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Abstract
Here a thick (semi-infinite) layer of polar liquid crystal having a free surface is considered. The temperature of the sample is assumed to be in the vicinity of the nematic (N)-monolayer smectic A (SA1) phase transition and considerably higher than the temperature of possible (“virtual”) SA1-bilayer smectic A phase with long-range antiferroelectric order (SA2) transition. Therefore, the bilayer smectic ordering, induced by the interaction between polar molecules and the free surface of liquid crystal, decays much more rapidly with increasing distance to the free surface than the free surface-induced monolayer smectic ordering. Using this assumption the dependnence of both the monolayer and bilayer smectic order parameters on the temperature and the distance to the free surface are determined. It is shown that the latter dependence for the monolayer smectic order parameter has an approximately exponential character and the depth of the free surface-induced monolayer smectic A ordering penetration into bulk liquid crystal increases with the approaching of the N-SA1 transition point. At certain temperature below the N-SA1 transition point this penetration depth achieves an infinite value. The bilayer smectic order parameter also decays almost exponentially with increasing distance to the free surface. However it's magnitude and the depth of the bilayer smectic ordering penetration into bulk liquid crystal are practically independent of temperature. The results obtained are compared with the experiment.