Theory of phase transitions in liquid crystals and plastic crystals

The properties of the layered, or smectic, liquid crystals are explained in terms of progressive freezing-out of rotational and translational degrees of freedom within each smectic plane. McMillan's dipole-dipole interaction model is extended to include intermolecular repulsions. In the self-consistent field approximation there are three ordered phases: the smectic C phase in which molecules are rotationally ordered but free to translate randomly; the smectic B phase in which molecules rotate freely around their long molecular axes but are positioned on a two dimensional hexagonal lattice; and the smectlc H phase which has both rotational and hexagonal translational order. By considering both the intermolecular dipole-dipole and intermolecular phenyl or benzene group interactions the properties of the phases with two dimensional hexagonal lattices are discussed. The smectic H phase results from ordering of the dipoles. We also get a smectic E phase with a herringbone structure resulting from ordering of the phenyl groups, and a smectic G phase resulting from order of both dipoles and phenyl groups. A Landau or continuum theory of the orientational phase transitions in crystalline methane is derived on the basis of molecular and lattice symmetry arguments. Coupling of the orientational order parameter to lattice distortions via the strain tensor is shown to make the methane J -methane II transition first order in this classical approximation. The symmetry breaking at a (001) surface of methane I is shown to result in (i) tetragonal surface distortions, (ii) rotational ordering on the surface, and (iii) temperature dependent surface phonon modes. Orientational fluctuations in the disordered methane I phase are briefly discussed.U of I OnlyThesi