A two-region transport model for interpreting T₁-T₂ measurements in complex systems

Area of Science:

• Physics
• Materials Science
• Chemistry

Background:

• Understanding nuclear magnetic resonance (NMR) signal behavior in porous materials is crucial for various applications.
• Surface relaxivity variations within porous systems can significantly alter NMR signal characteristics.
• Existing models may not fully capture the complex interplay of diffusion and spin physics in heterogeneous pore structures.

Purpose of the Study:

• To develop and validate a 1D two-region coupled pore model for elucidating eigenmode interactions in regions with differing surface relaxivity.
• To investigate the influence of surface relaxivity, pore connectivity, and pore size ratio on NMR signal behavior.
• To connect mathematical modeling with the underlying diffusion dynamics and spin physics.

Main Methods:

• Development of a 1D two-region coupled pore model with discrete pore coupling.
• Numerical solution of the model to simulate correlation experiments.
• Analysis of eigenmodes and eigenfunctions to understand their contribution to the signal.
• Comparison with experimental data from physical systems like microporous glass beads, hydrate formers, and beeswax.

Main Results:

• The model demonstrates the role of negative eigenmodes in signal generation.
• Overlap of T1 and T2 eigenmodes is shown to be key in producing a time-domain signal increase with inversion recovery time (t1).
• Simulations align with experimental observations of T1-T2 time-domain signal rise in tested physical systems.

Conclusions:

• The developed coupled pore model effectively explains NMR signal behavior influenced by varying surface relaxivity.
• Eigenmode interactions, particularly the overlap of T1 and T2 modes, are fundamental to the observed time-domain signal increase.
• The model provides a framework for understanding diffusion and spin physics in complex porous materials.