Masashi Torikai

Free-energy functional method for inverse problem of self assembly

A new theoretical approach is described for the inverse self-assembly problem, i.e., the reconstruction of the interparticle interaction from a given structure. This theory is based on the variational principle for the functional that is constructed from a free energy functional in combination with Percuss approach [J. Percus, Phys. Rev. Lett. 8, 462 (1962)]. In this theory, the interparticle interaction potential for the given structure is obtained as the function that maximizes the functional. As test cases, the interparticle potentials for two-dimensional crystals, such as square, honeycomb, and kagome lattices, are predicted by this theory. The formation of each target lattice from an initial random particle configuration in Monte Carlo simulations with the predicted interparticle interaction indicates that the theory is successfully applied to the test cases.

Nematic Ordering of a Liquid Crystalline Homeotropic Cell

Nematic ordering in a very thin system under the homeotropic anchoring condition is studied in the framework of the Maier–Saupe model. The first order transition disappears and continuous change of phase occurs at the system with thickness smaller than a certain critical thickness. To study the mechanism of the continuous change of phase, nonuniformity due to the boundary effect is described in terms of an effective field which is conjugate to the order parameter, and behaviour of the system is analysed by observing loci of the effective fields on the phase diagram of the bulk. It is found that the continuous change is mediated by an unstable state; a metasteble high-temperature phase changes to a metastable low-temperature one continuously via an unstable phase between them. This mechanism is an analogue of the phenomenon occurring in a freely suspended film of a certain chiral smectic material.

A Change of Structure and Discrete Soliton at Smectic in an Electric Field

Phase transition from chiral smectic Cα phase ( ) to smectic C phase (SmC) driven by an electric field is studied from a standpoint of discrete soliton concept, while similar phenomenon occurring at a transition from chiral smectic C phase (SmC*) to SmC is characterized by a condensation of solitons of sine Gordon equation. As a pitch of without the field is very short, an equation describing a change of a helical structure is difference equation and the soliton excited at the phase transition should be a discrete type. It is shown that for the pitch larger than three layers, soliton density, which is identical to a wave number of the structure, decreases to zero making a devils staircase as the field is increased. Though the transition is a continuous type and an interaction between discrete solitons is repulsive like the case of SmC*, a range of the interaction is shorter than the one for the continuous solitons. On the other hand, for the pitch smaller than three, the wave number increases reaching a bi-layer structure as the field is increased, and finally at a critical field the bi-layer structure changes to the uniform SmC continuously. Three-layer structure is proved to be marginal at the -SmC transition.

Field Induced SmCα*-SmC Transition and Discrete Soliton Excitation

The helical structure of the chiral smectic Cα phase (SmCα*) is unwound by an electric field and a field induced SmCα*-smectic C phase transition occurs at a certain field strength, which is similar to the chiral smectic C phase (SmC*) where the transition is interpreted as a condensation of solitons. The pitch of SmCα* without the field is very short and the soliton excited at the phase transition should be a discrete type, in contrast with SmC* where the pitch is large enough and a continuum theory is applied. It is shown that the SmCα*-SmC transition is of the second order like the SmC*-SmC transition, while the interaction between discrete solitons is quite short range and the condensation process of solitons occurs drastically. The dependence of wave number of the helical structure on the field strength is possibly something like staircase. At high field region, discrete soliton lattices of short period become unstable showing fragile property.

Change of Order of Nematic Phase Transition in Uniaxially Anchored Systems

ABSTRACT Nematic phase transition with both uniaxial and biaxial order parameters is studied in the two kind of external fields where are conjugate to the order parameters, respectively. A global phase diagram on the fields versus temperature space is obtained in the mean field theory, which is similar topologically to the phase diagram of the three-state Potts in three dimension. From this phase diagram, the phase diagram of the system in the uniaxial field is derived, and the result is applied to the phase transition of the thin system anchored uniaxially, i.e., by the homeotropic and planer walls.

Isotropic, Nematic and Smectic A Phase Behaviour in a Fictitious Field

Phase behaviours of liquid crystals under external fields, conjugate to the nematic order and smectic order, are studied within the framework of mean field approximation developed by McMillan. It is found that phase diagrams, of temperature vs interaction parameter of smectic A order, show several topologically different types caused by the external fields. The influences of the field conjugate to the smectic A phase, which is fictitious field, are precisely discussed.

Symmetry of Nematic Phase and Oblique Axial Order

Nematic order is usually described by a uniaxial order parameter, or occasionally by a biaxial order parameter together with the uniaxial one, in a typical configuration. In a general case of a system exposed to two different types of external fields, e.g., an electric field and a magnetic field, an additional order parameter, here called an oblique axial order parameter, is shown to be necessary, in addition to the above order parameters, to describe transition phenomena of the system correctly. The symmetry of the phase with the triplet of the order parameters is discussed. Effect of the oblique axial order are demonstrated practically in two phenomena: (i) qualitative change of the phase transition when the oblique axial order is neglected; (ii) disappearance of phase transition between ordered phases with different ordering axes when an oblique axial field conjugate to the oblique axial order parameter exists.

Equation of State for Parallel Rigid Spherocylinders

The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto’s method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto’s original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto’s original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2.

On Discrete Soliton and Soliton Lattice at SmCα∗-SmC Transition Driven by an Electric Field

Unwinding process of Smectic Cα* phase (SmCα*) to smectic C phase (SmC) in an electric field looks similar to a transition from chiral smectic C phase (SmC*) to SmC which is interpreted as a soliton condensation. As a pitch of the helical structure is quite short in the former, a discrete description is required and the soliton accompanying with should be a discrete type, while in the latter, the soliton is a kink of sine-Gordon equation. Under the condition of constant tilt at SmCα*, it has been elucidated that for the helical pitch larger than four-layer the transition is second order and a wave number versus field relation makes a devils staircase. Here, a free energy curve for the wave number is proved to be non-differentiable at any rational wave number, monotonous and convex, corresponding to the devils staircase structure of the wave number. This non-analytic property contrasts with the case of continuous description in SmC*, where the free energy curve is analytic. In the framework of the present model, a change of apparent optical axis and switching current is calculated, which are compared with experimental results reported so far.

Molecular theoretic study of Freedericksz transition. Symmetry breaking of oblique axial order

Freedericksz transition, which is usually analyzed by an elastic theory, is studied on the basis of statistical mechanical ground, where nematics with positive dielectric anisotropy in homogeneous anchoring cell is exposed to an electric field in the direction of wall normal. In low temperature region, an oblique axial symmetry breaking occurs, which is nothing but the Freedericksz transition. In high temperature and high field region, biaxial nematic phase with principal axis parallel to the field direction at interior area of the system is proved to appear. A phase diagram on the field versus temperature plane is obtained and compared with the one at a bulk with common biaxial symmetry, where both of electric and magnetic fields are applied in directions perpendicular to each other. In the latter, no symmetry breaking occurs, in contrast with the former case above-mentioned, and the reason why this difference occurs is elucidated.