Dimensional dependence of the Stokes-Einstein relation and its violation

We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violation with dimension in simple hard sphere glass formers. The analysis suggests that this SER violation disappears around dimension du = 8, above which it is not observed. The critical exponent associated with the violation appears to evolve linearly in 8 - d, below d = 8, as predicted by Biroli and Bouchaud [J. Phys.: Condens. Matter 19, 205101 (2007)], but the linear coefficient is not consistent with the prediction. The SER violation with d establishes a new benchmark for theory, and its complete description remains an open problem. © 2013 AIP Publishing LLC.

The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method.

While the Stokes-Einstein (SE) equation predicts that the diffusion coefficient of a solute will be inversely proportional to the viscosity of the solvent, this relation is commonly known to fail for solutes, which are the same size or smaller than the solvent. Multiple researchers have reported that for small solutes, the diffusion coefficient is inversely proportional to the viscosity to a fractional power, and that solutes actually diffuse faster than SE predicts. For other solvent systems, attractive solute-solvent interactions, such as hydrogen bonding, are known to retard the diffusion of a solute. Some researchers have interpreted the slower diffusion due to hydrogen bonding as resulting from the effective diffusion of a larger complex of a solute and solvent molecules. We have developed and used a novel micropipette technique, which can form and hold a single microdroplet of water while it dissolves in a diffusion controlled environment into the solvent. This method has been used to examine the diffusion of water in both n-alkanes and n-alcohols. It was found that the polar solute water, diffusing in a solvent with which it cannot hydrogen bond, closely resembles small nonpolar solutes such as xenon and krypton diffusing in n-alkanes, with diffusion coefficients ranging from 12.5x10(-5) cm(2)/s for water in n-pentane to 1.15x10(-5) cm(2)/s for water in hexadecane. Diffusion coefficients were found to be inversely proportional to viscosity to a fractional power, and diffusion coefficients were faster than SE predicts. For water diffusing in a solvent (n-alcohols) with which it can hydrogen bond, diffusion coefficient values ranged from 1.75x10(-5) cm(2)/s in n-methanol to 0.364x10(-5) cm(2)/s in n-octanol, and diffusion was slower than an alkane of corresponding viscosity. We find no evidence for solute-solvent complex diffusion. Rather, it is possible that the small solute water may be retarded by relatively longer residence times (compared to non-H-bonding solvents) as it moves through the liquid.