Exact Evaluation of the Salt Concentration Dependence of Interparticle Distance in Colloidal Crystals by Ultra-Small-Angle X-ray Scattering. 2. The Universality of the Maximum in the Interparticle Distance−Salt Concentration Relationship

We have investigated the salt concentration dependence of the interparticle distance in colloidal crystals in dispersion by the ultra-small-angle X-ray scattering (USAXS) technique. USAXS gives us the internal, global, and general information for the structure of colloidal crystals. The nearest neighbor interparticle distance (2 D exp ) increased at low salt concentration with increasing ionic strength in the dispersion. After passing through a maximum, 2 D exp decreased. The maximum value of 2 D exp was nearly equal to the calculated distance (2 D 0 ), assuming uniform distribution of the particles in the dispersion. This quite unique tendency, which we reported in our previous letter ( Langmuir 1994, 10, 4423), was found to be universal by systematic USAXS experiments for various kinds of latices which were different in size and charged state. The salt concentration at the maximum of the 2 D exp vs [salt] profile was different for each latex particle, but it was found that this position is scaled by κ a (κ -1, Debye length; a, particle radius): the condition of κ a = 1.3 is the maximum point for all latices studied. The theories proposed for colloidal interaction to date cannot explain this curious phenomenon. These observations by USAXS seem to be predicting some possibility of transition in structure and in interaction at this maximum position.