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

Microenvironment-mediated cancer dormancy: Insights from metastability theory

Dormancy is an evolutionarily conserved protective mechanism widely observed in nature. A pathological example is found during cancer metastasis, where cancer cells disseminate from the primary tumor, home to secondary organs, and enter a growth-arrested state, which could last for decades. Recent studies have pointed toward the microenvironment being heavily involved in inducing, preserving, or ceasing this dormant state, with a strong focus on identifying specific molecular mechanisms and signaling pathways. Increasing evidence now suggests the existence of an interplay between intracellular as well as extracellular biochemical and mechanical cues in guiding such processes. Despite the inherent complexities associated with dormancy, proliferation, and growth of cancer cells and tumor tissues, viewing these phenomena from a physical perspective allows for a more global description, independent from many details of the systems. Building on the analogies between tissues and fluids and thermodynamic phase separation concepts, we classify a number of proposed mechanisms in terms of a thermodynamic metastability of the tumor with respect to growth. This can be governed by interaction with the microenvironment in the form of adherence (wetting) to a substrate or by mechanical confinement of the surrounding extracellular matrix. By drawing parallels with clinical and experimental data, we advance the notion that the local energy minima, or metastable states, emerging in the tissue droplet growth kinetics can be associated with a dormant state. Despite its simplicity, the provided framework captures several aspects associated with cancer dormancy and tumor growth.

Long-Range Surface-Directed Polymerization-Induced Phase Separation: A Computational Study

The presence of a surface preferably attracting one component of a polymer mixture by the long-range van der Waals surface potential while the mixture undergoes phase separation by spinodal decomposition is called long-range surface-directed spinodal decomposition (SDSD). The morphology achieved under SDSD is an enrichment layer(s) close to the wall surface and a droplet-type structure in the bulk. In the current study of the long-range surface-directed polymerization-induced phase separation, the surface-directed spinodal decomposition of a monomer-solvent mixture undergoing self-condensation polymerization was theoretically simulated. The nonlinear Cahn-Hilliard and Flory-Huggins free energy theories were applied to investigate the phase separation phenomenon. The long-range surface potential led to the formation of a wetting layer on the surface. The thickness of the wetting layer was found proportional to time t*1/5 and surface potential parameter h 1 1/5. A larger diffusion coefficient led to the formation of smaller droplets in the bulk and a thinner depletion layer, while it did not affect the thickness of the enrichment layer close to the wall. A temperature gradient imposed in the same direction of long-range surface potential led to the formation of a stripe morphology near the wall, while imposing it in the opposite direction of surface potential led to the formation of large particles at the high-temperature side, the opposite side of the interacting wall.

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.

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.

Phase separation in swelling and deswelling hydrogels with a free boundary

We present a full kinetic model of a hydrogel that undergoes phase separation during swelling and deswelling. The model accounts for the interfacial energy of coexisting phases, finite strain of the polymer network, and solvent transport across free boundaries. For the geometry of an initially dry layer bonded to a rigid substrate, the model predicts that forcing solvent into the gel at a fixed rate can induce a volume phase transition, which gives rise to coexisting phases with different degrees of swelling, in systems where this cannot occur in the free-swelling case. While a nonzero shear modulus assists in the propagation of the transition front separating these phases in the driven-swelling case, increasing it beyond a critical threshold suppresses its formation. Quenching a swollen hydrogel induces spinodal decomposition, which produces several highly localized, highly swollen phases which coarsen and are then ejected from free boundary. The wealth of dynamic scenarios of this system is discussed using phase-plane analysis and numerical solutions in a one-dimensional setting.

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.

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.

Phase separation of binary mixtures in thin films: Effects of an initial concentration gradient across the film

We study the kinetics of phase separation of a binary (A,B) mixture confined in a thin film of thickness D by numerical simulations of the corresponding Cahn-Hilliard-Cook (CHC) model. The initial state consisted of 50% A:50% B with a concentration gradient across the film, i.e., the average order parameter profile is Ψav(z,t=0)=(2z/D-1)Ψg,0≤z≤D, for various choices of Ψg and D. The equilibrium state (for time t→∞) consists of coexisting A-rich and B-rich domains separated by interfaces oriented perpendicular to the surfaces. However, for sufficiently large Ψg, a (metastable) layered state is formed with a single interface parallel to the surfaces. This phenomenon is explained in terms of a competition between domain growth in the bulk and surface-directed spinodal decomposition (SDSD) that is caused by the gradient. Thus, gradients in the initial state can stabilize thin-film morphologies which are not stable in full equilibrium. This offers interesting possibilities as a method for preparing novel materials.

Phase separation of thin-film polymer mixtures under in-plane electric fields

Phase-separation dynamics of polymer thin-film mixtures of polystyrene (PS) and poly(methyl methacrylate) (PMMA) are observed while an in-plane electric field is applied, instead of the out-of-plane fields usually employed previously. The phase separation is accompanied by the formation of PS dewetting holes at zero or weak fields. The dewetting velocity at 0.25 μm/min is a few times slower than that seen in regular bilayer dewetting. With the increasing of the field strength, we observe the formation of PS droplets in PMMA matrix, a reversal from zero- or low-field conditions. The PS dewetting holes are also suppressed. At further increased fields, PS droplets quickly penetrate up to the top of the PMMA matrix, leading to smaller and more irregular final PS droplets. This is manifested in the dramatic decrease in the growth exponent of the droplet size L from L∼t1.5 to L∼t0.1. These morphology changes are explained by the electrostatic energy resulted from the PS and PMMA dielectric contrast.

Kinetics of phase separation in thin films: lattice versus continuum models for solid binary mixtures

A description of phase separation kinetics for solid binary (A,B) mixtures in thin film geometry based on the Kawasaki spin-exchange kinetic Ising model is presented in a discrete lattice molecular field formulation. It is shown that the model describes the interplay of wetting layer formation and lateral phase separation, which leads to a characteristic domain size l(t) in the directions parallel to the confining walls that grows according to the Lifshitz-Slyozov t;{13} law with time t after the quench. Near the critical point of the model, the description is shown to be equivalent to the standard treatments based on Ginzburg-Landau models. Unlike the latter, the present treatment is reliable also at temperatures far below criticality, where the correlation length in the bulk is only of the order of a lattice spacing, and steep concentration variations may occur near the walls, invalidating the gradient square approximation. A further merit is that the relation to the interaction parameters in the bulk and at the walls is always transparent, and the correct free energy at low temperatures is consistent with the time evolution by construction.

Dynamical effects and phase separation in cooled binary fluid films

We study phase separation in thin films using a model based on the Navier-Stokes Cahn-Hilliard equations in the lubrication approximation, with a van der Waals potential to account for substrate-film interactions. We solve the resulting thin-film equations numerically and compare to experimental data. The model captures the qualitative features of real phase-separating fluids, in particular, how concentration gradients produce film thinning and surface roughening. The ultimate outcome of the phase separation depends strongly on the dynamical back reaction of concentration gradients on the flow, an effect we demonstrate by applying a shear stress at the film's surface. When the back reaction is small, the phase domain boundaries align with the direction of the imposed stress, while for larger back-reaction strengths, the domains align in the perpendicular direction.

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.

Spinodal decomposition in thin films: molecular-dynamics simulations of a binary Lennard-Jones fluid mixture

We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of binary fluids (AB), confined in a slit pore of width D. The pore walls are assumed to be flat and structureless and attract one component of the mixture (A) with the same strength. The pairwise interactions between the particles are modeled by the Lennard-Jones potential, with symmetric parameters that lead to a miscibility gap in the bulk. In the thin-film geometry, an interesting interplay occurs between surface enrichment and phase separation. We study the evolution of a mixture with equal amounts of A and B, which is rendered unstable by a temperature quench. We find that A-rich surface enrichment layers form quickly during the early stages of the evolution, causing a depletion of A in the inner regions of the film. These surface-directed concentration profiles propagate from the walls towards the center of the film, resulting in a transient layered structure. This layered state breaks up into a columnar state, which is characterized by the lateral coarsening of cylindrical domains. The qualitative features of this process resemble results from previous studies of diffusive Ginzburg-Landau-type models [S. K. Das, S. Puri, J. Horbach, and K. Binder, Phys. Rev. E 72, 061603 (2005)], but quantitative aspects differ markedly. The relation to spinodal decomposition in a strictly two-dimensional geometry is also discussed.

Bombardment-induced tunable superlattices in the growth of Au-Ni films

Highly ordered superlattices are typically created through the sequential deposition of two different materials. Here, we report our experimental observation of spontaneous formation of superlattices in coevaporation of Au and Ni under energetic ion bombardment. The superlattice periodicities are on the order of a few nanometers and can be adjusted through the energy and flux of ion beams. Such a self-organization process is a consequence of the bombardment-induced segregation and uphill diffusion within the advancing nanoscale subsurface zone in the film growth. Our observations suggest that ion beams can be employed to make tunable natural superlattices in the deposition of phase-separated systems with strong bombardment-induced segregation.

Molecular dynamics study of phase separation kinetics in thin films

We use molecular dynamics to simulate experiments where a symmetric binary fluid mixture (AB), confined between walls that preferentially attract one component (A), is quenched from the one-phase region into the miscibility gap. Surface enrichment occurs during the early stages, yielding a B-rich mixture in the film center with well-defined A-rich droplets. The droplet size grows with time as l(t) proportional t(2/3) after a transient regime. The present atomistic model is also compared to mesoscopic coarse-grained models for this problem.

Kinetics of phase separation in thin films: simulations for the diffusive case

We study the diffusion-driven kinetics of phase separation of a symmetric binary mixture (AB), confined in a thin-film geometry between two parallel walls. We consider cases where (i) both walls preferentially attract the same component (A), and (ii) one wall attracts and the other wall attracts (with the same strength). We focus on the interplay of phase separation and wetting at the walls, which is referred to as surface-directed spinodal decomposition (SDSD). The formation of SDSD waves at the two surfaces, with wave vectors oriented perpendicular to them, often results in a metastable layered state (also referred to as "stratified morphology"). This state is reminiscent of the situation where the thin film is still in the one-phase region but the surfaces are completely wet, and hence coated with thick wetting layers. This metastable state decays by spinodal fluctuations and crosses over to an asymptotic growth regime characterized by the lateral coarsening of pancakelike domains. These pancakes may or may not be coated by precursors of wetting layers. We use Langevin simulations to study this crossover and the growth kinetics in the asymptotic coarsening regime.

Phase behavior and local structure of a binary mixture in pores: Mean-field lattice model calculations for analyzing neutron scattering data

We investigate the phase behavior of an asymmetric binary liquid A-W mixture confined between two planar homogenous substrates (slit pore). Molecules of species W interact preferentially with the solid walls via a long-range potential. Assuming nearest-neighbor attractions between the liquid molecules, we employ a lattice-gas model and a mean-field approximation for the grand potential. Minimization of this potential yields the density profiles of thermodynamically stable phases for fixed temperature, chemical potentials of both species, pore width and strengths of attraction. This model is used to analyze experimental small-angle neutron-scattering (SANS) data on the microscopic structure of the binary system isobutyric acid (iBA)+heavy water (D2O) inside a mesoscopic porous matrix (controlled-pore glass of about 10 nm mean pore width). Confinement-independent model parameters are adjusted so that the theoretical liquid-liquid coexistence curve in the bulk matches its experimental counterpart. By choosing appropriate values of the pore width and the attraction strength between substrates and water we analyze the effect of confinement on the phase diagram. In addition to a depression of the liquid-liquid critical point we observe surface induced phase transitions as well as water-film adsorption near the walls. The temperature dependence of the structure of water-rich and iBA-rich phases of constant composition are discussed in detail. The theoretical predictions are consistent with results of the SANS study and assist their interpretation.