X-Ray Scattering from Freestanding Polymer Films with Geometrically Curved Surfaces

We show that the x-ray surface scattering from a freestanding polymer film exhibits features that cannot be explained by the usual stochastic formalism for surfaces with random height fluctuations. Instead, a geometric description of the film morphology assuming two curved surfaces characterized by a radius of curvature and a lateral cutoff length successfully accounts for the phase difference between the Kiessig fringes of the nominal "specular" and "off-specular" components of the scattering. The formalism allows one to distinguish unambiguously between conformal and anticonformal curvature morphologies at long length scales.