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Measuring accurate translational self-diffusion coefficients (Dt ) 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 (VH ) 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 Dt values of three isosteric Cp2 MCl2 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(M) power laws from the Stokes-Einstein equation. Some pitfalls in establishing log (Dt ) 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.

We have reported a new Stokes–Einstein relation (SER) for size determination and tested it by different nanoparticles. We assumed that the breakdown for SER results from local increases in viscosity. Here we investigate hydrodynamics of solvent near dendrimers to further test generality of our new theory. We discuss simulations of dendrimers in comparison to nanoparticles, experimental data on dendrimers from literature, and our theory. Local viscosity and local diffusivity of solvent near dendrimers are estimated by persistence times and exchange times, respectively. We find that the local dynamics of solvent near dendrimers of low density stay almost the same as that of bulk solvent. While the motions of solvent particles slow down near dendrimers of high density. This is similar with changes in local dynamics of solvent near nanoparticles. According to the causes we proposed for the deviation of SER, this is consistent with our findings that the SER works for the dendrimers of low density, while it fails for the dendrimers of high density. The new SER is then tested to predict size of the dendrimers accurately. Taking this together with the results for the nanoparticles, we believe that the new theory is general. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 1380–1392

By means of molecular dynamics simulations we investigate the Stokes–Einstein behaviour of the Gaussian Core Model liquid at high densities. From a recent analysis at moderately high densities, we found that the Stokes–Einstein factor grows linearly with the viscosity. We show that at high densities the behaviour is similar, but there are slight departures at lower temperatures and higher densities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Values of the melting temperature at normal pressure , of the slope of the melting line, and of the activation energies for the diffusion coefficient and viscosity are corrected.

An empirical relation between diffusion coefficients and viscosities is proposed which interpolates between the kinetic theory of dilute gases and the Stokes-Einstein equation of liquids. This extended Stokes-Einstein-relationship is tested with experimental examples. It is useful for studies of reaction processes over large density ranges.