TWISTING TRANSITION IN A CAPILLARY FILLED WITH CHIRAL SMECTIC-C LIQUID-CRYSTAL

We consider a cylindrical capillary filled with the chiral smectic C phase of a liquid crystal. The smectic layers are stacked along the capillary axis, and at the capillary wall the director is assumed to be parallel to the wall. Non-chiral materials in these conditions exhibit a disclination line which coincides with the capillary axis. In chiral smectic C material the tendency for macroscopic twist competes with the boundary conditions at the wall, and the disclination line can shift away from the capillary axis and form a helix. We calculate an approximate phase diagram for the system, which shows how the phase (helical or non-helical) depends on material parameters (elastic constants and chirality) and capillary radius. Both continuous and discontinuous phase transitions occur: the continuous transition should be observable in ordinary liquid crystals, while the discontinuous transition should be observable in main chain polymer liquid crystals. Observation of the discontinuous transition would provide information about a poorly known elastic constant.