SPIN-ECHO ATTENUATION OF RESTRICTED DIFFUSION AS A DISCORD OF SPIN PHASE-STRUCTURE

By using the particle probability density we analyze the spin echo att enuation of particles, diffusing in a bounded region. It provides a me ans to expand a nonuniform spin phase distribution into a series of wa ves that characterize the geometry and boundary conditions of confinem ent. Random motion disrupts the initial phase structure created by app lied gradients and consequently discords its structure waves. By assum ing the spin phase fluctuation and/or the randomness of spin phase dis tribution in the subensemble as a Gaussian stochastic process, we deri ve a new analytical expression for the echo attenuation related to the particle velocity correlation. For a diffusion in porous structure we get the expression featuring the same ''diffusive diffraction'' patte rns as those being found and explained by P. T. Callaghan and A. Coy ( ''Principles of Nuclear Magnetic Resonance Microscopy,'' Oxford Univ, Press, Oxford (1991); J. Chem. Phys. 101, 4599-4609 (1994)) with the u se of propagator theory. With the new approach we cast a new light on the phenomena and derive analitically how the diffusive diffractions a ppear when the sequence of finite or even modulated gradients are appl ied. The method takes into account the non-Markovian character of rest ricted diffusion, and therefore the echo dependence on the diffusion l engths and on the strength of applied gradient differs from the result s of authors assuming the Markovian diffusion either by dealing with t he diffusion propagators or by the computer simulation of Fick's diffu sion. (C) 1998 Academic Press.