High-Resolution NMR Measurement of Molecular Self-Diffusion by Fast Multi-Spin-Echo Diffusion Sequences

Abstract

There is currently much interest in probing the structure that is required to retrieve information about molecular transport processes. The spatial phase which accumulates during as well as the hydrodynamics of molecular species in solution. The steady growth of chemical and biomedical applicamolecular self-diffusion leads to signal attenuation in the ensemble average. This constitutes the basis for extracting tions including the measurement of molecular transport, the study of reaction dynamics, the identification of metabolites, D by traditional methods. Field gradients may in fact be applied in any arbitrary direction, permitting the measureand the measurement of their transport in vivo demands methods that are fast, accurate, and free from artifacts. It ment of individual components of the diffusion tensor in its principal-axis system. therefore seems worthwhile to develop experiments that could address both classes of issues with the same general The phenomenon of molecular self-diffusion in constant gradients was recognized early by Hahn (1) as a mechanism approach. NMR has proved to be a powerful technique on both counts; traditionally, however, NMR protocols for of echo attenuation. Later Stejskal and Tanner (4) developed pulsed-gradient methods that overcome problems associated structural work have relied on high-resolution strategies, while transport and relaxation have been investigated by with measurements of D in constant gradients; this was then followed by the development of other refinements (5–10) time-domain measurements. We report here a novel approach to the rapid measurement of molecular self-diffusion as well as a recent revival of interest in extremely large constant gradients (11) . coefficients D , employing high-resolution NMR. Our approach is based on encoding molecular self-diffusion as a NMR methods for measuring D , including PGSE (4) (pulsed-gradient spin echo) and PGSTE (6) (pulsed-gradilinewidth parameter, in a simple one-dimensional multiecho pulse sequence. The measurement protocols we report are ent stimulated echo), sample the echo top, the second half of the echo (FT-PGSE/DOSY) (8, 9) , or the entire echo. basically two-scan procedures—one with pulsed diffusion Each of these modes of operation has its own merits and encoding, and a second without—that can typically be exedemerits. When the echo top is sampled, the measurement cuted in under ten seconds if the signal-to-noise ratio is is free of susceptibility and inhomogeneity artifacts. The adequate. The sequences sample the tops of spin echoes and disadvantage of this mode of operation however is the loss of are hence completely free from inhomogeneity and susceptichemical-shift information, restricting its validity to singlebility artifacts. They are thus suited to the investigation of component systems. For multicomponent systems, the measolution-state self-diffusion in heterogeneous environments. surement must be performed by sampling either the second We also emphasize that our methods are suitable for singlehalf of the echo or the entire echo. This mode is, however, component systems as well as for multicomponent systems, susceptible to inhomogeneity and susceptibility artifacts. and are applicable regardless of echo modulations. They Further, if the echo time t is varied, echo modulation must may be readily performed on the present generation of highbe taken into account. Clearly, satisfactory experiments need resolution NMR spectrometers that support gradient-accelerto be developed to handle multicomponent systems in heteroated spectroscopy. geneous liquid-like environments. Self-diffusion is measured in magnetic resonance by Our earlier work (12) in this direction involved the develapplying either steady or pulsed field gradients (1–4) , so opment of novel two-dimensional methods employing sinthat there is a variation of the field over the sample. This gle-quantum or multiple-quantum echoes. The disadvantage renders the Larmor precession frequency position-depenof the 2D family of methods (12–14) , however, is the meadent, providing the frequency or phase labeling of molecules surement time (an hour or longer) , since a pair of 2D experiments is required, one with evolution-dependent and a second with evolution-independent diffusion encoding. * To whom correspondence should be addressed.