Theoretical description of fluctuations in free-standing smectic-A films including spatial non-uniformity of their elastic characteristics

A theoretical study is reported of fluctuations in smectic layer displacements and of the correlations between them in free-standing smectic-A films formed of liquid-crystal compounds with smectic-A-isotropic liquid (Sm-A-I) and Sm-A-nematic (Sm-A-N) bulk phase transitions. The study took into account the dependence of the elastic constants for bending, K, and tension (compression), B, of smectic layers on distance to the free film surfaces. The calculations are compared with the results obtained within Hołyst’s model for spatially uniform, free-standing smectic-A films. It has been established that, below the temperature at which smectic order in the bulk of a 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 temperatures considerably above the Sm-A-I and Sm-A-N phase transitions, their inclusion results in considerable discrepancies from the predictions of Hołyst’s model. Fiz. Tverd. Tela (St. Petersburg) 41, 1882–1889 (October 1999)