No abstract

A SANS study of 0.073 c micellar solutions of sodium alkyl sulfates with chain length from n C = 9 to 16 was carried out. Micelles were assumed to be ellipsoids which may grow only in the direction of their axis of symmetry. The structure factor was calculated in terms of the one-component macrofluid model by assuming DLVO potential. The contact radius and the strength of the interaction potential were handled as free fitting parameters; the electrostatic potential and the apparent micellar charge on the contact surface were derived from the latter. The assumptions imposed on the conformation of the micellar cores are sustained by the best-fit parameters of the form-factor. For n C = 9−13 the mean aggregation numbers are in good, or at least, in acceptable agreement with the predictions of a recent thermodynamic theory of micellization. The difference found between the mean core and contact radii suggests that an unknown repulsive interaction may be present which prevents the micelles from astructurally possiblecloser approach. Although the surface potential indicates that the outgoing conditions for deriving the DLVO potential are violated, the agreement of the electric charge derived partly from the DLVO potential, partly from the nonlinearized Gouy−Chapman model supports the practical applicability of the well-known DLVO potential formula to interpreting SAS results.

Small-angle neutron- (SANS) and X-ray-scattering (SAXS) patterns obtained at 40 °C from 0.0729 m D2O solution of cesium dodecyl sulfate (CsDDS) have been simultaneously evaluated in terms of the conventional two-shell model, a three-shell model created for demonstration purposes, and a newly developedand partly testedfour-component model. The simultaneous fitting is based on the fact that the two types of coherent scattering patterns differ only in the neutron- and X-ray scattering lengths. For comparison, the SANS and SAXS patterns were evaluated separately, too. In contrast to the two- and three-shell models, the four-component model is able to represent the continuously varying spatial distribution of the scattering contrast. From the results, it seems that the most reliable data are obtained from fitting the four-component model simultaneously to both patterns. Along with (approximate) core- and counterion profiles, application of the latter model can result in the spatial distribution of the solvent molecules around the micellar center. If an atom or a molecular group has well-distinguishable scattering contrast relative to both types of scattering (such as Cs+ counter-, and -SO4 -- headgroup-ions), utilization of the four-component model enables their molecular volumes to be treated as variable model parameters, thus providing a unique method for determining their hydration properties in a structured nonsimple liquid.

Multishell models used for calculating the elementary scattering amplitude from micelles are replaced by the Fourier transforms of the probability density functions of finding the hydrophobic (methyl and methylene) groups as well as the headgroup and counterions at a particular distance from the micellar center. Model variables are the aggregation number and two width parameters respectively characterizing the Gaussian core and the exponential counterion profiles. Application of the model to almost spherical sodium nonyl-, decyl and undecyl sulfate micelles leads to reasonable best-fit values. Aggregation numbers are tested by a recent thermodynamic model of micellization. Within the limits set by the finite resolution of the method, the group-density functions render possible to determine the spatial distribution of any physical quantity inside and around the micelles that depends only on the number of the molecular groups present. As an example, the relative dielectric permittivity is discussed.