Extraction of reliable molecular information from diffusion NMR spectroscopy: hydrodynamic volume or molecular mass?

Measuring accurate translational self-diffusion coefficients (Dt) by NMR with modern spectrometers has become rather routine. On the contrary, the derivation of reliable molecular information therefrom still remains a non-trivial task. In this paper, two established approaches to estimate molecular size in terms of hydrodynamic volume (VH) or molecular weight (MW) are compared. Ad-hoc designed experiments allow the critical aspects of their application to be explored, by translating relatively complex theoretical principles in practical take-home messages. For instance, comparing the Dt of three isosteric Cp2MCl2 complexes (Cp = cyclopentadienyl, M = Ti, Zr, Hf), having significantly different molecular mass, provided an empirical demonstration that VH is the critical molecular property affecting Dt. This central concept served to clarify the assumptions behind the derivation of Dt = ƒ(MW) power laws from the Stokes-Einstein equation. Some pitfalls in establishing Log(Dt) vs Log(MW) linear correlations for a set of species have been highlighted by further investigations on selected examples. The effectiveness of the Stokes-Einstein equation itself in describing aggregation or polymerization of differently shaped species has been explored by comparing e.g. a ball-shaped silsesquioxane cage with its cigar-like dimeric form, or styrene with polystyrene macromolecules.