Influence of surface interactions on spinodal decomposition

Mechanisms of alignment of lamellar-forming block copolymer under shear flow

The potential applications of block copolymer thin films, utilising their self-assembly capabilities, are enhanced when achieving long-range ordering. In this study we explain the experimental alignment of lamellae under shear flow findings [S. Pujari et al. Soft Matter, 2012, 8, 5258] and classify the alignment mechanisms based on shear rate and segregation, uncovering similarities to the systems subjected to electric fields, suggesting a common pathway of lamellae orientations. However, the presence of thin films surfaces introduces distinct features in the lamellae orientation under shear compared to electric fields. Notably, we observe the emergence of a three-dimensional rotation alongside the conventional two-dimensional rotation. Furthermore, a transient regime has been identified within the melting mechanism, which confirms the existence of the checkboard pattern proposed by Schneider et al. [Macromolecules, 2018, 51, 4642]. These findings significantly enhance our understanding of block copolymer alignments and shed light on the intricate interplay between external fields and the lamellar structure.

Perpendicular Phase Separation in Confined Binary Liquids: Unveiling Novel Kinetics and Stabilization Mechanisms for Nanofilms

We investigated the dynamics of a binary mixture confined within van der Waals walls using molecular dynamics simulations. We discovered a novel phenomenon named perpendicular separations of two phases (PSTP). In the initial stage, central water molecules diffused, subsequently condensing symmetrically within the confinement's midplane. In the later stage, as water droplets nucleate and grow, the resin separates perpendicularly into two films due to the action of bubblers and vdW walls, resulting in a hollow nanochannel. The mechanisms and conditions underlying PSTP are discussed. The results indicate that the concentration (C) of resin in the middle region is linearly decreased with temporal power (C(t,T) ∝ a(T)t1/3). We propose a new mechanism for stabilizing nanochannels and films: dynamic "soft pillars" that prevent Rayleigh-like instability. Our findings could shed light on the manufacture of nanofilms and organic nanochannels, which could help advance biodetection and energy fields.

Coarsening dynamics of ternary polymer solutions with mobility and viscosity contrasts

Using phase-field simulations, we investigate the bulk coarsening dynamics of ternary polymer solutions undergoing a glass transition for two models of phase separation: diffusion only and with hydrodynamics. The glass transition is incorporated in both models by imposing mobility and viscosity contrasts between the polymer-rich and polymer-poor phases of the evolving microstructure. For microstructures composed of polymer-poor clusters in a polymer-rich matrix, the mobility and viscosity contrasts significantly hinder coarsening, effectively leading to structural arrest. For microstructures composed of polymer-rich clusters in a polymer-poor matrix, the mobility and viscosity contrasts do not impede domain growth; rather, they change the transient concentration of the polymer-rich phase, altering the shape of the discrete domains. This effect introduces several complexities to the coarsening process, including percolation inversion of the polymer-rich and polymer-poor phases-a phenomenon normally attributed to viscoelastic phase separation.

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.

Impact of the prequench state of binary fluid mixtures on surface-directed spinodal decomposition

Using lattice Boltzmann simulations we investigate the impact of the amplitude of concentration fluctuations in binary fluid mixtures prior to demixing when in contact with a surface that is preferentially wet by one of the components. We find a bicontinuous structure near the surface for an initial, prequench state of the mixture close to the critical point where the amplitude of concentration fluctuations is large. In contrast, if the initial state of the mixture is not near the critical point and concentration fluctuations are relatively weak, then the morphology is not bicontinuous but remains layered until the very late stages of coarsening. In both cases, it is the morphology of a depletion layer rich in the nonpreferred component that dictates the growth exponent of the thickness of the fluid layer that is in direct contact with the substrate. In the early stages of demixing, we find a growth exponent consistent with a value of 1/4 for a prequench state away from the critical point, which is different from the usual diffusive scaling exponent of 1/3 that we recover for a prequench state close to the critical point. We attribute this to the structure of a depletion layer that is penetrated by tubes of the preferred fluid, connecting the wetting layer to the bulk fluid even in the early stages if the initial state is characterized by concentration fluctuations that are large in amplitude. Furthermore, we find that in the late stages of demixing the flow through these tubes results in significant in-plane concentration variations near the substrate, leading to dropletlike structures with a concentration lower than the average concentration in the wetting layer. This causes a deceleration in the growth of the wetting layer in the very late stages of the demixing. Irrespective of the prequench state of the mixture, the late stages of the demixing process produce the same growth law for the layer thickness, with a scaling exponent of unity usually associated with the impact of hydrodynamic flow fields.

Surface-directed spinodal decomposition on morphologically patterned substrates

This paper is the second in a two-part exposition on surface-directed spinodal decomposition (SDSD), i.e., the interplay of kinetics of wetting and phase separation at a surface which is wetted by one of the components of a binary mixture. In our first paper [P. Das, P. K. Jaiswal, and S. Puri, Phys. Rev. E 102, 012803 (2020)2470-004510.1103/PhysRevE.102.012803], we studied SDSD on chemically heterogeneous and physically flat substrates. In this paper, we study SDSD on a chemically homogeneous but morphologically patterned substrate. Such substrates arise in a vast variety of technological applications. Our goal is to provide a theoretical understanding of SDSD in this context. We present detailed numerical results for domain growth both inside and above the grooves in the substrate. The morphological evolution can be understood in terms of the interference of SDSD waves originating from the different surfaces comprising the substrate.

Surface-directed spinodal decomposition on chemically patterned substrates

Surface-directed spinodal decomposition (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical study of SDSD on a chemically patterned substrate. We consider simple surface patterns for our simulations, but most of the results apply for arbitrary patterns. In layers near the surface, we observe a dynamical crossover from a surface-registry regime to a phase-separation regime. We study this crossover using layerwise correlation functions and structure factors and domain length scales.

Gelation Impairs Phase Separation and Small Molecule Migration in Polymer Mixtures

Surface segregation of the low molecular weight component of a polymeric mixture is a ubiquitous phenomenon that leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer-polymer ( O P ) and oligomer-gel ( O G ) systems following a temperature quench that induces demixing of components. We compute equilibrium and time varying migrant (oligomer) density profiles and wetting layer thickness in these systems using coarse grained molecular dynamics (CGMD) and mesoscale hydrodynamics (MH) simulations. Such multiscale methods quantitatively describe the phenomena over a wide range of length and time scales. We show that surface migration in gel-oligomer systems is significantly reduced on account of network elasticity. Furthermore, the phase separation processes are significantly slowed in gels leading to the modification of the well known Lifshitz-Slyozov-Wagner (LSW) law ℓ ( τ ) ∼ τ 1 / 3 . Our work allows for rational design of polymer/gel-oligomer mixtures with predictable surface segregation characteristics that can be compared against experiments.

Mass-transfer driven spinodal decomposition in a ternary polymer solution

Nonsolvent induced phase separation (NIPS) is a widely occuring process used in industrial membrane production, nanotechnology and Nature to produce microstructured polymer materials. A variety of process-dependent morphologies are produced when a polymer solution is exposed to a nonsolvent that, following a period where mass is exchanged, precipitates and solidifies the polymer. Despite years of investigation, both experimental and theoretical, many questions surround the pathways to the microstructures that NIPS can produce. Here, we provide simulation results from a model that simultaneously captures both the processess of solvent/nonsolvent exchange and phase separation. We show that the time it takes the nonsolvent to diffuse to the bottom of the film is an important timescale, and that phase separation is possible at times both much smaller and much larger than this scale. Our results include both one-dimensional simulations of the mass transfer kinetics and two- and three-dimensional simulations of morphologies at both short and long times. We find good qualitative agreement with experimental heuristics, but we conclude that an additional model for the vitrification process will be key for fully explaining experimental observations of microstructure formation.

Lateral phase separation in polymer-blend thin films: surface bifurcation

We use simulations of a binary polymer blend confined between selectively attracting walls to identify and explain the mechanism of lateral phase separation via a transient wetting layer. We first show that equilibrium phases in the film are described by one-dimensional phase equilibria in the vertical (depth) dimension, and demonstrate that effective boundary conditions imposed by the film walls pin the film profile at the walls. We then show that, prior to lateral phase separation, distortion of the interface in a transient wetting layer is coupled to lateral phase separation at the walls. Using Hamiltonian phase portraits, we explain a "surface bifurcation mechanism" whereby the volume fraction at the walls evolves and controls the dynamics of the phase separation. We suggest how solvent evaporation may assist our mechanism.

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.

Breakup of a transient wetting layer in polymer blend thin films: unification with 1D phase equilibria

We show that lateral phase separation in polymer blend thin films can proceed via the formation of a transient wetting layer which breaks up to give a laterally segregated film. We show that the growth of lateral inhomogeneities at the walls in turn causes the distortion of the interface in the transient wetting layer. By addressing the 1D phase equilibria of a polymer blend thin film confined between selectively attracting walls, we show that the breakup of a transient wetting layer is due to wall-blend interactions; there are multiple values of the volume fraction at the walls which solve equilibrium boundary conditions. This mechanism of lateral phase separation should be general.

Fluid-fluid demixing of off-critical colloid-polymer systems confined between parallel plates

We investigate the off-critical demixing of colloid-polymer systems confined between two parallel plates, where the surface potential is short ranged. We study the case where the minority phase completely wets the surfaces. We find that initially the sample separates as in bulk, until the size of the domains becomes sufficiently large such that further growth is restricted by the plate spacing. The behaviour of the droplets is then determined by the wettability of the walls. We furthermore explore a sample where the loss of wetting phase material to the surfaces causes a shift from a morphology associated with an unstable sample, showing spinodal decomposition, to that associated with a metastable sample. This underlines the importance of the rich interplay between the viscosity contrast and the local volume fraction on the observed morphologies.

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.

Scenarios of heterogeneous nucleation and growth studied by cell dynamics simulation

The dynamics of phase transformation due to homogeneous nucleation has long been analyzed using the classic Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. However, the dynamics of phase transformation due to heterogeneous nucleation has not been studied systematically even though it is vitally important technologically. In this report, the author studies the dynamics of heterogeneous nucleation theoretically and systematically using the phenomenological time-dependent Ginzburg-Landau (TDGL)-type model combined with the cell dynamics method. In this study the author focuses on the dynamics of phase transformation when the material is sandwiched by two supporting substrates. This model is supposed to simulate phase change storage media. Since both homogeneous and heterogeneous nucleations can occur simultaneously, the author predicts a few scenarios of phase transformation including homogeneous nucleation regime, heterogeneous nucleation regime, and the homogeneous-heterogeneous coexistence regime. These predictions are directly confirmed by numerical simulation using the TDGL model. The outcome of the study was that the KJMA formula has limited use when heterogeneous nucleation exists, but it could still give some information about the microscopic mechanism of phase transformation at various stages during phase transformation.

Wetting-layer formation mechanisms of surface-directed phase separation under different quench depths with off-critical compositions in polymer binary mixture

Focusing on the off-critical condition, the quench depth dependence of surface-directed phase separation in the polymer binary mixture is numerically investigated by combination of the Cahn-Hilliard-Cook theory and the Flory-Huggins-de Gennes theory. Two distinct situations, i.e., for the wetting, the minority component is preferred by the surface and the majority component is preferred by the surface, are discussed in detail. The simulated results show that the formation mechanism of the wetting layer is affected by both the quench depth and the off-critical extent. Moreover, a diagram, illustrating the formation mechanisms of the wetting layer with various quench depths and compositions, is obtained on the basis of the simulated results. It is found that, when the minority component is preferred by the surface, the growth of the wetting layer can exhibit pure diffusion limited growth law, logarithmic growth law, and Lifshitz-Slyozov growth law. However, when the majority component is preferred by the surface, the wetting layer always grows logarithmically, regardless of the quench depth and the off-critical extent. It is interesting that the surface-induced nucleation can be observed in this case. The simulated results demonstrate that the surface-induced nucleation only occurs below a certain value of the quench depth, and a detailed range about it is calculated and indicated. Furthermore, the formation mechanisms of the wetting layer are theoretically analyzed in depth by the chemical potential gradient.

Influence of electric field on the phase transitions of the hexagonal cylinder phase of diblock copolymers

We have used the cell dynamic simulations (CDS) method to study the evolution of asymmetric and symmetric diblock copolymers under electric fields. For symmetric diblock copolymers, long-range-ordered lamellar phases form readily under electric fields. For asymmetric diblock copolymers, sphere-to-cylinder phase transitions occur rapidly when strong electric fields are applied, but it takes longer for the system to form hexagonal cylinder structures. The results of these simulations suggest that the sphere phase is stable under weak electric fields, but a threshold electric intensity exists for the sphere-to-cylinder phase transition. In addition, we also studied the kinetic pathways of the transition of the lamellar phase to the hexagonal cylinder phase of the asymmetric diblock copolymers under electric fields. Hexagonal cylinder structures form when the lamellar phase is subjected to a sudden temperature jump. The scattering functions suggest that the hexagonal cylinder structures are very regular and possess very few flaws.

Numerical treatment of the dynamics of a conserved order parameter in the presence of walls

We discuss how the diffusive dynamics of a conserved order parameter should be numerically treated when impenetrable wall surfaces are present and interact with the degrees of freedom characterized by the order parameter. We derive the discretization scheme for the dynamics, paying particular attention to the conservation of the order parameter in the strict numerical sense. The discretized chemical potential, or the functional derivative of the free energy, contains a surface contribution inversely proportional to the grid spacing Delta z, which was proposed heuristically in a recent paper of Henderson and Clarke [Macromol. Theory Simul. 14, 435 (2005)]. Although apparently that surface contribution diverges in the continuum limit Delta z --> 0, we can show, by an analytic argument and numerical calculations, that this divergence does not yield any anomalies, and that our discretization scheme is well defined in this limit. We also discuss the correspondence of our treatment to the model proposed by Puri and Binder [Phys. Rev. A 46, R4487 (1992)] extensively used for the present problem.

Long-range ordered structures in diblock copolymer melts induced by combined external fields

The structure of diblock copolymer melts under a single external electric or shear field, as well as under combined orthogonal external fields was investigated using a cell dynamic system. The phase structure was determined by coupling the effects of the external fields with the original structure of the bulk free of external fields. The single electric or shear field generated long-range cylinders in asymmetric A4mB6m diblock copolymers and distorted lamellae in symmetric A5mB5m diblock copolymers. Successive orthogonal shear followed by an electric external field generated long-range lamellae in symmetrical A5mB5m systems. However, the simultaneous orthogonal electric and shear fields could more easily form long-range lamellae than the sequential orthogonal fields. The dynamical processes in diblock copolymer melts under orthogonal fields have been also examined.

Spinodal decomposition, power laws, and wetting at a triple point

We study numerically the dynamics of phase separation in ternary mixtures at a triple point. For the full range of compositions and for different interaction parameters, the long time growth is in accord with a universal law. The early time behavior is governed by the structure of the spinodal region, including the possibility of a two step separation and decomposition originating at a surface and propagating into the bulk. The appearance of the domains is governed by the wetting properties of the mixture and the growth of a wetting layer follows again the universal law; a result that we can interpret with a simple phenomenological model.

Surface-directed phase separation with off-critical composition: analytical and numerical results

We study the interplay of wetting and phase separation in an unstable binary mixture (AB) with off-critical composition, placed in contact with a surface which prefers the component A. We consider surface potentials V(z) approximately z(-n), where z is the distance from the surface, and present analytical arguments and detailed numerical results to elucidate wetting-layer kinetics for arbitrary mixture compositions. If the preferred component is the minority phase, the wetting-layer thickness exhibits a potential-specific behavior at early times tau, R1 approximately tau(1/(n+2)), before crossing over to the universal growth law, R1 approximately tau(1/3). On the other hand, if the preferred component is the majority phase, there is a crossover from potential-specific growth (as before) to a slower growth regime.

Phase separation under two-dimensional Poiseuille flow

The spinodal decomposition of a two-dimensional binary fluid under Poiseuille flow is studied by numerical simulation. We investigated time dependence of domain sizes in directions parallel and perpendicular to the flow. In an effective region of the flow, the power-law growth of a characteristic length in the direction parallel to the flow changes from the diffusive regime with the growth exponent alpha=1/3 to a new regime. The scaling invariance of the growth in the perpendicular direction is destroyed after the diffusive regime. A recurrent prevalence of thick and thin domains which determines log-time periodic oscillations has not been observed in our model. The growth exponents in the infinite system under two-dimensional Poiseuille flow are obtained by the renormalization group.

Critical properties and phase separation in lattice Boltzmann fluid mixtures

Basic equilibrium properties of lattice Boltzmann (LB) fluid mixtures (coexistence curve, surface tension, interfacial profile, correlation length) are calculated to characterize the critical phenomena occurring in these model liquids and to establish a reduced variable description allowing a comparison with real fluid mixtures. We observe mean-field critical exponents and amplitudes so that the LB model may be useful for modeling high molecular weight polymer blends and other fluid mixtures approximated over a wide temperature range by mean-field theory. We also briefly consider phase separation under quiescent and shearing conditions and point out the strong influence of interacting boundaries on the qualitative form of the late-stage phase-separation morphology.

Power laws and crossovers in off-critical surface-directed spinodal decomposition

We study the dynamics of phase separation in binary mixtures near a surface with a preferential attraction for one of the components of the mixture. We obtain detailed numerical results for a range of mixture compositions. In the case where the minority component is attracted to the surface, wetting layer growth is characterized by a crossover from a surface-potential-dependent growth law to a universal law. We formulate a simple phenomenological model to explain our numerical results.

Wetting in a phase separating polymer blend film: quench depth dependence

We have used 3He nuclear reaction analysis to measure the growth of the wetting layer as a function of immiscibility (quench depth) in blends of deuterated polystyrene and poly(alpha-methylstyrene) undergoing surface-directed spinodal decomposition. We are able to identify three different laws for the surface layer growth with time t. For the deepest quenches, the forces driving phase separation dominate (high thermal noise) and the surface layer grows with a t(1/3) coarsening behavior. For shallower quenches, a logarithmic behavior is observed, indicative of a low noise system. The crossover from logarithmic growth to t(1/3) behavior is close to where a wetting transition should occur. We also discuss the possibility of a "plating transition" extending complete wetting to deeper quenches by comparing the surface field with thermal noise. For the shallowest quench, a critical blend exhibits a t(1/2) behavior. We believe this surface layer growth is driven by the curvature of domains at the surface and shows how the wetting layer forms in the absence of thermal noise. This suggestion is reinforced by a slower growth at later times, indicating that the surface domains have coalesced. Atomic force microscopy measurements in each of the different regimes further support the above. The surface in the region of t(1/3) growth is initially somewhat rougher than that in the regime of logarithmic growth, indicating the existence of droplets at the surface.

Filler-induced composition waves in phase-separating polymer blends

The influence of immobile filler particles (spheres, fibers, platelets) on polymer-blend phase separation is investigated computationally using a generalization of the Cahn-Hilliard-Cook (CHC) model. Simulation shows that the selective affinity of one of the polymers for the filler surface leads to the development of concentration waves about the filler particles at an early stage of phase separation in near critical composition blends. These "target" patterns are overtaken in late-stage phase separation by a growing "background" spinodal pattern characteristic of blends without filler particles. The linearized CHC model is used to estimate the number of composition oscillations emanating from isolated filler particles. In far-off-critical composition blends, an "encapsulation layer" grows at the surface of the filler rather than a target pattern. The results of these simulations compare favorably with experiments on filled phase-separating ultrathin blend films in which the filler particles are immobilized on a solid substrate.