Transitions and modulated phases in chiral tilted smectic liquid crystals

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Abstract
Modulated phases that occur in tilted chiral smectic liquid crystals are discussed within mean-field theory in thin films and in bulk. A chiral term in the free energy containing three order parameters and one gradient can make the free energy of certain defects negative or the bend elastic constant negative. Assuming various possible behaviors for these defect energies we find either a striped state with parallel defect walls or a lattice of hexagonal unit cells containing disclinations bounded by intersecting defect walls in films. Rather different transitions to the striped phase occur when this elastic constant is either positive or zero. The multicritical point that separates these two transitions is discussed. Finally, possible modulated phases in bulk, three-dimensional systems are discussed and it is shown that, because of a competition between two different modulations, the transitions to the new modulated phases are always first order. Possible consequences for designing molecules for chiral smectic-C phases with increased polarizations are discussed.