Thermal fluctuations in smectic-<Emphasis Type="Italic">A</Emphasis> films on the surface of solid substrates

The static and dynamic characteristics of layer displacement fluctuations in smectic-A films supported on the surface of a solid substrate are calculated with due regard for the profiles of the flexural and tensile (compressive) moduli of smectic layers. The difference in the surfaces bounding the film and the asymmetry of the profiles of the elastic moduli with respect to the central layer of the film are taken into account. The profiles of fluctuations of smectic-layer displacements and the correlations between these fluctuations are determined for the films formed by liquid-crystal compounds that can undergo a bulk smectic-A-nematic phase transition. The dynamic correlation functions derived for these fluctuations are used for calculating the correlations between the intensities of x-ray scattering by a film at different instants of time. It is demonstrated that, in smectic-A films supported on the surface of a solid substrate, unlike free-standing smectic-A films, the effect of temperature on the dynamics of layer displacement fluctuations can be observed in experiments on dynamic x-ray scattering from films that are not very thick (the number of layers N ～ 20) and at considerably smaller recoilmomentum components in the film plane.