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

The accurate distribution of countercations (Rb+ and Sr2+) around a rigid, spherical, 2.9‐nm size polyoxometalate cluster, {Mo132}42−, is determined by anomalous small‐angle X‐ray scattering. Both Rb+ and Sr2+ ions lead to shorter diffuse lengths for {Mo132} than prediction. Most Rb+ ions are closely associated with {Mo132} by staying near the skeleton of {Mo132} or in the Stern layer, whereas more Sr2+ ions loosely associate with {Mo132} in the diffuse layer. The stronger affinity of Rb+ ions towards {Mo132} than that of Sr2+ ions explains the anomalous lower critical coagulation concentration of {Mo132} with Rb+ compared to Sr2+. The anomalous behavior of {Mo132} 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–{Mo132} interaction. [ABSTRACT FROM AUTHOR]