Monte Carlo simulations of phase separation in chemically reactive binary mixtures

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.

Effect of hydrodynamic interactions on the evolution of chemically reactive ternary mixtures

We investigate the structural evolution of an A/B/C ternary mixture in which the A and B components can undergo a reversible chemical reaction to form C. We developed a lattice Boltzmann model for this ternary mixture that allows us to capture both the reaction kinetics and the hydrodynamic interactions within the system. We use this model to study a specific reactive mixture in which C acts as a surfactant, i.e., the formation of C at the A/B interface decreases the interfacial tension between the A and B domains. We found that the dynamics of the system is different for fluids in the diffusive and viscous regimes. In the diffusive regime, the formation of a layer of C at the interface leads to a freezing of the structural evolution in the fluid; the values of the reaction rate constants determine the characteristic domain size in the system. In the viscous regime, where hydrodynamic interactions are important, interfacial reactions cause a slowing down of the domain growth, but do not arrest the evolution of the mixture. The results provide guidelines for controlling the morphology of this complex ternary fluid.

Fast growth in phase-separating A-B-copolymer ternary mixtures with a chemical reaction

We study the dynamics of phase separation of a binary A-B- polymer mixture with copolymer C, which is produced by the reaction of two counterpart reactive polymers A and B at the interface via the chemical reaction A+B right harpoon over left harpoon C. For low interfacial energy between the A and B phases, where the copolymer prefers to locate at interfaces, we show that the chemical reaction accelerates the phase separation of the system dramatically, because the backward reaction always drives the creation of immiscible A and B pairs at interfaces, which speed up the phase separation of the system, while the forward reaction process becomes more and more difficult as the interfaces are gradually saturated by copolymers. We also indicate that for a fixed chemical reaction rate constant, as the initial concentration of the copolymers increases, the domain growth at the late stage is speeded up as a result of the backward chemical reaction. However, when the interfacial energy is high, both forward and backward reactions coexist due to the occurrence of unsaturated interfaces, but the relative strength of reaction rates has no appreciable effect on domain growth during spinodal decomposition, because the interfacial energy dominates phase separation.

Ordering of the lamellar phase under a shear flow

The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free energy and the evolution follows a convection-diffusion equation. Lamellas order preferentially with the normal along the vorticity direction. Typical lengths grow as gamma t(5/4) (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3.

Influence of extended dynamics on phase transitions in a driven lattice gas

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transition in a driven lattice gas with nearest-neighbor exclusion on a square lattice. A slight extension of the microscopic dynamics with allowing the next-nearest-neighbor hops results in dramatic changes. Instead of the phase separation into high- and low-density regions in the stationary state the system exhibits a continuous transition belonging to the Ising universality class for any driving. The relevant features of the phase diagram are reproduced by an improved mean-field analysis.

Dynamics of spinodal decomposition in finite-lifetime systems: Nonlinear statistical theory based on a coarse-grained lattice-gas model

We study theoretically dynamics of the spinodal decomposition in finite-lifetime systems to clarify effects of the interparticle interactions beyond the Ginzburg-Landau-Wilson phenomenology. Our theory is based on the coarse-grained Hamiltonian derived from the interacting lattice-gas model with a finite lifetime. The information of a system is reduced to closed-form coupled integrodifferential equations for the single-point distribution function and the dynamical structure factor. These equations involve explicitly the interparticle interactions. The finite lifetime prevents the phase separation and the order formation in the cw creation case; domains cannot grow to be larger than an asymptotic characteristic size [k(max)(t --> infinity)](-1). Power-law dependence of k(max)(t --> infinity) on the interparticle interaction and the particle lifetime is also found numerically. The finite lifetime prevents the phase separation, i.e., the lower critical wave number k((1))(c) appears and domains of size larger than [k((1))(c)](-1) cannot grow.

Reply to "Comment on 'Surface restructuring, kinetic oscillations, and chaos in heterogeneous catalytic reactions' "

In my numeration, the criticism of my simulations of kinetic oscillations in NO reduction by H2 on Pt(100) [V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999)] by Kuzovkov, Kortlüke, and von Niessen [preceding paper, Phys. Rev. 63, 023101 (2001)] contains 19 comments. I show that four comments are irrelevant. The other 15 comments are wrong, because they either contradict the basic principles of the theory of phase transitions, Monte Carlo simulations, and catalytic chemistry or ignore numerous experimental data on adsorbate-induced restructuring of the Pt(100) surface.

Simulation of enzymatic cellular reactions complicated by phase separation

We present two-dimensional Monte Carlo simulations of enzymatic cellular reaction occurring via the Michaelis-Menten scheme in the case of attractive interactions between the reaction products. The model employed predicts phase separation in the cell provided that the reaction is relatively fast. The shape of the corresponding patterns varies from a few separate islands to a large patch located in the center of the cell. The fluctuations of the reaction rate during such regimes are found to be much higher than those predicted by the Poissonian distribution.

Wetting-driven structure formation of a binary mixture in the presence of a mobile particle pinning potential

We investigate the pattern formation on the solid substrate of phase-separating films containing mobile wetting particles with a preferential attraction for one component of the mixtures. The presence of mobile particles under the surface-particle interaction modulation breaks the isotropy of the bulk phase-separating process, leading to the formation of orientational structure due to the interplay between phase separation and wetting particle ordering under a modulated pinning potential at the late stage. Simulations suggest that the phase-separation morphology can be changed through the adjustment of the wettable-phase-particle interaction and the surface-particle interaction. It provides some important insights into this "wetting-directed spinodal decomposition."

Phase transitions and steady-state microstructures in a two-temperature lattice-gas model with mobile active impurities

The nonequilibrium, steady-state phase transitions and the structure of the different phases of a two-dimensional system with two thermodynamic temperatures are studied via a simple lattice-gas model with mobile active impurities ("hot/cold spots") whose activity is controlled by an external drive. The properties of the model are calculated by Monte Carlo computer-simulation techniques. The two temperatures and the external drive on the system lead to a rich phase diagram including regions of microstructured phases in addition to macroscopically ordered (phase-separated) and disordered phases. Depending on the temperatures, microstructured phases of both lamellar and droplet symmetry arise, described by a length scale that is determined by the characteristic temperature controlling the diffusive motion of the active impurities.

Compositional patterning in systems driven by competing dynamics Of different length scale

We study an alloy system where short-ranged, thermally driven diffusion competes with externally imposed, finite-ranged, athermal atomic exchanges, as is the case in alloys under irradiation. Using a Cahn-Hilliard-type approach, we show that when the range of these exchanges exceeds a critical value labyrinthine concentration patterns at a mesoscopic scale can be stabilized. Furthermore, these steady-state patterns appear only for a window of the frequency of forced exchanges. Our results suggest that ion beams may provide a novel route to stabilize and tune the size of nanoscale structural features in materials.

Stationary state in a two-temperature model with competing dynamics

A two-dimensional half-filled lattice gas model with nearest-neighbor attractive interaction is studied where particles are coupled to two thermal baths at different temperatures T1 and T2. The hopping of particles is governed by the heat bath at temperature T1 with probability p and the other heat bath (T2) with probability 1-p independently of the hopping direction. On a square lattice the vertical and horizontal interfaces become unstable while interfaces are stable in the diagonal directions. As a consequence, particles condense into a tilted square in the novel ordered state. The p dependence of the resulting nonequilibrium stationary state is studied by a Monte Carlo simulation and dynamical mean-field approximation as well.

Steady-state compartmentalization of lipid membranes by active proteins

Using a simple microscopic model of lipid-protein interactions, based on the hydrophobic matching principle, we study some generic aspects of lipid-membrane compartmentalization controlled by a dispersion of active integral membrane proteins. The activity of the proteins is simulated by conformational excitations governed by an external drive, and the deexcitation is controlled by interaction of the protein with its lipid surroundings. In response to the flux of energy into the proteins from the environment and the subsequent dissipation of energy into the lipid bilayer, the lipid-protein assembly reorganizes into a steady-state structure with a typical length scale determined by the strength of the external drive. In the specific case of a mixed dimyristoylphosphatidylcholine-distearoylphosphatidylcholine bilayer in the gel-fluid coexistence region, it is shown explicitly by computer simulation that the activity of an integral membrane protein can lead to a compartmentalization of the lipid-bilayer membrane. The compartmentalization is related to the dynamical process of phase separation and lipid domain formation.