In this paper, we outline a simple procedure for analyzing small angle neutron scattering (SANS) spectra from interacting colloids containing a continuous distribution of particle sizes. In particular, the effects of polydispersity on the apparent interparticle structure factor S′(Q) observed by SANS is investigated. We find that the oscillations in S′(Q) are significantly damped in comparison to those of the true structure factor S(Q). When our procedure is extended to the analysis of SANS spectra from nonspherical particles, we find that orientational averaging affects S′(Q) in a qualitatively similar way. The applicability of the procedure to the analysis of real data is demonstrated with spectra taken from water-in-oil microemulsions, ionic micelles, and interacting proteins.

The intensity distribution of the critical scattering from sodium di-2-ethylhexylsulfosuccinate AOT -D20 -n-alkane water-in-oil (W/0) microemulsions has been measured over an extensive range of droplet volume fractions (3 -30 vol %) and temperatures (22 to 43'C) in the critical region.The water/surfactant molar ratio of the microemulsion was kept at a constant value of 40.8, for which previous experiments on the temperature variation have been well documented. A structural model of W/O microemulsions based on well-defined surfactant-coated water droplets is firmly established up to a volume fraction of about 20 vol % for all temperatures studied. Data analysis assumes that the cloud points and subsequent phase separation are caused by concentration fluctuations of polydisperse droplets. The major conclusions drawn from the analysis are as follows. (1) The order parameter of the critical phenomenon can be taken to be the volume fraction of the dispersed droplets. (2) The size and polydispersity of the droplets remain essentially constant in the vicinity of the critical point (for a fixed water/surfactant ratio). (3) The critical phenomenon is driven by an increased attraction between the droplets as the critical point is approached. (4) The critical point can be approached by either raising the temperature at fixed volume fraction or by varying the carbon number of the oil solvent at fixed volume fraction and temperature. (5) The nature of the droplets does not change upon a phase separation into two coexisting microemulsions. The data also gives some evidence that the droplet picture of the microemulsion breaks down at sufficiently high concentrations of water and surfactant.

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The temperature dependence of the size and polydispersity of the water core in a pure three-component microemulsion consisting of decane + AOT + D20 has been observed by small-angle neutron scattering. At each temperature, as the molar ratio X = [DzO]/[AOT] is varied from 8 to 49, a linear increase in the radius is observed from about 25 to 90 A. The extrapolated value of the radius at vanishing water concentration is nonzero, indicating substantial water penetration into the charged head group region of the inverted micelle. From the slope and extrapolated radius of this line we can deduce the effective area and volume occupied by the hydrated head group at each temperature. The polydispersity in size is appreciable even at room temperature and it increases steadily as the temperature is raised. The Q dependence of the intensity distribution does not follow the Ornstein-Zernike form, but instead it can be well described as scattering from a collection of polydispersed spheres as the critical point (37 "C for 6% DzO) is approached.