An analytic expression for the double quantum 1H nuclear magnetic resonance build-up and decay from a Gaussian polymer chain with dynamics governed by a single relaxation time

Abstract

An analytic result for the double quantum ¹H nuclear magnetic resonance build-up and decay is presented for a polymer chain with Gaussian statistics. The analytic expression is obtained for the particular case of bond vector dynamics governed by a single relaxation time. The result is used to check the accuracy of the commonly used second moment approximation applied to the same problem. This approximation is shown to differ significantly from our exact result over the entire range of relaxation times, set by the relevant interaction constant. We show that this measurement technique is peculiarly sensitive to slow dynamics, and that these slow motions reveal themselves in an experimental time window t that is, curiously, much smaller than the timescale τ of the dynamics being probed. We found t∼τ^1/3, which enables a wide range of bond vector dynamics to be measured.