Extraction of Reliable Molecular Information from Diffusion NMR Spectroscopy: Hydrodynamic Volume or Molecular Mass?

Measuring accurate translational self-diffusion coefficients (D_t ) by NMR techniques with modern spectrometers has become rather routine. In contrast, the derivation of reliable molecular information therefrom still remains a nontrivial task. In this paper, two established approaches to estimating molecular size in terms of hydrodynamic volume (V_H ) or molecular weight (M) are compared. Ad hoc designed experiments allowed the critical aspects of their application to be explored by translating relatively complex theoretical principles into practical take-home messages. For instance, comparing the D_t values of three isosteric Cp₂ MCl₂ complexes (Cp=cyclopentadienyl, M=Ti, Zr, Hf), having significantly different molecular mass, provided an empirical demonstration that V_H is the critical molecular property affecting D_t . This central concept served to clarify the assumptions behind the derivation of D_t =ƒ(M) power laws from the Stokes-Einstein equation. Some pitfalls in establishing log (D_t ) versus log (M) linear correlations for a set of species have been highlighted by further investigations of selected examples. The effectiveness of the Stokes-Einstein equation itself in describing the aggregation or polymerization of differently shaped species has been explored by comparing, for example, a ball-shaped silsesquioxane cage with its cigar-like dimeric form, or styrene with polystyrene macromolecules.