Determination of Intermolecular Distances of Macroions and the Correlations with their Solution Behaviors

The intermolecular distance between macroions is essential to dictate and regulate the solution or phase behaviors of macroions. However, direct measurements of the intermolecular distance between macroions in different phase states especially in dilute solutions, is very challenging. Here, small-angle X-ray scattering (SAXS) and analytical ultracentrifuge (AUC) techniques are applied to determine the intermolecular distance for a 2.42-nm-size, spherical uranyl peroxide molecular cluster U₆₀. Upon the addition of simple counterions into U₆₀ dilute aqueous solutions, counterion-mediated attraction would induce the formation of U₆₀ dimers, that would further grow and self-assemble into 2-D sheet structures. Depending on the valences of counterions, the 2-D sheets would either stay as standalone tough sheet structures or they would further bend and be enclosed into single-layered spherical blackberry structures. Moreover, upon increasing the concentration of multivalent counterions, the U₆₀ aqueous solution can undergo phase transition (e.g., gelation). Inter-macroionic distances of U₆₀ are obtained under these different scenarios. The gradual increment of inter-U₆₀ distance demonstrates a nice correlation with the macroscopic phasal transitions of U₆₀: from single crystals to gels, then to solutions containing self-assembled standalone sheet structures, and to solutions containing self-assembled blackberry structures.