Interpretation of Pulsed-Field-Gradient NMR in Terms of Molecular Displacements

TL;DR

This paper analyzes how Pulsed-Field-Gradient NMR signals relate to molecular displacements, highlighting conditions where mean-square displacement dominates and providing diagnostics for complex fluids.

Contribution

It clarifies the relationship between NMR signals and molecular displacements, especially in complex fluids with memory effects, and introduces diagnostics for identifying when mean-square displacement is the primary factor.

Findings

NMR signal relates to mean-square displacement in simple solutions.

Higher moments influence NMR signals in complex fluids.

Diagnostics can identify when mean-square displacement dominates.

Abstract

The relationship for Pulsed-Field-Gradient NMR between the amplitude $I(t)$ of the spin echo and the molecular displacement ${\bf X}(t)$ is examined. $I(t)$ of a single species in a simple solution is determined by the mean-square displacement $\bar{X(t)^{2}}$. With polydisperse species, or molecular probes in complex fluids showing memory effects, $I(t)$ in general includes large contributions from all higher even moments $\bar{X(t)^{2n}}$. Conditions under which the NMR signal is indeed determined by the molecular mean-square displacement are noted. A diagnostic that sometimes identifies when these conditions are not met is presented.