Combining PGSE NMR with homonuclear dipolar decoupling

A new robust approach for combining multiple-pulse homonuclear decoupling and PGSE NMR is introduced for accurately measuring molecular diffusion coefficients in systems with nonvanishing static homonuclear dipolar couplings. Homonuclear decoupling suppresses dipolar dephasing during the gradient pulses but its efficiency and scaling factor for the effective gradient vary across the sample because of the large variation of the frequency offset caused by the gradient. The resulting artifacts are reduced by introducing a slice selection scheme. The method is demonstrated by (19)F PGSE NMR experiments in a lyotropic liquid crystal.     

13C PGSE NMR experiment with heteronuclear dipolar decoupling to measure diffusion in liquid crystals and solids

A new PGSE NMR experiment, designed to measure molecular diffusion coefficients in systems with nonvanishing static dipolar coupling, is described. The fast static dipolar dephasing of the single-quantum (13)C coherences is removed by multiple-pulse heteronuclear decoupling. The resulting slow dephasing of the (13)C coherences allows for inserting appropriate gradient pulses into the pulse sequence. The presence of the large magnetic field gradient reduces the efficiency of the decoupling sequences which is compensated for by introducing a scheme of sequential slice selection across the sample. The method is demonstrated by (19)F-decoupled (13)C PGSE NMR experiments in a lyotropic nematic and lamellar liquid crystal.     

MAG-PGSTE: a new STE-based PGSE NMR sequence for the determination of diffusion in magnetically inhomogeneous samples

A new stimulated echo based pulsed gradient spin-echo sequence, MAG-PGSTE, has been developed for the determination of self-diffusion in magnetically inhomogeneous samples. The sequence was tested on two glass bead samples (i.e., 212-300 and <106 microm glass bead packs). The MAG-PGSTE sequence was compared to the MAGSTE (or MPFG) (P.Z. Sun, J.G. Seland, D. Cory, Background gradient suppression in pulsed gradient stimulated echo measurements, J. Magn. Reson. 161 (2003) 168-173; P.Z. Sun, S.A. Smith, J. Zhou, Analysis of the magic asymmetric gradient stimulated echo sequence with shaped gradients, J. Magn. Reson. 171 (2004) 324-329; P.Z. Sun, Improved diffusion measurement in heterogeneous systems using the magic asymmetric gradient stimulated echo (MAGSTE) technique, J. Magn. Reson. 187 (2007) 177-183; P. Galvosas, F. Stallmach, J. K?rger, Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios, J. Magn. Reson. 166 (2004) 164-173, P. Galvosas, PFG NMR-Diffusionsuntersuchungen mit ultra-hohen gepulsten magnetischen Feldgradienten an mikropor?sen Materialien, Ph.D. Thesis, Universit?t Leipzig, 2003, P.Z. Sun, Nuclear Magnetic Resonance Microscopy and Diffusion, Ph.D. Thesis, Massachusetts Institute of Technology, 2003] sequence and Cotts 13-interval [R.M. Cotts, M.J.R. Hoch, T. Sun, J.T. Marker, Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems, J. Magn. Reson. 83 (1989) 252-266] sequence using both glass bead samples. The MAG-PGSTE and MAGSTE (or MPFG) sequences outperformed the Cotts 13-interval sequence in the measurement of diffusion coefficients; more interestingly, for the sample with higher background gradients (i.e., the <106 microm glass bead sample), the MAG-PGSTE sequence provided higher signal-to-noise ratios and thus better diffusion measurements than the MAGSTE and Cotts 13-interval sequences. In addition, the MAG-PGSTE sequence provided good characterization of the surface-to-volume ratio for the glass bead samples.     

Spectral simulations incorporating gradient coherence selection.

Computer-aided methods can considerably simplify the use of the product operator formalism for theoretical analysis of NMR phenomena, which otherwise becomes unwieldy for anything but simple spin systems and pulse sequences. In this report, two previously available programming approaches using symbolic algebra (J. Shriver, Concepts Magn. Reson. 4, 1-33, 1992) and numerical simulation using object-oriented programming (S. A. Smith, T. O. Levante, B. H. Meier, and R. R. Ernst, J. Magn. Reson. A 106, 75-105, 1994) have been extended to include the use of gradient operators for simulation of spatially localized NMR spectroscopy and gradient coherence selection. These methods are demonstrated using an analysis of the response of an AX(3) spin system to the STEAM pulse sequence and verified with experimental measurements on lactate.     

13C-1H HSQC experiment of probe molecules aligned in thermotropic liquid crystals: sensitivity and resolution enhancement in the indirect dimension

The spectra of molecules oriented in liquid crystalline media are dominated by partially averaged dipolar couplings. In the 13C-1H HSQC, due to the inefficient hetero-nuclear dipolar decoupling in the indirect dimension, normally carried out by using a pi pulse, there is a considerable loss of resolution. Furthermore, in such strongly orienting media the 1H-1H and 13C-1H dipolar couplings leads to fast dephasing of transverse magnetization causing inefficient polarization transfer and hence the loss of sensitivity in the indirect dimension. In this study we have carried out 13C-1H HSQC experiment with efficient polarization transfer from 1H to 13C for molecules aligned in liquid crystalline media. The homonuclear dipolar decoupling using FFLG during the INEPT transfer delays and also during evolution period combined with the pi pulse heteronuclear decoupling in the t1 period has been applied. The studies showed a significant reduction in partially averaged dipolar couplings and thereby enhancement in the resolution and sensitivity in the indirect dimension. This has been demonstrated on pyridazine and pyrimidine oriented in the liquid crystal. The two closely resonating carbons in pyrimidine are better resolved in the present study compared to the earlier work [H.S. Vinay Deepak, Anu Joy, N. Suryaprakash, Determination of natural abundance 15N-1H and 13C-1H dipolar couplings of molecules in a strongly orienting media using two-dimensional inverse experiments, Magn. Reson. Chem. 44 (2006) 553-565].     

Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan [J. Magn. Reson.129, 74–84 (1997)], and based on the multiple propagator approach of Caprihanet al.[J. Magn. Reson. A118, 94–102 (1996)], allows for the calculation of the echo attenuation,E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid–surface interactions. In particular, theq-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (δ a²/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry.     

Cross-relaxation effects in stimulated-echo-type PGSE NMR experiments by bipolar and monopolar gradient pulses

Exchange of longitudinal spin polarization by dipolar cross relaxation between nonequivalent spins results in a modulation of the stimulated echo signal on increasing the encoding/decoding delays and in a multiexponential decay on increasing the diffusion time. These artifacts are suppressed by 180° pulses inserted in the middle of the gradient encoding/decoding periods. The efficiency of the gradient encoding is preserved if bipolar gradient pulses are used instead of monopolar pulses. The behavior of the different pulse sequences is demonstrated by ¹⁹F PGSE NMR experiments in a lyotropic liquid crystal in both isotropic micellar and oriented nematic phases.     

Assessing signal enhancement in distant dipolar field-based sequences

The possibility of improving the signal-to-noise efficiency of NMR signal refocused by long-range dipolar interactions has been discussed recently [R.T. Branca, G. Galiana, W.S. Warren, Signal enhancement in CRAZED experiments, J. Magn. Reson. 187 (2007) 38-43]. For systems where T(1)>T(2), by including an extra radio-frequency pulse in a standard CRAZED sequence, it is possible to increase the available signal by exploiting its sensitivity to T(1) relaxation. Here, we use analytical calculations to investigate the source of this improved signal and determine the maximum enhancement provided by the method.     

Pulsed-Field-Gradient NMR Study of Anisotropic Molecular Translational Diffusion in nOCB Liquid Crystals

Pulsed-field-gradient nuclear magnetic resonance (NMR) combined with magic echo decoupling is applied to study anisotropic diffusion in samples with strong static dipolar spin interactions. The approach, due to its moderate demands on the NMR hardware, can be implemented on standard commercial equipment for routine diffusion studies of liquid crystals. Using a microimaging probe, measurement of diffusion in arbitrary spatial direction is possible. Hence, the principal components of the diffusion tensor are directly obtained. Anisotropic diffusion is investigated in the thermotropic mesophases of a homologous series of nOCB liquid crystals and an analogous compound with hydroxyl groups. The geometric average diffusion coefficient changes continuously at the isotropic–nematic phase transition. Experimental data are described in terms of the molecular translation models in the nematic phase and for the second-order nematic–smectic A phase transition. The diffusion anisotropy is higher for the sample with terminal hydroxyl groups suggesting significant molecular association via hydrogen bonding.     

Optimizing delays in the MBOB,broadband HMBC,and broadband XLOC NMR pulse sequences

The MBOB, broadband HMBC, and broadband XLOC NMR pulse sequences (A. Meissner and O. W. S?rensen (2000, Magn. Reson. Chem. 38, 981-984; 2001, 39, 49-52)) were introduced as a means of obtaining heteronuclear long-range correlation spectra with broadband excitation over an interval of heteronuclear long-range J coupling constants. However, it is not trivial what combination of delays to choose for a given purpose, particularly if one-bond and long-range correlation spectra are obtained simultaneously as in MBOB. This paper presents a way to determine sets of delays for MBOB, broadband HMBC, and broadband XLOC resolving the problem. The results tabulated suit various ranges of J coupling constants and transverse relaxation times.     

Double-quantum-filtered rotational-resonance MAS NMR in the presence of large chemical shielding anisotropies

Double-quantum filtration under rotational resonance MAS NMR conditions where the chemical shielding anisotropies involved exceed the differences in isotropic chemical shielding is considered by means of numerical simulations and (13)C MAS NMR experiments. The responses of two different pulse sequences, suitable for double-quantum filtration specifically under rotational resonance conditions, to large chemical shielding anisotropies are compared. In the presence of large chemical shielding anisotropies a very recently introduced pulse sequence (T. Karlsson, M. Edén, H. Luthman, and M. H. Levitt, J. Magn. Reson. 145, 95-107, 2000) suffers losses in double-quantum-filtration efficiencies. The double-quantum-filtration efficiency of another pulse sequence (N. C. Nielsen, F. Creuzet, R. G. Griffin, and M. H. Levitt, J. Chem. Phys. 96, 5668-5677, 1992) is less afflicted by the presence of large chemical shielding anisotropies. Both sequences deliver double-quantum-filtered lineshapes that sensitively reflect chemical shielding tensor orientations. It is further shown that double-quantum-filtered rotational-resonance lineshapes of spin systems composed of more than two spins offer a suitable experimental approach for determining chemical shielding tensor orientations for cases where conventional rotational-resonance experiments are not applicable due to the presence of additional background resonances.     

Unwanted signal leakage in excitation sculpting with single axis gradients

Excitation sculpting (T-L. Hwang and A. J. Shaka, J. Magn. Reson. A 112, 275-279 (1995)) used for solvent suppression and selective excitation in NMR bases its success on the ability to remove baseline and phase errors created by the application of selective rf pulses. This is achieved by the application of two pulsed field gradient (PFG) echoes in sequence. It is essential that the two pairs of PFGs select the coherence transfer steps independently of each other, which is conveniently achieved if they are applied along orthogonal spatial axes. Here, the much more common case where both PFG pairs must be applied along a single axis is investigated. This is shown to lead to complications for certain ratios of PFG strengths. The original theory of excitation sculpting is restated in the spherical basis for convenience. Some of the effects can only be explained by invoking the dipolar demagnetizing field.     

Short-time restricted diffusion in a static gradient and the attenuation of individual coherence pathways

We experimentally explore some of the implications of a recent theoretical study [J. Magn. Reson. 64 (2003) 145] for the measurement of restricted diffusion in connected porous media in a static gradient. In particular, we examine how restriction affects the short-time attenuation of different coherence pathways, all excited with the same sequence of slice-selective radiofrequency (RF) pulses, and how the various pathways make the transition to the long-time or tortuosity regime. We confirm that every pathway contains equivalent diffusional information and, for short times, yields the surface-to-volume ratio (S/V) of the confining space. We find also, in agreement with the theoretical predictions, that different pathways are controlled by different time scales and, thus, exhibit different sensitivity to restriction. This property might be exploited when designing optimal sequences to study restricted motion.     

The extended Fourier transform for 2D spectral estimation.

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to infinity one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals.     

An improved broadband decoupling sequence for liquid crystals and solids

Recently we developed an efficient broadband decoupling sequence called SPARC-16 for liquid crystals ?J. Magn. Reson. 130, 317 (1998). The sequence is based upon a 16-step phase cycling of the 2-step TPPM decoupling method for solids ?J. Chem. Phys. 103, 6951 (1995). Since then, we have found that a stepwise variation of the phase angle in the TPPM sequence offers even better results. The application of this new method to a liquid crystalline compound, 4-n-pentyl-4'-cyanobiphenyl, and a solid, L-tyrosine hydrochloride, is reported. The reason for the improvement is explained by an analysis of the problem in the rotating frame.     

Effects of finite-width pulses in the pulsed-field gradient measurement of the diffusion coefficient in connected porous media

We analytically compute the apparent diffusion coefficient D(app) for an open restricted geometry, such as an extended porous medium, for the case of a pulsed-field gradient (PFG) experiment with finite-width pulses. In the short- and long-time limits, we give explicit, model-independent expressions that correct for the finite duration of the pulses and can be used to extract the pore surface-to-volume (S/V) ratio as well as the tortuosity. For all times, we compute D(app) using a well-established model form of the actual time-dependent diffusion coefficient D(t) that can be obtained from an ideal narrow-pulse PFG. We compare D(app) and D(t) and find that, regardless of pulse widths and geometry-dependent parameters, the two quantities deviate by less than 20%. These results are in sharp contrast with the studies on closed geometries [J. Magn. Reson. A 117 (1995) 209], where the effects of finite gradient-pulse widths are large. The analytical results presented here can be easily adapted for different pulse protocols and time sequences.     

Comparative Studies of Phase-Cycling Schemes for Multiple π-Pulse Sequences

Recently, a new phase cycling scheme was introduced by this laboratory for use in biological solid-state NMR experiments involving multiple π-pulses with characteristics that suggested it may enhance the sensitivity of these kind of experiments (Y. Li and J. N. S. Evans, 1995,Chem. Phys. Lett.241,79 and Erratum, 1995,ibid.246,527; Y. Li and J. N. S. Evans, 1996,J. Magn. Reson. B111,296). The new sequence followed the supercycled concept proposed a decade ago for heteronuclear decoupling experiments. In this paper, more detailed experiments demonstrate that the claim of enhanced sensitivity was unfounded, and in fact the supercycle proposed differs little from the established XY-8 and XY-16 based supercycles.     

Recoupling of chemical-shift anisotropy powder patterns in MAS NMR

A comparison of three different implementations of the chemical-shift recoupling experiment of Tycko et al. [R. Tycko, G. Dabbagh, P.A. Mirau, Determination of chemical-shift-anisotropy lineshapes in a two-dimensional magic-angle-spinning NMR experiment, J. Magn. Reson. 85 (1989) 265-274] is presented. The methods seek to reduce the effects of artefacts resulting from pulse imperfections and residual C-H dipolar coupling in organic solids. An optimised and constant time implementation are shown to give well-defined and artefact free powder pattern lineshapes in the indirectly observed dimension for both sp2 and sp3 carbon sites. Experimental setup is no more demanding than for the original experiment, and can be implemented using standard commercial hardware.