M. Mauri, Y. Thomann, H. Schneider, K. Saalwächter.
Spin Diffusion NMR at Low Field for the Study of Multiphase Solids.
Solid State Nucl. Magn. Reson. 34, 125-141 (2008). DOI
The use of spin-diffusion NMR for the measurement of domain sizes in multiphase
materials is becoming increasingly popular, in particular for the study of
heterogeneous polymers. Under conditions where T1 relaxation can be neglected, which is mostly the case at
high field, analytical and approximate solutions to the evolution of spin
diffusion are available. In order to extend the technique to more general
conditions, we performed a comprehensive study of the diffusion of magnetization
in a model copolymer at low field, where T1 tends to be of the same order of magnitude as the typical
spin-diffusion time. In order to study the effects of T1 and to delineate the optimal T1 values for back correction prior to applying the
initial-rate approximation, we developed a numerical simulation based on the
diffusion equation and including longitudinal relaxation. We present and discuss
the limits of simple correction strategies for initial-slope analysis based on
apparent relaxation times from saturation-recovery experiments or the
spin-diffusion experiments themselves. Our best strategy faithfully reproduces
domain sizes obtained by both TEM investigations and full simultaneous fitting
of spin-diffusion and saturation-recovery curves. Full fitting of such
independent data sets not only yields correct domain sizes, but also the true
longitudinal relaxation times, as well as spin-diffusion coefficients. Effects
of interphases with distinct mobility on spin-diffusion curves, as well as
practical hints concerning the reliable component decomposition of the detected
low-resolution FID signal by help of different magnetization filters are also
discussed in detail.