X-ray scattering from smectic films on a substrate

The combined effect of thermal fluctuations and substrate roughness replica tion in smectic liquid-crystalline films on a substrate is described. For t hat purpose a theory is developed which is an extension of existing continu um models. Both thermal fluctuations and roughness replication can be quant ified in terms of the surface tension and the elastic constants for compres sion and bending of the smectic material. Model calculations show the effec t of the various parameters. It is shown that the growth of roughness due t o thermal fluctuations largely cancels the diminishment due to roughness re plication. This explains why previous x-ray scattering measurements could b e satisfactorily described in terms of fractal correlation functions. [S106 3-651X(99)14802-5].