Two-dimensional exchange NMR of powder samples. II. The dynamic evolution of two-time distribution functions

Abstract

Theoretical as well as experimental examples concerning the evolution of the two-time distribution S2‖0 (ω1,ω2 ;tm) as a function of the mixing time tm are presented, where S2‖0 is identical with the two-dimensional (2D) absorption spectrum rendered by 2D exchange NMR spectroscopy of static powder samples. The model calculations comprise standard models like isotropic rotational diffusion or overall isotropic reorientation combined with discrete internal rotational jumps to simulate the chain dynamics of polymers. In any case, the 2D spectrum directly reflects the main aspects of the underlying motional mechanism. An axially symmetric coupling (η=0) between spin and lattice is assumed throughout. Thus, the angular information contained in a 2D spectrum is completely specified by a one-dimensional jump angle distribution supplied with each spectrum. In connection with the simulations the numerical mapping of a discrete distribution function into a space of new variables is discussed. In the experimental section 2H NMR spectra of chain deuterated linear polystyrene above its glass transition temperature are shown, which are compared with the model calculations.