Accurate Determination of the Quantity and Spatial Distribution of Counterions around a Spherical Macroion.

The accurate distribution of countercations (Rb and Sr ) around a rigid, spherical, 2.9-nm size polyoxometalate cluster, {Mo } , is determined by anomalous small-angle X-ray scattering. Both Rb and Sr ions lead to shorter diffuse lengths for {Mo } than prediction. Most Rb ions are closely associated with {Mo } by staying near the skeleton of {Mo } or in the Stern layer, whereas more Sr ions loosely associate with {Mo } in the diffuse layer. The stronger affinity of Rb ions towards {Mo } than that of Sr ions explains the anomalous lower critical coagulation concentration of {Mo } with Rb compared to Sr . The anomalous behavior of {Mo } can be attributed to majority of negative charges being located at the inner surface of its cavity. The longer anion-cation distance weakens the Coulomb interaction, making the enthalpy change owing to the breakage of hydration layers of cations more important in regulating the counterion-{Mo } interaction.