Determination of the Effective Hydrodynamic Radii of Small Molecules by Viscometry

The effective hydrodynamic radii of small uncharged molecules in dilute aqueous solution were determined using Einstein's classical theory of viscosity. The radii thus obtained are those of a hypothetical sphere whose hydrodynamic behavior is the same as that of the solute molecule plus that water of hydration which is too firmly bound to partake in the viscous shearing process. The results obtained compare favorably with radii determined from molecular models constructed in accordance with atomic dimensions compiled by Pauling. Although the application of the Einstein theory to molecules whose size is comparable to that of water represents a considerable extrapolation, the results suggest that this deviation from the assumptions of the theory, in the case of the molecules studied, is of second order importance. Employing the viscometric radii, we have formulated an empirical correction of the Stokes-Einstein diffusion equation. This correction is similar in form to those previously proposed by Cunningham (22) and Millikan (21) and is of particular significance when the solute molecule is comparable in size to the discontinuities of the surrounding medium. The molecular radii of a number of small organic molecules obtained by means of the corrected Stokes-Einstein equation do not differ significantly from the radii obtained from molecular models of these compounds.