An exact expression for the transverse nuclear magnetic resonance relaxation of a dynamic scale invariant polymer chain governed by a single relaxation time

Abstract

An exact analytic calculation of the transverse nuclear magnetic resonance (NMR) relaxation function, due to dipolar interactions, is presented for a polymer chain considered at the scale invariant level of description. The calculation is possible for the particular case where the dynamics of the bond vectors are governed by a single relaxation time. This exact result is used to check the accuracy of two approximation methods when they are applied to the single relaxation time case. The well known second moment approximation is shown to be seriously wrong when the time scale of the bond dynamics is comparable or greater than the NMR time scale set by the dipolar interactions. A more recent method, based on a representation of the chain dynamics in terms of hybrid Fourier components defined over the experimental time interval, is shown to give excellent agreement with the exact result over the entire range of relaxation times.