The heterogeneous collision velocity for hydrated ions in aqueous solutions is similar to 10(4) cm/s

The heterogeneous collision velocity v(o), units of centimeters/second) is the average velocity of a solution particle toward a surface. v(o) thus defines the maximum flux of the particles to the surface. Einstein argued that v(o) in condensed phases and in gases may be deduced in a precisely analogous manner and that v(o) in aqueous solution therefore should be similar to 10(4) cm/s (for particles with a mass of 100 Da). Values of v(o) for several aqueous monovalent cations (Na+, K+, Rb+, Cs+ and NH4+) were estimated from steady-state limiting current measurements through single gramicidin A channels spanning lipid bilayer membranes. The collisional and diffusional current components were separated by making use of the different viscosities of H2O and D2O solutions. The transfer of ions from the bulk solution to the channel entrance is modeled using a hemispherical entrance and an extension of the classical analysis of diffusion to a (hemi)sphere in which we relax the assumption that the jump distance (associated with three-dimensional diffusion of an ion in the bulk phase) be small compared to the hemispherical capture radius. Our estimate of v(o) agrees well with the prediction of Einstein. We therefore conclude that ion dehydration (only partially hydrated ions can pass through the gramicidin A channel) cannot be a rate-controlling step-a conclusion that is consistent with known rate constants for water exchange for these ions.