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We present results from the molecular dynamics simulation of surface-directed spinodal decomposition in binary fluid mixtures (A + B) with off-critical compositions. The aim is to elucidate the role of composition ratio in the early time wetting kinetics under the influence of long-range surface potential. In our simulations, the attractive part of surface potential varies as V(z) = −ϵa/zn, with ϵa being the surface-potential strength. The surface prefers the "A" species to form the wetting layer. Its thickness [R1(t)] for the majority wetting (number of A-type particles [NA] > number of B-type particles [NB]) grows as a power-law with an exponent of 1/(n + 2). This is consistent with the early time kinetics in the form of potential-dependent growth present in the Puri–Binder model. However, for minority wetting (NA < NB), the growth exponent in R1(t) is less than 1/(n + 2). Furthermore, on decreasing the field strength ϵa, we recover 1/(n + 2) for a minority wetting case. We provide phenomenological arguments to explain the early time wetting kinetics for both cases. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present the phase separation dynamics of a binary (AB), simple fluid (SF), and amphiphilic polymer (AP) mixture using dissipative particle dynamics simulation at d = 3. We study the effect of different AP topologies, including block copolymers, ring block copolymers (RCP), and miktoarm star polymers, on the evolution morphologies, dynamic scaling functions, and length scale of the AB mixture. Our results demonstrate that the presence of APs leads to significantly different evolution morphologies in SF. However, the deviation from dynamical scaling is prominent, mainly for RCP. Typically, the characteristic length scale for SF follows the power law R(t) ∼ tϕ, where ϕ is the growth exponent. In the presence of high AP, we observe diffusive growth (ϕ → 1/3) at early times, followed by saturation in length scale (ϕ → 0) at late times. The extent of saturation varies with constraints imposed on the APs, such as topology, composition ratio, chain length, and stiffness. At lower composition ratios, the system exhibits inertial hydrodynamic growth (ϕ → 2/3) at asymptotic times without clearly exhibiting the viscous hydrodynamic regime (ϕ → 1) at earlier times in our simulations. Our results firmly establish the existence of hydrodynamic growth regimes in low surfactant-influenced phase separation kinetics of binary fluids and settle the related ambiguity in d = 3 systems. [ABSTRACT FROM AUTHOR]

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We study the ordering kinetics of an assembly of active Brownian particles (ABPs) on a two-dimensional substrate. We use a coarse-grained equation for the composition order parameter ψ (r , t) ,where r and t denote space and time, respectively. The model is similar to the Cahn-Hilliard equation orModel B (MB) for a conserved order parameter with an additional activity term of strength λ. This model has been introduced by Wittkowski et al., Nature Comm. 5, 4351 (2014), and is termed Active Model B (AMB). We study domain growth kinetics and dynamical scaling of the correlation function for the AMB with critical and off-critical compositions. The quantity P = s i g n (λ × ψ 0) governs the asymptotic growth kinetics for the off-critical AMB, where ψ 0 denotes the average order parameter. For negative P ,the domain growth law is the usual Lifshitz-Slyozov growth law with L (t , λ) ∼ t 1 / 3 . For positive P ,the growth law shows a crossover to a novel growth law L (t , λ) ∼ t 1 / 4 . Further, the correlation function shows good dynamical scaling for the off-critical AMB but the scaling function has a dependency on ψ 0 and λ. We also study the effects of both additive and multiplicative noise on the AMB. [ABSTRACT FROM AUTHOR]

We present detailed results from a molecular dynamics (MD) simulation of phase-separation kinetics in polymer mixtures. Our MD simulations naturally incorporate hydrodynamic effects. We find that polymeric phase separation (with dynamically symmetric components) is in the same universality class as segregation of simple fluids: the degree of polymerization only slows down the segregation kinetics. For d = 2 polymeric fluids, the domain growth law is L(t) ∼ tø with f showing a crossover from 1/3 → 1/2 → 2/3. For d = 3 polymeric fluids, we see the crossover ø = 1/3 → 1. Our MD simulations do not yet access the inertial hydrodynamic regime (with L ∼ t2/3) of phase separation in 3-d fluids. [ABSTRACT FROM AUTHOR]

We undertake a comprehensive Monte Carlo (MC) study of the ordering kinetics in nematic liquid crystals (NLCs) in 3 dimensions by performing deep quenches from the isotropic (T > Tc) to the nematic (T < Tc) phase. The inter-molecular potential between the nematogens, represented by continuous O(3) spins with inversion symmetry, is accurately mimicked by the generalised Lebwohl Lasher (GLL) model. It incorporates second- and fourth-order Legendre interactions, and their relative interaction strength is λ. For , we observe canted morphologies with a λ-dependent angle of tilt between the neighbouring rod-like molecules. For , the molecules align to yield uniform states. The coarsening morphologies obey generalized dynamical scaling in the two regimes, but the scaling function is not robust with respect to λ. The structure factor tail in the canted regime follows the Porod law: , implying that the coarsening dynamics is due to the annihilation of interfacial defects. This is unexpected, as the GLL model is characterised by a continuous order parameter. The uniform regime on the other hand, exhibits the expected generalized Porod decay: , characteristic of scattering from string defects. Finally, the domain growth obeys the Lifshitz-Allen-Cahn law: for all values of λ. Our results for the novel canted regime are relevant for a large class of systems with orientational ordering, e.g., active matter, membranes, LC elastomers, etc. We hope that our work triggers off stimulating investigations in them. [ABSTRACT FROM AUTHOR]

We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links a can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in a radical way. Small a does not prevent the system from a complete ordering, but this occurs in an extremely (logarithmically) slow manner. However, larger values of this parameter destroy complete ordering, due to frustration, and the evolution is comparatively faster (algebraic). Our study shows a precise correspondence between the kind of developing order, ferromagnetic versus frustrated, and the speed of evolution. The aging properties of the system are studied by focusing on the scaling properties of two-time quantities, the autocorrelation and linear response functions. We find that the contribution of an equilibrium and an aging part to these functions occurs differently in the various regions of the phase diagram of the model. When quenching inside the ferromagnetic phase, the two-time quantities are obtained by the addition of these parts. Instead, in the paramagnetic phase, these two contributions enter multiplicatively. Both of the scaling forms are shown with excellent accuracy, and the corresponding scaling functions and exponents have been determined and discussed. [ABSTRACT FROM AUTHOR]

We focus on understanding the influence of the two-component coupling in ferronematics, a colloidal suspension of magnetic nanoparticles in nematic liquid crystals. Using coarse-grained Landau-de Gennes free energies, we study the ordering dynamics of this complex fluid in d = 2 and present a range of analytical and numerical results. Our main observations are: i) slaved coarsening for quench temperatures T intermediate to the critical temperatures of the uncoupled components, ii) slower growth similar to the Lifshitz-Slyozov law for symmetric magneto-nematic coupling, iii) sub-domain morphologies dominated by interfacial defects for asymmetric coupling strengths. These novel results will serve to guide future experiments on this technologically important system. [ABSTRACT FROM AUTHOR]

Phase separation kinetics of a binary (A,B) mixture contained in a thin film of thickness D induced by a quench from the one-phase region into the miscibility gap is studied by simulations using a Cahn-Hilliard-Cook model. The initial randomly mixed state (50% A, 50% B) contains a concentration gradient perpendicular to the film, while the surfaces of the film are 'neutral' (no preference for either A or B). In thermal equilibrium, a pattern of large A-rich and B-rich domains must result, separated by domain walls oriented perpendicularly to the external surfaces of the thin film. However, it is shown that for many choices of D and the strength of the initial gradient Ψg, instead a very long-lived metastable layered structure forms, with two domains separated by a single interface parallel to the external walls. The transient time evolution that leads to this structure is interpreted in terms of a competition between domain growth in the bulk and surface-directed spinodal decomposition caused by the gradient during the initial stages. A surprising and potentially useful finding is that a moderate concentration gradient perpendicular to the film does not favor the layered structure but facilitates the approach toward the true equilibrium with just two domain walls perpendicular to the film. This mechanism may have useful applications in producing layered materials. [ABSTRACT FROM AUTHOR]

In this paper, we study the evolution of phase-separating binary mixtures which are subjected to alternate cooling and heating cycles. An initially homogeneous mixture is rapidly quenched to a temperature T1c, where Tc is the critical temperature. The mixture undergoes phase separation for a while and is then suddenly heated to a temperature T2>Tc. These cycles are repeated to create a domain morphology with multiple length scales, i.e., the structure factor is characterized by multiple peaks. For phase separation in d = 2 systems, we present numerical and analytical results for the emergence and growth of this multiple-scale morphology. [ABSTRACT FROM AUTHOR]

We use molecular dynamics to study the kinetics of surface enrichment (SE) in a stable homogeneous mixture (AB), placed in contact with a surface which preferentially attracts A. The SE profiles show a characteristic double-exponential behavior with two length scales: ξ-, which rapidly saturates to its equilibrium value, and ξ+, which diverges as a power-law with time (ξ+∼tθ). We find that hydrodynamic effects result in a crossover of the growth exponent from θ≃0.5 to θ≃1.0. There is also a corresponding crossover in the growth dynamics of the SE layer thickness. [ABSTRACT FROM AUTHOR]

Reports on the experimentally relevant problem of a stable binary mixture in contact with a surface which has a preference for one of the components of the mixture. Focus on the dynamics of surface enrichment resulting from a surface field turned on at zero time; Asymptotic behavior of various characteristics of the enrichment profiles.

We present a phenomenological model for the dynamics of binary alloys in contact with a surface which has a preferential attraction for one of the components of the alloy. The bulk system is described by the usual Cahn–Hilliard equation whereas the surface is mimicked by two boundary conditions. We also present numerical results from this model for the case when the system temperature is above the bulk critical temperature. Specific predictions are made which should be verifiable experimentally. [ABSTRACT FROM AUTHOR]

Abstract.: We study phase ordering kinetics in symmetric and asymmetric binary mixtures, undergoing an order-disorder transition below the critical temperature. Microscopically, we model the kinetics via the antiferromagnetic Ising model with Kawasaki spin-exchange kinetics. This conserves the composition while the order parameter (staggered magnetization) is not conserved. The order-parameter correlation function and structure factor show dynamical scaling, and the scaling functions are independent of the mixture composition. The average domain size shows a power-law growth: $ L_{\sigma}(t)\sim t^{\alpha}$ . The asymptotic growth regime has $\alpha = 1/2$ , though there can be prolonged transients with $\alpha < 1/2$ for asymmetric mixtures. Our unambiguous observation of the asymptotic universal regime is facilitated by using an accelerated Monte Carlo technique. We also obtain the coarse-grained free energy from the Hamiltonian, as a function of two order parameters. The evolution of these order parameters is modeled by using Model C kinetics. As for the microscopic dynamics, the average domain size of the nonconserved order-parameter (staggered magnetization) field exhibits a power-law growth: $L_{m}(t)\sim t^{1/2}$ at later times, irrespective of the mean value of the conserved order-parameter (composition) field. Graphical abstract: [ABSTRACT FROM AUTHOR]

Abstract.: In this paper, we study the random field Ising model (RFIM) in an external magnetic field h . A computationally efficient graph-cut method is used to study ground state (GS) morphologies in this system for three different disorder types: Gaussian, uniform and bimodal. We obtain the critical properties of this system and find that they are independent of the disorder type. We also study GS morphologies via pinned-cluster distributions, which are scale-free at criticality. The spin-spin correlation functions (and structure factors) are characterized by a roughness exponent $ \alpha \simeq 0.5$ . The corresponding scaling function is universal for all disorder types and independent of h. Graphical abstract: [ABSTRACT FROM AUTHOR]

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 (leq) in the steady state suggests apower-law dependence on the reaction rate ε: leq ~ ε-δ with δ ≂ 1.0. [ABSTRACT FROM AUTHOR]

We study domain kinetics in ferroelectric films, subsequent to a rapid quench below the critical temperature. We model the kinetics via the time-dependent Ginzburg-Landau (TDGL) equation for the Ginzburg-Landau-Devonshire (GLD) free energy, which is a functional of the electric polarization vector . The nature of ordering dynamics depends on the strength of coupling between Px and Py. For , domain growth is mediated by the annihilation of vortex defects with the growth law . For , the corresponding defects are sharp interfaces between four-fold-degenerate ground states. The resultant growth law is purely diffusive: . [ABSTRACT FROM AUTHOR]

We study the phase-separation kinetics of a binary (AB) mixture confined in a thin film of thickness D with a temperature gradient. Starting from a Kawasaki-exchange kinetic Ising model, we use a master-equation approach to systematically derive an extension of the Cahn-Hilliard model for this system. We study the effect of temperature gradients perpendicular to the film with “neutral” (no preference for either A or B) surfaces. We highlight the rich phenomenology and pattern dynamics which arises from the interplay of phase separation and the temperature gradient. [ABSTRACT FROM AUTHOR]