Computer simulation of the spin-echo spatial distribution in the case of restricted self-diffusion

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Accurate modeling of confined particle diffusion is crucial for understanding various physical phenomena.
• The standard spin-echo self-diffusion attenuation method relies on approximations that fail under certain conditions.

Purpose of the Study:

• To investigate a proper stochastic treatment for spin-echo self-diffusion attenuation of confined particles.
• To identify the limitations of existing models and propose improvements for diffusion in restricted geometries.

Main Methods:

• Numerical simulation of diffusion as random steps between reflecting parallel planes.
• Calculation of spin-echo signal spatial distribution from simulated trajectories.
• Comparison of simulation results with diffusion propagator and modified Langevin equation models.

Main Results:

• The diffusion propagator approach (Gaussian approximation) agrees with simulations only for small displacements.
• Strong deviations occur at longer gradient sequences due to increased boundary interactions.
• Replacing the velocity correlation function with the Oppenheim-Mazur solution improves agreement for intermediate displacements.

Conclusions:

• The Gaussian approximation is insufficient for describing spin echo diffusion in confined pores.
• Higher-order cumulants may be necessary for accurate modeling of diffusion in closed pores.
• Boundary conditions and correlation dynamics significantly influence diffusion at larger displacements.