Makiko Nonomura

Study on multicellular systems using a phase field model.

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell. The dynamics of each cell is based on the criteria for minimizing the surface area and retaining a certain volume. The effects of cell adhesion and excluded volume are also taken into account. The proposed model can be used to find the position of the membrane and/or the cortex of each cell without the need to adopt extra variables. This model is suitable for numerical simulations of a system having a large number of cells. The two-dimensional results of cell division, cell adhesion, rearrangement of a cell cluster, chemotaxis, and cell sorting as well as the three-dimensional results of cell clusters on the substrate are presented.

Kinetics of morphological transitions between mesophases

We investigate the dynamics of morphological transitions between mesoscopic structures on the basis of the model equation for microphase separation of block copolymers. The phase diagram for the modulated structures is obtained by means of the single-wavenumber approximation. In order to study the time evolution of domains, we derive a coupled set of equations for the amplitudes of the modulated structures in the weak-segregation regime. Simulations of the transitions between lamellar and hexagonal structures are carried out in two dimensions and the results are compared with the theory. Simulations in three dimensions are also presented.

Periodic Precipitation during Droplet Evaporation on a Substrate

We present a model of motion and evaporation of a droplet of a solute along with precipitation. It is demonstrated that the model can simulate the formation of stripe patterns parallel to the droplet edge resulting from periodic precipitation.

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.

Decay rate of concentration fluctuations in microemulsions

Using a variational method, we derive a set of equations of motion for ternary fluids with oil, water, and surfactant. The equations are written in terms of two local concentrations of the components and a local average velocity field. Choosing the free energy functional suitable for microemulsions, we study the dynamics of concentration fluctuations. The time-correlation function of the concentration fluctuations is shown to be generally given by two exponential functions due to the dynamic cross coupling between the two concentration fields. A formula of the stress tensor and the explicit form of the effective diffusion constant arising from the hydrodynamic interaction are also obtained.

Growth of Mesophases in Morphological Transitions

By using the model equation for microphase separation of block copolymers, we study dynamics of morphological transitions between mesophases. A coupled set of equations for the amplitudes of the modulated structures is derived in the weak segregation regime. This theory is applied to kinetics of the transition between a lamellar structure and a hexagonal structure and the results are compared with computer simulations in two dimensions.

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.

Morphology of microphase separated domains in rod-coil copolymer melts.

We investigate the morphology of microphase separated domains in 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 show in the weak segregation regime that the elastic energy in the rod-block rich domains affects drastically the structures of microphase separated domains. A coil-to-rod transition is incorporated into the model system to examine the elastic and anisotropic effects. The effects of the external electric field are also investigated to control the domain morphology.

Microphase separation in rod-coil copolymers

We investigate the morphology and kinetics of microphase separation of diblock copolymers where each chain consists of a rod-like block and a flexible block. Simplified phenomenological model systems are introduced, which are coarse-grained in terms of the local concentration of blocks and the local director field of the rod part. Computer simulations of this set of time–evolution equations in two dimensions show that existence of the rod blocks drastically affects the structures of microphase-separated domains due to the elastic energy in the rod-block-rich domains.