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.

Field Dependence of Chemical Shift Resolution in Solids

As undergraduates we learn that the chemical shift resolution in an NMR spectrum increases with increasing field strength. This is true because the number of Hz in a ppm increases with field and inequivalent resonances are more separated (in Hz) at higher field.

Will one always get better chemical shift resolution at higher field? You may be surprised to learn that the answer is - no. In certain cases for liquids, where dynamic processes are occuring at a rate comparable to the frequency difference between resonances (i.e. on the NMR time scale) one may even get less resolution at higher fields due to line width changes at higher field.

In the MAS or CPMAS spectra of solids one obtains liquid-like spectra of solid materials. In the cases where dipolar coupling is effectively removed by either or both MAS and high power decoupling, the width of the resonances often depends on a chemical shift distribution associated with a particular site. Just like chemical shielding anisotropy, this distribution increases (in Hz) with the magnetic field strength. As a result, the chemical shift resolution does not improve on going to higher field as the widths of the MAS lines increase (in Hz) as a function of field. Two examples of this are shown below. The first figure is the ²⁹Si CPMAS spectrum of the clay kaolinite at 11.7 T (top trace) and 21.1 T (bottom trace). Both spectra were acquired with MAS rates exceeding the span of the chemical shift tensors. One can see that there is little if any improvement in the chemical shift resolution at higher field.

The second figure is the ¹⁹F MAS spectrum of the perfluorinated polymer, Nafion at 11.7 T (top trace) and 21.1 T (bottom trace). The MAS rates for each spectrum were chosen such that the dipolar coupling between the fluorines was effectively averaged by the MAS and that the spinning sidebands would be coincident (in ppm) in the spectra. Again, one can see that there is little if any improvement in the chemical shift resolution at higher field.

Thank you to Victor Terskikh and Eric Ye of the National Ultrahigh-Field NMR Facility for Solids for providing the figures for this post.

The 500 MHz 1H NMR Spectrum of Butane

n-Butane is a very simple molecule. Should it not then give a very simple ¹H NMR spectrum? The figure below shows two calculated 500 MHz proton spectra for n-butane. Which spectrum most closely represents the true spectrum of n-butane?The answer is the very complicated spectrum B. The spectra were calculated with the following parameters:

Spectrum B
Spectrometer frequency = 500 MHz
δ1 = δ4 = 0.333 ppm
δ2 = δ3 = 1.271 ppm
³J₁₂ = ³J₃₄ = 7.11 Hz
⁴J₁₃ = ⁴J₂₄ = -0.07 Hz
³J₂₃ = 6.77 Hz
LB = 0.5 Hz

Spectrum A

Spectrometer frequency = 500 MHz
δ1 = δ4 = 0.333 ppm
δ2 = δ3 = 1.271 ppm
³J₁₂ = ³J₃₄ = 7.11 Hz
⁴J₁₃ = ⁴J₂₄ = -0.07 Hz
³J₂₃ = 0 Hz

LB = 0.5 Hz

The only difference between the simulations is that in spectrum B a coupling of 6.77 Hz was assumed between the two methylene groups whereas in spectrum A the same coupling was taken to be zero. The reason spectrum spectrum B is so complicated is that despite the fact that both the methyl groups and both the methylene groups are chemically equivalent, they are not magnetically equivalent. This is true for both spectrum A and spectrum B however, in spectrum A the second order effects are small based on the parameters used in the simulation.

Thank you to Adrian Dingle for inspiring me to create this post.

Distortions in QCPMG Spectra from Pulse Miscalibrations

A standard QCPMG NMR pulse sequence consists of a 90^o pulse followed by a train of 180^o pulses. Ideally, the resulting spikelet envelope should outline the static lineshape from a conventiaonal Hahn-echo experiment. If the first pulse deviates from 90^o due to incorrect calibration, the QCPMG spikelet pattern does not change significantly, the only effect is somewhat lower overall intensity (first figure). At the same time the miscalibrated subsequent pulses lead to significantly distorted spikelet patterns (second figure). The 180^o pulse misset by as little as 20^o-30^o, could produce considerable oscillations in the spikelet intensity across the envelope. This illustrates that QCPMG NMR experiments are much more sensitive to proper setup of the 180^o pulses than the Hahn-echo experiment. The QCPMG spectra shown were calculated in SIMPSON for a central transition of a spin 3/2 nucleus resonating at 295 MHz (⁸⁷Rb at 21.1 T), C_Q=10 MHz, η_Q=0.7, CS anisotropy= -200 ppm, coincidental EFG and CSA tensors, ω_RF/2π= 200 kHz.

Many thanks to Eric Ye of the National Ultra-high Field NMR Facility for Solids for contributing this post.

13C NMR with 1H and 31P Decoupling

NMR users are very familiar with the advantages of proton decoupling when observing ¹³C. The ¹³C NMR spectra of phosphorus containing compounds can be made simpler by applying ³¹P decoupling either on its own or in addition to proton decoupling. The figure below shows the ¹³C NMR spectrum of dimethyl methylphosphonate with all possible combinations of proton and ³¹P decoupling. The data collection required a triple resonance probe with the appropriate band pass filters.

31P - 13C HMQC

When most people think about HMQC or HSQC spectra they think about protons and ¹³C or protons and ¹⁵N. Although these are by far the most common spins to probe, the HMQC technique can be applied to other spin pairs as well. In earlier posts to this BLOG, this was demonstrated for protons and ¹¹B and ³¹P and ¹⁰⁹Ag. This post shows an application of the technique to ³¹P and ¹³C. Measurements made between spin pairs, where one of the spins is not a proton, require a triple resonance probe and the appropriate filters.

The figure below shows ³¹P detected ³¹P - ¹³C HMQC data for dimethyl methylphosphonate with ¹³C decoupling during the acquisition and ¹H decoupling during the entire sequence. The spectra on the top and left-hand sides of the plots are separately run one dimensional ³¹P and ¹³C spectra, respectively, both with proton decoupling. The methyl carbon of dimethyl methylphosphonate has ¹J_CP = 142 Hz whereas the methoxy carbons have ²J_CP = 6 Hz. Two HMQC spectra were run. The one on the left was optimized for 142 Hz and the one on the right was optimized for 6 Hz. Each spectrum shows a correlation according to its coupling constant. The data were collected on a 500 MHz instrument with the appropriate bandpass filters on each channel.

90 Degree Pulse Determinations

In the routine procedure of R.F. pulse optimization, distorted nutation curves can sometimes be observed, as can be seen in the calculated graph below. This is usually due to the short recycle delay time (D1) not sufficient for complete relaxation. With increasingly shorter delay time, the maximum of the nutation curve shifts to lower flip angle, which makes the curve asymmetric. Under this circumstance, the 90 degree pulse determined from the maximum of the intensity will be inaccurate. On the other hand, if the recycle delay time is not too short, say 1 to 2 times of T1, the length of 180 degree pulse can still be determined with reasonable accuracy.

Many thanks to Eric Ye of the National Ultra-high Field NMR Facility for Solids for contributing this post.

The Selective 1D Gradient NOESY

Many students run very long 2D NMR experiments to find one particular piece of information. This is especially true for 2D NOESY experiments where perhaps only a single NOE correlation is sought. Depending on the amount of compound available, 2D NOESY measurements often take hours or tens of hours to acquire and can cost alot of money in instrument user fees. Many people do not realize that there are selective 1D analogs to the non selective 2D experiments. These 1D experiments rely on shaped pulses for selective excitation and take only a small fraction of the time required to run the comparable non selective 2D experiment. Previously I have posted entries in this BLOG on the very useful 1D selective gradient TOCSY experiment. The figure below demonstrates the use of the 1D selective gradient NOESY experiment for bis(phenylthio)methane compared to the standard proton NMR spectrum. In this case, the methylene protons were selectively irradiated and the NOE's were observed on the phenyl rings. The experiment took less than 5 minutes to acquire.

The Background from a Dirty NMR Probe

Have you ever wondered why the manager of your NMR equipment gets on your case about wiping down NMR tubes before putting them in the NMR probe? The figure below should answer your question. It shows the ¹H NMR spectrum of a clean empty NMR tube inside an NMR probe before and after the NMR probe has been cleaned.

Over time, the "stuff" from your hands and residue on the outside of your NMR tubes builds up on the inside of the inserts inside the coil of the NMR probe. This "stuff" contains protons and results in a background signal in all subsequent NMR spectra. I have seen inserts of NMR probes so dirty that samples have "stuck" inside the probe. The offending gunk resembles grey-black bubble gum or perhaps dirty dried nasal effluent. Periodically NMR probes must be cleaned to remove this offensive residue. This can usually be accomplished by gently inserting and removing a cotton swab soaked in alcohol inside the coil insert. For the particular case in the figure above, the NMR probe could not be cleaned in this way and had to be disassembled by a service engineer and cleaned in an ultrasonic bath.

WIPE YOUR NMR TUBES BEFORE PUTTING THEM IN AN NMR PROBE !!

Thank you to Dr. Michael Lumsden who manages the NMR Facility at Dallousie University for suggesting this post, kindly sharing his tale and providing the figure.

Spin Echos for Uncoupled Spins

The spin echo is one of the most fundamental building blocks for NMR pulse sequences. Its main purpose is to refocus chemical shifts. The simplest spin echo is that for uncoupled spins where only the offset, Ω (i.e. the frequency difference between the carrier and the resonance) need be considered. The pulse sequence is represented in the upper portion of the figure with the vector and product operator representations below. A 90_x pulse is first given to create magnetization along the -y axis of the rotating frame. During the first delay period, τ, the magnetization rotates in the x-y plane at a rate, Ω. The 180_x pulse rotates the magnetization 180 degrees about the x axis. During the second delay period, the magnetization again rotates in the x-y plane at a rate, Ω in the same direction as during the first delay. At the end of the second delay, the magnetization is on the y axis and the collection of the FID is started. It is important to note that the echo will always have its maximum at 2τ after the 90 degree pulse regardless of its offset, Ω or the duration of τ. The value of τ however is limited by the T₂.

What is T1ρ and How is it Measured?

The time constant for the build up of magnetization along the direction of the main magnetic field, B_o, (the z axis) either after a pulse or upon initially exposing a sample to the magnetic field is called the T₁ relaxation time or spin-lattice relaxation time. It is this relaxation time which determines the rate at which a pulse sequence can be repeated. The time constant for the decay of magnetization in the x-y plane of the rotating frame of reference after a pulse is called the T₂ relaxation time, the spin-spin relaxation time or the transverse relaxation time. It is this relaxation time which determines the natural line width of a particular resonance. There is another relaxation time constant of interest to NMR spectroscopists - T₁ρ. T₁ρ is the time constant for the decay of magnetization along the radio frequency field, B₁, of an applied spin locking pulse in the rotating frame of reference. It is analogous to T₁ except it describes relaxation along the radio frequency field of the pulse (which is static in the rotating frame) rather than relaxation along B_o. T₁ρ's are of interest in ROESY, TOCSY and cross polarization experiments. The T₁ρ is measured by first applying a 90 degree pulse to an equilibrium magnetization vector. A spin locking pulse is then applied. The phase of this pulse is shifted 90 degrees with respect to the excitation pulse such that the field of the spin locking pulse is coincident with the spin vector in the rotating frame of reference. During the spin locking pulse, the large magnetization vector (which was initially polarized in B_o) decays to its equilibrium value in the much smaller field, B₁, with time constant, T₁ρ. The T₁ρ is measured by analysing the intensity of the NMR signal in spectra collected as a function of the duration of the spin locking pulse. This is illustrated in the figure below.

Ottawa U Takes Delivery of a Bruker AVANCE III 400

The Bruker AVANCE III 400 NMR spectrometer for solids was delivered to Ottawa U last week and is currently being installed. It will be available for use in February. With the addition of this instrument, the Ottawa U campus boasts 7 NMR instruments (8, including the Bruker AVANCE II 900 on the NRC campus ). For some photos of the installation, follow this link.

Weak One-bond or Multiple Bond Correlations in 1H / 13C HMQC / HSQC Spectra

Many people are quite surprised to see either unusually weak one-bond correlations or weak multiple bond correlations in their ¹H / ¹³C HMQC / HSQC spectra. These people must be reminded that there is nothing "magic" about these experiments - the responses are based solely on an assigned delay proportional a reciprocal coupling constant. The large scale success of the ¹H / ¹³C HMQC / HSQC techniques can be attributed to the fact that most one-bond ¹H - ¹³C coupling constants are very similar ( ~ 145 Hz). The pulse sequences are therefore run with a delay based on a 145 Hz coupling constant. When one-bond coupling constants are significantly different than 145 Hz then the correlation will be either very weak or absent in the spectrum. Also, if multiple bond couplings are unusually large then those multiple bond correlations may be present in the spectrum. The figure below is an example. In the 500 MHz HMQC spectrum of an alkyne (optimized for 145 Hz coupling), one can see an unusually small one-bond correlation between the terminal alkyne proton and its attached carbon. There is also a weak two-bond correlation between the terminal alkyne proton and the other alkyne carbon.