Crossover in growth laws for phase-separating binary fluids: molecular dynamics simulations

Phase separation dynamics in a symmetric binary mixture of ultrasoft particles

Phase separation plays a key role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The interaction among these aggregates is soft, i.e., they can significantly overlap at a small energy cost. From a computer simulation point of view, these complex macromolecular aggregates are generally modeled by soft particles. The effective interaction between two particles is defined via the generalized exponential model of index n, with n = 4. Here, using molecular dynamics simulations, we study the phase separation dynamics of a size-symmetric binary mixture of ultrasoft particles. We find that when the mixture is quenched to a temperature below the critical temperature, the two components spontaneously start to separate. Domains of the two components form, and the equal-time order parameter reveals that the domain sizes grow with time in a power-law manner with an exponent of 1/3, which is consistent with the Lifshitz-Slyozov law for conserved systems. Furthermore, the static structure factor shows a power-law decay with an exponent of 4, consistent with the Porod law.

Pattern dynamics of density and velocity fields in segregation of fluid mixtures

We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H.

Growth kinetics and morphology characterization of binary polymeric fluid under random photo-illumination

We present a comprehensive study using dissipative particle dynamics simulations to investigate phase separation kinetics (PSK) in three-dimensional (3d) polymeric fluids under random photo-illumination. We consider two scenarios: polymer blends with active radicals at one end of each immiscible chain and block copolymer (BCP) melts with photosensitive bonds linking incompatible blocks. The phase separation (PS) is induced by temperature quench of the initial homogeneously mixed system. Simultaneously, the system experiences random photo-illumination, simulated by two concurrent random events: (a) the recombination of active radicals in polymer blends and (b) the breaking of photosensitive bonds in BCP chains. Variations in the bond-breaking probability, Pb, mimic the change in light intensity. The length scale follows power law growth, R(t) ∼ tϕ, where ϕ represents the growth exponent. Increasing Pb results in a gradual transition in growth kinetics from micro-PS to macro-PS, accompanied by corresponding transition probabilities for both systems. Micro-PSK dominates the evolution process at low Pb values. The scaling functions exhibit data overlap for most scaled distances, indicating the statistical self-similarity of evolving patterns. Our study enhances the understanding of PSK in polymeric fluids, revealing the impact of photosensitive bonds and active radicals. Furthermore, it suggests the potential for designing novel polymeric materials with desired properties.

Surface-directed spinodal decomposition of fluids confined in a cylindrical pore

The surface-directed spinodal decomposition of a binary liquid confined inside a cylindrical pore is investigated using molecular dynamics simulations. One component of the liquid wets the pore surface while the other remains neutral. A variety of wetting conditions are studied. For the partial wetting case, after an initial period of phase separation, the domains organize themselves into pluglike structures and the system enters into a metastable state. Therefore, a complete phase separation is never achieved. Analysis of domain growth and the structure factor suggests a one-dimensional growth dynamics for the partial wetting case. As the wetting interaction is increased beyond a critical value, a transition from the pluglike to tubelike domain formation is observed, which corresponds to the full wetting morphology. Thus, a complete phase separation is achieved as the wetting species moves towards the pore surface and forms layers enclosing the nonwetting species residing around the axis of the cylinder. The coarsening dynamics of both the species are studied separately. The wetting species is found to follow a two-dimensional domain growth dynamics with a growth exponent 1/2 in the viscous hydrodynamic regime. This was substantiated by the Porod tail of the structure factor. On the other hand, the domain grows linearly with time for the nonwetting species. This suggests that the nonwetting species behaves akin to a three-dimensional bulk system. An appropriate reasoning is presented to justify the given observations.

Segregation of fluids with polymer additives at domain interfaces: a dissipative particle dynamics study

This paper investigates the phase separation kinetics of ternary fluid mixtures composed of a polymeric component (C) and two simple fluids (A and B) using dissipative particle dynamics simulations with a system dimensionality of d = 3. We model the affinities between the components to enable the settling of the polymeric component at the interface of fluids A and B. Thus, the system evolves to form polymer coated morphologies, enabling alteration of the fluids' interfacial properties. This manipulation can be utilized across various disciplines, such as the stabilization of emulsions and foams, rheological control, biomimetic design, and surface modification. We probe the effects of various parameters, such as the polymeric concentration, chain stiffness, and length, on the phase separation kinetics of the system. The simulation results show that changes in the concentration of flexible polymers exhibit perfect dynamic scaling for coated morphologies. The growth rate decreases as the polymeric composition is increased due to reduced surface tension and restricted connectivity between A- and B-rich clusters. Variations in the polymer chain rigidity at fixed composition ratios and degrees of polymerization slow the evolution kinetics of AB fluids marginally, although the effect is more pronounced for perfectly rigid chains. Whereas flexible polymer chain lengths at fixed composition ratios slow down the segregation kinetics of AB fluids slightly, varying the chain lengths of perfectly rigid polymers leads to a significant deviation in the length scale and dynamic scaling for the evolved coated morphologies. The characteristic length scale follows a power-law growth with a growth exponent ϕ that shows a crossover from the viscous to the inertial hydrodynamic regime, where the values of ϕ depend on the constraints imposed on the system.

Growth and aging in a few phase-separating active matter systems

Via computer simulations we study evolution dynamics in systems of continuously moving active Brownian particles. The obtained results are discussed against those from the passive 2D Ising case. Following sudden quenches of random configurations to state points lying within the miscibility gaps and to the critical points, we investigate the far-from-steady-state dynamics by calculating quantities associated with structure and characteristic length scales. We also study aging for quenches into the miscibility gap and provide a quantitative picture for the scaling behavior of the two-time order-parameter correlation function. The overall structure and dynamics are consistent with expectations from the Ising model. This remains true for certain active lattice models as well, for which we present results for quenches to the critical points.

Particle-based mesoscopic model for phase separation in a binary fluid mixture

A mesoscopic simulation model to study the phase separation in a binary fluid mixture in three dimensions (3D) is presented here by augmenting the existing particle-based multiparticle collision dynamics (MPCD) algorithm. The approach describes the nonideal equation of the fluid state by incorporating the excluded-volume interaction between the two components within the framework of stochastic collision, which depends on the local fluid composition and velocity. Calculating the nonideal contribution to the pressure both from simulation and analytics shows the model to be thermodynamically consistent. A phase diagram to explore the range of parameters that give rise to phase separation in the model is investigated. The interfacial width and phase growth obtained from the model agree with the literature for a wide range of temperatures and parameters.

Hydrodynamic effects in kinetics of phase separation in binary fluids: Critical versus off-critical compositions

Via hydrodynamics-preserving molecular dynamics simulations we study growth phenomena in a phase-separating symmetric binary mixture model. We quench high-temperature homogeneous configurations to state points inside the miscibility gap, for various mixture compositions. For compositions at the symmetric or critical value we capture the rapid linear viscous hydrodynamic growth due to advective transport of material through tubelike interconnected domains. For state points very close to any of the branches of the coexistence curve, the growth in the system, following nucleation of disconnected droplets of the minority species, occurs via a coalescence mechanism. Using state-of-the-art techniques, we have identified that these droplets, between collisions, exhibit diffusive motion. The value of the exponent for the power-law growth, related to this diffusive coalescence mechanism, has been estimated. While the exponent nicely agrees with that for the growth via the well-known Lifshitz-Slyozov particle diffusion mechanism, the amplitude is stronger. For the intermediate compositions we observe initial rapid growth that matches the expectations for viscous or inertial hydrodynamic pictures. However, at later times these types of growth cross over to the exponent that is decided by the diffusive coalescence mechanism.

Universal fast mode regime in wetting kinetics

We present simulation results from a comprehensive molecular dynamics (MD) study of surface-directed spinodal decomposition (SDSD) in unstable symmetric binary mixtures at wetting surfaces. We consider long-ranged and short-ranged surface fields to investigate the early stage wetting kinetics. The attractive part of the long-ranged potential is of the form V(z)∼z^{-n}, where z is the distance from the surface and n is the power-law exponent. We find that the wetting-layer thickness R_{1}(t) at very early times exhibits a power-law growth with an exponent α=1/(n+2). It then crosses over to a universal fast-mode regime with α=3/2. In contrast, for the short-ranged surface potential, a logarithmic behavior in R_{1}(t) is observed at initial times. Remarkably, similar rapid growth is seen in this case too. We provide phenomenological arguments to understand these growth laws. Our MD results firmly establish the existence of universal fast-mode kinetics and settle the related controversy.

Power-law coarsening in network-forming phase separation governed by mechanical relaxation

A space-spanning network structure is a basic morphology in phase separation of soft and biomatter, alongside a droplet one. Despite its fundamental and industrial importance, the physical principle underlying such network-forming phase separation remains elusive. Here, we study the network coarsening during gas-liquid-type phase separation of colloidal suspensions and pure fluids, by hydrodynamic and molecular dynamics simulations, respectively. For both, the detailed analyses of the pore sizes and strain field reveal the self-similar network coarsening and the unconventional power-law growth more than a decade according to ℓ ∝ t1/2, where ℓ is the characteristic pore size and t is the elapsed time. We find that phase-separation dynamics is controlled by mechanical relaxation of the network-forming dense phase, whose limiting process is permeation flow of the solvent for colloidal suspensions and heat transport for pure fluids. This universal coarsening law would contribute to the fundamental physical understanding of network-forming phase separation.

Initial correlation dependence of aging in phase separating solid binary mixtures and ordering ferromagnets

Following quenches of initial configurations having long range spatial correlations, prepared at the demixing critical point, to points inside the miscibility gap, we study aging phenomena in solid binary mixtures. Results on the decay of the two-time order-parameter autocorrelation functions, obtained from Monte Carlo simulations of the two-dimensional Ising model, with Kawasaki exchange kinetics, are analyzed via state-of-the art methods. The outcome is compared with that obtained for the ordering in uniaxial ferromagnets. For the latter, we have performed Monte Carlo simulations of the same model using the Glauber mechanism. For both types of systems we provide comparative discussion of our results with reference to those concerning quenches with configurations having no spatial correlation. We also discuss the role of structure on the decay of these correlations.

Janus Nanoparticles Enable Entropy-Driven Mixing of Bicomponent Hydrogels

Mixing incompatible polymers in water to form homogeneous hydrogels possessing both hydrophilic and lipophilic components is challenging due to high enthalpic penalty and negligible entropic gain in total Gibbs free energy. Here we performed dissipative particle dynamics simulations and machine learning to uncover the influence of Janus nanoparticles on immiscible polymer mixtures with high water content and to predict the phase behavior of bicomponent hydrogels. An intriguing transition from kinetically arrested demixing to spontaneous mixing was observed with increasing particle concentration and decreasing particle size. The analysis reveals that the mixing is driven by a significant entropic gain of small nanoparticles being well dispersed in aqueous solvent of high-volume fraction. This finding highlights an entropy-driven mixing mechanism for nanocomposite bicomponent hydrogels. Supervised machine learning algorithms were used to establish a microstructure phase diagram with respect to particle concentration and radius, in which homogeneous, percolated, clustered, and separated phases, as well as corresponding phase boundaries, were clearly identified.

Pattern, growth, and aging in aggregation kinetics of a Vicsek-like active matter model

Via molecular dynamics simulations, we study kinetics in a Vicsek-like phase-separating active matter model. Quantitative results, for isotropic bicontinuous pattern, are presented on the structure, growth, and aging. These are obtained via the two-point equal-time density-density correlation function, the average domain length, and the two-time density autocorrelation function. Both the correlation functions exhibit basic scaling properties, implying self-similarity in the pattern dynamics, for which the average domain size exhibits a power-law growth in time. The equal-time correlation has a short distance behavior that provides reasonable agreement between the corresponding structure factor tail and the Porod law. The autocorrelation decay is a power-law in the average domain size. Apart from these basic similarities, the overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation. The functional forms of these have been quantified. An exceptionally rapid growth in the active system occurs due to fast coherent motion of the particles, mean-squared-displacements of which exhibit multiple scaling regimes, including a long time ballistic one.

Role of a polymeric component in the phase separation of ternary fluid mixtures: a dissipative particle dynamics study

We present the results from dissipative particle dynamics (DPD) simulations of phase separation dynamics in ternary (ABC) fluids mixture in d = 3 where components A and B represent the simple fluids, and component C represents a polymeric fluid. Here, we study the role of polymeric fluid (C) on domain morphology by varying composition ratio, polymer chain length, and polymer stiffness. We observe that the system under consideration lies in the same dynamical universality class as a simple ternary fluids mixture. However, the scaling functions depend upon the parameters mentioned above as they change the time scale of the evolution morphologies. In all cases, the characteristic domain size follows l(t) ∼ tφ with dynamic growth exponent φ, showing a crossover from the viscous hydrodynamic regime (φ = 1) to the inertial hydrodynamic regime (φ = 2/3) in the system at late times.

Ballistic aggregation in systems of inelastic particles: Cluster growth, structure, and aging

We study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.

Effect of bond-disorder on the phase-separation kinetics of binary mixtures: A Monte Carlo simulation study

We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashion, the system follows the dynamical scaling for the modest number of disordered sites. For a higher number of disordered sites, the evolution morphology illustrates a lamellar pattern formation. Our MC results are consistent with the Lifshitz-Slyozov power-law growth in all the cases.

Dissipative particle dynamics study of phase separation in binary fluid mixtures in periodic and confined domains

We investigate the phase separation behavior of binary mixtures in two-dimensional periodic and confined domains using dissipative particle dynamics. Two canonical problems of fluid mechanics are considered for the confined domains: square cavity with no-slip walls and lid-driven cavity with one driven wall. The dynamics is studied for both weakly and strongly separating mixtures and different area fractions. The phase separation process is analyzed using the structure factor and the total interface length. The dynamics of phase separation in the square cavity and lid-driven cavity are observed to be significantly slower when compared to the dynamics in the periodic domain. The presence of the no-slip walls and the inertial effects significantly influences the separation dynamics. Finally, we show that the growth exponent for the strongly separating case is invariant to changes in the inter-species repulsion parameter.

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.

Intermittent dynamics and logarithmic domain growth during the spinodal decomposition of a glass-forming liquid

We use large-scale molecular dynamics simulations of a simple glass-forming system to investigate how its liquid-gas phase separation kinetics depends on temperature. A shallow quench leads to a fully demixed liquid-gas system whereas a deep quench makes the dense phase undergo a glass transition and become an amorphous solid. This glass has a gel-like bicontinuous structure that evolves very slowly with time and becomes fully arrested in the limit where thermal fluctuations become negligible. We show that the phase separation kinetics changes qualitatively with temperature, the microscopic dynamics evolving from a surface tension-driven diffusive motion at high temperature to a strongly intermittent, heterogeneous, and thermally activated dynamics at low temperature, with a logarithmically slow growth of the typical domain size. These results elucidate the microscopic mechanisms underlying a specific class of viscoelastic phase separation.

Phase separation in ternary fluid mixtures: a molecular dynamics study

We present detailed results from molecular dynamics (MD) simulations of phase separation in ternary (ABC) fluid mixtures for d = 2 and d = 3 systems. Our MD simulations naturally incorporate hydrodynamic effects. The domain growth law is l(t) ∼ t(ϕ) with dynamic growth exponent ϕ. Our data clearly indicate that a ternary fluid mixture reaches a dynamical scaling regime at late times with a gradual crossover from ϕ = 1/3 → 1/2 → 2/3 in d = 2 and ϕ = 1/3 → 1 in d = 3 resulting from the hydrodynamic effect in the system. These MD simulations do not yet access the inertial hydrodynamic regime (with l(t) ∼ t(2/3)) of phase separation in ternary fluid mixtures in d = 3.

Phase separation of fluids in porous media: a molecular dynamics study

We present comprehensive molecular dynamics results for phase-separation kinetics of fluids in a porous medium. This system is modeled by a symmetric Lennard-Jones fluid mixture with a quenched random field. The presence of disorder slows down domain growth from power-law to a logarithmic form. It also modifies the correlation functions and structure factors which characterize the morphology. In particular, the structure-factor tail shows a non-Porod behavior, which is the consequence of scattering from rough interfaces.

Non-Porod behavior in systems with rough morphologies

Many experiments yield multi-scale morphologies which are smooth on some length scales and fractal on others. Accurate statements about morphological properties, e.g., roughness exponent, fractal dimension, domain size, interfacial width, etc. are obtained from the correlation function and structure factor. In this paper, we present structure factor data for two systems: (a) droplet-in-droplet morphologies of double-phase-separating mixtures; and (b) ground-state morphologies in dilute anti-ferromagnets. An important characteristic of the scattering data is a non-Porod tail, which is associated with scattering off rough domains and interfaces.

Fragmentation and limits to dynamical scaling in viscous coarsening: an interrupted in situ x-ray tomographic study

X-ray microtomography was used to follow the coarsening of the structure of a ternary silicate glass experiencing phase separation in the liquid state. The volumes, surfaces, mean, and Gaussian curvatures of the domains of minority phase were measured after reconstruction of the 3D images and segmentation. A linear growth law of the characteristic length scale ℓ∼t was observed. A detailed morphological study was performed. While dynamical scaling holds for most of the geometrical observables under study, a progressive departure from scaling invariance of the distributions of local curvatures was evidenced. The latter results from a gradual fragmentation of the structure in the less viscous phase that also leads to a power-law size distribution of isolated domains.

Phase separation in antisymmetric films: a molecular dynamics study

We have used molecular dynamics (MD) simulations to study phase-separation kinetics in a binary fluid mixture (AB) confined in an antisymmetric thin film. One surface of the film (located at z = 0) attracts the A-atoms, and the other surface (located at z = D) attracts the B-atoms. We study the kinetic processes which lead to the formation of equilibrium morphologies subsequent to a deep quench below the miscibility gap. In the initial stages, one observes the formation of a layered structure, consisting of an A-rich layer followed by a B-rich layer at z = 0; and an analogous structure at z = D. This multi-layered morphology is time-dependent and propagates into the bulk, though it may break up into a laterally inhomogeneous structure at a later stage. We characterize the evolution morphologies via laterally averaged order parameter profiles; the growth laws for wetting-layer kinetics and layer-wise length scales; and the scaling properties of layer-wise correlation functions.

Aging and crossovers in phase-separating fluid mixtures

We use state-of-the-art molecular dynamics simulations to study hydrodynamic effects on aging during kinetics of phase separation in a fluid mixture. The domain growth law shows a crossover from a diffusive regime to a viscous hydrodynamic regime. There is a corresponding crossover in the autocorrelation function from a power-law behavior to an exponential decay. While the former is consistent with theories for diffusive domain growth, the latter results as a consequence of faster advective transport in fluids for which an analytical justification has been provided.

Surface-directed spinodal decomposition: a molecular dynamics study

We use molecular dynamics simulations to study surface-directed spinodal decomposition in unstable binary AB fluid mixtures at wetting surfaces. The thickness of the wetting layer R1 grows with time t as a power law (R1∼tθ). We find that hydrodynamic effects result in a crossover of the growth exponent from θ≃1/3 to 1. We also present results for the layerwise correlation functions and domain length scales.