Liquid nuclear magnetic resonance behaviors related to intermolecular dipolar interactions were investigated theoretically and experimentally in highly polarized two-component spin systems. A modified CRAZED pulse sequence was designed to investigate relative signal intensities with considerations of spin transverse relaxation, longitudinal relaxation, molecular diffusion, and optimal radio-frequency flip angles. The dissipation of the demagnetizing field due to relaxation and diffusion processes during the detection period was taken into account as well. For the first time, vigorous analytical expressions of the spin dynamics, including all the effects mentioned above, were derived from the combination of the demagnetizing field model and product operator formalism. In the regime where the linear approximation (γμoMot《1) is valid, these explicit analytical expressions can quantitatively describe the signal behaviors related to intermolecular dipolar interactions. All the theoretical predictions based on the analytical expressions for the directly excited component are in excellent agreement with experimental observations reported previously. Several valuable insights for the indirectly excited component were gained from the analytical expressions and verified by experimental measurements, including optimal radio-frequency flip angles, unusual relative signal intensities for n522 and n52, and unconventional diffusion and multi-exponential longitudinal relaxation processes, where n is the ratio of the coherence-selection gradient areas in the CRAZED pulse sequence. In addition, n-order diffusion coefficients of the directly and indirectly excited spins during the evolution period predicted by the demagnetizing field picture are found to be the same as those obtained with the combination of the intermolecular multiple-quantum picture and Gaussian phase distribution approximation which is valid in the case of unrestricted isotropic diffusion. These results suggest that a combination of the demagnetizing field model and product operator formalism provides excellent predictive power and computational convenience for diffusion and relaxation behaviors in two-component systems. These quantitative studies may also provide an opportunity to probe specific sources of new contrast for medical MR imaging.

To date, both the intermolecular multiple-quantum coherence (MQC) and demagnetizing field models have led to fully quantitative predictions of NMR signals in a highly polarized system using the CRAZED and similar sequences. In this paper, measurements of apparent MQC diffusion rates, Dn app, for a specific apparent coherence order, n, were used to investigate the equivalent between the intermolecular MQC and demagnetizing field treatments. A number of physical effects were analyzed both theoretically and experimentally. These effects include molecular diffusion, variation in dipolar correlation distance, radiation damping, inhomogeneous broadening, and spin relaxation, all of which may alter the NMR signal. Two variations of a two-pulse CRAZED sequence, where the signal attenuation is almost entirely caused by the diffusion weighting, were designed to accurately measure and characterize Dn app during the evolution period. Apparent diffusion rates were extracted from a least-squares fitting of a series of 1H spectra, measured with varying diffusion weighting factors. Complete theoretical formations were explicitly derived from both the intermolecular MQC and demagnetizing field treatments. Numerical simulations based on the demagnetizing field treatment were performed and it was found that the model can be used to predict the apparent diffusion rates. A novel diffusion model for intermolecular MQC is proposed in which the phase shift of each individual spin on different molecules is considered to be uncorrelated. This model successfully predicts the unconventional diffusion behaviors of intermolecular MQCs, specifically for differences of apparent diffusion rates between inter-and intramolecular MQCs. Our theoretical predictions and experimental confirmation demonstrate, for the first time, that Dn app for intermolecular MQCs of order n are characterized by Dn app5nDT for n>2 and D0 app52DT for n50, where DT is the translational molecular diffusion rate of the single quantum coherences. These results do not coincide with Dn5n2DT for n>0 which is a general relationship for an intramolecular n-quantum coherence. These works about the apparent diffusion rates during the evolution period of the CRAZED sequences provide additional evidence to support the argument of the equivalence between the intermolecular MQC and demagnetizing field models. The general results derived from both intermolecular MQC and demagnetizing field treatments in this report can reasonably explain new observations of diffusion phenomena in nonlinear spin echoes by Kimmich and co-workers. Even though the theoretical prediction about intermolecular MQC diffusion is verified only with specific experiments using tailor-made pulse sequences, it is demonstrated that the function dependence of diffusion rate on coherence order is general. These results provide independent evidence to support the intermolecular MQC theory proposed by Warren and co-workers.

Intermolecular zero-quantum and double-quantum coherences (iZQCs and iDQCs) are frequently discussed in literature since they may provide novel contrast mechanisms in magnetic resonance imaging and possibilities for high-resolution spectra in an inhomogeneous and unstable magnetic field. In a previous paper [J. Chem. Phys. 115, 10769 (2001)], we have studied both theoretically and experimentally the properties of iZQC and iDQC nuclear magnetic resonance (NMR) Signals related to intermolecular dipolar interactions in two-component systems. In this paper, the investigation is extended to homonuclear intermolecular single-quantum coherences (iSQCs) from the second-order spin interactions, which have not been observed and studied previously. Selective excitation was used to suppress the strong conventional single-spin single-quantum signals. A combination of dipolar field treatment and Torrey equation was used to derive a general theoretical expression for the time evolution of spins with arbitrary flip angles of rf pulses. The expression was used to predict the optimal conditions for iSQCs among highly polarized spins in liquid. Dependence of the iSQC signals on the experimental parameters was measured and analyzed to verify the theoretical predictions. For the first time, signals from pure homonuclear two-spin iSQCs free of much larger conventional single-spin single-quantum signals, and intermolecular iSQC cross peaks in homonuclear pulsed-field gradient COSY experiments were observed and characterized, in one-and two-dimensional (1D and 2D) experiments, respectively. The use of coherence-selection gradients tilted at the magic angle results in the suppression of iSQC cross peaks. It provides strong evidence that the observed signals originate from distant dipolar interactions. Relaxation and diffusion properties of iSQCs in multiple-component samples were characterized and analyzed as well as the optimal rf flip angles. Theoretical and experimental results presented herein demonstrate that the signals from the homonuclear second-order iSQCs not only have a similar signal intensity as iZQCs or iDQCs, all of which are much stronger than that from three-spin iSQCs reported previously, but also provide spatial information related to dipolar correlation scales similar to iZQCs and iDQCs, which is not present in conventional SQC experiments. All 1D and 2D NMR experimental observations based on single- and multiple-component samples are in excellent agreement with the theoretical predictions. The quantitative study of iSQCs provides a better understanding of their unique mechanisms, and may find useful applications in NMR analyses such as sample purification and/or preparation of metabolites, biofluids, and natural compounds dissolved in nondeuterated solvents.

Although the theories and potential applications of intermolecular multiple-quantum coherences iMQCs have been under active investigations for over a decade, discussion of iMQC NMR signal formation was mainly confined in the time domain. In this paper, a full line-shape theory was developed to describe iMQC signals in the frequency domain. Relevant features of the line shape, such as peak height, linewidth, and phase, were investigated in detail. Predictions based on the theory agree well with experimental and simulated results. Since radiation-damping effects always couple with iMQCs in highly polarized liquid-state NMR systems, and strongly radiation-damped signals have many spectral characteristics similar to those of iMQCs, a detailed comparison was also made between them from different spectral aspects. With detailed comparison of peak height, linewidth, and phase, this work demonstrates that the iMQC and radiation-damping phenomena result from two completely different physical mechanisms despite that both present similar signal features and coexist in highly polarized liquid-state NMR systems.

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