Kohtaro Yamada

Formation and stability of double gyroid in microphase-separated diblock copolymers

We investigate the morphology and kinetics of microphase separation of diblock copolymers by means of a mode expansion method. In a weak segregation limit, we employ two-wavenumber approximation to study the formation and stability of a double gyroid structure and derive the phase diagram of the microphase separated states. We have studied the kinetics of structural transitions due to temperature change by solving the coupled set of amplitude equations for the fundamental modes. We focus our attention on the morphological evolution from a double gyroid to a lamellar structure and to a hexagonal structure.

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.

Fluoride ion dynamics and relaxation in KSn2F5 studied by 19F nuclear magnetic resonance and impedance spectroscopy

Ion dynamics in the two-dimensional fluoride ion conductor KSn2F5 have been studied by 19F nuclear magnetic resonance (NMR) and impedance spectroscopy. The electrical relaxation behaviour of the investigated material is represented in the conductivity and electric modulus formalisms. The values of the dc conductivity and the hopping frequency of mobile ions and their respective activation energies are estimated from the analysis of the conductivity spectra using Almond–West formalism. The activation energies for conduction and ion hopping processes are almost identical, with values of 0.53 and 0.54 eV, respectively, suggesting that the concentration of charge carriers is independent of temperature. The Roling scaling approach to the conductivity spectra is applied in order to gain insight into the temperature dependence of the relaxation mechanism. The scaling law successfully collapses the conductivity spectra into a single curve, indicating a temperature-independent relaxation mechanism. Moreover, chemical exchange simulation of the 19F NMR spectra is introduced. The discrepancy between the values of the activation energies deduced from the electrical and NMR experiments are discussed according to Ngais coupling model.

Interface between Lamellar and Gyroid Structures in Diblock Copolymer Melts

We investigate the properties of a planer interface separating a lamellar structure and a gyroid structure in AB-type diblock copolymers. Depending on the relative orientation between lamellar and interface planes, we find that there are three different structures of an interface. Motion of an interface invading the unstable state is also studied numerically.

Microphase separation in rod–coil copolymers

We investigate the morphology and kinetics of microphase separation in rod–coil diblock copolymers where each chain consists of a stiff rod block and a flexible coil block. A simplified phenomenological model system is introduced, which is coarse grained in terms of the local concentration difference between the two blocks and the local director field of the rod part. Computer simulations of this set of time-evolution equations in two dimensions reveal that the elastic energy in the rod-block-rich domains affects drastically the domain structures formed in the course of microphase separation. The effects of the external electric field are investigated to examine the domain stability and control the domain morphology. Our recent study of morphological transitions in three dimensions for coil–coil copolymers is also briefly described.

Metastable and unstable structures in microphase separated diblock copolymers

We investigate possible intermediate structures in the process of microphase separation in diblock copolymers. By employing the two-mode expansion valid in the weak-segregation regime, we have found that the Fddd structure and diamond structure of interconnected domains can be metastable whereas the hexagonally perforated lamellar structure and FCC structure exist as a saddle point of the free energy landscape and hence these are unstable.

Most stable patterns among three-dimensional Turing patterns

It is known that Turing systems in two dimensions produce spotted, striped, and labyrinthine patterns. In three dimensions, a greater variety of patterns is possible. By numerical simulation of the FitzHugh-Nagumo type of reaction-diffusion system, we have obtained not only lamellar, hexagonal and spherical structures (BCC and FCC) but also gyroid, Fddd, and perforated lamellar structures. The domains of these three structures constitute interconnected regular networks, a characteristic occurring in three dimensions. Moreover, we derive the Lyapunov functional by reducing the system, and we evaluate this functional by introducing the asymptotic solutions of each structure by the mode-expansion method and direct simulation of the time evolution equation.