Probe Tuning and 90 Degree Pulses

In order to get meaningful results from multiple-pulse NMR pulse sequences, it is essential that the 90° and 180° pulses are calibrated at the power levels used in the sequences (see this post for example). The calibrations are usually done on a standard sample in a well tuned and matched probe. The calibrations are typically stored in a file which is called up when setting up particular NMR experiments. It is important to know that these calibrations are correct for the particular sample of interest only when the probe is well tuned and matched. For samples of high ionic strength, it may not be possible to properly tune and match the probe and the 90° and 180° pulses for these samples will be longer than those previously calibrated, resulting in questionable data. In these cases, the pulses must be calibrated on the problematic sample. The figure below addresses the question of how important proper tuning and matching are with respect to the 90° pulse duration. The ¹H 90° pulses for a sample HDO in a 500 MHz broadband probe were measured by the fast nutation method for various states of probe tuning and matching. In the left-hand side of the figure, pulses were calibrated for a perfectly matched probe as a function of tuning frequency. One can see that the 90° pulse is at a minimum when the probe is perfectly tuned and increases as the probe is detuned in either direction. In the right-hand side of the figure, pulses were calibrated for a perfectly tuned probe as a function of probe mismatch. One can see that the 90° pulse is at a minimum in a perfectly matched probe and increases as a function of the degree of mismatch (in units of screen divisions on the spectrometer display). It is interesting to note that the 90° pulse duration is more forgiving to mismatch than to errors in probe tuning.

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.

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

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.

90 Degree Pulses for I = n/2 Quadrupolar Nuclei in the Solid State

The 90 degree pulse for an I = n/2 quadrupolar nucleus in the solid state depends on the strength of the rf pulse with respect to the quadrupolar frequency. If the strength of the pulse is much greater than the quadrupolar frequency, the pulse is non-selective and excites all transitions equally. If however it is much less than the quadrupolar frequency, then the pulse is selective to the central (m = 1/2 - m = -1/2) transition. The duration of the pulse producing a maximum signal is shorter for selective vs. non-selective pulses at a similar power level. In solution, where the quadrupolar interactions is averaged by random isotropic molecular motion or in the solid state, if the symmetry around the I = n/2 nucleus is cubic, the quadrupolar frequency is small with respect to the strength of the rf pulses and the pulses are non-selective. When the symmetry around the I = n/2 nucleus in the solid state is non-cubic, the quadrupolar frequency is significant and the pulses are very often selective to the central transition. This is illustrated in the figures below for the ²³Na MAS spectrum of a mixture of NaCl (cubic) and Na₂SO₄ (non-cubic). The first figure shows the ²³Na MAS spectrum labelling each component of the mixture. The second figure shows the effect of increasing the pulse duration. One can clearly see that the 90 degree pulse for NaCl is close to twice that of Na₂SO₄.