Fluctuations in thin smectic-<i>A</i>films

Abstract

The smectic layer displacement fluctuation profile, \ensuremath{\sigma}(r)=〈${\mathit{u}}^{2}$(r)${\mathrm{〉}}^{1/2}$, has been calculated for thin smectic-A films. In thin smectic-A films the calculated fluctuation amplitudes are only \ensuremath{\sigma}\ensuremath{\approxeq}4 \AA{}, compared to \ensuremath{\sigma}\ensuremath{\approxeq}8 \AA{} in a macroscopic sample. The fluctuations are suppressed at the two free surfaces by the surface tension, grow rapidly away from each surface, and have a parabolic profile near the center of the film. These results are in quantitative agreement (\ifmmode\pm\else\textpm\fi{}0.1 \AA{}) with recent x-ray measurements.