A method is developed for calculating the small-angle x-ray scattering originating from within the interior of a thin film under grazing incidence illumination. This offers the possibility of using x-ray scattering to probe how the structure of polymers is modified by confinement. When the diffuse scattering from a thin film is measured over a range of incident angles, it is possible to separate the contributions to scattering from the interfaces and the contribution from the film interior. Using the distorted-wave Born approximation the structure factor, $S\left(q\right)$, of the film interior can then be obtained. We apply this method to analyze density fluctuations from within the interior of a silicon supported molten polystyrene (PS) film. Measurements were made as a function of film thickness ranging from one to ten times the polymer radius of gyration $\left(R_g\right)$. The compressibility, calculated by extrapolating the measured $S\left(q\right)$ to $q=0$, agrees well with that of bulk PS for thick films, but thinner films exhibit a peak in $S\left(q\right)$ near $q=0$. This peak, which grows with decreasing thickness, is attributed to a decreased interpenetration of chains and a consequent enhanced compressibility.

• Received 12 May 2010

DOI:https://doi.org/10.1103/PhysRevE.82.011804