Unified derivation of the dipolar field and relaxation terms in the Bloch-Redfield equations of liquid NMR

Abstract

The standard theory of NMR relaxation in liquids ͑with molecular motion described as a classical Brownian motion, and including intermolecular spin-spin couplings͒ is re-examined, taking great care not to drop significant contributions from the dipolar coupling between distant molecules. This results in ''modified Bloch-Redfield equations'' for the spins in a single molecule, valid at all spin temperatures, which contain both the usual relaxation terms and a coupling of each spin with a classical average dipolar field. Delicate issues raised in this derivation, like the neglect of quantum correlations between spins on different molecules at ͑repeated͒ initial times, are discussed with the help of exact calculations ͑for all spin temperatures͒ performed on a simplified model which includes equal couplings between all N spins of a system. The same model is used to compare the merits of different forms of ''high temperature'' approximation. We also propose an iterative scheme for solving the ''modified Bloch-Redfield equations,'' in which the starting point is the well understood solution of the problem without dipolar field. Finally, a short discussion is given of the relation between ''quantum correlations'' and ''quantum coherences'' in the perspective of multiple-pulse and multiple-quantum experiments. These two notions are very simply related in the strict first approximation of weak order, and have often not been clearly distinguished. However, in the second order approximation, which is required whenever dipolar field effects manifest themselves, unrelated spins may display observable coherences although they are not coupled ͑hence not correlated͒.

Quasiequilibrium states in thermotropic liquid crystals studied by multiple-quantum NMR

“…The very small dipolar interactions between distant spins in solution and even in gases have been shown to generate macroscopic signals if the spatial symmetry of the sample is broken [39][40][41][42][43][44]. These long range couplings could be expected to be more pronounced in a LC due to the restricted molecular diffusion [45] and the instrinsic asymmetry on the sample inntroduced by the molecular alignment.…”

Optimal conditions for magnetization reversal of nanocluster assemblies with random properties

“…One sometimes calls it the radiation damping, following Bloembergen and Pound [12]. However the latter term is rather a misnomer, as has been stressed by a number of researchers [13][14][15], since the coupling of a spin system with a resonator does strongly influences spin dynamics, but not necessarily damping it. For instance, this effect enhances nuclear magnetic resonance signals, which is widely used in NMR techniques [16][17][18].…”

Controlling the dipole-dipole interaction using NMR composite rf pulses

“…It can be simply verified that conditions (26) and (27) are equivalent. For higher orders the condition of order n for a magic sequence is simply:…”

“…Both experimental confirmations of predictions from the classic formalism and theoretical advances now support that the classical formalism correctly describe the NMR evolution. In this formalism, the spin ensemble is described by the local magnetization m( r, t) whose evolution can be described in the rotating frame by the mesoscopic Bloch-Redfield equation 27 which takes into account the coupling between magnetic moments due to the distant dipolar field:…”