Description of dynamic x-ray scattering from freely standing smectic-A films

The consequent description of the x-ray scattering from the free standing smectic-A films is suggested. Calculations are based on the discrete model for the film dynamics. The scattering intensity temporal autocorrelation function is obtained within the framework of this approach neglecting the multiple scattering and refraction effects. It is shown that the behavior of this function crucially depends on the film thickness. In particular, in thin films containing less than 10(3) layers the time dependence of has damping oscillation character. This behavior is determined by an acoustic mode that describes the film motion caused by the action of the surface tension. For thick films containing more than 10(4) layers the dynamics of the intensity temporal autocorrelation function is determined either by an acoustic mode or by a wide spectrum of modes depending on the x-ray geometry. In both the cases the autocorrelation function is a relaxation one. The results obtained are compared with the experiments on the coherent soft and hard x-ray scattering.