Nematic order director fluctuations in cylindrical capillaries

Order director fluctuations in a nematic liquid crystal confined to cylindrical cavity are studied within the framework of the Frank elastic theory. In particular, eigenmodes of director fluctuations around the planar radial structure, characterized by a disclination line along the symmetry axis of the cylinder, are analyzed for K(11)not equal K(22)not equal K-33. The disclination line is modeled by a concentric cylindrical core; its relevant properties are described by radius, anchoring strength, and surface rotational viscosity. The eigenmodes turn out to have a peculiar phase-shifted geometrical character. The main features of the spectrum of fluctuations' eigenmodes, typical for the spectra of coupled excitations, are determined by the radial symmetry of the structure. The results of an eigenmode-based stability analysis with respect to the escape in the axial direction are in qualitative agreement with the phase diagram, obtained by comparison of the free energies of the planar and escaped radial structures.