Structure of twist-grain-boundary-C phases.

We study properties of the Renn-Lubensky twist-grain-boundary-C (TGB(C)) phase, with layer normal rotating in a plane perpendicular to the pitch axis, and the Bordeaux TGB(C) phase, with the layer normal rotating on a cone parallel to the pitch axis near the upper critical twist k(c2) marking the transition to the cholesteric phase. We introduce a generalized model free energy for the smectic-C phase that allows either TGB(C) phase to be stable, and we calculate k(c2) and the order-parameter profile, which shows only modest spatial variation, for both phases.