Phase separation in two-dimensional fluid mixtures

Spatiotemporal Mapping of Hole Nucleation and Growth during Block Copolymer Terracing with High-Speed Atomic Force Microscopy

As a platform for investigating two-dimensional phase separation, we track the structural evolution of block copolymer thin films during thermal annealing with environmentally controlled atomic force microscopy (AFM). Upon thermal annealing, block copolymer films with incommensurate thickness separate into a terraced morphology decorated with holes. With in situ imaging at 200 °C, we follow the continuous progression of terrace formation in a single region of a cylinder-forming poly(styrene-block-methyl methacrylate) thin film, beginning with the disordered morphology on an unpatterned silicon substrate and continuing through nucleation and coarsening stages. Topographic AFM imaging with nanoscale resolution simultaneously captures ensemble hole growth statistics while locally tracking polymer diffusion through measurements of the film thickness. At early times, we observe homogeneous hole nucleation and isotropic growth, with kinetics following the predictions of classical nucleation theory. At later times, however, we find anomalous hole growth which arises due to the combination of Ostwald ripening and coalescence mechanisms. In each case, our real-space observations highlight the importance of hole interactions for determining coarsening kinetics, mediated either through the interconnected phase for Ostwald ripening or through binary collision events for coalescence.

Controlling cluster size in 2D phase-separating binary mixtures with specific interactions

By varying the concentration of molecules in the cytoplasm or on the membrane, cells can induce the formation of condensates and liquid droplets, similar to phase separation. Their thermodynamics, much studied, depends on the mutual interactions between microscopic constituents. Here, we focus on the kinetics and size control of 2D clusters, forming on membranes. Using molecular dynamics of patchy colloids, we model a system of two species of proteins, giving origin to specific heterotypic bonds. We find that concentrations, together with valence and bond strength, control both the size and the growth time rate of the clusters. In particular, if one species is in large excess, it gradually saturates the binding sites of the other species; the system then becomes kinetically arrested and cluster coarsening slows down or stops, thus yielding effective size selection. This phenomenology is observed both in solid and fluid clusters, which feature additional generic homotypic interactions and are reminiscent of the ones observed on biological membranes.

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.

Advancing micro-scale cooling by utilizing liquid-liquid phase separation

Achieving effective cooling within limited space is one of the key challenges for miniaturized product design. State-of-the-art micro-scale cooling enhancement techniques incorporate flow disturbances and boiling to reach high performance. However, these methods face the inherent issues of extra pressure drop, flow instability and dry-out that limits heat flux. Here we demonstrate that substantial cooling capability enhancement, up to 2.5 times, is realized by introducing the phase separation of a triethylamine (TEA)/water mixture at the micro-scale. Our experiments show that the enhancement behavior is closely related to the system’s initial composition, temperature, and flow conditions. Moreover, the mixture system exhibits reduced pressure drop after separation, which makes it more promising in serving practical applications. The results reveal new possibilities for liquid coolant selection and provide the experimental foundation for further research in this area.

Kinetics of Vapor-Solid Phase Transitions: Structure, Growth, and Mechanism

The kinetics of the separation between low and high density phases in a single component Lennard-Jones model is studied via molecular dynamics simulations, at very low temperatures, in the space dimension d=2. For densities close to the vapor branch of the coexistence curve, disconnected nanoscale clusters of the high density phase exhibit essentially ballistic motion. Starting from nearly circular shapes, at the time of nucleation, these clusters grow via sticky collisions, gaining filamentlike nonequilibrium structure at a later time, with a very low fractal dimensionality. The origin of the latter is shown to lie in the low mobility of the constituent particles, in the corresponding cluster reference frame, due to the (quasi-long-range) crystalline order. Standard self-similarity in the domain pattern, typically observed in the kinetics of phase transitions, is found to be absent. This invalidates the common method, that provides a growth law comparable to that in solid mixtures, of quantifying growth. An appropriate alternative approach, involving the fractality, quantifies the growth of the characteristic "length" to be a power law with time, the exponent being strongly temperature dependent. The observed growth law is in agreement with the outcome of a nonequilibrium kinetic theory.

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.

Morphological evolution of domains in spinodal decomposition

Domain growth in spinodal decomposition is usually described by a single time-evolving length scale. We show that the evolution of morphology of domains is nonmonotonic. The domains elongate rapidly at first and then, with the help of hydrodynamics, return to a more circular shape. The initial elongation phase does not alter with hydrodynamics. A small deviation from critical composition changes the morphology dramatically.

Hydrodynamic effects on spinodal decomposition kinetics in planar lipid bilayer membranes

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, domain growth in the presence of hydrodynamic interactions both within the (effectively) two-dimensional membrane and in the three-dimensional solvent in which the membrane is immersed has received little attention. In this work, we explore the role of hydrodynamic effects on spinodal decomposition kinetics via continuum simulations of a convective Cahn-Hilliard equation for membrane composition coupled to the Stokes equation. Our approach explicitly includes hydrodynamics both within the planar membrane and in the three-dimensional solvent in the viscously dominated flow regime. Numerical simulations reveal that dynamical scaling breaks down for critical lipid mixtures due to distinct coarsening mechanisms for elongated versus more isotropic compositional lipid domains. The breakdown in scaling should be readily observable in experiments on model membrane systems.

Distance of closest approach of two arbitrary hard ellipses in two dimensions

The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [Vieillard-Baron, J. Chem. Phys. 56, 4729 (1972); Perram and Wertheim, J. Comput. Phys. 58, 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals.

Universal dynamic exponent at the liquid-gas transition from molecular dynamics

The liquid-gas system is expected to exhibit distinct dynamic behavior in the fluid's critical region (model H). We present molecular dynamics simulations of a Lennard-Jones fluid model starting from specially designed, near-equilibrium, initial conditions. By following the fluid's relaxation towards equilibrium, we calculate the requisite transport coefficients in the critical region. The results yield the scaling behavior of the thermal diffusion coefficient D(T) approximately xi(-1.023+/-0.018) (xi is the correlation length) and a nonconventional divergent heat conductivity, all of which are in accord with mode-coupling and renormalization group predictions, as well as some experimental data.

Smoothed particle hydrodynamics model for phase separating fluid mixtures. II. Diffusion in a binary mixture

A previously formulated smoothed particle hydrodynamics model for a phase separating mixture is tested for the case when viscous processes are negligible and only mass and energy diffusive processes take place. We restrict ourselves to the case of a binary mixture that can exhibit liquid-liquid phase separation. The thermodynamic consistency of the model is assessed and the potential of the model to study complex pattern formation in the presence of various thermal boundaries is illustrated.

Scale invariance in coarsening of binary and ternary fluids

Phase separation in binary and ternary fluids is studied using a two-dimensional lattice gas automata. The lengths given by the the first zero crossing point of the correlation function and the total interface length is shown to exhibit power law dependence on time. In binary mixtures, our data clearly indicate the existence of a regime having more than one length scale, where the coarsening process proceeds through the rupture and reassociation of domains. In ternary fluids; in the case of symmetric mixtures there exists a regime with a single length scale having dynamic exponent 1/2, while in asymmetric mixtures our data establish the break down of scale invariance.

Hydrodynamic bubble coarsening in off-critical vapor-liquid phase separation

Late-stage coarsening in off-critical vapor-liquid phase separation is reexamined. In the limit of bubbles of vapor distributed throughout a continuous liquid phase, it is argued that coarsening proceeds via inertial hydrodynamic bubble collapse. This replaces the Lifshitz-Slyozov-Wagner mechanism seen in binary liquid mixtures. The arguments are strongly supported by simulations in two dimensions using a novel single-component soft-sphere fluid.

Two-dimensional model of phase segregation in liquid binary mixtures

The hydrodynamic effects on the late stage kinetics of phase separation in liquid mixtures is studied using the model H. Mass and momentum transport are coupled via a nonequilibrium body force, which is proportional to the Peclet number alpha, i.e., the ratio between convective and diffusive molar fluxes. Numerical simulations based on this theoretical model show that phase separation in low viscosity, liquid binary mixtures is mostly driven by convection, thereby explaining the experimental findings that the process is fast, with the typical size of single-phase domains increasing linearly with time. However, as soon as sharp interfaces form, the linear growth regime reaches an end, and the process appears to be driven by diffusion, although the condition of local equilibrium is not reached. During this stage, the typical size of the nucleating drops increases like t(n), where 1/3< n <1/2, depending on the value of the Peclet number. As the Peclet number increases, the transition between convection- and diffusion-driven regimes occurs at larger times, and therefore for larger sizes of the nucleating drops.