Huzio Nakano

Nematic-Smectic Transition in an Aligned Rod System

The nematic-smectic transition in the system of completely aligned hard cylindrical rods is investigated, by making use of the method of symmetry breaking potential. In the second virial approximation the transition is found to occur in the 3-dimensional system but not in the 1- and 2-dimensional systems, in contrast with the result obtained by Wadati and Isihara that the 2-dimensional system also exhibits such a transition. It is shown that the transition is very like the second order one. A shape effect is also studied. Furthermore, by introducing an isotropic attractive intermolecular force, the dependence of the transition on the strength of that force as well as the length and diameter of the rod molecule is investigated.

Quantum Statistical-Mechanical Theory of Optical Activity

The expression for the electric current density induced in a system by an incident polarized beam is obtained on the basis of quantum statistical mechanical theory of linear response. It is expressed as a sum of time and space derivatives of the electric polarization and quadripole moment density and of the magnetization. In the case of the solution averaging over whole molecular orientations are applied. By solving the Maxwell equations with substitution of the averaged current density, what sort of polarized beam can travel through the solution is investigated. In the solution of randomly-oriented molecules the contribution from the quadripole moment density vanishes and the usual theory for the solution is attained. In the uniaxially symmetric case of molecular-orientation probability a linearly polarized beam travelling in the direction of the symmetry axis exhibits the optical rotation and circular dichroism, where the quadripole moment density contributes to the phenomena.

Statistical Theory of Cholesteric Ordering in Hard-Rod Fluids and Liquid Crystalline Properties of Polypeptide Solutions

A statistical theory of lyotropic cholesteric phase in the system of long coiled rod molecules is presented. Effects of molecular exclusion and of attractive intermolecular force are both taken into consideration. On the basis of the theoretical results, experiments on the cholesteric solutions of polypeptide are investigated, where use is made of the scaled particle theory on the fluid of hard rod molecules. It is thus found that the experimental dependences of cholesteric twisting power on temperature, concentration and molecular weight of the polymer and also the experimental curvature elasticity are explained satisfactorily.

Effect of Orientational Fluctuation on Nematic-Smectic A Transition in the System of Hard Rod Molecules

By applying the method of symmetry breaking potential to Zwanzigs three direction model for liquid crystal, the nematic-smectic as well as isotropic-nematic transitions are investigated. Particular attention is paid to the effect of orientational fluctuation on the nematic-smectic A transition. It is shown that the nematic-smectic A transition is reduced to the one of first order owing to that kind of fluctuation for the case of short molecule.

Molecular Statistical Theory of the Frank Elastic Constants of Liquid Crystals

The Frank elastic constants K 1, K 2, K 3 are calculated in the mean field approximation by assuming that the intermolecular force is the sum of hard rod repulsion (length L and width D) and Maier-...

Theory of Orientational Order in Chain Molecules —Phase Transitions in n-Alkanes and Lipid Membranes—

By assuming an attractive potential between molecules which depends on their orientations and configurations, an orientational phase transition accompanied with a configurational change of molecules are studied in mean field approximation. A “two state model”, in which only the state of “long” configuration causes the orientational order, is assumed. The phase transition temperature T c , the orientational order parameter S , the averaged extension of molecules, and the transition entropy are calculated as functions of the statistical weight of “long” configuration. The results are investigated with respect to the chain-length dependences. By analysing thermal data, the orientational order parameters adjacently below the transition temperature are estimated as S ∼0.95 for n-alkane crystals and as 0.7–0.8 for lipid membranes.

Phase Transitions in the Systems of Identical Rigid Molecules in Perfect Alignment-Relations of the Smectic A and Columnar Orderings in Liquid Crystals and the Crystalline Ordering to the Molecular Shape

The method of symmetry breaking potential is applied to the system of identical rigid molecules with simple typical shapes (rod with square cross-section, square plate and cube), which are perfectly aligned, to examine the occurrences of such various types of spatial ordering as in smectic, columnar and crystalline phases in relation to the molecular shape. A smectic A phase occurs in the system of rigid rod molecules much more easily than the close packed crystal structure does in the system of rigid sphere molecules. Columnar and crystalline phases do also similarly in the system of molecules of square plate and cube, respectively. It is also shown that the nematic-smectic A transition in the case of rigid rod molecules in perfect alignment is the second order one, in contrast with those in the others of typical first order transitions. The effect of orientational fluctuation is discussed in short.

On the Transition between Cholesteric and Nematic Phases in Magnetic Field

Abstract Singularities at the critical lines bounding the cholesteric and nematic phases on the magnetic field versus temperature plane are investigated. Critical exponents, α and γ, of the specific heat and magnetic susceptibility are found both unities. By regarding the inverse of pitch of the cholesteric structure as an order parameter, it is found that the exponents β and δ are zero and infinity, respectively, and these exponents satisfy the scaling relations, α + 2β + γ = 2 and α + β (δ + 1) = 2. In relation to the discommensurate charge density wave in layer structure materials, it is noted that the transition from the nematic to cholesteric phase occurring with the change of magnetic field and/or temperature is interpreted as a condensation process of solitons.

Faraday Rotation in a DMS Quantum Well

The present report concerns a theoretical study of the Faraday rotation in a quantum well system in a magnetic semiconductor; in particular, a (Cd, Mn)Te well confined by finite potential barriers of (Cd, Zn)Te. In this system, the oscillator strengths for right- and left-handed circularly polarized excitons increase as the width of the well is reduced, and the difference between them increases as well. On the other hand, the Zeeman shift decreases in comparison to the bulk value. It is shown that an enhancement of the Faraday rotation can occur in this system owing to the above difference in oscillator strength which increases to more than compensate for the reduction of the Zeeman shift.

Orientational Phase Transition in the System of Flexible Molecules

By assuming an attractive potential between molecules which depends on their relative orientations and respective molecular configurations, the phase transitions in the system of flexible molecules are studied in a mean field approximation. For simplicity, a two state model is adopted, where all configurations of a molecule are simply classified into “long” and “short” cases. It is found that the orientational transition is accompanied with a certain change in the molecular configuration for the case of long and flexible molecules (type I), whereas with a much smaller change in the case of short and rather rigid molecules (type II). In the intermediate case, transitions of the type I and II occur successively. Transitions observed in lipid membranes and in nematogenic homologous series can be understood on the basis of these analyses.