Magnetization evolution in connected pore systems

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Abstract
The equations governing magnetization evolution in fluid-filled pore systems are developed. Particular attention is given to the effect of coupling between pores. In pore systems with a range of pore sizes (and/or decay rates), the evolution of the total dipole moment is described exactly by a spectrum of decay rates, leading to multiple-exponential decay. We study this spectrum of decay rates as a function of coupling strength between pores, using perturbation theory, effective-medium theory, and matrix diagonalization. The spectrum of decay rates evolves from the individual pore decay-rate distribution, at zero coupling, to a δ-function distribution, at infinite coupling. The development of the spectrum of decay rates between the two extremes of weak and strong coupling is discussed. The three methods employed to study this problem are in good agreement. The effect of coupling between pores is important in NMR measurements when comparing different porous materials and in the study of the temperature dependence of characteristic decay rates in these materials.