Polymers dissolved in a chiral nematic liquid crystal: Model for twist-grain-boundary phases

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Abstract
We introduce a model of polymers dissolved in a chiral nematic liquid crystal. This model has equilibrium phases in which polymers adopt configurations identical to those of dislocations in the twist-grain-boundary (TGB) phases of smectic liquid crystals. We use this model to investigate lock-in to rotationally commensurate TGB phases. We also calculate elastic constants appearing in the long-wavelength elastic energy for rotationally incommensurate TGB phases introduced by Toner (unpublished). In developing the formalism for our calculation of these elastic constants, we present a new derivation, starting with the Frank free energy, of the Landau-Peierls elastic energy for a chiral nematic liquid crystal, and we calculate the elastic constants for the state consisting of a hexagonal lattice of parallel polymers dissolved in a nematic liquid crystal.