Gamma convolution models for self-diffusion coefficient distributions in PGSE NMR.

Area of Science:

• Nuclear Magnetic Resonance (NMR) Spectroscopy
• Materials Science
• Physical Chemistry

Background:

• Pulsed-field gradient spin echo (PGSE) NMR is a powerful technique for measuring molecular self-diffusion.
• Accurate modeling of self-diffusion coefficient distributions is crucial for interpreting PGSE NMR data.
• Existing models, such as gamma and lognormal distributions, have limitations in capturing complex diffusion behaviors.

Purpose of the Study:

• To introduce a novel, closed-form signal attenuation model for PGSE NMR.
• To utilize gamma convolutions of n gamma distributions (n⩾1) for representing self-diffusion coefficient distributions.
• To demonstrate the superior fitting capabilities of the proposed model compared to existing distributions.

Main Methods:

• Development of a closed-form signal attenuation model based on gamma convolutions.
• Simulation studies to validate the model's performance.
• Application of the model to experimental PGSE NMR data from poly(vinyl alcohol) and polystyrene samples.

Main Results:

• The gamma convolution model accurately represents uni-modal self-diffusion coefficient distributions.
• The model encompasses the gamma distribution (n=1) and approaches the lognormal distribution (n→∞).
• The proposed model demonstrated superior goodness of fit compared to gamma and lognormal distributions and was comparable to the inverse Laplace transform for experimental data.

Conclusions:

• The gamma convolution model offers a versatile and accurate approach for analyzing PGSE NMR data.
• This model provides improved characterization of self-diffusion coefficients in complex systems.
• The findings advance the application of NMR spectroscopy in materials science and physical chemistry.