Determination of Intermolecular Distances in Dilute Solutions of Macroions and Their Direct Correlations with Self-Assembly and Macrophase Transitions

This work demonstrates new attempts to determine the intermolecular distances between charged macroionic solutes in their dilute solutions, which regulate the solute’s microphase (self-assembly) and macrophase transitions. Small-angle X-ray scattering (SAXS) and analytical ultracentrifuge (AUC) techniques were applied to determine the intermolecular distances for the 2.42 nm-sized, spherical uranyl peroxide molecular cluster {U₆₀} in their self-assembled states in dilute aqueous solution and concentrated phases, respectively. The counterion-mediated attraction among {U₆₀} leads to characteristic, inter-{U₆₀} distances in solutions, which increase gradually with decreasing the strength of introduced counterions (e.g., lower valency). The gradual increment of inter-{U₆₀} distance demonstrates a nice correlation with the macroscopic phase transitions of {U₆₀}, from single crystals to concentrated fluids containing rigid 2-D sheets, then to dilute solutions containing a small amount of standalone, floating 2-D sheets of {U₆₀}, and finally to dilute solutions containing a limited amount of self-assembled single-layered, spherical blackberry structures of different sizes from the bending of more flexible 2-D sheets.