Effect of the inhomogeneous structure of freely suspended smectic-A films on the dynamics of fluctuations of smectic-layer displacements

The dynamics of fluctuations of smectic-layer displacements in freely suspended smectic-A films is studied theoretically with due regard for the dependence of the transverse-bending moduli K and extension (or compression) of smectic-B layers on the distance to the free surfaces of the films. The temperature dependences of the dynamic correlation functions are calculated for fluctuations of layer displacements in films of various thicknesses and then used to calculate the correlations between the X-ray intensities scattered by the film at different moments of time. The calculations were performed within a wide temperature range. It is shown that the influence of temperature on the X-ray dynamics of fluctuations of layer displacements in freely suspended smectic-A films can be detected in the experiments on the dynamical scattering by rather thick films (layer number N ≥ 100) at considerably high values of the recoil-momentum component in the film plane (≥10⁶ cm^?1).