Thermal Fluctuations of Freely Suspended Smectic-A Films from Mesoscopic to Molecular Length Scales

The thermal fluctuations of freely suspended smectic-A films have been studied with diffuse x-ray scattering. Using a $\left(2+2\right)$ scattering geometry at a synchrotron source the spectral dependence of the displacement-displacement correlation function has been determined from mesoscopic to molecular dimensions. At long in-plane length scales the fluctuations of the smectic layers were found to be conformal; i.e., all layers of the film fluctuated in unison. At decreasing length scales conformality was progressively lost, starting between the top and bottom layers of the film.