rf pulses, delays and gradients used in the pulse program; the only difference is that the receiver is not turned on to collect data. Dummy scans are typically used to ensure that a spin system is in a steady state before data are collected. For example, One may collect a spectrum using a relaxation delay short with respect to the T₁'s of some of the resonances in the spectrum. The first scan may find the system at equilibrium, as the sample may have sat in the magnet for a few minutes while the probe was being tuned and matched or the magnet was being shimmed. The second and subsequent scans will find the system not at equilibrium, as the system has been perturbed by the rf pulses of the preceding scan(s) and not allowed to fully relax. The data from the first and seccond scan are therefore not the same. After several scans, although not at equilibrium, the system will be in a steady state before each additional scan and therefore each subsequent scan will collect similar data. An example of the use of dummy scans is shown in the figure below. The bottom trace shows a single scan ¹³C NMR spectrum of a concentrated solution of menthol in CDCl3 after the sample had sat in the magnet for a minute or so. The top trace shows a similar single scan acquisition preceded by 16 dummy scans. The relaxation delay was set to 1 second and the acquisition time for the FID was 1 second. 90° pulses were used in both spectra. One can see that some of the resonances in the top spectrum are attenuated in comparison to the bottom spectrum. The ¹³C signal from the CDCl₃ (which has a long T₁) is missing in the spectrum acquired with dummy scans. The dummy scans have selectively presaturated the solvent.

Household Dust (Bunnies)

Many people will be celebrating Easter this coming weekend. Children will be searching for Easter eggs left by the Easter Bunny. A word of caution though: Not all bunnies are cute!

Household dust bunnies seem to magically reproduce and grow. They must be collected regularly either with a broom or a vacuum cleaner and disposed of. What exactly is household dust? A bit of internet searching reveals that household dust is composed largely of fibers from clothing, dead human skin and the bodies of dust mites - a very disgusting mixture indeed. The top trace in the figure below is the ¹³C CPMAS NMR spectrum of a sample of household dust. The middle trace is a similar spectrum of clothing fibers from a sample of dryer lint. The difference spectrum (in the bottom trace) is consistent with a complex mixture of proteins and largely represents the spectrum of dead human skin and the bodies of dust mites.

Free and Inexpensive NMR Processing Software for Students

Processing NMR data has just become more affordable for students. Our friends at Advanced Chemistry Development have recently decided to make their NMR processing software free of charge to academics. As a student, you can put this software on your personal laptop or PC and process your NMR data at home or anywhere your travels take you. You can register and download the software here. They have even started a BLOG dealing with use of the software. I think I speak for all students when I say "Thanks guys!!"

Also, our friends at Bruker Biospin have recently introduced an inexpensive personal student license for their TOPSPIN software which can be purchased online.
There are other excellent NMR processing software options available. I mention specifically those above as the University of Ottawa currently holds network licenses for them and our students are most familiar with them.

Watergate vs Presaturation

Biochemists and protein chemists are often interested in observing the NH protons in their samples. Since the NH protons usually undergo slow chemical exchange with water, it is desirable to run the samples in H₂O rather than D₂O so the NH protons will not exchange with the deuterium in the solvent which would make them invisible in the ¹H NMR spectrum. In practice, a mixture of 10% D₂O and 90% H₂O is used as a solvent so that a deuterium lock can be established and used while running the spectrum. The very high concentration of water compared to the very low concentration of solute necessitates the use of solvent suppression methods.

Both presaturation and WATERGATE are efficient techniques used to suppress strong water signals from proton NMR spectra, however, there are differences between the two methods of which the user must be aware. Presaturation employs a selective, long, low power pulse to saturate the water resonance. This pulse is usually several seconds in duration during which exchange can occur between the unsaturated NH protons and the saturated water protons. If this exchange occurs, the NH protons become partially saturated to an extent related to the rate of chemical exchange between the NH and the water. The intensity of the NH protons in the spectrum is non-quantitative. WATERGATE, on the other hand, uses a pair of gradients surrounding a composite pulse which in effect inverts all but the water signal. The duration of the composite pulse is about 4 orders of magnitude shorter than a presaturation pulse, so exchange between the NH protons and the solvent occurs to a much lesser extent during the WATERGATE sequence compared to presaturation. As a result, the NH region is much less attenuated and more quantitative in a spectrum collected using WATERGATE compared to a similar spectrum run with presaturation. This is illustrated in the figure below which shows the NH region of the ¹H spectrum of a small disaccharide substituted peptide.One can see that some of the NH's are greatly attenuated in the spectrum acquired with presaturation compared to the spectrum run using WATERGATE. The more attenuated the signal, the faster the chemical exchange for that particular NH with water.

The WATERGATE suppression sequence is very similar to the gradient spin echo sequences used to measure diffusion constants and DOSY spectra. As a result, when WATERGATE suppression is used, one expects diffusion losses for small molecules (which diffuse quickly) compared to large molecules (which diffuse slowly). This effect is demonstrated in the figure below which shows the NH/aromatic region of the ¹H spectrum of a partially degraded ¹⁵N labelled 10 kDa protein.Here, one can see the same exchange losses pointed out in the previous figure for the presaturation spectrum compared to the WATERGATE spectrum. In addition, one can see that the intensity of a very sharp peak marked in yellow (likely due to a CH proton from free histidine) is less intense in the WATERGATE spectrum compared to the presaturation spectrum. This loss is due to the fast diffusion of the small free amino acid compared to the very large protein. In conclusion, one must be aware of the differences between the two solvent suppression methods if quantitative results are being sought.

I would like to thank Roger Tam from Robert Ben's Laboratory and Allison Sherratt from Natalie Goto's Laboratory for kindly providing the samples of the peptide and protein, respectively.

Fast 90 Degree Pulse Determination

Almost all NMR measurements rely on the correct calibration of 90° pulses. This is traditionally done by collecting a series of spectra as a function of pulse duration, finding a null for the 180° or 360° pulse and calculating the 90° pulse by simple division by 2 or 4 in the case of the 180° and 360° nulls, respectively. This determination, although trivial, can be very time consuming. Wu and Otting* have presented a much faster method of determining a 90° pulse based on measuring the nutation of a magnetization vector directly. Continuous nutation is depicted in the figure below. Here, the sample is subjected to continuous irradiation about the x axis. While being irradiated, the magnetization vector rotates in the z-y plane at a nutation frequency proportional to the pulse power. The magnetization on the -y axis is defined by a sine function. Fourier transformation of this magnetization gives an antiphase doublet centered at zero whose splitting Δν is twice the nutation frequency. The reciprocal of the nutation frequency is the time it takes the magnetization vector to rotate one complete cycle in the z-y plane and therefore the time it takes to rotate by one quarter of a cycle (i.e. the 90° pulse duration) is defined as 1/(2 Δν). The problem with continuous irradiation is that the sample must be irradiated at the same time magnetization is being detected. To eliminate this problem, a scheme similar to homonuclear decoupling is used where the radiation is turned off long enough to sample a data point. This is depicted in the figure below.Here each dwell period is divided up into a period for irradiation and a period for detection. The duty cycle for the irradiation is the fraction of time for which the sample is being irradiated. The magnetization is sampled when the power is off. As in the case for continuous irradiation, the magnetization vector still rotates in the z-y plane however, the rotation is slower as it is scaled according to the duty cycle. The duration of the 90° pulse is d/(2 Δν), where d is the duty cycle for irradiation. An example of this is shown in the figure below. The nutation spectrum was measured for HDO using a duty cycle, d = 0.10 and a power level of 12 dB (Bruker). Since the response of the amplifiers is linear, the 90° pulses at higher power levels can be calculated. Each decrease by 6 dB cuts the duration of the 90° pulse in half. In this case the 90° pulse at 0 dB was calculated to be 10.93 µsec at 0 dB based on the measured 90° pulse of 43.71 µsec at 12 dB. This pulse agrees to within a couple of percent of that measured by the more traditional method however, the measurement took only a few seconds. You can use a program called "pulsecal" on newer Bruker spectrometers to do this in complete automation.

--

* Peter S.C. Wu and Gottfried Otting J. Mag. Res. 176, 115 (2005).

Faster Relaxation Time Measurements in Solids

T₁ relaxation times are typically measured with the inversion recovery technique. In this method the magnetization is inverted and its recovery is monitored as a function of time. For nuclei with long T₁'s, the measurements are very time consuming as a recycle delay of at least five times T₁ must be used between scans. Typical T₁'s for ¹³C in the solid state range from several seconds to tens of minutes, so their direct measurement via the inversion recovery method could be prohibitively long.

High resolution ¹³C solid state NMR spectra of solids are routinely measured with cross polarization and magic angle spinning (CPMAS) in order to take advantage of the signal enhancement due to magnetization transfer between the abundant protons and isotopically dilute ¹³C nuclei. Additionally, the recycle delay needed for this measurement depends on the T_1ρ of the protons rather than the T₁ of the ¹³C. Proton T_1ρ's are typically shorter than ¹³C T₁'s by at least an order of magnitude, so many more scans can be collected per unit data collection time compared to a direct one-pulse measurement.

One might think that ¹³C T₁'s can simply be measured with cross polarization using a simple inversion recovery scheme by applying a 90° pulse to the ¹³C spins immediately following the contact pulse and then following their recovery over time. This method would have both the advantages of signal enhancement due to CP and more scans per unit time. The problem however, is that the enhanced magnetization of the inverted spins relaxes back to its unenhanced Boltzmann value and not its enhanced value. So, in order to measure the T₁, the direct ¹³C magnetization would have to be measured first (without CP) which would be very time consuming. This difficulty can be eliminated with the pulse sequence introduced by Torchia in 1978^* shown in the figure below.
This sequence uses a simple two step phase cycle to subtract out the effect of the direct ¹³C Boltzmann magnetization. The first part of the sequence uses a (90°_-y) pulse to return the CP enhanced magnetization to the z axis. The decay of the enhanced magnetization down to its Boltzmann value is followed using a (90°_x) pulse with detection of signals on the -y axis. The second part of the sequence uses a (90°_y) pulse to put the CP enhanced magnetization on the -z axis. The recovery of the enhanced inverted magnetization back to its equilibrium Boltzmann value is followed using a (90°_x) pulse with detection of signals on the y axis. The addition of the first and second parts of the experiment by way of the phase cycle allows for a simple calculation of the ¹³C T₁ with both the advantages of CP enhancement and the ability to collect more scans per unit time. An illustration of this method is shown in the figure below where the ¹³C T₁'s of glycine were measured. (The small peak in the spectrum is a spinning sideband of the carbonyl carbon)

* D.A. Torchia, J. Mag. Res. 30, 613, (1978).

NMR WIKI

An excellent resource for NMR users has been gaining more and more popularity on the web over the last few years. The brainchild of Evgeny Fadeev (Director of the Biomolecular Spectroscopy Facility at the University of California Irvine), NMR Wiki is an information sharing site offering a question and answer forum, job postings, a pulse sequence library, course material, history, information on meetings etc.... I think this is a fantastic place to learn more about NMR and Evgeny is to be commended for his efforts.

The Scale on an NMR Spectrum

Some people new to NMR spectroscopy have trouble with the meaning on the scales of their NMR spectra. Usually the data are plotted with a chemical shift scale (δ). This scale increases to the left and is usually reported in units of parts per million (ppm). The chemical shift of a resonance in a sample, δ_sample , in ppm is defined as follows:where ν_sample is the absolute frequency of the sample resonance and ν_reference is the absolute frequency of an agreed upon reference compound. For ¹H, ¹³C and ²⁹Si NMR, tetramethylsilane (TMS) is the agreed upon reference standard. When the scale is plotted in this manner, the peak positions are relative to that of the standard compound. This scale is particularly useful, as it independent of a single absolute frequency and therefore does not depend on the magnetic field strength, which varies from laboratory to laboratory. Spectra recorded using magnets of unequal field strength can be compared more easily.

Scales are also plotted in frequency units (Hz), usually with the reference compound assigned a value of 0 Hz. This scale also increases to the left and is usually of use when coupling constants (which are independent of field) are being measured.

Although absolute electronic shielding values are inconvenient to measure, one may hear people refer to one resonance being "more shielded" or "less shielded" than another, The shielding constant, σ, for a particular nucleus in a particular environment can be expressed by rearranging the Larmor equation.The shielding scale increases to the right.

In the age of continuous wave NMR spectrometers, NMR spectra were measured by irradiating the sample with continuous wave radiation and sweeping the magnetic field from a low value (on the left) to a high value (on the right). The scales were sometimes plotted in magnetic field units and one still hears about one peak being described as "upfield" or "downfield" from another. These terms have little relevance in FT NMR and should be avoided.

Some of the older literature reported ¹H NMR peak positions on a τ scale. Here, τ was equal to (10 ppm - δ ) and the scale increased to the right. This is no longer in use and has caused considerable confusion. It should be avoided.

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.

Pulse Power Expressed in Hz

On several occasions I have been asked what it means when a power level for a pulse is expressed in frequency units (e.g. "The proton decoupling power was 75 kHz"). The frequency here is the precession frequency about the magnetic field due to the pulse in the rotating frame of reference and NOT the frequency within the pulse itself. The power level expressed in Hz is simply the reciprocal of the time required for a magnetization vector to travel 360° (one cycle) under the influence of the pulse (i.e. the reciprocal of the 360° pulse duration). The algebra is as follows where the power level in Hz is expressed with respect to the 90° pulse rather than the 360° pulse.

Field Homogeneity and VT Gas

In order to obtain optimum resolution, NMR spectroscopists always correct the inhomogeneity of the magnetic field around the sample by adjusting the current in the the room temperature shim coils. The magnetic field homogeneity around the sample depends not only on the quality of the superconducting magnet but also on the magnetic susceptibility of the materials in the vicinity of the coil and the sample. The careful selection of materials in probe manufacturing and their use around the coil are essential for being able to produce a homogeneous field in the vicinity of the sample using the shim coils. This is one of the reasons why high resolution NMR probes are very expensive. One "material" near the coil which is often overlooked by the NMR user is the VT (variable temperature) gas being passed over the sample. The two most common VT gasses are air and nitrogen. One might think that these are very similar to one another as dry air is approximately 80% nitrogen. The magnetic susceptibility between the two however, is quite large and they will distort the magnetic field around the sample to differing extents. This is demonstrated in the figure below. A sample of CHCl₃ in acetone-d₆ was placed in a 500 MHz magnet equipped with a probe using air as the VT gas. The magnet was shimmed and the spectrum acquired is shown in the top trace. The air source was then replaced by a source of nitrogen gas at the same flow rate. The spectrum was measured again without re-shimming the magnet and is displayed in the lower trace. The difference in line shape and width is due to the difference in magnetic susceptibilities between the two gases. It should be noted that a spectrum of similar quality to the one obtained using air can be obtained after re-shimming the magnet to correct for the susceptibility difference.

Measuring Power

Anyone who takes care of NMR equipment knows that visits from service engineers are very expensive. These visits can often be avoided by becoming familiar with the components of the NMR spectrometer and learning how to make simple diagnostic measurements. These measurements can be sent to service engineers who can provide advice on replacement parts. One such measurement is the determination of the output power from the amplifiers of the spectrometer. This measurement requires an oscilloscope with a band width greater than the output frequency from the amplifier. Since properly functioning amplifiers put out tens to hundreds of watts, the output must be attenuated in order to prevent damage to the oscilloscope. An attenuator of 30 or 40 dB (rated for at least 10 watts of CW power) is suitable. Also, the measurement must be made at 50 Ω impedance. The spectrometer must be set up to take pulses at regular intervals (e.g. 10 µsec pulses every second). For oscilloscopes with only a 1 MΩ input impedance setting, the measurement can be made according to the following figure using a "T" connector and a low power 50 Ω terminator to match the impedance. The "T" connector and 50 Ω terminator are not required if the oscilloscope has in input impedance setting of 50 Ω. In this case, the connections can be made according to the following figure. The output power (in Watts) is determined by the peak to peak voltage, V_pp , of the pulse as follows.

NMR Facility now on Twitter

The University of Ottawa NMR Facility is now on Twitter ( http://twitter.com/Uottawanmr ). NMR users at the University of Ottawa can check here for timely news specifiic to the NMR Facility (for example if an instrument is out of service for repair).

Gradient Recovery Times

Many pulse sequences employ pulsed field gradients for coherence selection thereby minimizing or eliminating the need for phase cycling. The routine use of pulsed field gradients has dramatically reduced the data collection times needed for many 2D experiments and therefore increased the throughput and productivity of NMR spectrometers. The field gradient coils in modern high resolution NMR probes surround the rf coils and are powered by an amplifier in the NMR spectrometer console. When a pulsed field gradient (typically 1 -2 msec in duration) is applied, the sample is no longer in a homogeneous magnetic field. When the gradient is turned off, the system must recover from the disturbance. This recovery is not instantaneous. Pulse sequences typically have delays of 50 - 200 μsec following a gradient pulse to allow for recovery of field homogeneity. The time for recovery after a gradient pulse depends on the design of the NMR probe, the strength and shape of the gradient pulse as well as the shielding between the gradient coils and the shim coils. One can measure the time required for recovery by applying a gradient pulse, and then collecting an NMR spectrum after a variable delay. In the figures below, the gradient recovery time was measured using a console equipped with gradients of maximum strength 50 G/cm, and a narrow bore 500 MHz broadband probe adapted to fit in a wide bore magnet. The duration of the gradient pulses was set to 1 msec. The first figure below shows the proton NMR data for a sample of doped 1% H₂O in D₂O with a line width of approximately 4 Hz with short term recovery times from 1 to 20 µsec.The top trace shows the data for a rectangular gradient at 100 % strength. The middle trace shows the results for a rectangular gradient of 50% of full strength and the bottom trace shows the data using a sine bell shaped gradient pulse of 100 % strength. One can see that for the rectangular gradients the full intensity of the line is recovered in as little as 10 µsec. When the sine bell shaped gradient pulse is used, the full intensity of the line is recovered in less than 1 microsecond. This faster recovery is the result of the gradual rise and fall of the gradient strength in the sine bell shaped pulse.

A 4 Hz line is not a very sensitive gauge for the measurement of recovery times, so the experiments were repeated for a sample with a line of ~0.3 Hz in width where the line shape could be examined in detail at longer recovery times. The second figure shows the proton NMR data for a sample of 1% CHCl₃ in acetone-d₆ with a line width of approximately 0.3 Hz with long term recovery times from 50 to 800 msec.The top trace shows the data for a rectangular gradient at 100 % strength. The middle trace shows the results for a rectangular gradient of 50% of full strength and the bottom trace shows the data using a sine shaped gradient pulse of 100 % strength. One can see that in all cases a reasonable line shape is recovered in ~ 400 msec. The shape of the gradient pulse does not seem to influence the time required to recover a good line shape.

What is this Holiday Treat?

Things are beginning to wind down at the University of Ottawa as the end of exams approaches and we all look forward to a few holidays. I would like to wish all readers a happy and safe holiday season.

I leave you with a little puzzle. The ¹³C MAS NMR spectrum of one of my favorite holiday treats is shown below. What is it? Leave a comment to this post with your guess. (hint: cross polarization was attempted but was quite inefficient).

Defining the Excitation Profile

The excitation profile of an rf pulse is determined by its Fourier transform. The Fourier transform of rectangular pulses of monochromatic radiation, typically used in NMR measurements, are (sin(x) /x) (or sinc(x)) functions. The sinc(x) function has a large central lobe with satellite lobes of alternating positive and negative sign. In order to obtain uniform excitation and therefore quantitative data, one must ensure that the excitation pulse is sufficiently short to allow the entire spectral width of interest to fit within a small region of the central sinc(x) lobe. The pulse must also have sufficient amplitude to produce a 90° rotation of the magnetization. The excitation profile of four pulses is shown in the figure below.The data were obtained by measuring a 300 MHz ¹H NMR spectrum of HDO as a function of transmitter frequency. The power level for each of the pulses was set such that the pulses provided a 90° flip angle for an on-resonance signal. Each spectrum was phased independently. The first zero crossings of the sinc(x) function are at + 1/(PW) and -1/(PW) where PW is the duration of the pulse. It is therefore important that the spectral width of interest be less than ~1/(10PW) to ensure uniform excitation. One can see that a 10 µsec pulse provides essentially flat excitation across 40 kHz whereas 50, 100 and 200 µsec pulses do not.

Variable Temperature NMR - Thermal Equilibrium

When doing variable temperature NMR, students often ask me how long they should wait for thermal equilibrium in their sample before collecting NMR data. The answer depends of course on the amount of gas flow around the sample and the temperature difference between the current and desired sample temperature. The position of the thermocouple in an NMR probe is typically right below the sample. It takes time between when the thermocouple reports the desired temperature and when the sample is at the desired temperature. During this time there is a large thermal gradient across the sample as well as convection currents which will affect the line width of NMR resonances. These effects are demonstrated in the figure below. For this measurement, the temperature of the probe was set to 50°C with an air flow of 800 L/hour. Once the thermocouple read 50°C, a sample of D₂O was placed in the probe and 30 minutes was allowed to pass, after which the sample was presumed to be at thermal equilibrium. The lock was established and the magnet was then shimmed. The sample was removed and allowed to sit at room temperature for 30 minutes. It was then reintroduced to the probe at 50°C. ¹H NMR spectra of the residual HDO were then collected at 30 second intervals for a period of 10 minutes. As soon as the room temperature sample is reintroduced to the warm probe, it begins to warm up. During the this time, the thermal gradients and convection currents are large and the line width is adversely affected. As the sample temperature approaches 50°C the thermal gradients are smaller and the line becomes narrower. After approximately 6 minutes the width of the line changes very little. The sample appears to be at thermal equilibrium after 10 minutes.

Purge Pulses and Spin Locking Pulses

Both spin locking pulses and purge pulses are very useful components of multipulse NMR experiments. Spin locking pulses are long pulses applied at the same phase as the transverse magnetization. While being applied, the magnetization is polarized along the static field of the spin locking pulse, B₁, in the rotating frame. The magnetization is therefore locked to the axis of the applied pulse in much the same way that an equilibrium magnetization vector is locked to the static magnetic field, B_o. Purge pulses are long pulses applied at a phase 90° from the transverse magnetization. While the pulse is being applied, the transverse magnetization precesses about the static field of the pulse, B₁, exactly like the way transverse magnetization precesses about B_o during a delay. If the pulse is long enough, the magnetization will dephase as a result of the B₁ inhomogeneity of the rf pulse and be lost.

A long high power pulse can behave as both a spin locking pulse and a purge pulse as demonstrated in the vector diagram below. Imagine a spectrum consisting of two singlets. If the transmitter is set to the frequency of one of the singlets and a 90°_x pulse is applied, both magnetization vectors are rotated to the -y axis. During a delay equal to one quarter of the reciprocal frequency difference between the singlets, the "on resonance" singlet will remain stationary while the "off resonance" singlet will rotate by 90° onto the x axis. If a long high power pulse is now applied along the y axis, it will behave as a spin locking pulse for the "on resonance" singlet and a purge pulse for the "off resonance" singlet. An example of this is shown in the figure below for a sample of methylene chloride and chloroform where the transmitter was set on the methylene chloride resonance. The top trace represents a simple one pulse measurement. The spectrum in the bottom trace was collected by applying a 90°_x pulse followed by a delay equal to one quarter of the reciprocal frequency difference between the methylene chloride and chloroform. A 1 msec y pulse was then applied at the same power level as the 90° pulse followed by detection. One can see that the resonance of methylene chloride is unaffected compared to the one pulse measurement while that of the chloroform has been completely suppressed.

B1 Homogeneity

High resolution NMR spectroscopists spend a great deal of time shimming the magnet to ensure that the static magnetic field, B_o is homogeneous. This is because the transverse magnetization precesses about B_o. The Larmor equation implies that if there is a distribution in B_o across the volume of the sample, there will be a distribution of frequencies for each resonance line (i.e. the NMR resonances will be broad). The more homogeneous B_o across the sample volume, the sharper the NMR lines.

There is another field we must consider when doing NMR experiments - the magnetic field due to the RF pulse in the rotating frame of reference. In the rotating frame of reference, during the application of a pulse, an "on resonance" NMR line experiences an effective field, B_eff equal to the magnetic field due to the pulse, B₁. B₁ is a static magnetic field in the rotating frame of reference. Due to the finite dimensions of the coil in the probe with respect to the sample, the B₁ field will not be homogeneous across the entire volume of the sample. For example, a 90° pulse for the sample in the center of the coil will not be equal to a 90° pulse for the sample near the edges of the coil. While an x phased pulse is being applied to an equilibrium magnetization vector, the magnetization will precess about the x' axis in the rotating frame in the z-y' plane exactly like transverse magnetization precesses about the z axis in the x-y plane. While the magnetization precesses in the z-y' plane during the pulse, it is affected by the inhomogeneity in the B₁ field. The inhomogeneity of the B₁ field can be measured by doing a simple pulse calibration, applying longer and longer pulses well beyond that needed for a 360° pulse. After the pulse, the magnetization vectors precess again about B_o, and can be measured. The magnitude of the magnetization for a 90°, (90° + 360°), (90° + 720°) ..... etc. pulse will depend on the B₁ homogeneity. An example of this is shown in the figure below. The figure shows a simple ¹H pulse calibration for the decoupler coil of a 5 mm broadband NMR probe. The B₁ homogeneity is expressed as the ratio of intensity for an 810° pulse compared to that from a 90° pulse. In this case the B₁ homogeneity is 0.43. Much higher B₁ homogeneity would be expected for an inverse detection probe.

Why are MRI Scanners so Loud?

If you have ever had a magnetic resonance image (I prefer the term NMR image) taken in a hospital, you have undoubtedly heard very loud noises while the instrument collected the data. These noises are the result of the application of magnetic field gradients by way of the gradient coils inside the main magnetic field. The magnetic field gradients are applied in short pulses and are used to spatially encode the sample (person) such that the Larmor frequency of the protons in one region of the sample differs from that in other regions. It is this spatial frequency labelling which allows for the generation of the image. The time dependant magnetic field generated by the pulsed magnetic field gradients interacts with the main magnetic field with a force exactly like the one we are all familiar with when we move two magnets in close proximity to one another. Since the pulsed field gradient coils are held in a rigid form within the main magnet, they are unable to move any great distance however the sudden application of a gradient pulse generates a very strong force which physically slams the gradient coils inside the rigid form making a loud noise from the vibration. The larger the main magnetic field or the stronger the gradient pulses, the greater the force generated and the louder the noise.

These noises can sometimes be heard in high resolution NMR probes equipped with pulsed field gradients. Recently, a student approached me concerned that the NMR spectrometer was making a soft "tick" noise for every scan collected in his gradient COSY experiment. Immediately I thought perhaps the probe was arcing so I turned down the RF power. The noise persisted. Upon closer inspection, I found that the gradient strength was set unnecessarily high for the measurement. When the gradient strength was turned down, the "tick" noise ceased.

NMR and Food Chemistry - Popcorn

Both liquid state and solid state NMR have become very important tools in the food industry for both research and quality control. Since starch is a very important biopolymer and a major constituent in many foods, a great deal of work has been done on its chemical and physical characterization. Starches are 1 -4 linked polymers of glucose. Native starches are a mixture of a linear polymer (amylose) and a branched polymer (amylopectin). Furthermore, the starches are of two main types differing in their crystal structures and water content: the A type (cereal starches) and the B type (tuber starches). In addition to A or B starches, the starch granules in plants can have some amorphous starch as well. Corn starch is of the A type.

Popcorn is a snack enjoyed by millions around the world. As a child, I remember being fascinated at watching it pop and wondering what was going on. Much study has been devoted to the physics of popping corn. Essentially, every kernel of corn is a pressure vessel. When cooked, the moisture trapped within the starchy endosperm of the kernel is superheated. When the steam pressure inside the kernel becomes high enough the hull (pericarp) of the kernel explodes and the superheated water in the starch granules suddenly vaporizes, expands and rapidly cools making a solid foam out of the starchy endosperm. Each starch granule is a bubble in the solid foam.

Although much work has been done to understand starch and much work has been done to understand the popping of corn, I was unable to find any efforts directed to the chemical changes in corn starch before and after popping. This prompted me to collect a few spectra to address the issue. The first figure below shows the starch region of the ¹³C CPMAS spectra of unpopped corn (bottom trace), popped corn (middle trace) and cooked but unpopped corn (upper trace). The spectrum of unpopped corn is a mixture of A type starch (with a characteristic three line pattern in the C1 region) and amorphous starch (with a broad distribution of overlapping lines in the C1 region). The spectra of popped corn and cooked but unpopped corn are essentially identical and characteristic of amorphous starch. The data indicate that the heating and dehydration of the corn transform the crystalline A starch into amorphous starch. The observation is consistent with published studies on the hydration of starches. Aside from this change, there is no evidence for any other chemical transformation in the starch.

The second figure shows an expansion of the C1 region highlighting the conversion of crystalline A type starch into amorphous starch.

Probe Arcing

Probe arcing can occur during the application of an rf pulse. It is the passage of a spark between a localized area of high voltage inside the probe to ground. In cases of severe probe arcing, one can hear a "snap" during the application of a pulse. If the probe is removed from the magnet and the cover is removed, one can see the arcing as a small "bolt of lightning" between the high voltage area and ground. When a probe arcs, the integrity of the pulse is affected and one will observe FIDs of irreproducible amplitude and phase. Needless to say, the quality of data collected on an arcing probe will be severely compromised. If a probe is permitted to arc for extended periods of time, some of the electronic components inside the probe can be permanently damaged. The amplifiers can also be damaged as arcing will cause mismatching and high levels of reflected power. Here are a few things you can do to help stop probe arcing.

1. Use lower pulse power levels.
2. If the location of the arcing can be found visually (i.e. you can see the spark), then the high voltage area and the path to ground can be wrapped with teflon tape.
3. Round off any sharp edges inside the probe as these are the areas of highest local voltage. In particular, any solder joints around the coil should be smooth.
4. Keep the coil and capacitors as far away from ground as possible.
5. Purge the inside of the probe body continuously with nitrogen gas.