Spinodal decomposition in 3-space

Hydrodynamic coarsening in striped pattern formation with a conservation law

We observed in numerical simulations that the interaction of striped-pattern-forming instability and a neutrally stable zero mode induces patterns of domains of upflow hexagons coexisting with domains of downflow hexagons. They appear only when hydrodynamic flow is present.

Orientational order transition of the striped microphase structure of a copolymer-homopolymer mixture under oscillatory particles

Based on the three-order-parameter model, we investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-homopolymer mixtures in the presence of periodic oscillatory particles. Under suitable conditions, although the macrophase separation of a system is almost isotropic, the microphase separation of the system will be significantly perturbed by the oscillatory field, and composition fluctuations are suppressed anisotropically. The isotropy of the microphase will be broken up. By changing the oscillatory amplitude and frequency, we observe the orientational order transition of a striped microphase structure from the isotropic state to a state parallel to the oscillatory direction, and from the parallel state to a state perpendicular to the oscillatory direction. We examine, in detail, the microstructure and orientational order parameter as well as the domain size in the process of orientational order transition under the oscillatory field. We study also how the microphase structure changes with the composition ratio of homopolymers and copolymers in mixtures. The results suggest that our model system may provide a simple way to realize orientational order transition of soft materials.

Long-range ordered structures in diblock copolymer melts induced by combined external fields

The structure of diblock copolymer melts under a single external electric or shear field, as well as under combined orthogonal external fields was investigated using a cell dynamic system. The phase structure was determined by coupling the effects of the external fields with the original structure of the bulk free of external fields. The single electric or shear field generated long-range cylinders in asymmetric A4mB6m diblock copolymers and distorted lamellae in symmetric A5mB5m diblock copolymers. Successive orthogonal shear followed by an electric external field generated long-range lamellae in symmetrical A5mB5m systems. However, the simultaneous orthogonal electric and shear fields could more easily form long-range lamellae than the sequential orthogonal fields. The dynamical processes in diblock copolymer melts under orthogonal fields have been also examined.

Phase separation of a polymer blend driven by oscillating particles

We study the possible formation of ordered structures of a binary polymer blend by introducing mobile particles in a periodically oscillating driving field. The particles which have a preferential attraction to one of the immiscible phases, will significantly perturb the phase separation of the system and breakup the isotropy of the system, so that some interesting structures such as lamellar and cylinder phases are observed by appropriate selection of the simulation parameters. We examine in detail the dependence of formed morphology and domain size on the oscillating fields, the relative composition of mixtures, the diffusion coefficient, and quench depth, and then discuss how to realize stable and highly ordered structures.

Simulating the morphology and mechanical properties of filled diblock copolymers

We couple a morphological study of a mixture of diblock copolymers and spherical nanoparticles with a micromechanical simulation to determine how the spatial distribution of the particles affects the mechanical behavior of the composite. The morphological studies are conducted through a hybrid technique, which combines a Cahn-Hilliard (CH) theory for the diblocks and a Brownian dynamics (BD) for the particles. Through these "CH-BD" calculations, we obtain the late-stage morphology of the diblock-particle mixtures. The output of this CH-BD model serves as the input to the lattice spring model (LSM), which consists of a three-dimensional network of springs. In particular, the location of the different phases is mapped onto the LSM lattice and the appropriate force constants are assigned to the LSM bonds. A stress is applied to the LSM lattice, and we calculate the local strain fields and overall elastic response of the material. We find that the confinement of nanoparticles within a given domain of a bicontinous diblock mesophase causes the particles to percolate and form essentially a rigid backbone throughout the material. This continuous distribution of fillers significantly increases the reinforcement efficiency of the nanoparticles and dramatically increases the Young's modulus of the material. By integrating the morphological and mechanical models, we can isolate how modifications in physical characteristics of the particles and diblocks affect both the structure of the mixture and the macroscopic behavior of the composite. Thus, we can establish how choices made in the components affect the ultimate performance of the material.

Competition of spiral-defect chaos and rolls in Rayleigh-Bénard convection under shear flow

Computer simulations of domain coarsening of Rayleigh-Bénard convective patterns under horizontal shear flow are carried out. The model calculations reported here explicitly include the hydrodynamic interaction of the order parameter field and provide a description of the spiral-defect chaos which competes with the roll pattern. We observe shear banding at moderate strain rates.

Effects of macromolecular crowding on protein folding and aggregation studied by density functional theory: dynamics

Inside the living cell is inherently crowded with proteins and other macromolecules. Thus, it is indispensable to take into account various interactions between the protein and other macromolecules for thorough understanding of protein functions in cellular contexts. Here we focus on the excluded volume interaction imposed on the protein by surrounding macromolecules or "crowding agents." We have presented a theoretical framework for describing equilibrium properties of proteins in crowded solutions [A. R. Kinjo and S. Takada, Phys. Rev. E (to be published)]. In the present paper, we extend the theory to describe nonequilibrium properties of proteins in crowded solutions. Dynamics simulations exhibit qualitatively different morphologies depending on the aggregating conditions, and it was found that macromolecular crowding accelerates the onset of aggregation while stabilizing the native protein in the quasiuniform phase before the onset of aggregation. It is also observed, however, that the aggregation may be kinetically inhibited in highly crowded conditions. The effects of crowding on folding and unfolding of proteins are also examined, and the results suggest that fast folding is an important factor in preventing aggregation of denatured proteins.

Hydrodynamic interactions in ordering process of two-dimensional quenched block copolymers

The hydrodynamic coarsening of microphase separation in two-dimensional diblock copolymers is studied using numerical simulations. Results for symmetric and asymmetric block copolymers are compared. In contrast to the formation of the hexagonal phase where hydrodynamic flow appears not to be effective in enhancing domain coarsening, the late-time evolution of the lamellar phase proceeds faster, thus leading to a different power-law scaling with the addition of coupling of the velocity field to the order parameter.

Renormalization group and perfect operators for stochastic differential equations

We develop renormalization group (RG) methods for solving partial and stochastic differential equations on coarse meshes. RG transformations are used to calculate the precise effect of small-scale dynamics on the dynamics at the mesh size. The fixed point of these transformations yields a perfect operator: an exact representation of physical observables on the mesh scale with minimal lattice artifacts. We apply the formalism to simple nonlinear models of critical dynamics, and show how the method leads to an improvement in the computational performance of Monte Carlo methods.

Crossover from the hydrodynamic regime to the thermal fluctuation regime in a two-dimensional phase-separating binary fluid containing surfactants

Extensive simulations were carried out to investigate the crossover between the hydrodynamic regime at intermediate stage and the thermal fluctuation regime at late stage in a phase-separating binary fluid/surfactant system in two dimensions. The existence of the crossover and its dependence on the surfactant concentration were analyzed using Kawasaki and Ohta's interface kinetic equation [Physica A 118, 175 (1983)]. The analysis showed that there should exist a critical surfactant concentration, above which thermal fluctuations dominate phase separation at all times. Simulations suggested that the crossover exists and the hydrodynamic regime shrinks when surfactant concentration increases. Simulations also demonstrated that the trapped surfactants seen in a previous study [Phys. Rev. E 59, 2109 (1999)] can remain trapped for a time much longer than the time needed to form well segregated domains, in spite of the presence of significant thermal fluctuations.

Hierarchical model in multiphase flow

A hierarchical model for two-phase flow is constructed. The model has two layered systems one corresponding to the macroscopic hydrodynamics described by the Navier-Stokes equation and the other to the interfacial dynamics described by the Cahn-Hilliard-type equation. Numerical simulations in some simple cases are carried out to examine the validity of the model. As an application of the model simulations of two colliding droplets under shear flow are presented.

Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions

We investigate the domain growth and phase separation of hydrodynamically correct binary immiscible fluids of differing viscosity as a function of minority phase concentration in both two and three spatial dimensions using dissipative particle dynamics. We also examine the behavior of equal-viscosity fluids and compare our results to similar lattice-gas simulations in two dimensions.

Two-dimensional model of phase segregation in liquid binary mixtures

The hydrodynamic effects on the late stage kinetics of phase separation in liquid mixtures is studied using the model H. Mass and momentum transport are coupled via a nonequilibrium body force, which is proportional to the Peclet number alpha, i.e., the ratio between convective and diffusive molar fluxes. Numerical simulations based on this theoretical model show that phase separation in low viscosity, liquid binary mixtures is mostly driven by convection, thereby explaining the experimental findings that the process is fast, with the typical size of single-phase domains increasing linearly with time. However, as soon as sharp interfaces form, the linear growth regime reaches an end, and the process appears to be driven by diffusion, although the condition of local equilibrium is not reached. During this stage, the typical size of the nucleating drops increases like t(n), where 1/3< n <1/2, depending on the value of the Peclet number. As the Peclet number increases, the transition between convection- and diffusion-driven regimes occurs at larger times, and therefore for larger sizes of the nucleating drops.

Evolution of speckle during spinodal decomposition

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time tau as R=[Btau](n) with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector k can be collapsed onto a scaling function Cov(deltat,t), where deltat=k(1/n)B(tau(2)-tau(1)) and t=k(1/n)B(tau(1)+tau(2))/2. Both analytically and numerically, the covariance is found to depend on deltat only through deltat/t in the small-t limit and deltat/t (1-n) in the large-t limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large t. In addition, the two-time, two-point order-parameter correlation function is found to scale as C(r/(B(n)sqaureroot[tau1(2n)+tau2(2n)]),tau1/tau2), even for quite large distances r. The asymptotic power-law exponent for the autocorrelation function is found to be lambda approximately 4.47, violating an upper bound conjectured by Fisher and Huse.