Related Experiment Video
Updated: May 9, 2026

NMR 15N Relaxation Experiments for the Investigation of Picosecond to Nanoseconds Structural Dynamics of Proteins
Published on: November 1, 2024
Numerical analysis of NMR diffusion measurements in the short gradient pulse limit
Benjamin F Moroney1, Timothy Stait-Gardner, Bahman Ghadirian
1Nanoscale Organisation and Dynamics Group, University of Western Sydney, Penrith, NSW 2751, Australia.
Abstract:
Pulsed gradient spin-echo (PGSE) NMR diffusion measurements provide a powerful technique for probing porous media. The derivation of analytical mathematical models for analysing such experiments is only straightforward for ideal restricting geometries and rapidly becomes intractable as the geometrical complexity increases. Consequently, in general, numerical methods must be employed. Here, a highly flexible method for calculating the results of PGSE NMR experiments in porous systems in the short gradient pulse limit based on the finite element method is presented. The efficiency and accuracy of the method is verified by comparison with the known solutions to simple pore geometries (parallel planes, a cylindrical pore, and a spherical pore) and also to Monte Carlo simulations. The approach is then applied to modelling the more complicated cases of parallel semipermeable planes and a pore hopping model. Finally, the results of a PGSE measurement on a toroidal pore, a geometry for which there is presently no current analytical solution, are presented. This study shows that this approach has great potential for modelling the results of PGSE experiments on real (3D) porous systems. Importantly, the FEM approach provides far greater accuracy in simulating PGSE diffraction data.
Related Concept Videos
NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Two-Dimensional (2D) NMR: Overview
The first step is the preparation period, during which nucleus A is excited with a radiofrequency pulse.
NMR Spectrometers: Resolution and Error Correction
Double Resonance Techniques: Overview
Spin decoupling is usually achieved by...
¹³C NMR: ¹H–¹³C Decoupling
A broadband decoupling technique is used to simplify these complex, sometimes overlapping, signals. Broadband decoupling relies on a...
