The solutions of ionic micelles of dodecyl-, tetradecyl-and hexadecyl-trimethylammonium chlorides were studied by small-angle X-ray scattering (SAXS). The SAXS curves showed a single, broad peak. The interference functions S ( Q ) were obtained from the scattering curves. The radial distribution function g(r) was calculated from S ( Q ) and the distances between nearest neighboring micelles were evaluated. The intermicellar distances (r,) evaluated from g (r) were close to the average distance calculated by assuming a uniform distribution of the micelles throughout the solution. This fact indicates that the intermicelle attractive force through the intermediary of counterions was weak, because the number of charges on the micelles was small. A difference between rm and the Bragg spacing calculated from the overall intensity of scattered X-ray was noticed but it was not large enough to invalidate our previous interpretation that the Bragg spacing is an approximate measure of the ordered structure. By taking into account the paracrystalline distortion, the lattice factor Z ( Q ) was calculated. Excellent agreement was obtained with the structure factor S (Q) for a face-centered cubic lattice structure when the distortion factor was assumed to be about 0.2. The number of peaks of the lattice factor decreased with increasing distortion factor. This suggests the incorrectness of the often expressed view that the single broad peak is not reminiscent of some kind of ordering: in this view the large distortion, which exists in solutions and at ambient temperatures, has been overlooked.
Introduction [l]In previous papers, we have studied aqueous solutions of macroions such as polyacrylate [a], poly-L-lysine [3] and polystyrenesulfonate [4] by the small-angle X-ray scattering (SAXS) technique. The scattering curves of the macroion solutions showed a single, broad peak under suitable conditions. From this peak position, we estimated the approximate intermacroion distance (2 Dexp) by assuming the Bragg equation. The 2 Dexp value was revealed to be considerably smaller than the average intermacroion distance (2 Do), which was calculated by assuming a uniform distribution of the solutes throughout the solution.This fact indicates the presence of non-space-filling ordering, in other words, a two-state structure in which some of the macroions are localized in ordered regions of a high density with an intermacroionic distance of 2 Dexp whereas the rest are in disordered regions of a low density. Accordingly, we have suggested that the macroion ordering is due to an intermacroion attraction through the intermediary of its counterions [l -41. Recently, this intermacroion attraction was supported by a theoretical. consideration [S, 61.The information obtained by the SAXS measurements on "invisible" macroions has been confirmed by independent microscopic observation on suspensions of polymer latex particles, which are large enough to be seen by the naked eye with an ultramicroscope [7-103. The situation in this case is straightforwa...
