Mesoscopic simulation of phase behaviors and structures in an amphiphile-solvent system.

We have performed a three-dimensional simulation of mesoscopic structures in a mixture of AB amphiphilic molecule and C solvent by employing the density-functional theory under the conditions that (i) the size of the AB is much larger than C and (ii) the affinity between A and B is much larger than the affinity between B and C. First, we have calculated the free energy of five periodic structures, i.e., the lamellar phase, hexagonally packed cylinders, body-centered-cubic spheres, face-centered-cubic spheres, and gyroid phase for different sets of the concentration of AB (ϕ[over ¯]_{AB}) and the χ parameter (χ_{AC}). By comparing the free energies for these structures, the χ_{AC}-ϕ[over ¯]_{AB} phase diagram has been obtained. In addition to these periodic structures, it has been shown that nonperiodic structures such as spherical and rodlike micelles can be obtained although they might be metastable phase.

Turing patterns in three dimensions.

We investigate three-dimensional Turing patterns in two-component reaction diffusion systems. The FitzHugh-Nagumo equation, the Brusselator, and the Gray-Scott model are solved numerically in three dimensions. Several interconnected structures of domains as well as lamellar, hexagonal, and spherical domains are obtained as stable motionless equilibrium patterns. The relative stability of these structures is studied analytically based on the reduction approximation. The relation with the microphase-separated structures in block copolymers is also discussed.

Fddd structure in AB-type diblock copolymers.

It is well known that lamellar structure, hexagonal structure of cylinder domains, gyroid and body-centred cubic structure of spherical domains all exist as equilibrium structures in AB-type diblock copolymers. We shall show in the present letter that, in addition to the above four phases, there is another equilibrium phase, the so-called Fddd structure which is an interconnected but uniaxial structure. We confirm this conclusion by two different methods. One is the mode-expansion including a substantial number of modes. The other is direct simulations of the time-evolution equation in three dimensions.

Interconnected Turing patterns in three dimensions.

We study numerically the Turing pattern in three dimensions in a FitzHugh-Nagumo-type reaction-diffusion system. We have found that interconnected periodic domain structures such as a gyroid, Fddd, and perforated lamellar structures appear in three dimensions, which never exist in lower dimensions. The stability analysis of these structures is also performed by means of a mode expansion.