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.