Fluctuations in thin smectic-Afilms

Abstract

The smectic layer displacement fluctuation profile, σ(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 σ≊4 Å, compared to σ≊8 Å 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 (±0.1 Å) with recent x-ray measurements.