An Exact Evaluation of Salt Concentration Dependence of Interparticle Distance in Colloidal Crystals by Ultra-Small-Angle X-ray Scattering. 3. Confirmation of Solid−Liquid Transition by Three-Dimensional Paracrystal Analysis

In our previous works ( Langmuir 1994, 10, 4423; 1996, 12, 5588), we performed a systematic ultra-small-angle X-ray scattering (USAXS) study for structure and its change as a function of salt concentration very carefully and found that the interparticle distance in colloidal crystal showed a maximum at κ a = 1.3 (κ -1, Debye length; a, radius of particle). This observation could not be explained by present concepts and theories for colloidal interaction like Derjaguin−Landau−Verwey−Overbeek (DLVO). However, it was confirmed that this phenomenon is universal by experiments for various latex particles which were different in size and charged state. By the analysis of the interparticle structure factor, S ( q ), it was suggested that the point at κ a = 1.3 is the solid−liquid transition point. In this study, the USAXS data have been further analyzed by three-dimensional (3D) paracrystal theory to obtain more quantitative information about this curious, unexpected phenomenon. The S ( q ) profiles obtained by USAXS were excellently reproduced by the 3D-paracrystal lattice factor, Z ( q ), for face-centered cubic symmetry. The g -factor, which represents the degree of distortion, was found to be about 0.1−0.15 near the transition point, which was in good agreement with α*-law for solid−liquid transition. Possible new factors, which should be taken into account to explain this phenomenon, were duly discussed.