Propagator representation of anomalous diffusion: the orientational structure factor formalism in NMR

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Understanding molecular dynamics in porous media is crucial for various applications.
• Surface diffusion plays a significant role in the behavior of liquids confined in porous materials.
• Fractional diffusion equations are effective in describing anomalous diffusion processes.

Purpose of the Study:

• To investigate the relationship between molecular fluctuations, surface diffusion, and fractal dimensions in porous media.
• To apply the radial Fourier transform and fractional diffusion equations to analyze diffusive displacements.
• To utilize field-cycling Nuclear Magnetic Resonance (NMR) experiments for characterizing static and dynamic fractal properties.

Main Methods:

• Calculation of moments of diffusive displacements using non-Gaussian propagators from fractional diffusion equations.
• Application of the Fourier propagator to NMR correlation and spectral density functions within the orientational structure factor formalism.
• Analysis of experimental data from liquids in porous silica glass.

Main Results:

• Low-frequency molecular fluctuations in porous media are attributed to surface diffusion-mediated reorientations.
• Field-cycling NMR experiments provide quantitative information on static and dynamic fractal dimensions.
• A surface fractal dimension (df=2.5) explains experimental results for liquids in porous silica glass.
• The mean squared displacement scales as proportional, variantt(2/dw), with dw=1 for bulk-mediated surface diffusion and dw=2 when the bulk phase is frozen.

Conclusions:

• Surface diffusion is a key mechanism governing molecular dynamics in porous materials.
• Field-cycling NMR is a powerful technique for probing fractal properties of surfaces and diffusion.
• The study provides a framework for understanding complex molecular behavior in confined environments.