Long-range interlayer interactions in ferroelectric liquid crystals

Some smectic liquid crystals exhibit a series of phases, including ferroelectric, antiferroelectric, and ferrielectric commensurate structures as well as an incommensurate phase. A long-standing problem has been to understand the origin of the long-range interaction responsible for this rich variety of phases. We study a model that incorporates thermal fluctuations in the flexing of layers and find that it supports commensurate and incommensurate structures. The vibrational entropy competes with an assumed helical interaction between nearest-neighbor layers. An increase in temperature then leads to an unwinding of the helix that proceeds at first through commensurate phases and then into an incommensurate phase. This result is consistent with the experimentally observed "distorted clock model."