Hydrodynamic interactions and concentration dependence of orientational relaxation times of ions in dilute solution

Abstract

We derived a theoretical expression for the limiting concentration dependence of ionic rotational friction coefficients using the approximations of point force and point torque and a form of hydrodynamic interaction between a pair of ions, the central ion rotating and the neighbor one translating or rotating. The pairwise hydrodynamic interactions were calculated by the reflection method and summed over all the surrounding ions in solution using the ionic distribution function due to the Debye–Hückel theory. Ionic rotational friction coefficients are predicted to increase linearly with concentration in dilute enough solution; the slope is determined by the translation rather than rotation of the countercation. The limiting slope increases with an increase in the surface charge density of the countercation if the charge effect on the cation friction coefficient is taken into account. The continuum theory has been applied to aqueous MNO3 solutions (M=Li, Na, K, Cs) at 25 °C for comparison with experiment; the theoretical predictions are in qualitative agreement with experiment.