Quantitative characterization of intermolecular dipolar interactions of two-component systems in solution nuclear magnetic resonance

Abstract

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 (γμ0M0t≪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 n=−2 and n=2, 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.