Determination of Intermolecular Distances in Dilute Solutions of Macroions and Their Direct Correlations with...

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.