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Percolation Model of Nuclear Magnetic Relaxation in Porous Media: Slow Diffusion
Author(s) -
Mendelson Kenneth S.
Publication year - 1991
Publication title -
israel journal of chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.908
H-Index - 54
eISSN - 1869-5868
pISSN - 0021-2148
DOI - 10.1002/ijch.199100011
Subject(s) - chemistry , percolation (cognitive psychology) , mean squared displacement , relaxation (psychology) , diffusion , porous medium , percolation threshold , random walk , exponential decay , square lattice , exponential function , continuous time random walk , condensed matter physics , anomalous diffusion , thermodynamics , porosity , physics , ising model , nuclear physics , statistics , mathematical analysis , mathematics , quantum mechanics , molecular dynamics , computational chemistry , electrical resistivity and conductivity , knowledge management , innovation diffusion , computer science , biology , psychology , social psychology , organic chemistry , neuroscience
Nuclear magnetic relaxation in a porous medium is simulated by a random walk on the open sites of a percolation lattice. This model is used to study relaxation in the case that diffusion to the pore surface is slow compared to relaxation at the surface. The computed decay curves can be fit by sums of exponentials. For slow diffusion the principal relaxation time is independent of the surface relaxation rate. It is inversely proportional to the diffusion coefficient and directly proportional to the mean square displacement of the walkers. It appears that a measurement of nuclear magnetic relaxation in the slow diffusion range will yield only an average pore size. This pore size is given by the root mean square displacement to the surface for a random walker starting with equal probability from any point in the pore space.