Reaction-induced ordering phenomena in binary polymer mixtures

Interplay of phase segregation and chemical reaction: Crossover and effect on growth laws

By combining the nonconserved spin-flip dynamics driving ferromagnetic ordering with the conserved Kawasaki-exchange dynamics driving phase segregation, we perform Monte Carlo simulations of the nearest-neighbor Ising model. This kind of mixed dynamics is found in a system consisting of a binary mixture of isomers, simultaneously undergoing a segregation and an interconversion reaction among themselves. Here, we study such a system following a quench from the high-temperature homogeneous phase to a temperature below the demixing transition. We monitor the growth of domains of both the winner; the isomer, which survives as the majority; and the loser, the isomer that perishes. Our results show a strong interplay of the two dynamics at early times, leading to a growth of the average domain size of both the winner and loser as ∼t^{1/7}, slower than a purely phase-segregating system. At later times, eventually the dynamics becomes reaction dominated and the winner exhibits a ∼t^{1/2} growth, expected for a system with purely nonconserved dynamics. On the other hand, the loser at first show a faster growth, albeit, slower than the winner, and then starts to decay before it almost vanishes. Further, we estimate the time τ_{s} marking the crossover from the early-time slow growth to the late-time reaction-dominated faster growth. As a function of the reaction probability p_{r}, we observe a power-law scaling τ_{s}∼p_{r}^{-x}, where x≈1.05, irrespective of the temperature. For a fixed value of p_{r} too, τ_{s} appears to be independent of the temperature.

Phase separation in the presence of fractal aggregates

Liquid-liquid phase separation in diverse manufacturing and biological contexts often occurs in the presence of aggregated particles or complex-shaped structures that do not actively participate in the phase separation process, but these "background" structures can serve to direct the macroscale phase separation morphology by their local symmetry-breaking presence. We perform Cahn-Hilliard phase-field simulations in two dimensions to investigate the morphological evolution, wetting, and domain growth phenomena during the phase separation of a binary mixture in contact with model fractal aggregates. Our simulations reveal that phase separation initially accelerates around the fractal due to the driving force of wetting, leading to the formation of the target composition patterns about the fractals, as previously observed for circular particles. After the formation of a wetting layer on the fractal, however, we observe a dramatic slowing-down in the kinetics of phase separation, and the characteristic domain size eventually "pins" to a finite value or approaches an asymptotic scaling regime as an ordinary phase if the phase separation loses memory of the aggregates when the scale of phase separation becomes much larger than the aggregate. Furthermore, we perform simulations to examine the effects of compositional interference between fractals with a view to elucidating interesting novel morphological features in the phase-separating mixture. Our findings should be helpful in understanding the qualitative aspects of the phase separation processes in mixtures containing particle aggregates relevant for coating, catalyst, adhesive, and electronic applications as well as in diverse biological contexts, where phase separation occurs in the presence of irregular heterogeneities.

Segregation disrupts the Arrhenius behavior of an isomerization reaction

Coexistence of segregation and interconversion or isomerization reaction among molecular species leads to fascinating structure formation in the biological and chemical worlds. Using Monte Carlo simulations of the prototype Ising model, we explore the chemical kinetics of such a system consisting of a binary mixture of isomers. Our results reveal that even though the two concerned processes are individually Arrhenius in nature, the Arrhenius behavior of the isomerization reaction gets significantly disrupted due to an interplay of the nonconserved dynamics of the reaction and the conserved diffusive dynamics of segregation. The approach used here can be potentially adapted to understand reaction kinetics of more complex reactions.

Lattice Boltzmann simulation for phase separation with chemical reaction controlled by thermal diffusion

This study investigates phase separation behavior and pattern formation in a binary fluid with chemical reaction controlled by thermal diffusion. By incorporating the Arrhenius equation into the lattice Boltzmann method (LBM), the coupling effects of the pre-exponential factor K, viscosity [Formula: see text], and thermal diffusion D on phase separation were successfully evaluated. The effect of the competition between thermal diffusion and concentration on the phase separation morphology and dynamics of binary mixtures under a chemically reacting controlled by slow cooling is assessed based on the extended LBM. The calculations indicated that increases in viscosity and thermal diffusion can obtain interconnected structures (ISs) and lamellar structures (LSs) for cases with small K. However, concentric phase-separated structures (CSs) were observed in cases with large K. The increase in the degree and efficiency of phase separation were significantly greater in cases with decreased viscosity and increased thermal diffusion.

Photo-induced bond breaking during phase separation kinetics of block copolymer melts: a dissipative particle dynamics study

Using a dissipative particle dynamics (DPD) simulation method, we study the phase separation dynamics in block copolymer (BCP) melts in d = 3, subjected to external stimuli such as light. An initial homogeneous BCP melt is rapidly quenched to a temperature T < T_c, where T_c is the critical temperature. We then allow the system to undergo alternate light "on" and "off" cycles. An on-cycle breaks the stimuli-sensitive bonds connecting both the blocks A and B in the BCP melt, and during the off-cycle, the broken bonds recombine. By simulating the effect of light, we isolate scenarios where phase separation begins with the light off (set 1); the cooperative interactions within the system allow it to undergo microphase separation. When the phase separation starts with the light on (set 2), the system undergoes macrophase separation due to bond breaking. Here, we report the role of alternate cycles on domain morphology by varying the bond-breaking probability for both set 1 and set 2, respectively. We observe that the scaling functions depend upon the conditions mentioned above that change the time scale of the evolving morphologies in various cycles. However, in all the cases, the average domain size respects the power-law growth: R(t) ∼t^φ at late times, where φ is the dynamic growth exponent. After a short-lived diffusive growth (φ∼ 1/3) at early times, φ illustrates a crossover from the viscous hydrodynamic (φ∼ 1) to the inertial hydrodynamic (φ∼ 2/3) regimes at late times.

Impact of particle arrays on phase separation composition patterns

We examine the symmetry-breaking effect of fixed constellations of particles on the surface-directed spinodal decomposition of binary blends in the presence of particles whose surfaces have a preferential affinity for one of the components. Our phase-field simulations indicate that the phase separation morphology in the presence of particle arrays can be tuned to have a continuous, droplet, lamellar, or hybrid morphology depending on the interparticle spacing, blend composition, and time. In particular, when the interparticle spacing is large compared to the spinodal wavelength, a transient target pattern composed of alternate rings of preferred and non-preferred phases emerges at early times, tending to adopt the symmetry of the particle configuration. We reveal that such target patterns stabilize for certain characteristic length, time, and composition scales characteristic of the pure phase-separating mixture. To illustrate the general range of phenomena exhibited by mixture-particle systems, we simulate the effects of single-particle, multi-particle, and cluster-particle systems having multiple geometrical configurations of the particle characteristic of pattern substrates on phase separation. Our simulations show that tailoring the particle configuration, or substrate pattern configuration, a relative fluid-particle composition should allow the desirable control of the phase separation morphology as in block copolymer materials, but where the scales accessible to this approach of organizing phase-separated fluids usually are significantly larger. Limited experiments confirm the trends observed in our simulations, which should provide some guidance in engineering patterned blend and other mixtures of technological interest.

Physics of active emulsions

Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call active emulsions. These systems are driven by external energy input, for example provided by an external fuel reservoir. The external energy input gives rise to novel phenomena that are not present in passive systems. For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions. Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled, and they can divide spontaneously. In this review, we discuss the physics of phase separation and emulsions and show how the concepts that govern such phenomena can be extended to capture the physics of active emulsions. This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development of novel applications in chemical engineering and models for the origin of life.

Structuring polymer gels via catalytic reactions

We use computer simulations to investigate how a catalytic reaction in a polymer sol can induce the formation of a polymer gel. To this aim we consider a solution of homopolymers in which freely-diffusing catalysts convert the originally repulsive A monomers into attractive B ones. We find that at low temperatures this reaction transforms the polymer solution into a physical gel that has a remarkably regular mesostructure in the form of a cluster phase, absent in the usual homopolymer gels obtained by a quench in temperature. We investigate how this microstructuring depends on catalyst concentration, temperature, and polymer density and show that the dynamics for its formation can be understood in a semi-quantitative manner using the interaction potentials between the particles as input. The structuring of the copolymers and the AB sequences resulting from the reactions can be discussed in the context of the phase behaviour of correlated random copolymers. The location of the spinodal line as found in our simulations is consistent with analytical predictions. Finally, we show that the observed structuring depends not only on the chemical distribution of the A and B monomers but also on the mode of formation of this distribution.

Particles with selective wetting affect spinodal decomposition microstructures

We have used mesoscale simulations to study the effect of immobile particles on microstructure formation during spinodal decomposition in ternary mixtures such as polymer blends.

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.

Polymer networks with bicontinuous gradient morphologies resulting from the competition between phase separation and photopolymerization

Poly(ethyl acrylate)/poly(methyl methacrylate) (PEA/PMMA) polymer networks (IPNs) with spatially graded bicontinuous morphology were designed and controlled by taking advantage of the spinodal decomposition process induced by photopolymerization of the MMA monomer. Spatial gradients of the quench depth, induced by the gradients of light intensity, were generated along the path of the excitation light travelling through the mixture. Bicontinuous structures with uniaxial gradient of characteristic length scales were obtained by two different methods: simply irradiating the mixture with strong light intensity along the Z-direction and using the so-called computer-assisted irradiation (CAI) method with moderate intensity to generate the light intensity gradient exclusively in the XY plane. These experimental results suggest that the combination of these two irradiation methods could provide polymer materials with biaxially co-continuous gradient morphology. An analysis method using the concept of spatial correlation function was developed to analyze the time-evolution of these graded structures. The experimental results obtained in this study suggest a promising method to design gradient polymers in the bulk state (3D) as well as on the surface (2D) by taking advantage of photopolymerization.

Molecular dynamics study of phase separation in fluids with chemical reactions

We present results from the first d=3 molecular dynamics (MD) study of phase-separating fluid mixtures (AB) with simple chemical reactions (A⇌B). We focus on the case where the rates of forward and backward reactions are equal. The chemical reactions compete with segregation, and the coarsening system settles into a steady-state mesoscale morphology. However, hydrodynamic effects destroy the lamellar morphology which characterizes the diffusive case. This has important consequences for the phase-separating structure, which we study in detail. In particular, the equilibrium length scale (ℓ(eq)) in the steady state suggests a power-law dependence on the reaction rate ε:ℓ(eq)∼ε(-θ) with θ≃1.0.

Suppression of Ostwald ripening in active emulsions

Emulsions consisting of droplets immersed in a fluid are typically unstable since they coarsen over time. One important coarsening process is Ostwald ripening, which is driven by the surface tension of the droplets. Stability of emulsions is relevant not only in complex fluids but also in biological cells, which contain liquidlike compartments, e.g., germ granules, Cajal bodies, and centrosomes. Such cellular systems are driven away from equilibrium, e.g., by chemical reactions, and thus can be called active emulsions. In this paper, we study such active emulsions by developing a coarse-grained description of the droplet dynamics, which we analyze for two different chemical reaction schemes. We first consider the simple case of first-order reactions, which leads to stable, monodisperse emulsions in which Ostwald ripening is suppressed within a range of chemical reaction rates. We then consider autocatalytic droplets, which catalyze the production of their own droplet material. Spontaneous nucleation of autocatalytic droplets is strongly suppressed and their emulsions are typically unstable. We show that autocatalytic droplets can be nucleated reliably and their emulsions stabilized by the help of chemically active cores, which catalyze the production of droplet material. In summary, different reaction schemes and catalytic cores can be used to stabilize emulsions and to control their properties.

Centrosomes are autocatalytic droplets of pericentriolar material organized by centrioles

Centrosomes are highly dynamic, spherical organelles without a membrane. Their physical nature and their assembly are not understood. Using the concept of phase separation, we propose a theoretical description of centrosomes as liquid droplets. In our model, centrosome material occurs in a form soluble in the cytosol and a form that tends to undergo phase separation from the cytosol. We show that an autocatalytic chemical transition between these forms accounts for the temporal evolution observed in experiments. Interestingly, the nucleation of centrosomes can be controlled by an enzymatic activity of the centrioles, which are present at the core of all centrosomes. This nonequilibrium feature also allows for multiple stable centrosomes, a situation that is unstable in equilibrium phase separation. Our theory explains the growth dynamics of centrosomes for all cell sizes down to the eight-cell stage of the Caenorhabditis elegans embryo, and it also accounts for data acquired in experiments with aberrant numbers of centrosomes and altered cell volumes. Furthermore, the model can describe unequal centrosome sizes observed in cells with perturbed centrioles. We also propose an interpretation of the molecular details of the involved proteins in the case of C. elegans. Our example suggests a general picture of the organization of membraneless organelles.

Self-organization in living cells: networks of protein machines and nonequilibrium soft matter

Microscopic self-organization phenomena inside a living cell should not represent merely a reduced copy of self-organization in macroscopic systems. A cell is populated by active protein machines that communicate via small molecules diffusing through the cytoplasm. Mutual synchronization of machine cycles can spontaneously develop in such networks - an effect which is similar to coherent laser generation. On the other hand, an interplay between reactions, diffusion and phase transitions in biological soft matter may lead to the formation of stationary or traveling nonequilibrium nanoscale structures.

Nanosize pattern formation in overdamped stochastic reaction-diffusion systems with interacting adsorbate

We study overdamped stochastic model describing adsorption or desorption processes with nonequilibrium chemical reactions on the surface. It is shown that internal noise satisfying the fluctuation-dissipation relation at small intensities governs transitions between ordered thermodynamical dense and diluted phases. These phase transitions are characterized by an increase of fluctuations of the coverage filed and correlation radius of spatial modulation. At large noise intensity a transition towards disordered phase with chaotic spatial configuration is realized. We have shown that organized stationary patterns are of nanometer range. We define that both period of stationary structures and corresponding correlation radius depend on the noise intensity.

Surface patterning of low-dimensional systems: the chirality of charged fibres

Charged surfaces are interesting for their ability to have long-range correlations and their ability to be dynamically tuned. While the configurations of charged planar surfaces have been thoroughly mapped and studied, charged cylindrical surfaces show novel features. The surface patterning of cylindrically confined charges is discussed with emphasis on the role of chiral configurations. The origins of surface patterns due to competing interactions in charged monolayers are summarized along with their associated theoretical models. The electrostatically induced patterns described in this paper are important in many low-dimensional biological systems such as plasma membrane organization, filamentous virus capsid structure or microtubule interactions. A simple model effectively predicting some features of chiral patterns in biological systems is presented. We extend our model from helical lamellar patterns to elliptical patterns to consider asymmetrical patterns in assemblies of filamentous aggregates.

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.

Insights Into Crowding Effects on Protein Stability From a Coarse-Grained Model

Proteins aggregate and precipitate from high concentration solutions in a wide variety of problems of natural and technological interest. Consequently, there is a broad interest in developing new ways to model the thermodynamic and kinetic aspects of protein stability in these crowded cellular or solution environments. We use a coarse-grained modeling approach to study the effects of different crowding agents on the conformational equilibria of proteins and the thermodynamic phase behavior of their solutions. At low to moderate protein concentrations, we find that crowding species can either stabilize or destabilize the native state, depending on the strength of their attractive interaction with the proteins. At high protein concentrations, crowders tend to stabilize the native state due to excluded volume effects, irrespective of the strength of the crowder-protein attraction. Crowding agents reduce the tendency of protein solutions to undergo a liquid-liquid phase separation driven by strong protein-protein attractions. The aforementioned equilibrium trends represent, to our knowledge, the first simulation predictions for how the properties of crowding species impact the global thermodynamic stability of proteins and their solutions.

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.

Liquid-liquid phase transition of protein aqueous solutions isothermally induced by protein cross-linking

We experimentally demonstrated that liquid-liquid phase separation (LLPS) of protein aqueous solutions can be induced by isothermal protein oligomerization. This phenomenon is analogous to LLPS induced by the polymerization of small organic molecules in solution. Specifically, using glutaraldehyde for protein cross-linking, we observed the formation of protein-rich liquid droplets for bovine serum albumin and chicken egg lysozyme at 25 degrees C. These droplets evolved into cross-linked protein microspheres. If the aqueous solutions of the protein monomer do not show LLPS at temperatures lower than the oligomerization temperature, protein-rich droplets are not observed. We experimentally linked the formation of these droplets to the increase of LLPS temperature during protein oligomerization. When macroscopic aggregation competes with LLPS, a rationale choice of pH, polyethylene glycol, and salt concentrations can be used to favor LLPS relative to aggregation. Although glutaraldehyde has been extensively used to cross-link protein molecules, to our knowledge, its use in homogeneous aqueous solutions to induce LLPS has not been previously described. This work contributes to the fundamental understanding of both phase transitions of protein solutions and the morphology of protein condensed phases. It also provides guidance for the development of new methods based on mild experimental conditions for the preparation of protein-based materials.

Hexagonal phase induced by a reversible photo-cross-link reaction in a polymer mixture

A hexagonal phase was found during the synthesis of interpenetrating polymer networks composed of polystyrene (PS) and poly(methyl methacrylate) (PMMA). By using confocal microscopy, it was found that the regularity of this hexagonal phase further increases upon de-cross-linking of the PS networks in the matrix phase by irradiation with shorter uv wavelengths. We conclude that the cooperation between the cross-link-induced suppression of phase separation and the elastic repulsion between the dispersed PMMA-rich domains is responsible for the emergence of this hexagonal phase.

Facile approach to the fabrication of a micropattern possessing nanoscale substructure

On the basis of the combined technologies of photolithography and reaction-induced phase separation (RIPS), a facile approach has been successfully developed for the fabrication of a micropattern possessing nanoscale substructure on the thin film surface. This approach involves three steps. In the first step, a thin film was prepared by spin coating from a solution of a commercial random copolymer, polystyrene-r-poly(methyl methacrylate) (PS-r-PMMA) and a commercial crosslinker, trimethylolpropane triacrylate (TMPTA). In the second step, photolithograph was performed with the thin film using a 250 W high-pressure mercury lamp to produce the micropattern. Finally, the resulting micropattern was annealed at 200 degrees C for a certain time, and reaction-induced phase separation occurred. After soaking in chloroform for 4 h, nanoscale substructure was obtained. The whole processes were traced by atomic force microscopy (AFM), X-ray photoelectron spectrometry (XPS), and Fourier transform infrared (FTIR) spectroscopy, and the results supported the proposed structure.

Imaging with Chemical Analysis: Adsorbed Structures Formed during Surface Chemical Reactions

Imaging surfaces and interfaces with structural and chemical specificity has been essential for understanding a variety of phenomena occurring in adsorbed layers during surface chemical reactions. A recent achievement of chemical imaging with spectroscopic analysis is the experimental proof of theoretically predicted spontaneous formation of regular patterns of metal adatoms during surface chemical reactions. An attractive feature of this finding is that the reaction rate and adlayer coverage can be employed to precisely control the morphology of the structures. The mechanisms of these self-organisation phenomena, driven by the interplay between energetic principles and kinetics, opens a conceptually novel route to creating a wide range of surface-supported functional structures at the micro- and nanometre length scales.

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 self-organization phenomena in active Langmuir monolayers

Langmuir monomolecular layers, formed by amphiphilic molecules at liquid-air interfaces and containing a fraction of chiral molecules, are theoretically investigated. These monolayers can be brought out of thermal equilibrium by applying a gradient of small molecules across the interface, resulting in the leakage flow. We show that, when splay coupling between the orientation field and the local concentration of chiral molecules in the monolayer is taken into account, this nonequilibrium soft matter system can show complex wave behavior, including the development of target wave patterns, spiral waves, and dense regions filled with inwardly propagating waves.

Lattice Boltzmann simulations of phase separation in chemically reactive binary fluids

We use a lattice Boltzmann method to study pattern formation in chemically reactive binary fluids in the regime where hydrodynamic effects are important. The coupled equations solved by the method are a Cahn-Hilliard equation, modified by the inclusion of a reactive source term, and the Navier-Stokes equations for conservation of mass and momentum. The coupling is twofold, resulting from the advection of the order parameter by the velocity field and the effect of fluid composition on pressure. We study the evolution of the system following a critical quench for a linear and for a quadratic reaction source term. Comparison is made between the high and low viscosity regimes to identify the influence of hydrodynamic flows. In both cases hydrodynamics is found to influence the pathways available for domain growth and the eventual steady states.

Spatial modulation in cross-linked binary polymer blends

Spatial modulation means that the free energy of the composite mixture is minimized at a finite wavenumber, which defines the primary length scale, the maximum size possible, of the evolving phases. Although spatial modulation may appear in different systems in different ways and is not necessarily a thermodynamic precept, here it is expressed as a thermodynamic consequence of short-range interfacial forces pitted against long-range elastic forces. Cross-linked chains bring about new thermodynamic interactions based on their conformations and the fractal dimensions of the chain networks to which they tether and belong. Interplay among these different interactions during phase ordering brings about the spatial modulation and the spatial pattern. Here, the underlying processes are only succinctly outlined.