Unconventional diffusion behaviors of intermolecular multiple-quantum coherences in nuclear magnetic resonance

Abstract

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, Dnapp, 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 Dnapp during the evolution period. Apparent diffusion rates were extracted from a least-squares fitting of a series of H1 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 Dnapp for intermolecular MQCs of order n are characterized by Dnapp=nDT for n⩾2 and D0app=2DT for n=0, where DT is the translational molecular diffusion rate of the single quantum coherences. These results do not coincide with Dn=n2DT 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.