Koji Okano

Concentration fluctuation of stiff polymers. II. Dynamical structure factor of rod‐like polymers in the isotropic phase

The dynamical structure factor of the solution of rod‐like polymers is calculated by using a newly proposed kinetic equation. The initial decay rate of the structure factor is obtained as a power series of the scattering vector k. It is found that (i) the coefficient of k2, which gives the cooperative diffusion constant, increases with concentration due to the excluded volume of rod and (ii) the coefficient of k4 changes sign from positive to negative. These results agree qualitatively with experiments.

Concentration fluctuation of stiff polymers. III. Spinodal decomposition

We discuss the dynamics of the formation of liquid crystalline phase of rod‐like polymer solutions, particularly the behavior of spinodal decomposition which should be observed when the system is suddenly brought into a thermodynamically unstable region. The growth rate of the concentration fluctuation is calculated as a function of the wave number. It is shown that these growth rates are governed by the translational motion, not the rotational motion. The dynamical structure factor in the isotropic phase is also calculated.

Concentration fluctuation of stiff polymers. I. Static structure factor

The static structure factor g(k) of the concentrated solution of stiff polymers is calculated based on the generalized random phase approximation (RPA) which accounts for the nematic interaction (i.e., the interaction causing the nematic phase of stiff polymers) between the segments. The structure factor is obtained in the form of power series expansion with respect to k. The result is: (i) the correlation length ξ is independent of the nematic interaction, and is given by the conventional RPA; (ii) the sign of the coefficient of k4 changes from positive to negative as the nematic interaction is increased; and (iii) the structure factor of rigid rod, which can be calculated exactly, shows no anomaly below the critical concentration c*, but suddenly shows anomaly above c*.

Diffusion coefficients of interacting Brownian particles

Starting from a N‐particle diffusion equation, the effective particle (self‐) and concentration diffusion coefficients of interacting Brownian particles are studied theoretically. These two diffusion coefficients defined by distinct ways are different for interacting systems. By taking into account both potential and hydrodynamic interactions, the expression for the frequency‐dependent particle diffusion coefficient exact to linear order in number density is derived. Detailed calculations of both diffusion coefficients are performed for model systems of hard spheres with a repulsive or an attractive long‐range potential. The effects of potential and hydrodynamic interactions on these two diffusion coefficients are clarified. The velocity autocorrelation function is also calculated and non‐Markovian behaviors are discussed.

van der Waals‐Lifshitz forces between anisotropic ellipsoidal particles

van der Walls‐Lifshitz forces between an ellipsoidal particle and a dielectric wall as well as between two ellipsoidal particles suspended in a liquid are calculated on the basis of the theory of McLachlan. The materials constituting the ellipsoids may be anisotropic. It is assumed, however, that in each ellipsoid the principal axes of the tensor of dielectric permeability coincide with those of the ellipsoid. The obtained formulas include those for spheroids by Kihara and Honda as well as those for spheres by Dzyaloshinskii, Lifshitz and Pitaevskii as particular cases. The variations of the free energies of interaction with respect to the mutual orientations of the interacting bodies are discussed. The three‐body forces among three ellipsoids as well as among two ellipsoids and a wall are also calculated.

Dynamic properties of concentrated suspensions of charged polystyrene spheres.

Ordered structure formation of charged polystyrene spheres was studied by measuring the order-disorder phase diagrams as well as the mechanical properties. The phase diagrams indicate that the ordering of polystyrene spheres obeys Lindemanns law of crystal melting, in which the Lindemanns parameter is about 5%. The rigidity of about 10(3) dyn/cm(2) was observed in the ordered suspension of polystyrene spheres as measured by a torsional quartz crystal method. The steady flow properties of suspensions of polystyrene spheres showed a remarkable change from a Bingham body to a Newtonian liquid at the transition point. The limit of elasticity in the ordered phase was about 1 dyn/cm(2). The viscosity in the disordered phase was well explained by the free volume theory of liquids. It is concluded from these facts that the ordered phase of polystyrene spheres is a real crystal whereas the disordered phase is a liquid. Properties of ordered structures in biological systems are also discussed.

Theory of anomalous ultrasonic absorption and dispersion of nematic liquid crystals just above the clearing point

Abstract The dynamic heat capacity of nematic liquid crystals just above the clearing point is calculated as an extension of our previous theory of static heat capacity. The present theory explains semi-quantitatively the available experimental results of anomalous ultrasonic absorption and dispersion.

Ultrasonic measurements of two-component lipid bilayer suspensions

Two-component lipid bilayers of dipalmitoylphosphatidylcholine and dimyristoylphosphatidylcholine were studied by measuring ultrasonic velocity and absorption at 3 MHz. The phase diagram of the two-component lipid bilayers is discussed based upon the transition anomalies of the ultrasonic velocity as well as absorption, and it is suggested that this binary system has two critical points. The bulk modulus of lipid bilayers was determined from the ultrasonic velocity to be (2.2-3.0) x 10(10) dyne/cm2, whereas the bulk viscosity calculated from the absorption was 10-20 P except for the transition regions.

A theory of the anomalous heat capacity and thermal expansion of nematic liquid crystals above the clearing point

Abstract the anomalous part of the specific heat capacity and hte isobaric thermal expansion coefficient of nematic liquid crystals above the transition point are calculated on the basis of the continuum fluctuation theory of de Gennes.

Anomalous Ultrasonic Absorption and Dispersion of Nematic Liquid Crystals near the Clearing Point

The attenuation coefficient of longitudinal ultrasonic waves in the nematic-isotropic phase transition regions of liquid crystals has been measured as a function of both temperature and frequency. A sharp maximum is observed in the attenuation coefficient at the phase transition temperature Tc. The temperature dependence of the velocity has also been measured at 2 MHz, and a sharp minimum is observed at Tc. The anomalous changes of the ultrasonic propagation properties in the nematic phase near Tc are analysed and discussed by a phenomenological treatment based on the Landau-Khalatonikov theory of critical slowing down. On the other hand, behaviors in the isotropic phase near Tc are discussed in terms of the theory proposed recently by Imura and Okano. It is concluded that the anomalies are associated with the nematic-isotropic phase transition which is of first order even though it is nearly of second order.