Akihiko Matsuyama

Theory of solvation‐induced reentrant coil–globule transition of an isolated polymer chain

This paper discusses the conformational phase change of an isolated polymer chain which is capable of forming physical bonds with solvent molecules. On the basis of the mean‐field theory of Flory type, we derive a formula for the temperature dependence of the expansion factor of the chain. Our theory takes account of the extra mixing entropy change induced by the solvation. We predict that the physical‐bond formation between polymer and solvent molecules causes a reentrant conformational change between coiled and globular state when temperature is varied. We also show that the polymer chain exhibits a sharp collapse near the Θ temperature as the temperature is increased to the lower critical solution temperature of the polymer solution. This behavior can be interpreted in terms of the breakup of the polymer–solvents complex. The result is compared with the observed coil–globule transition on poly (N‐isopropylacrylalmide) in water.

Phase diagrams of polymer dispersed liquid crystals

A simple model is introduced to describe liquid crystal transitions and phase separations in binary mixtures of a flexible polymer and a liquid crystal. By combining the McMillan theory for the smectic A phase of liquid crystals with the Flory–Huggins theory for the isotropic mixing of two components, we examine binodal and spinodal lines on the temperature-concentration plane. We predict the appearance of phase separations such as the smectic A-nematic, smectic A-isotropic, and smectic A-nematic-isotropic phase separations. We also find a tricritical point caused by the interference between a second-order liquid crystal transition and a phase separation.

Phase separations in liquid crystal-colloid mixtures

We present a mean-field theory to describe phase separations in mixtures of a nematic liquid crystal and a colloidal particle. The theory takes into account an orientational ordering of liquid crystals and a crystalline ordering of colloidal particles. We calculate phase diagrams on the temperature-concentration plane, depending on interactions between a liquid crystal and a colloidal surface and a coupling between nematic and crystalline ordering. We find various phase separation processes, such as a nematic-crystal phase separation and nematic-isotropic-crystal triple point. Inside binodal curves, we find new unstable and metastable regions which are important in phase ordering dynamics. We also find a stable nematic-crystalline (NC) phase, where colloidal particles dispersed in a nematic phase can form a crystalline structure. The coexistence between two NC phases with different concentrations can be appear though the coupling between nematic and crystalline ordering.

Theory of binary mixtures of a rodlike polymer and a liquid crystal

We present a mean field theory to describe phase separations in mixtures of a low molecular-weight-liquid crystalline (LC) molecule and a rigid-rodlike polymer (rod) such as carbon nanotubes (CNTs) and LC polymers. By taking into account two orientational order parameters of the rod and the LC, we find three nematic phases (N(0),N(1),N(2)) on the temperature-concentration plane, depending on the attractive or repulsive interactions between the rod and the LC. We discuss the phase behavior of the systems where the rod and the LC are oriented to be parallel or perpendicular with each other and find that the phase diagrams of the parallel alignment are different from that of the perpendicular one. We predict the appearances of a lower critical solution temperature (LCST) and an upper one, a tricritical point, a critical point, and the first- and the second-order nematic-isotropic phase transitions. The theory can qualitatively describe the phase diagram with a LCST observed in a rod/LC mixture. We also predict a variety of phase separations in CNT/LC mixtures.

Volume phase transitions of nematic gels under an external field

The effect of external (magnetic or electric) fields on the swelling of nematic gels dissolved in an isotropic solvent are discussed. We calculate the swelling ratio of the gel, orientational order parameter, and phase diagrams on a temperature–swelling ratio plane under an external field. For a weak external field, we find a first-order volume phase transition between two nematic gels with different orientational ordering. Upon increasing the strength of an external field, a critical point appears on the phase diagram. We also discuss the swelling of nematic gels as a function of the strength of an external field for various temperatures.

Nematic ordering-induced volume phase transitions of liquid crystalline gels

We present a mean field theory to describe swelling behaviors of a nematic gel immersed in a low molecular weight liquid crystal solvent under an external field such as magnetic and electric fields. We calculate the equilibrium concentration of the gel, orientational order parameters, and elongation of the gel. As a result of a nematic ordering between the gel and solvent inside the gel, the shape of the gel is discontinuously (or continuously) elongated with increasing the strength of the external field. We examine the condition for a nematic ordering-induced first- and second-order volume phase transition of the gel.

Phase separations in mixtures of a liquid crystal and a nanocolloidal particle

We present a mean field theory to describe phase separations in mixtures of a liquid crystal and a nanocolloidal particle. By taking into account a nematic, a smectic A ordering of the liquid crystal, and a crystalline ordering of the nanoparticle, we calculate the phase diagrams on the temperature-concentration plane. We predict various phase separations, such as a smectic A-crystal phase separation and a smectic A-isotropic-crystal triple point, etc., depending on the interactions between the liquid crystal and the colloidal surface. Inside binodal curves, we find new unstable and metastable regions, which are important in the phase ordering dynamics. We also find a crystalline ordering of the nanoparticles dispersed in a smectic A phase and a nematic phase. The cooperative phenomena between liquid-crystalline ordering and crystalline ordering induce a variety of phase diagrams.

MEAN FIELD THEORY FOR SOLUTIONS OF MAIN-CHAIN LIQUID CRYSTALLINE POLYMERS

A mean field theory is introduced to describe the nematic-isotropic phase transitions (NIT) in solutions of main-chain liquid crystalline polymers (MLCPs) which consist of rigid mesogens and spacers with various degrees of flexibility. The theory takes into account not only the nematic ordering of mesogens but also the partial ordering, or straightening, of spacer segments in the nematic phase. On the basis of the Onsager-type excluded volume interactions and the Maier–Saupe model for orientational dependent–attractive interactions between rigid segments, we derive the free energy for solutions of the MLCP. We find two different nematic phases: One is a weak nematic phase which is almost formed by the ordering of the mesogens. The other is a high nematic phase where the straightened segments on the spacers and the mesogens are highly ordered. The two different nematic phases and phase behaviors are discussed in the phase diagrams on the temperature-concentration plane.

Theory of polymer-dispersed cholesteric liquid crystals

A mean field theory is presented to describe cholesteric phases in mixtures of a polymer and a cholesteric liquid crystal. Taking into account an anisotropic coupling between a polymer and a liquid crystal, we examine the helical pitch, twist elastic constant, and phase separations. Analytical expressions of the helical pitch of a cholesteric phase and the twist elastic constant are derived as a function of the orientational order parameters of a polymer and a liquid crystal and two intermolecular interaction parameters. We also find isotropic-cholesteric, cholesteric-cholesteric phase separations, and polymer-induced cholesteric phase on the temperature-concentration plane. We demonstrate that an anisotropic coupling between a polymer and a liquid crystal can stabilize a cholesteric phase in the mixtures. Our theory can also apply to mixtures of a nematic liquid crystal and a chiral dopant. We discuss the helical twisting power, which depends on temperature, concentration, and orientational order parameters. It is shown that our theory can qualitatively explain experimental observations.

Mean Field Theory of Crystalline Ordering in Colloidal Solutions

A mean field model is introduced to describe phase separations and crystalline ordering in colloidal solutions. We introduce translational order parameters for crystalline ordering of cubic crystal...