Analysis of three-site T2-T2 exchange NMR

Abstract

T2-T2 exchange NMR is a unique method to investigate the pore space and fluid dynamics in porous media. While two-site relaxation exchange is well understood, three-site exchange is not. We analyze the solutions for three-site T2-T2 exchange NMR analytically and by computer simulation. Three main results are obtained. First, the exchange map can be asymmetric in the case of microscale vortex motion in violation of the principle of detailed balance. Second, the apparent longitudinal relaxation times and/or apparent transverse relaxation times can be complex valued. In the case of complex apparent transverse relaxation times, the three-site exchange map coalesces to a two-site exchange map with characteristic oscillations in the time domain. As a result of the oscillations, the shorter relaxation time is less than expected. Third, there can be negative cross-peaks in the exchange map for certain combinations of longitudinal and transverse relaxation times or if the mixing period is shorter than the evolution and detection periods. In view of these results experimental exchange maps may need to be reevaluated.