Charge regulation as a stabilization mechanism for shell-like assemblies of polyoxometalates

We show that the equilibrium size of single-layer shells composed of polyoxometalate macroions is inversely proportional to the dielectric constant of the medium in which they are dispersed. This behavior is consistent with a stabilization mechanism based on Coulomb repulsion combined with charge regulation. We estimate the cohesive energy per bond between macroions on the shells to be approximately -6kT. This number is extracted from analysis based on a charge regulation model in combination with a model for defects on a sphere. The value of the cohesive bond energy is in agreement with the model-independent critical aggregate concentration. This observation points to a new class of thermodynamically stable shell-like objects. We point out the possible relevance our findings have for certain surfactant systems.