4 – NMR of Liquid Crystals*

The properties of a particle undergoing circular rotational motion in an N-fold cosine potential is investigated in detail. The rate equation for the probability function is given and order parameters are defined. The self-correlation functions of cos nϕ and sin nϕ (ϕ is the azimuthal angle) are calculated. The neutron incoherent scattering law is derived. The elastic incoherent structure factor is calculated directly. The jump model among N equidistant sites and the continuous rotational diffusion model are found as limiting cases. The problem of a more general potential is also discussed.

Random motion of a uniaxial rotator in an N-fold cosine potential: Correlation functions and neutron incoherent scattering law

Article de synthese sur les phases smectiques de substances avec des molecules type bâtonnet en structure en couche. Les phases nematiques ne sont considerees que dans le contexte du polymorphisme

Polymorphism in Thermotropic Liquid Crystals

In order to elucidate the structure of methane solids in phase III, orientational orderings of molecules are studied on the basis of a model potential consisting of a crystalline field (one‐body potential), octopole–octopole type, octopole–hexadecapole type, and hexadecapole–hexadecapole type potentials, which are obtained through a multipole expansion of the sum of interatomic Lennard‐Jones type potentials. It is assumed that carbon atoms are fixed at sites of a fcc lattice, and that the orientational order has the period not larger than twice the lattice constant of the carbon fcc lattice. In the framework of classical molecular field approximation, we solve consistency equations for molecular fields, and examine stabilities of various solutions which branch off from phase I (disordered phase) or from phase II (partially ordered phase). To this end, Landau’s theorem on the phase transition of second order is extended such that it allows us to determine possible space groups for the lower temperature pha...

Theory of phase transitions in solid methanes. XII. Orientational order of molecules in phase III

Following a very brief historical review, x-ray diffraction by nematic and smectic liquid crystals is critically examined in terms of the data available and the structural models and molecular theories that have been proposed to explain it. Studiesof TBBA are used to illustrate some of the principal mesophases that have been distinguished. Other types of liquid crystals and their phase transitions are also briefly reviewed. This analysis shows that careful experimental work is still needed to decide the kinds of models that best describe the various types of mesophases that have been shown to exist.

X-Ray Diffraction by Liquid Crystals

The molecular theory of the smectic $B$ and $H$ phases is extended to the smectic $E$ and VI phases by including the phenyl-phenyl interaction in addition to the dipole-dipole potential used previously. This phenyl-phenyl interaction contains quadrupole-quradrupole, dispersive, and exchange terms. The possibility of both dipolar and "herringbone" order is considered in the self-consistent-field approximation. Four phases are found, all with a two-dimensional hexagonal lattice assumed: (1) a disordered phase (smectic $B$); (2) an oriented phase in which dipoles align (smectic $H$); (3) a herringbone phase with phenyl groups ordered (smectic $E$); (4) and a herringbone phase with both phenyl groups and dipoles ordered (smectic VI). In the phases with dipolar order the director is tilted with respect to the normal to the plane. The transitions vary in order. The temperature dependence of the order parameters, entropy, and specific heat are computed.

Molecular theory of the smectic E , H , and VI phases

Molecular order in the smectic E phase

An order parameter for orientational phase transitions in solid methane is obtained on the basis of molecular symmetry arguments. A Landau theory of the I-II transition at constant volume is proposed. Then coupling of the order parameter and the lattice strain tensor is introduced. In the case of light methane ${\mathrm{CH}}_{4}$, coupling to the lattice makes the I-II phase transition first order. It is suggested that these lattice effects are at least as important as crystalline field effects in the methane transition. Finally, applications to other plastic crystal phase transitions of molecules of symmetry ${T}_{d}$, ${C}_{3h}$, and ${D}_{3h}$ are mentioned.

Lattice distortions and phase transitions in crystalline methanes

Theory of angular-resolved photoemission at low energy and high atomic number: 1 T-TaS 2

Molecular and lattice symmetry effects on the order of plastic crystal-crystal phase transitions are discussed in the context of Landau theory.

R. Jay Meyer

Papers

Molecular theory of the smectic E , H , and VI phases

Molecular order in the smectic E phase

Lattice distortions and phase transitions in crystalline methanes

Theory of angular-resolved photoemission at low energy and high atomic number: 1 T-TaS 2

Symmetry Considerations for Plastic Crystal-Crystal Phase Transitions