Apparent diffusion behaviour of intermolecular double-quantum coherence modulated by a distant dipolar field in solution NMR

A modified correlated spectroscopy (COSY) revamped with asymmetric Z-gradient echo detection sequence was designed to investigate the influence of diffusion behaviour on intermolecular double-quantum coherence signal attenuation during the pre-acquisition period. Theoretical formulas were deduced and experimental measurements and simulations were performed. It is found that the diffusion behaviour of intermolecular double-quantum coherence in the pre-acquisition period may be different from that of conventional single-quantum coherence, depending on the relative orientation of diffusion weighting gradients to coherence selection gradients. When the orientation of the diffusion weighting gradients is parallel or anti-parallel to the orientation of the coherence selection gradients, the diffusion is modulated by the distant dipolar field. This study is helpful for understanding the signal properties in intermolecular double-quantum coherence magnetic resonance imaging.     

Intermolecular double-quantum coherence imaging without coherence selection gradients and its application in in vivo MRI

In the COSY Revamped with Asymmetric Z-gradient Echo Detection (CRAZED) experiments, magnetization is modulated by the distant dipolar field (DDF) generated by coherence selection gradient (CSG) commonly in sinusoidal wave-form and results in detectable intermolecular multiple-quantum coherence (iMQC) signal. IMQCs have some attractive features, but their intrinsic weak signal intensity prevents their widespread applications. In this paper, a new phase cycling scheme was applied to obtain intermolecular double-quantum coherence (iDQC) signal. It is found that DDF can arise from nonspherical sample geometry or background inhomogeneous field in the absence of CSGs, which is more efficient than that created from CSGs. The experimental results show that the resulting DDF can refocus the ± iDQC signals simultaneously and thus enhance the signal intensity to about two folds of that from the conventional CRAZED sequence. Theoretical prediction and experiments give coincident results.     

Apparent diffusion behaviors of spins in the presence of distant dipolar field in two-component solution NMR

The diffusion behaviors of spins in the presence of distant dipolar field in two-component spin systems during the second evolution period of a modified CRAZED sequence before acquisition were investigated. Theoretical formulas were deduced based on the distant dipolar field model. The simulation results and experimental observations are consistent with the theoretical predictions. This study shows that the relative intensities of signals from intermolecular zero-quantum coherences (iZQCs) and intermolecular double-quantum coherences (iDQCs) have the same diffusion attenuation characteristic under the combined effect of diffusion weighting gradients and distant dipolar field during the second evolution period. This diffusion attenuation may be different from that of conventional single-quantum coherence signal, depending on the relative orientation of the diffusion weighting gradients to the coherence selection gradients. The results presented herein are helpful for understanding the effect of distant dipolar field from a spin system on the diffusion behavior of other spin system and the signal properties in the iZQC or iDQC magnetic resonance imaging.     

Chemical exchange saturation transfer by intermolecular double-quantum coherence

A number of contrast enhancement effects based on the use of intermolecular multiple-quantum coherences, or distant dipolar field effects are known. This phenomenon is characterized by the dependence on the mth power of the initial magnetization (where m is the coherence order used). In this paper, we describe the contrast enhancement based on chemical exchange saturation transfer and NOE, which is achieved by the use of intermolecular double-quantum coherences (iDQC). The method was validated using clinically relevant systems based on glycosaminoglycans and a sample of cartilage tissue, showing that the CEST contrast, as well as, NOE are enhanced by iDQC.     

Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a gamma-encoded pulse sequence from the C/R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for (13)C and (31)P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [(13)C(3)]alanine.     

Structural anisotropy and internal magnetic fields in trabecular bone: coupling solution and solid dipolar interactions

We investigate the use of intermolecular multiple-quantum coherence to probe structural anisotropy in trabecular bone. Despite the low volume fraction of bone, the bone-water interface produces internal magnetic field gradients which modulate the dipolar field, depending on sample orientation, choice of dipolar correlation length, correlation gradient direction, and evolution time. For this system, the probing of internal magnetic field gradients in the liquid phase permits indirect measurements of the solid phase dipolar field. Our results suggest that measurements of volume-averaged signal intensity as a function of gradient strength and three orthogonal directions could be used to non-invasively measure the orientation of structures inside a sample or their degree of anisotropy. The system is modeled as having two phases, solid and liquid (bone and water), which differ in their magnetization density and magnetic susceptibility. A simple calculation using a priori knowledge of the material geometry and distribution of internal magnetic fields verifies the experimental measurements as a function of gradient strength, direction, and sample orientation.     

Separation and characterization of different signals from intermolecular three-spin orders in solution NMR

In this paper, signals originating from a pure specific coherence of intermolecular three-spin orders were separated and characterized experimentally in highly polarized two-component spin systems. A modified CRAZED sequence with selective radio-frequency excitation was designed to separate the small signals from the strong conventional single-spin single-quantum signals. General theoretical expressions of the pulse sequence with arbitrary flip angle pulses were derived using dipolar field treatment. The expressions were used to predict the relaxation and diffusion properties and optimal experimental parameters such as flip angles. For the first time, relaxation and diffusion properties of pure intermolecular single-quantum, double-quantum, and triple-quantum coherences of three-spin orders were characterized and analyzed in one-dimensional experiments. All experimental observations are in excellent agreement with the theoretical predictions. The theoretical results show that the quantum-mechanical treatment leads to exactly the same predictions as the dipolar field treatment. The quantitative study of intermolecular multiple-quantum coherences of three-spin orders presented herein provides a better understanding of their mechanisms.     

Heteronuclear Double-Quantum MAS NMR Spectroscopy in Dipolar Solids

A new pulse sequence for high-resolution solid-state heteronuclear double-quantum MAS NMR spectroscopy of dipolar-coupled spin-12 nuclei is introduced. It is based on the five-pulse sequence known from solution-state NMR, which is here applied synchronously to both spin species. The heteronuclear double-quantum (HeDQ) spinning-sideband patterns produced by this experiment are shown to be sensitive to the heteronuclear distance, as well as the relative orientations of the chemical-shift and dipolar tensors. In particular, it is shown that the HeDQ patterns exhibit an enhanced sensitivity to the chemical shielding tensors as compared with the single-quantum spinning-sideband patterns. The detection of HeDQ patterns via the I and S spins is discussed. The isolated (13)C-(1)H spin pair in deuterated ammonium formate with (13)C in natural abundance was chosen as a model system, and the perturbing influence of dipolar couplings to surrounding protons on the (13)C-(1)H DQ coherence is discussed. The pulse sequence can also be used as a heteronuclear double-quantum filter, hence providing information about heteronuclear couplings, and thus allowing the differentiation of quaternary and CH(n) bonded carbons. The elucidation of (13)C-(1)H dipolar proximities is presented for a sample of bisphenol A polycarbonate with (13)C in natural abundance, recorded with a broadband version of the synchronized five-pulse sequence.     

Intermolecular double-quantum NMR techniques to probe microstructures on porous media

In heterogeneous systems the amplitude of the intermolecular double-quantum (DQ) signal depends on sample heterogeneity over a correlation distance dc=pi/(gammaGct). In this paper two different CRAZED-type sequences were applied in a porous medium phantom. One of these sequences gives rise to a DQ-T2 weighted signal, while the other one gives rise to a DQ-T2* weighted signal. Experimental results indicate that tuning of the correlation distance dc in a porous medium can alter the DQ signal in a manner which depends on the microstructure. This is evident only using the CRAZED-type sequence which gives rise to a DQ-T2* weighted signal.     

Efficient double-quantum excitation in rotational resonance NMR

We present a new technique for double-quantum excitation in magic-angle-spinning solid-state NMR. The method involves (i) preparation of nonequilibrium longitudinal magnetization; (ii) mechanical excitation of zero-quantum coherence by spinning the sample at rotational resonance, and (iii) phase-coherent conversion of the zero-quantum coherence into double-quantum coherence by frequency-selective spin inversion. The double-quantum coherence is converted into observable magnetization by reversing the excitation process, followed by a pi/2 pulse. The method is technically simple, does not require strong RF fields, and is feasible at high spinning frequencies. In [(13)C(2),(15)N]-glycine, with an internuclear (13)C-(13)C distance of 0.153 nm, we achieve a double-quantum filtering efficiency of approximately 56%. In [11, 20-(13)C(2)]-all-E-retinal, with an internuclear (13)C-(13)C distance of 0.296 nm, we obtain approximately 45% double-quantum filtering efficiency.     

Heteronuclear intermolecular single-quantum coherences in liquid nuclear magnetic resonance

This paper analyses the heteronuclear Cosy Revamped by Asymmetric Z-gradient Echo Detection pulse sequence. General theoretical expressions of the pulse sequence with arbitrary flip angles were derived by using dipolar field treatment and signals originating from heteronuclear intermolecular single-quantum coherences （iSQCs） in highly-polarized two spin-1/2 systems were mainly discussed in order to find the optimal flip angles. The results show that signals from heteronuclear iSQCs decay slower than those from intermolecular double-quantum coherences or intermolecular zero-quantum coherences. Magical angle experiments validate that the signals are from heteronuclear iSQCs and insensitive to the imperfection of radio-frequency flip angles. All experimental observations are in excellent agreement with theoretical predictions. The quantum-mechanical treatment leads to similar predictions to the dipolar field treatment.     

DIRECT MEASUREMENT OF TRANSVERSE RELAXATION TIME OF INTERMOLECULAR MULTIPLE QUANTUM COHERENCES IN NMR

A one-dimensional NMR method is presented for measuring the transverse relaxation time, T_2,n, of intermolecular multiple quantum coherences (IMQCs) of coherence order n in highly polarized spin systems. The pulse sequence proposed in this paper effectively suppresses the effects of radiation damping, molecular diffusion, inhomogeneity of magnetic field, and variations of dipolar correlation distance, all of which may affect quantitation of T_2,n. This pulse sequence can be used to measure not only IMQC transverse relaxation time T_2,n(n>1) quickly and directly, but also the conventional transverse relaxation time. Experimental results demonstrate that the quantitative relationship between T_2,n(n≥1) and T₂ is T_2,n≈T₂/n. These results will be helpful for understanding the fundamental properties and mechanisms of IMQCs.     

Diffraction-like phenomena in a periodic magnetization distribution at 1.5 T using the distant dipolar field (DDF)

In the CRAZED experiment (COSY revamped by asymmetric Z-gradient echo detection, Warren et al.), a spatially anisotropic magnetization distribution is created by application of a magnetic field gradient (strength G, duration tau) which in turn generates a response called the distant dipolar field (DDF). The DDF is a source of intermolecular multiple-quantum coherences (iMQC) which contain information on the distance d=pi/(gammaGtau) between pairs of dipolar-coupled spins. Diffraction-like phenomena may result for periodically structured samples. In this study, we report the observation of diffraction owing to the DDF at 1.5 T using a clinical whole-body tomograph. Based on the semi-classical treatment of the problem by Robyr and Bowtell, diffraction conditions were obtained for a CRAZED-type pulse sequence that selects iMQC of order N. The predicted distinct difference in N=2 and N not equal2 coherences, i.e., a dominant continuous course as a function of tau (N=2) and prominent diffraction peaks otherwise, could be verified in CRAZED experiments in a periodically structured sample selecting coherence orders N=2 and N=3. The diffractive signal component contains information on the geometric structure of the sample. Applications of this technique may permit the detection of changes in composition and geometry of periodic structures.     

Double-quantum excitation in the NMR of spinning solids by pulse-assisted rotational resonance

We describe a new technique for double-quantum excitation in magic-angle-spinning NMR of powdered solids. The technique is designed to efficiently excite double-quantum coherence in the vicinity of a rotational resonance condition. The offset from rotational resonance allows the double-quantum filtered signals to be observed with high resolution and sensitivity. The method uses rotational excitation of zero-quantum coherence, assisted by radiofrequency pulse cycles. The zero-quantum coherence is converted into double-quantum coherence by a frequency-selective inversion sequence. Experiments on [(13)C(2), (15)N]-glycine demonstrate a double-quantum filtering efficiency of approximately 41% at a sample rotation frequency of 8.300 kHz, which is 1.600 kHz away from the n = 1 rotational resonance. We achieve 32% double-quantum filtering efficiency at a spinning frequency of 9.250 kHz, which is 2.550 kHz away from rotational resonance.     

Multispin moments edited by multiple-quantum NMR: application to elastomers

The spin system response to the five-pulse sequence used for measurements of double-quantum and triple-quantum buildup curves is evaluated in the initial excitation/reconversion regime. The multispin dipolar network that is present also in many soft solids like elastomers was considered. It is proved rigorously that the relevant quantity for analysis of double-quantum build-up curves in the initial regime is the second van Vleck moment. The higher-order moments edited by double-quantum as well as higher-order coherences in the multiple-quantum build-up experiments are different from van Vleck moments. These results can be applied to compare (1)H residual moments edited by double-quantum and triple-quantum experiments with those measured by other NMR methods. The sensitivity of multiple-quantum coherences to the changes in the values of residual dipolar couplings for cross-linked natural rubber under uniaxial elongation is also discussed. Under such conditions (1)H second van Vleck moments were measured for different elongation ratios of a cross-linked natural rubber. Moreover, (1)H triple-quantum edited moments were also measured for the same sample under uniaxial compression. The dependence of the second van Vleck moment and the time of the maximum of the double-quantum buildup curve on the cross-link density of natural rubber measured at low magnetic field was also investigated.     

Solvent-localized NMR spectroscopy using the distant dipolar field: a method for NMR separations with a single gradient

Solvent-localized NMR (SOLO) is a new method which allows the separation of NMR spectra of substances dissolved in different solvents. It uses the selective HOMOGENIZED pulse sequence to produce a two-dimensional NMR spectrum resulting from intermolecular zero-quantum coherences in one distinct solvent. The detected signal is locally refocused by the action of the distant dipolar field, which is created by a frequency selective pulse only in regions containing the selected solvent. The prerequisites are that the different solvents have sufficiently different chemical shifts to be excited separately and that compartments with different solvents are spatially separated by more than the typical diffusion distance. Here, the method is demonstrated for the solvents water and DMSO on a length scale of 0.5 mm. Because signal in the spectra is refocused locally, SOLO is insensitive to variations in the magnetic field which may result from inhomogeneities or structures in the sample. This makes applications in strongly structured samples possible. SOLO is the first method that achieves localization of NMR signal with a single gradient pulse. Therefore, it can be used in conventional NMR spectrometers with one-axis gradient systems and lends itself to a wide range of applications including in vivo NMR.     

Sample restriction using magnetic field gradients in high-resolution solid-state NMR

Many solid-state NMR experiments are sensitive to inhomogeneity in the radiofrequency field. We propose a method to restrict the sample volume, in magic angle spinning experiments, using a static magnetic field gradient and a selective pulse. The position of the gradient is calculated for our experimental configuration and we have simulated the effects of selective pulses to determine the excited volume. The resulting sequences are applied to a sample of sodium acetate using frequency-switched Lee–Goldburg proton–proton homonuclear dipolar decoupling. A gain of a factor of 2 on the carbon resolution is experimentally observed.     

High-resolution absorptive intermolecular multiple-quantum coherence NMR spectroscopy under inhomogeneous fields

Intermolecular multiple-quantum coherence (iMQC) is capable of improving NMR spectral resolution using a 2D shearing manipulation method. A pulse sequence termed CT-iDH, which combines intermolecular double-quantum filter (iDQF) with a modified constant-time (CT) scheme, is designed to achieve fast acquisition of high-resolution intermolecular zero-quantum coherences (iZQCs) and intermolecular double-quantum coherences (iDQCs) spectra without strong coupling artifacts. Furthermore, double-absorption lineshapes are first realized in 2D intermolecular multi-quantum coherences (iMQCs) spectra under inhomogeneous fields through a combination of iZQC and iDQC signals to double the resolution without loss of sensitivity. Theoretically the spectral linewidth can be further reduced by half compared to original iMQC high-resolution spectra. Several experiments were performed to test the feasibility of the new method and the improvements are evaluated quantitatively. The study suggests potential applications for in vivo spectroscopy.     

Enhanced sensitivity to residual dipolar couplings of elastomers by higher-order multiple-quantum NMR

The homonuclear and heteronuclear residual dipolar couplings in elastomers reflect changes in the cross-link density, temperature, the uniaxial and biaxial extension or compression as well as the presence of penetrant molecules. It is shown theoretically that for an isolated methyl group the relative changes in the intensity of the homonuclear double-quantum buildup curves in the initial time regime due to variation of the residual dipolar coupling strength is less sensitive than the changes in the triple-quantum filtered NMR signal when considering the same excitation/reconversion time. For a quadrupolar nucleus with spin I=2 the sensitivity enhancement was simulated for four-quantum, triple-quantum, and double-quantum buildup curves. In this case the four-quantum build-up curve shows the highest sensitivity to changes of spin couplings. This enhanced sensitivity to the residual dipolar couplings was tested experimentally by measuring 1H double-quantum, triple-quantum, and four-quantum buildup curves of differently cross-linked natural rubber samples. In the initial excitation/reconversion time regime, where the residual dipolar couplings can be measured model free, the relative changes in the intensity of the four-quantum buildup curves are about five times higher than those of the double-quantum coherences. For the first time proton four-quantum coherences were recorded for cross-linked elastomers.     

Quantum Treatment of Intermolecular Multiple-Quantum Coherences with IntramolecularJCoupling in Solution NMR

A recently introduced density matrix picture for dipolar effects in solution NMR (1996,J. Chem. Phys.105,874) gave complete solutions for intermolecular multiple-quantum coherences for single-component samples without scalar couplings. This paper, for the first time, shows that this quantum picture can lead to explicit signal expressions for multicomponent samples of molecules with internal scalar couplings (here assumed to generate a first-order spectrum) and long-range dipolar couplings. Experimental observation of a triplet in the indirectly detected dimension for a heteronuclear CRAZED sequence (¹³CHCl₃sample, ZQ or 2Q coherences) gives clear evidence that the coupling is due to the intermolecular dipolar coupling. We also make comparisons with classical pictures which introduce the dipolar demagnetization field in multicomponent spin systems.