Quantification of pore size distribution using diffusion NMR: experimental design and physical insights

Area of Science:

• Materials Science
• Physical Chemistry
• Nuclear Magnetic Resonance Spectroscopy

Background:

• Pulsed field gradient (PFG) diffusion NMR is crucial for analyzing porous media microstructure.
• Estimating pore size distribution (PSD) from NMR data is an ill-posed problem with limited optimal design strategies.
• Existing methods lack robust criteria for selecting optimal experimental parameters.

Purpose of the Study:

• To develop a novel optimization framework for ill-posed problems, specifically for PFG diffusion NMR experiments.
• To enhance the accuracy and sensitivity of pore size distribution (PSD) estimation.
• To guide the selection of experimental parameters for improved microstructural characterization.

Main Methods:

• Formulation of a new optimization framework for ill-posed inverse problems.
• Development of a heuristic methodology to balance ill-posedness reduction and NMR signal intensity.
• Numerical simulations to evaluate the framework's effectiveness in PSD estimation.
• Analysis of experimental parameters like gradient strength, diffusion time, and mixing time.

Main Results:

• The proposed framework significantly improves the sensitivity of PFG experiments to pore sizes.
• Optimal experimental sets were identified, favoring increased gradient strength and varied parameters.
• The framework effectively selects favorable discrete pore sizes for PSD estimation.
• Evaluation of diffusion and mixing times reveals their impact on obtainable pore size information.

Conclusions:

• The developed optimization method is a valuable tool for quantifying PSDs in various specimens using diffusion NMR.
• The framework's applicability extends to designing sampling schemes for other ill-posed problems beyond NMR.
• This approach offers a systematic way to improve data acquisition and analysis in complex systems.