The boundary between liquidlike and solidlike behavior in magnetic resonance

Abstract

Recent experimental work in two-dimensional solution NMR (nuclear magnetic resonance) has demonstrated anomalous cross-peaks and additional resonances due to dipolar couplings between distant nuclei. These spectra have been analyzed either classically, using Bloch equations which include a mean-field approximation to the demagnetizing field, or quantum mechanically, using a full density matrix picture which shows that the peaks correspond to intermolecular multiple-quantum coherences (iMQCs). Here we use a density matrix treatment to predict intensities in solution for dipolar effects conventionally seen in solids; we also explore in detail the fundamental differences between dipolar effects in solids and liquids. For example, even though polarization transfer via the dipolar Hamiltonian in solution is not possible, indirect detection with substantial signal enhancement is possible. We find that, even for high-γ nuclei such as H1 or He3, solidlike dipolar effects are quite small unless the diffusion constant is roughly one million times smaller than that of water—which means that deviations between the quantum and classical treatments are barely observable in solution NMR, and that even solid He3 has liquidlike dipolar effects in agreement with experiment. However, the dipolar correlation function has an extremely unusual functional form—the long time falloff is proportional to t−3/2, not the exponential one commonly encounters. Because of this long falloff, solidlike dipolar effects can be substantial in solution electron spin resonance, and the classical picture of the demagnetizing field would fail in that case.