Analytical expression for the resolution function for small‐angle scattering in pinhole geometry are derived. The contributions to the resolution function due to wavelength spread, finite collimation and detector resolution are determined separately using Gaussian functions to approximate the contributions. A general resolution function is derived which is the result of the combined effect of the three contributions. An azimuthal‐integrated resolution function, which can be applied to scattering from a material with a circular symmetric scattering cross section, is calculated. This resolution function contains in addition a contribution from the averaging procedure itself. The analytical results are compared with the results of computer simulations. The comparison shows that Gaussian functions give a good description of the resolution function and that the widths agree with those calculated by the analytical expressions. The resolution function is applied in the analysis of two experimental examples: neutron scattering from latex particles [Wignall, Christen & Ramakrishnan (1988). J. Appl. Cryst.21, 438–451] and neutron scattering from lamellar structures of bilayer lipid membranes (Mortensen, Pfeiffer, Sackmann & Knoll, unpublished). The analytical expressions for the resolution function allow a least‐squares analysis to be performed and excellent agreement between experimental and theoretical scattering patterns are obtained.

Grazing-incidence small-angle X-ray or neutron scattering of thin polymer films reveals information about the ordering and preferential orientations of the phase-separated microdomains within the films. The grazing-incidence geometry enhances the surface sensitivity; however, the scattering has to be treated within the framework of the distorted-wave Born approximation. In this work, the case of thin films with lamellar mesostructure is studied, where the orientation of the lamellae is either perpendicular or parallel to the film interfaces. For perpendicular lamellae, Bragg rods are found, which are extended along the film normal, whereas for parallel lamellae, peaks along the film normal appear. The positions of the maxima present in the latter case are explained by accounting for refraction at the film surface and reflection at the film-substrate interface. The results are relevant for thin films of lamellar diblock copolymers.

Using tapping mode atomic force microscopy, we studied the influence of molar mass (13.9−183 kg/mol) on the lamellar orientation at the surface of thin films of symmetric polystyrene−polybutadiene diblock copolymers prepared via spin-coating and by slow solvent-casting. The ratio between film thickness and lamellar thickness was varied between 0.5 and 10. Whereas for film thicknesses between 1 and 10 times the lamellar thickness, a lamellar orientation parallel to the film surface is preferred for low molar masses (below ∼55 kg/mol), high molar mass samples (above ∼90 kg/mol) rather form lamellae oriented perpendicular to the surface. For film thicknesses equal to the lamellar thickness, the films do not exhibit any texture, whereas for film thicknesses equal to half the lamellar thickness, a weak surface structure could be observed. This is consistent with symmetric wetting, i.e., the same block adsorbs at both film interfaces, but their selectivity is only weak. Thus, entropic contributions like chain stretching along a wall and the enrichment of free chain ends at the interface become important, and both parallel and perpendicular orientations of lamellae in thin films can occur.

We have investigated the structural changes in thin films of lamellar poly(styrene-b-butadiene) diblock copolymers during treatment with saturated cyclohexane vapor, a solvent slightly selective for polybutadiene. Using real-time, in-situ grazing-incidence small-angle X-ray scattering (GISAXS), the swelling and the rearrangement of the lamellae were investigated with a time resolution of a few seconds, and the underlying processes on the molecular level were identified. After a few minutes in vapor, a transient state with a more well-defined and more long-range ordered lamellar orientation was encountered. Additional parallel lamellae formed which we attribute to the increased degree of coiling of the polymers in the swollen state. Eventually, the film became disordered. These changes are attributed to the increased mobility of the swollen polymers and the gradually decreasing segment-segment interaction parameter in the film as solvent is absorbed.