Microfriction correction factor to the Stokes–Einstein equation for small molecules determined by NMR diffusion measurements and hydrodynamic modelling

The Stokes-Einstein relationship relating the self-diffusion coefficient with the size of a diffusing particle (a hydrodynamic radius) breaks down in case of small molecules. We present a novel method extending the range of validity of the Stokes-Einstein relationship by means of introducing a molecule-specific microfriction correction factor. This factor equals to 1 in the ordinary form of the Stokes-Einstein formula for stick' boundary conditions when molecules of solvent are much smaller than the diffusing particle. We have determined the microfriction correction factors for series of small molecules (ranging in size from ethanol to 18-crown-6 ether and tetrakis(trimethylsilyl)silane) in a dilute hexane solution by a concerted use of the NMR diffusion measurements and the molecular hydrodynamic calculations. Both of the tested hydrodynamic modelling programmes, HydroNMR (Garcia de la Torre et al., J. Magn. Reson. 2000, 147, 138-146) and DiTe (Barone et al., J. Comput. Chem. 2008, 30, 2-13) provided very similar results after initial calibration on a molecular system, which is within the validity range of the Stokes-Einstein relationship (fullerene in hexane solution in this work).