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

Abstract

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.