Grain boundary structure in incommensurate smectics: a signature of phasons

The authors consider a tilt grain-boundary with small angle theta in an incommensurate smectic A_ic liquid crystal with ordering wavenumbers q₁, q₂ and sample thickness h in the direction normal to the layers. For q_i theta h<<1, a limit well within the reach of experiment, they find that the dislocation array which forms such a boundary has a spacing D approximately h^1/5 theta ^-4/5. This prediction, which is qualitatively different from that obtained for periodic smectics by Nallet and Prost, should serve as a decisive test for the existence of phasons and hence for the truly incommensurate nature of these systems.