Thermal fluctuations and x-ray scattering from free-standing smectic-A films.

The present paper is devoted to theoretical investigation of thermal fluctuations and correlations between them in free-standing smectic-A films (FSSAF's) formed of liquid crystal compounds with bulk smectic-A-isotropic (SmA-I) and SmA-nematic (SmA-N) phase transitions, as well as small angle x-ray scattering from these FSSAF's. The study took into account the dependence of the bending elastic constant K and the smectic layer compressibility B on the distance from the boundary free surfaces of the films. The results of calculation are compared with those obtained in the framework of the Holyst model [Phys. Rev. Lett. 65, 2153 (1990); Phys. Rev. A. 44, 3692 (1991)] for spatially uniform FSSAF's. It has been found that, well below the temperature at which the smectic order in the bulk liquid crystal disappears, taking into account the profiles of the elastic moduli K and B does not produce noticeable differences from this model. However, at maximum temperatures of existence of FSSAF's, our results are considerably different from the predictions of the Holyst model. The results obtained are applied to calculation of specular and diffuse x-ray reflectivities of FSSAF's in the whole temperature interval of their existence. Displacement of the molecular centers within the film layers along those normal to them and the deviation of the local orientational order in FSSAF's from the ideal are also taken into account. The results of calculation are in agreement with experiments on the small angle x-ray scattering from FSSAF's.