Theory of transitions among tilted hexatic phases in liquid crystals

We present a Landau theory for transitions among tilted hexatic phases in liquid-crystal films. Using the renormalization group, we then derive phase diagrams with four tilted hexatic phases: the hexatic-I and hexatic-F phases, an intermediate hexatic-L phase, and an unlocked phase. If the films are crystalline rather than hexatic, all these phases except the unlocked phase still exist. These results are consistent with recent experiments on thermotropic and lyotropic liquid crystals. We also study the five-armed ``star'' defect close to the hexatic-to-hexatic transitions. Near the first-order transition from hexatic-I to hexatic-F, the thickness of the arms increases as {}T-TIF{{}}^{{{-}}1/3}$ through a process similar to wetting. This thickening should be observable in thin tilted hexatic films.