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 perform ed a systematic ultrasmall-angle X-ray scattering (USAXS) study for structu re and its change as a function of salt concentration very carefully and fo und that the interparticle distance in colloidal crystal showed a maximum a t kappa a = 1.3 (kappa(-1), Debye length; a, radius of particle). This obse rvation could not be explained by present concepts and theories for colloid al interaction like Derjaguin-Landau-Verwey-Overbeek (DLVO). However, it wa s confirmed that this phenomenon is universal by experiments for various la tex particles which were different in size and charged state. By the analys is of the interparticle structure factor, S(q), it was suggested that the p oint at kappa a = 1.3 is the solid-liquid transition point. In this study, the USAXS data have been further analyzed by three-dimensional (3D) paracry stal theory to obtain more quantitative information about this curious, une xpected phenomenon. The S(q) profiles obtained by USAXS were excellently re produced by the SD-paracrystal lattice factor, Z(q), for face-centered cubi c symmetry. The g-factor, which represents the degree of distortion, was fo und to be about 0.1-0.15 near the transition point, which was in good agree ment with alpha*-law for solid-liquid transition. Possible new factors, whi ch should be taken into account to explain this phenomenon, were duly discu ssed.