Chemically frozen phase separation in an adsorbed layer

Phase transitions affected by natural and forceful molecular interconversion

If a binary liquid mixture, composed of two alternative species with equal amounts, is quenched from a high temperature to a low temperature, below the critical point of demixing, then the mixture will phase separate through a process known as spinodal decomposition. However, if the two alternative species are allowed to interconvert, either naturally (e.g., the equilibrium interconversion of enantiomers) or forcefully (e.g., via an external source of energy or matter), then the process of phase separation may drastically change. In this case, depending on the nature of interconversion, two phenomena could be observed: either phase amplification, the growth of one phase at the expense of another stable phase, or microphase separation, the formation of nongrowing (steady-state) microphase domains. In this work, we phenomenologically generalize the Cahn–Hilliard theory of spinodal decomposition to include the molecular interconversion of species and describe the physical properties of systems undergoing either phase amplification or microphase separation. We apply the developed phenomenology to accurately describe the simulation results of three atomistic models that demonstrate phase amplification and/or microphase separation. We also discuss the application of our approach to phase transitions in polyamorphic liquids. Finally, we describe the effects of fluctuations of the order parameter in the critical region on phase amplification and microphase separation.

Spinodal decomposition of chemically reactive binary mixtures

We simulate the influence of a reversible isomerization reaction on the phase segregation process occurring after spinodal decomposition of a deeply quenched regular binary mixture, restricting attention to systems wherein material transport occurs solely by diffusion. Our theoretical approach follows a diffuse-interface model of partially miscible binary mixtures wherein the coupling between reaction and diffusion is addressed within the frame of nonequilibrium thermodynamics, leading to a linear dependence of the reaction rate on the chemical affinity. Ultimately, the rate for an elementary reaction depends on the local part of the chemical potential difference since reaction is an inherently local phenomenon. Based on two-dimensional simulation results, we express the competition between segregation and reaction as a function of the Damköhler number. For a phase-separating mixture with components having different physical properties, a skewed phase diagram leads, at large times, to a system converging to a single-phase equilibrium state, corresponding to the absolute minimum of the Gibbs free energy. This conclusion continues to hold for the critical phase separation of an ideally perfectly symmetric binary mixture, where the choice of final equilibrium state at large times depends on the initial mean concentration being slightly larger or less than the critical concentration.

Traveling waves and global oscillations triggered by attractive molecular interactions in an excitable system

During pattern formation in spatially extended systems, different mechanisms with different characteristic length scales, e.g., reaction-diffusion processes or molecular interactions, can be active. Such multiscale effects may generate new phenomena, which are not observed in systems where pattern formation occurs on a single scale. Here, we derive and analyze a reaction-diffusion model of the FitzHugh-Nagumo type with short-range attractive molecular interactions of the activator species. The model exhibits a wave instability. Simulations in one and two dimensions show traveling waves with a wavelength set by the parameters of the molecular interaction in the model. In two dimensions, simulations reveal a labyrinthine arrangement of the waves in systems with isotropic diffusion, whereas parallel bands of counterpropagating waves are formed in simulations of a model with anisotropic diffusion. The latter findings are in good qualitative agreement with experimental observation in the catalytic NO+H_{2} reaction on an anisotropic Rh(110) surface. In addition we have identified a transition regime in the simulations, where a short scale instability triggers global oscillations in an excitable regime.

Nonequilibrium patterns in phase-separating ternary membranes

We present a nonequilibrium approach for the study of a two-dimensional phase-separating ternary mixture. When the component that promotes phase separation is dynamically exchanged with the medium, the separation process is halted and actively maintained finite-size segregation domains appear in the system. In addition to this effect, already reported in our earlier work [J. Gómez, F. Sagués, and R. Reigada, Phys. Rev. E 77, 021907 (2008)], the use of a generic Ginzburg-Landau formalism and the inclusion of thermal fluctuations provide a more dynamic description of the resulting domain organization. Its size, shape, and stability properties are studied. Larger and more circular and stable domains are formed when decreasing the recycling rate, increasing the mobility of the exchanged component, and the mixture is quenched deeper. We expect this outcome to be of applicability in raft phenomenology in plasmatic cell membranes.

Nonequilibrium microstructures in reactive monolayers as soft matter systems

Chemical systems provide classical examples of nonequilibrium pattern formation. Reactions in weak aqueous solutions, such as the extensively investigated Belousov-Zhabotinsky reaction, demonstrate a rich variety of patterns, ranging from travelling fronts to rotating spiral waves and chemical turbulence. Pattern formation in such systems is based on interplay between the reactions and diffusion. Intrinsically, this puts a restriction on the minimum length scale of the developing structures, which cannot be shorter than the diffusion length of the reactants. However, much smaller nonequilibrium structures, with characteristic lengths reaching down to nanoscales, are also possible. They are found in reactive soft matter, where energetic interactions between molecules are present as well. In these systems, chemical reactions and diffusion interfere with phase transitions, yielding active, stationary or dynamic microstructures. Nonequilibrium soft-matter microstructures are of fundamental importance for biological cells and may have interesting engineering applications. In this Minireview, we focus on the microstructures found in reactive soft-matter monolayers at solid surfaces or liquid-air interfaces.

Mass transport of alkali metal with pulses in a surface reaction

It is shown that the pulses which develop in the NO+H2 reaction on an alkali promoted Rh(110) surface reaction can transport alkali metal. This leads to the accumulation of a substantial alkali-metal concentration in the collision area of pulse trains. Realistic simulations revealed that the effect is due to the strong energetic interactions of the alkali metal with coadsorbates, i.e., the attractive interaction with coadsorbed oxygen and the effectively repulsive interaction with coadsorbed nitrogen.

Diatom structures templated by phase-separated fluids

An experimentally motivated model is proposed for the formation of fluid-phase templates corresponding to the porous silica skeletons of diatoms, single-cell organisms found in marine and freshwater environments. It is shown that phase-separation processes on a planar surface may give rise to a quasi-static mold that could direct the deposition of condensing silica to form complex arrays of pores. Calculations show that appropriate fluid templates can be generated for a wide variety of diatom species. The results could be of some biological relevance, but the most significant advance may be the identification of a synthetic strategy for generating complex porous architectures from simple, amorphous materials.

Formation of Regular Surface-Supported Mesostructures with Periodicity Controlled by Chemical Reaction Rate

We report a LEEM and XPEEM study of the formation of a variety of stationary two-dimensional metallic and oxygen structures in Au and Au + Pd adlayers on Rh(110) during water formation reaction. They result from chemically frozen spinodal decomposition and are created, preserved, or reversibly modified by tuning the reaction conditions. The wavelength of lamellar structures obtained at intermediate metal coverage is found to obey a power scaling law with respect to the reaction rate.

Nonequilibrium patterns and shape fluctuations in reactive membranes

A simple kinetic model of a two-component deformable and reactive bilayer is presented. The two differently shaped components are interconverted by a nonequilibrium reaction, and a phenomenological coupling between local composition and curvature is proposed. When the two components are not miscible, linear stability analysis predicts, and numerical simulations show, the formation of stationary nonequilibrium composition/curvature patterns whose typical size is determined by the reactive process. For miscible components, a linearization of the dynamic equations is performed in order to evaluate the correlation function for shape fluctuations from which the behavior of these systems in micropipet aspiration experiments can be predicted.

Promoter-induced reactive phase separation in surface reactions

Promoters are adsorbed mobile species which do not directly participate in a catalytic surface reaction, but can influence its rate. Often, they are characterized by strong attractive interactions with one of the reactants. We show that these conditions lead to a Turing instability of the uniform state and to the formation of reaction-induced periodic concentration patterns. Experimentally such patterns are observed in catalytic water formation on a Rh(110) surface in the presence of coadsorbed potassium.

Nonequilibrium orientational patterns in two-component Langmuir monolayers

A model of a phase-separating two-component Langmuir monolayer in the presence of a photoinduced reaction interconverting two components is formulated. An interplay between phase separation, orientational ordering, and reaction is found to lead to a variety of nonequilibrium self-organized patterns, both stationary and traveling. Examples of the patterns, observed in numerical simulations, include flowing droplets, traveling stripes, wave sources, and vortex defects.

Traveling waves in phase-separating reactive mixtures

A model of phase separation of chemically reactive ternary mixtures is constructed. In this model, spatially periodic structures that coherently propagate at a constant speed emerge through a Hopf bifurcation at a finite wave number. It is shown by computer simulations that both lamellar and hexagonal structures undergo a coherent propagating motion in two dimensions, and there are two types of traveling hexagons depending on the relative direction between the traveling velocity and the lattice vectors of the hexagonal structure. Amplitude equations for the traveling waves are derived, and the stability of the traveling and standing waves is discussed.

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.

Traveling waves and nonequilibrium stationary patterns in two-component reactive langmuir monolayers

A simple kinetic model of a two-component phase-separating Langmuir monolayer with a chemical reaction is proposed. Its analysis and numerical simulations show that nonequilibrium periodic stationary structures and patterns of traveling stripes can spontaneously develop. The nonequilibrium phase diagram of this system is constructed and the properties of the patterns are discussed.

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.

Self-propulsion of cellular structures in chemically reacting mixtures

An alternative model of phase-separating reactive mixtures is proposed. In this model both phase separation and chemical reactions simultaneously take place and a traveling coherent structure can be formed through a Hopf bifurcation at a finite wave number. Numerical simulations show that, depending on the parameters, either lamellar or hexagonal structures travel at constant speeds in two-dimensional systems.

Turing-type patterns on electrode surfaces

We report stationary, nonequilibrium potential and adsorbate patterns with an intrinsic wavelength that were observed in an electrochemical system with a specific type of current/electrode-potential (I-phi(DL)) characteristic. The patterns emerge owing to the interplay of a self-enhancing step in the reaction dynamics and a long-range inhibition by migration currents rather than by diffusion. Theoretical analysis revealed that this self-structuring of the electrode occurs in all electrochemical systems with an S-shaped I-phi(DL) characteristic in wide and well-accessible parameter ranges. This unusual pattern-forming instability in electrochemical systems has all the characteristics of the mechanism proposed by Turing in 1952 in the framework of an early theory of morphogenesis. Our finding might account for structure formation in certain biological systems that have gradients in the electric potential and may open new paths for fabricating patterned electrodes.

Phase separation with multiple length scales in polymer mixtures induced by autocatalytic reactions

A ternary polymer blend with two components photo-cross-linked independently in its miscible region undergoes phase separation, exhibiting morphology with multiple length scales. Contrary to the case of thermally induced phase separation, the morphology exhibits a unimodal-->multimodal transition. It is shown that these multiple length scales are caused by the inhomogeneous freezing kinetics of the cross-linking process. This inhomogeneity arises from the autocatalytic feedback driven by the couplings between concentration fluctuations and the photo-cross-linking reactions.

Modes selection in polymer mixtures undergoing phase separation by photochemical reactions

Phase separation kinetics and morphology of binary polymer mixtures (A/B) in the presence of photochemical reactions were investigated by using phase-contrast optical microscopy combined with digital image analysis. The polymers were chemically designed in such a way that two types of chemical reactions, intermolecular photodimerization and intramolecular photoisomerization, of polymer segments can be induced and controled by irradiation with ultraviolet light. Unlike the conventional case, the phase separation in the presence of these reactions is spontaneously frozen due to the suppression of the long-wavelength instabilities, resulting in stationary spatial structures with intrinsic periodicities. These characteristic length scales are determined by the competition between the two antagonistic interactions: phase separation as a relatively short-range activation and the photochemical reaction as a long-range inhibition. Furthermore, it was found that the spatial symmetry breaking of concentration fluctuations can emerge from the elastic stress associated with the nonhomogeneous kinetics of the reactions. Experimental data obtained with three types of reactions: A-A only cross-link, A-A and B-B simultaneous cross-links and the reversible A<-->B photoisomerization are described. These results do not only indicate that combination of chemical reactions and phase separation could provide a novel method to control the morphology of multiphase polymer materials, but also suggest that photoreactive polymers can be used as a chemical system to study the mode-selection process in polymers far from thermodynamic equilibrium. (c) 1999 American Institute of Physics.