Structure of the two-dimensional relaxation spectra seen within the eigenmode perturbation theory and the two-site exchange model

The form of the two-dimensional (2D) NMR-relaxation spectra - which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice (T-1) and spin-spin (T-2) relaxation times - has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T-1- and T-2-eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them - the presence of negative peaks - underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data. (C) 2010 Elsevier Inc. All rights reserved.