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  • Spin-echo spatial distribution long gradient pulses in the case of one-dimensional restricted self-diffusion [Elektronski vir]
    Duh, Andrej, 1969- ; Mohorič, Aleš, 1969- ; Stepišnik, Janez
    The question about the proper stohastic treatment of the spin-echo self-diffusion attenuation of confined particle that arises when short gradient pulse approximation fails is still open. In the ... following article we compare results of computer simulation of the spin-echo spatial distribution with the theoretical calculations for the PGSE sequence with long gradient pulses. For the sake of simplicity we investigate restricted self-diffusion for one-dimensional problem where the spin-bearing particles are trapped parallel perfectly reflecting planes and with gradient applied normal to the planes. Computer simulation of Brownian motion of the spins in confined space is implemented as numerical simulation of successive random steps, which are restricted to the space between two perfectly reflecting parallel planes. The spatial distribution of the spin-echo signal is calculated from the simulated trajectories when the magnetic field gradient is perpendicular to the plane boundaries. Theoretical calculation by the method of cumulant expansion in the Gaussian approximation (cumulants higher than second are negligible), where the Einstein's approximation of the VCF (hsort time VCF) is used, agreeswith the results of the simulation only for the particle displacement shorter than the size of the confinement. For a long gradient sequence, when the number of collisions between spins and walls increases, this approximation shows a strong deviation from the result of the simulation. Replacement of the short time VCF with the Oppenheim and Mazur solution gives a better approximation to the results of simulation. To get even closer fit tothe simulated signal we have made simple value estimation for cumulants higher than the second. It points out that for a long gradient sequence we should considered higher orders of cumulants for the proper treatment of restricted self-diffusion in an isolated pore.
    Source: EENC 2000 [Elektronski vir] (6 str.)
    Type of material - conference contribution
    Publish date - 2000
    Language - english
    COBISS.SI-ID - 5611286

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