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

The accurate distribution of countercations (Rb + and Sr 2+ ) around a rigid, spherical, 2.9‐nm size polyoxometalate cluster, {Mo 132 } 42− , is determined by anomalous small‐angle X‐ray scattering. Both Rb + and Sr 2+ ions lead to shorter diffuse lengths for {Mo 132 } than prediction. Most Rb + ions are closely associated with {Mo 132 } by staying near the skeleton of {Mo 132 } or in the Stern layer, whereas more Sr 2+ ions loosely associate with {Mo 132 } in the diffuse layer. The stronger affinity of Rb + ions towards {Mo 132 } than that of Sr 2+ ions explains the anomalous lower critical coagulation concentration of {Mo 132 } with Rb + compared to Sr 2+ . The anomalous behavior of {Mo 132 } 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 132 } interaction.