Analytical expressions for the scattering functions of ordered mesoscopic materials are derived and compared to experimentally determined scattering curves. Ordered structures comprising spheres (fcc, bcc, hcp, sc), cylinders (hex, sq), and lamellar structures are considered. The expressions take into account particle size distributions and lattice point deviations, domain size, core/shell structures, as well as peak shapes varying analytically between Lorentzian and Gaussian functions. The expressions allow one to quantitatively describe high-resolution synchrotron small-angle X-ray (SAXS) and neutron scattering (SANS) curves from lipid and block copolymer lyotropic phases, core/shell nanoparticle superstructures, ordered nanocomposites, and ordered mesoporous materials. In addition, the diffuse out-of-plane scattering of grazing incidence GISAXS and GISANS experiments of laterally ordered thin films can be quantitatively analyzed.

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Shear thinning and orientation of cylindrical surfactant and block copolymer micelles was investigated by rheo-SANS (small-angle neutron scattering) experiments. Shear thinning and orientation occur for shear rates (.)gamma tau(dis)>>1, where tau(dis) is the disentanglement time of the micelles. Micelles align in the flow direction with an orientational distribution that can be well described by an Onsager-type distribution function. Over nearly the whole range of concentrations and for all cylindrical micelles investigated, the shear viscosity eta follows a simple eta approximately e(-aS) behavior as a function of the orientational order parameter S with the same prefactor a.

We use scanning force microscopy and stepwise erosion in a radio-frequency (rf) plasma to obtain a three-dimensional volume image of an ultrathin poly(styrene-b-butadiene-b-styrene) triblock copolymer film. The free surface of the film exhibits domains of two distinctly different structures, i.e., hexagonal arrays of isolated dots and parallel stripes. A common forehand interpretation relates these surface morphologies to a cylindrical microdomain morphology with the cylinders oriented perpendicularly and parallel to the plane of the film, respectively. In contrast, our experiments show that the "dots" merge into parallel cylinders at some distance underneath the film surface. These results demonstrate that care has to be taken when the thin film morphology of block copolymers is inferred from their surface structure.

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