Heteronuclear spin interactions in solids and anisotropic liquids can be removed by phase modulated decoupling sequences with frequency sweep, such as
The interactions between different types of nuclear spins in heteronuclear spin systems lead to the splitting of NMR peaks. Unlike anisotropic liquids and solids, where both dipole-dipole and
The decoupling sequence called swept-frequency two-pulse phase modulation or SWf-TPPM is one of the commonly used heteronuclear dipolar decoupling schemes proposed for application in solid-state nuclear magnetic resonance [
As already remarked, the TPPM and SWf-TPPM family of sequences were originally developed for heteronuclear dipolar decoupling in solid-state NMR. Although the underlying principles of decoupling in isotropic and anisotropic systems are different, it would be interesting to know the behavior of these decoupling sequences in isotropic liquids and to understand their efficiency in removing scalar heteronuclear interactions. The spin dynamics during these sequences can be explored easily in the liquid state because of the smaller interaction strengths and the absence of many body effects.
In this report, an attempt is made to explore the efficiency of SWf-TPPM for heteronuclear decoupling in isotropic systems and compare the results with some commonly used broadband decoupling sequences in liquid state NMR, MLEV [
It can be observed in the literature that the efficiency of a decoupling sequence can be improved by combining different versions of the primitive cycle into extended supercycles in which some of the residual pulse imperfections are compensated [
The scheme for two-pulse phase modulation (TPPM) [
The SWf-TPPM sequence [
The multiplicative factors of pulse duration given in SWf-TPPM-11 follow a tangential path and it is possible to make new variants with less number of TPPM blocks keeping the pulse length variation tangential. In this manner, four other sequences are designed. They include SWf-TPPM-7 [
The profiles of (a) TPPM, (b) SWf-TPPM-4, (c) SWf-TPPM-5, (d) SWf-TPPM-6, (e) SWf-TPPM-7, and (f) SWf-TPPM-11 sequences. The pulse length, normalized with respect to the central pulse pair of various SWf-TPPM sequences, is plotted against the number of the TPPM blocks in the corresponding decoupling sequence. The ordinate denotes the multiplicative factors that determine the corresponding profile.
For each of these sequences, the effectiveness of decoupling was analyzed as a function of the proton offset and phase angle,
To analyze the effect of constructing supercycles on the efficiency of swept frequency phase modulated sequences, the parent SWf-TPPM-11 sequence was taken as
Proton decoupled 13C experiments of benzene dissolved in acetone-d6 were performed on a BRUKER AV spectrometer at a frequency of 300 MHz for proton. Eight scans were accumulated for each spectrum with 8 k data points in a time of 0.542 s. The FID was Fourier transformed after exponential multiplication with a 1 Hz damping function. The experiments were performed at a decoupler power corresponding to a
The 13C NMR spectrum of benzene with proton decoupling is measured as the decoupler radiofrequency offset was varied from 2 to 12 ppm with respect to TMS. The proton resonance frequency is at ~7.5 ppm and the 13C resonance appears at ~128 ppm. Since the RF field strength is constant the bandwidth of the decoupling can be considered as a measure of its efficiency. In the figures, intensity of the decoupled line corresponding to the 13C resonance of benzene is plotted with successive increments of offset frequencies.
The simulations required to understand and visualize the trajectories of nuclear magnetization vector corresponding to the decoupled nuclei in a simple spin system, benzene during various decoupling sequences, were carried out using a Bloch Simulator.
The efficiency of various SWf-TPPM sequences for heteronuclear decoupling in liquid state NMR is analyzed and the results are summarized below. Experiments were performed with the parent SWf-TPPM-11 and its variants, SWf-TPPM-7, SWf-TPPM-6, SWf-TPPM-5, SWf-TPPM-4, and TPPM.
In all these experiments, a constant phase angle of 15° is used with an RF power of 2.85 kHz. In TPPM, SWf-TPPM-5, and SWf-TPPM-4 the decoupling bandwidth is smaller than for sequences with more number of elements as shown in Figure
The relative intensities of the decoupled 13C spectra of benzene at an RF power of 2.85 kHz using (a) TPPM, SWf-TPPM-11, 7, 6, 5, and 4 decoupling sequences at a phase angle of 15° and (b) WALTZ-16, MLEV-16, and GARP decoupling sequences. The proton offset varies between 2 and 12 ppm with respect to TMS.
Experiments were conducted to study the effect of phase angles on the decoupling bandwidth in SWf-TPPM sequences with 4, 5, 6, 7, and 11 TPPM elements. In each case, there exists an optimum phase angle which gives us maximum decoupling bandwidth. For instance, a phase angle of 20° performs well in SWf-TPPM-11 and SWf-TPPM-5.In case of SWf-TPPM-7, SWf-TPPM-6, and SWf-TPPM-4, 25° is the optimum phase angle. The results for SWf-TPPM-11 and SWf-TPPM-7 are shown in Figures
The relative intensities of the decoupled 13C spectra of benzene at an RF power of 2.85 kHz using (a) SWf-TPPM-11 and (b) its supercycled version. Phase angles of 15, 20, 25, 30, 35, and 40° are used. The proton offset varies between 2 and 12 ppm with respect to TMS.
The relative intensities of the decoupled 13C spectra of benzene at an RF power of 2.85 kHz using (a) SWf-TPPM-7 and (b) its supercycled version. Phase angles of 15, 20, 25, 30, 35, and 40° are used. The proton offset varies between 2 and 12 ppm with respect to TMS.
In this situation let us think about some modifications to the existing sequences. An improvement in the effectiveness of decoupling at the points corresponding to the observed depressions of the curve is expected to give a larger decoupling bandwidth. Generally, improvement in the performance of a decoupling sequence can be achieved by uniting various combinations of the primitive cycle into extended supercycles. When we do so, some of the residual pulse imperfections are compensated. Decoupling experiments with the supercycled sequences show that there is significant improvement in its performance as shown in Figure
The case of supercycled sequence of SWf-TPPM-7 is similarly giving a marginal improvement in the efficiency of decoupling as shown in Figure
Thus, the effectiveness of SWf-TPPM-11 and 7 sequences is marginally enhanced on supercycling, the oscillatory behavior is removed, and the fluctuations in the intensities are suppressed. The price one pays is that these sequences are relatively lengthy and hence new sequences which are shorter are to be preferred. In an attempt to achieve this objective, the efficiency of decoupling for the supercycled SWf-TPPM-4 sequence was studied as a function of phase angle. Even though the sequence fails to suppress the fluctuations in intensities and to give effective decoupling at all the phase angles analyzed, it performs relatively well at the phase angle of 40°. The illustrations are given in the supporting information (see supporting information in Supplementary Material available online at
In the following sections, the trajectories of nuclear magnetization vector of the abundant nuclei in a simple spin system during TPPM and SWf-TPPM decoupling are traced out on the Bloch sphere and compared with those obtained from WALTZ-16, MLEV, and GARP decoupling sequences which are commonly used in liquids for removing heteronuclear couplings. Finally, an attempt has been done to interpret the efficiency of decoupling in correlation with the trajectories of proton magnetization vectors during the implementation of the corresponding decoupling sequences.
Figure
The simulated trajectory of proton magnetization vector during (a) TPPM decoupling at the resonance position and (b) TPPM with different offsets of 200 Hz increments from the resonance position (view from
Figure
The simulated trajectory of proton magnetization vector during (a) SWf-TPPM-11 at the resonance position and (b) SWf-TPPM-11 with different offsets of 50 Hz increments from the resonance position. The termini are marked. A phase angle of 15° is used with a decoupling power of 2.85 kHz.
Now, we analyze the time evolution of nuclear magnetization vector for the supercycled sequences by taking the example of SWf-TPPM-4. This supercycled sequence is a representative of the behavior shown by all other supercycled sequences and is depicted here because the crowded Bloch sphere in the other cases prevents drawing meaningful conclusions. Figure
The simulated trajectory of proton magnetization vector with different offsets of 50 Hz increments from the resonance position during (a) SWf-TPPM-4 and (b) supercycled SWf-TPPM-4 decoupling schemes. A phase angle of 40° is applied with a decoupling power of 2.85 kHz.
The group of proton magnetization trajectories, given by SWf-TPPM sequences at the implemented power level of 2.85 kHz, tells that the increased effective field in case of higher values of
Figures
The simulated trajectory of proton magnetization vector with different offsets of 50 Hz increments from the resonance position during (a) WALTZ-16 and (b) MLEV-16 decoupling schemes. The decoupling power is 2.85 kHz.
A careful analysis of the trajectories of proton magnetization vector during parent SWf-TPPM sequences and their supercycled sequences reveals that, in the former case, the magnetization vector rotates according to the specified sequence from +
The phase modulated decoupling sequences TPPM and SWf-TPPM and the variants of the latter were used for heteronuclear decoupling in isotropic liquids. The effectiveness of decoupling was analyzed for these sequences and compared with the other commonly used decoupling sequences in isotropic liquids such as WALTZ-16, MLEV-16, and GARP. The broadband decoupling sequences that we use in liquid state outperform TPPM based sequences in removing heteronuclear couplings with minimum RF power. The efficiency of TPPM based sequences as a function of phase angles has been experimentally determined. Interestingly, the efficiency of decoupling shows oscillatory behavior rather than a monotonic behavior. It has been noticed that the effectiveness of TPPM based sequences can be improved by combining the parent sequence into supercycles. The supercycled SWf-TPPM-11 and -7 sequences give us enhanced decoupling. The trajectories of nuclear magnetization vector of the abundant nuclei in a simple spin system during TPPM and SWf-TPPM decoupling were simulated on the Bloch sphere and compared with WALTZ-16, MLEV, and GARP decoupling sequences which are commonly used in liquids for removing heteronuclear couplings.
The author declares that there is no conflict of interests regarding the publication of this paper.
The experiments discussed here are done at the Central NMR facility of Indian Institute of Technology Delhi, New Delhi, and the author is extremely grateful to Professor Narayanan Kurur for his fruitful suggestions in this project. Financial support from the University Grants Commission (UGC), India, is gratefully acknowledged.