As an intermediate sample of ionic solutes between colloidal particles (macroions) and simple electrolyte ions, we made small-angle x-ray scattering (SAXS) measurements for aqueous solutions of poly(amido amine) dendrimers of three generations (G4, G7, and G10). The SAXS curves of univalent acid solutions showed a single scattering peak, as observed for synthetic macroions. The peak position was dependent on the dendrimer concentration but independent not only of the acid concentration (degree of protonation) but also of the counterion species. The effective charge density of the dendrimer determined by conductivity measurements was found to be insensitive to the acid concentration and the counterion species. The nearest neighbor interparticle distance ${2D}_{\exp }$ calculated from the peak position of the structure factor of G7 and G10 was obviously smaller, though slightly, than the average interparticle distance ${2D}_0$ calculated from molecular weights and concentrations of dendrimers, implying that acid solutions of dendrimers formed the two-state structures by the attractive force. The ultra-small-angle x-ray scattering curve for the hydrochloric acid solution did not show an upturn, which indicates the existence of large scale structural inhomogeneities such as localized ordered structures, probably due to the weak attraction and hence less clear distinction of the ordered and disordered regions. For sulfuric acid solutions, clear scattering peaks were not observed. The bivalent counterions were more strongly associated with the dendrimer ions than the univalent ones. The resulting low charge number of the dendrimers with the bivalent counterion was confirmed directly by the conductivity measurements. These observations confirm that the counterion-mediated attraction does exist even with the univalent counterions and point out that the frequently advanced claim that the effective potential is essentially repulsive with univalent counterions while attraction appears with bivalent counterions is not necessarily correct. It is noted that the intensity of the counterion-mediated attraction in dendrimer solutions is dictated by both the effective charge density and the effective charge number, in contrast with macroionic solutions or colloidal dispersions in which only the effective charge density appeared to be important.

• Received 14 March 2001

DOI:https://doi.org/10.1103/PhysRevE.64.051808