Comparison of USAXS information with RMSA prediction for the effect of added salt on colloidal crystal structure

Abstract

Charged colloidal particles form so-called colloidal crystals in dispersions because of electrostatic interparticle interactions between them. We performed a systematic and quantitative investigation of the effect of salt on the interparticle distance in colloidal crystals with the ultra-small-angle X-ray scattering (USAXS) technique. We accumulated a great deal of significant information about the mechanism of the colloidal crystal formation by USAXS. We found that the interparticle distance in colloidal crystals shows a maximum as a function of the added salt concentration. The maximum position of the interparticle distance was located around κa = 1.3 (κ−1 is the Debye length, and a is the particle radius). The behavior of the decrease of the interparticle distance with the increase of the added salt concentration at κa > 1.3 could be explained not quantitatively but qualitatively with the effective hard-sphere theory. Thus, it was suggested that the dependence of the interparticle distance on the salt concentration at κa > 1.3 was reasonable according to the classical theories, such as the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory. In this article, we advance this theoretical approach with the classical theory, that is, with the assumption of the only repulsive force for the interparticle interaction, to elucidate the origin of the curious behavior of the interparticle distance. We estimated the structure factor by the rescaled mean spherical approximation (RMSA) with a Yukawa-type interparticle interaction potential. A comparison between the prediction of the RMSA data and USAXS experimental data was performed. In this analysis, the charge renormalization procedure was applied. Although the origin of the behavior of the interparticle distance at κa < 1.3 is still a mystery, we concluded that the behavior at κa > 1.3 could be interpreted as a result from the DLVO manner. The effective surface charge number was on the order of several percentages of the analytical surface charge number. This experimental fact certainly proves the validly of our USAXS observation quantitatively and also predicts the existence of novel factors for κa ≤ 1.3, the real origin of colloidal crystal formation, which have never been taken into account previously. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 78–90, 2001