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

This article concerns the question of a proper stochastic treatment of the spin-echo self-diffusion attenuation of confined particles that arises when short gradient pulse approximation fails. Diffusion is numerically simulat ed as a succession of random steps when motion is restricted between two pe rfectly reflecting parallel planes. With the magnetic held gradient perpend icular to the plane boundaries, the spatial distribution of the spin-echo s ignal is calculated from the simulated trajectories. The diffusion propagat or approach (Callaghan, "Principles of Nuclear Magnetic Resonance Microscop y," Oxford Univ, Press, Oxford, 1991), which is just the same as the evalua tion of the spin-echo attenuation by the method of cumulant expansion in th e Gaussian approximation, with Einstein's approximation of the velocity cor relation function (VCF) (delta function), agrees with the results of simula tion only for the particle displacements that are much smaller than the siz e of the confinement. A strong deviation from the results of the simulation appears when the bouncing rate from the boundaries increases at intermedia te and long gradient sequences. A better fit, at least for intermediate par ticle displacements, was obtained by replacing the VCF with the Oppenheim-M azur solution of the Langevin equation (Oppenheim and Mazur, Physica 30, 18 33-1845, 1964), which is modified in a way to allow for spatial dependence of particle displacements. Clearly, interplay of the correlation dynamics a nd the boundary conditions is taking place for large diffusion displacement s. However, the deviation at long times demonstrates a deficiency of the Ga ussian approximation for the spin echo of diffusion inside entirely closed pores. Here, the cumulants higher than the second one might not be negligib le. The results are compared with the experiments on the edge enhancement b y magnetic resonance imaging of a pore, (C) 2001 Academic Press.