Hydrodynamical modes and light scattering in the liquid-crystalline cubic blue phases. I. Elastic theory.

Abstract

Light-scattering experiments reveal a strange behavior of thermal excitations in the liquid-crystalline cubic blue phases. To interpret the experiments we identify the hydrodynamical modes of the orientational pattern with pure displacements of the order parameter field. There are further modes that deform the orientational pattern, e.g., local rotations of the order parameter. An investigation of the elastic free energy shows that our identification of the hydrodynamical modes is valid as long as the wavelength is much smaller than the lattice constant. In this long-wavelength limit the additional deformation modes merely renormalize the eleastic constants of the displacement modes. We study the influence of two characteristic deformations, rotational and m=2 modes, and discuss the temperature and chirality behavior of the elastic constants. Also Keyes's [Phys. Rev. Lett. 65, 436 (1990)] idea of considering the phase transition to blue phase III as a melting of the cubic blue phases is critically reviewed.