Range of interlayer interactions in smectic-C liquid crystals

The fact that the elastic constant for bending a layer of smectic-C liquid crystal along its c director differs from the value for bending in the perpendicular direction has recently been shown to give rise to interactions between distant layers. The effect of this entropy-induced interaction is to favor a parallel or antiparallel alignment of the c directors in these nonadjacent layers. We calculate in detail the range and strength of this interaction in both infinite and finite samples, and find the results to depend mainly on the ratio of the average layer bending elastic constant to the layer compression modulus. At low values of this ratio, the interlayer interaction is of long range in a bulk sample, while at high values of the ratio it decays as the inverse cube of the interlayer distance. For a sample confined between rigid substrates parallel to the layers, the interaction is greatly reduced. For a free-standing film the interaction may be enhanced if the surface tension is weak, but may be diminished if the surface tension is strong.