Ambiguity in determining the shape of alkali alkyl sulfate micelles from small-angle scattering data

Model fitting to small-angle scattering patterns from a series of dilute sodium- and cesium alkyl sulfate micellar solutions results in two significantly different sets of best-fit parameters for each solution. One of the sets defines nearly monodisperse prolate ellipsoids; the other defines slightly, but significantly, polydisperse oblate ellipsoids. In the prolate and oblate minimum locations, the mean form and structure factors as well as the mean core volumes are equal within the experimental error such that the axial ratios are approximately the reciprocals of each other. The experimental finding is numerically generalized: it is demonstrated that, in a Q range, the upper limit of which depends on the axial ratio. the squared mean and the mean square of the scattering amplitude from homogeneous ellipsoids with equatorial radii and axial ratios, respectively (r,eta) and (r eta(2/3),1/eta) are indistinguishable in practice. In dilute solutions without added salt, neither the best-fit values of the model parameters nor the available thermodynamic models provide direct evidence for the conformation, although the prolate ellipsoidal shape is indirectly supported by experiment. The elongated conformation of ionic micelles in dense and/or salinated systems seems realistic.