Off-critical Mixtures Research Articles

Phase separation in binary fluid mixtures with symmetric and asymmetric Schmidt numbers: A DPD study.

We investigate the effect of the Schmidt number (Sc) on phase separation dynamics of two immiscible fluids in a two-dimensional periodic box using dissipative particle dynamics. The range of Sc investigated spans liquid-liquid separation processes. Phase separation is characterized by a domain size r(t), which typically follows a power law tβ in time t, where β is a characteristic exponent corresponding to the coarsening mechanism at play. The phase separation dynamics is studied for strongly (deep quench) separating mixtures. We consider cases of critical (ϕ ∼ 0.5) and off-critical (ϕ < 0.5) mixtures of fluids A and B for both ScA = ScB and ScA ≠ ScB. In all cases, the growth dynamics slow down with the increasing Schmidt number of either fluid. We observe the power law exponent β = 0.5 for symmetric (ScA = ScB) critical mixtures and β = 0.33 for all other cases. However, for off-critical mixtures, the exponent is 0.33 irrespective of the Schmidt number ratio of the two fluids. We explain these results from an analysis of the competition between diffusive effects vis-á-vis dynamical forces.

Universal finite-size scaling function for kinetics of phase separation in mixtures with varying number of components

From Kawasaki-exchange Monte Carlo simulations of the $q$-state Potts model, we present results for the kinetics of phase separation in multicomponent mixtures, for $q\ensuremath{\le}10$, in space dimension $d=2$. A particular focus has been on the quantification of finite-size scaling functions for various values of $q$ and quench depths. For a range of final quench temperatures, our analyses, via finite-size scaling and other state-of-the-art methods, show that the growth follows the Lifshitz-Slyozov behavior, expected for a diffusive mechanism, irrespective of the number of components. We show that the growth for different $q$ values and quench temperatures, in finite systems, can be described by a universal scaling function with a nonuniversal metric factor, originating from the differences in the amplitudes. We also demonstrate the morphological and kinetic equivalence between a $q$-component equal proportion mixture and an off-critical binary mixture, in the framework of the Ising model, with relative concentration of the minority component in the latter being ${x}_{c}=1/q$.

Two-dimensional steady states in off-critical mixtures with high interface tension

We present 2D steady concentration profiles of confined layers of off-critical polymer blends. The layer rests on a solid substrate and has a flat free surface due to very high surface tension. The profiles correspond to non-linear steady solutions of the Cahn-Hilliard equation in a rectangular domain. The free polymer-gas interface is considered to be sharp, while the internal interfaces are diffuse. We explore the rich solution structure (including laterally structured layers, stratified layers, checkerboard structures, oblique states and droplets) as a function of mean concentration.

Liquid mixture convection during phase separation in a temperature gradient

We simulate the phase separation of a low-viscosity binary mixture, assuming that the fluid system is confined between two walls that are cooled down to different temperatures below the critical point of the mixture, corresponding to quenches within the unstable range of its phase diagram. Spinodal decomposition patterns for off-critical mixtures are studied numerically in two dimensions in the creeping flow limit and for a large Lewis number, together with their dependence on the fluidity coefficient. Our numerical results reproduce the large-scale unidirectional migration of phase-separating droplets that was observed experimentally by Califano et al. [“Large-scale, unidirectional convection during phase separation of a density-matched liquid mixture,” Phys. Fluids 17, 094109 (2005)], who measured typical speeds that are quite larger than the Marangoni velocity. To understand this finding, we then studied the temperature-gradient-induced motion of an isolated droplet of the minority phase embedded in a continuous phase, showing that when the drop is near local equilibrium, its speed is of the same order as the Marangoni velocity, i.e., it is proportional to the unperturbed temperature gradient and the fluidity coefficient. However, far from local equilibrium, i.e., for very large unperturbed temperature gradients, the drop first accelerates to a speed that is larger than the Marangoni velocity, then, later, it decelerates, exhibiting an increase-decrease behavior, as described by Yin et al. [“Thermocapillary migration of nondeformable drops,” Phys. Fluids 20, 082101 (2008)]. Such behavior is due to the large nonequilibrium, Korteweg-driven convection, which at first accelerates the droplets to relatively large velocities, and then tends to induce an approximately uniform inside temperature distribution so that the drop experiences an effective temperature gradient that is much smaller than the unperturbed one and, consequently, decelerates.

Tuning the Morphology of Cellulose Acetate Gels by Manipulating the Mechanism of Phase Separation

The effect of dihydric alcohol (nonsolvent) addition on the rheological and microstructural behavior of cellulose acetate (CA) in a ternary CA, N,N-dimethylacetamide (DMA), nonsolvent system was investigated. Increasing the dihydric alcohol concentration led to enhanced steady shear viscosity and dynamic viscoelastic properties that were dependent on CA concentration. Changing the dihydric alcohol from 1,2-ethanediol to 1,4-butanediol and 1,6-hexanediol increased the moduli and decreased the concentration of nonsolvent at which the sol-gel transition occurred. At 10 wt % CA concentration the modulus and gel morphology of the 1,2-ethanediol and 1,4-butanediol systems were quite similar and distinctly different from that of 1,6-hexanediol. In the former, the gel morphologies were more heterogeneous, evident of more extensive coarsening, and likely obtained via nucleation and growth and spinoidal decomposition of off-critical mixtures. The latter exhibited more uniform dense network morphology, indicative of a spinoidal decomposition of near-critical mixtures. The gels were fractal in nature and exhibited different fractal dimensions in-line with the observed differences in microstructure; D ∼ 1.87 ± 0.02 (1,2-ethanediol and 1,4-butanediol) and D ∼ 1.97 ± 0.02 (1,6-hexanediol). However, at 15 wt % CA content, the gels exhibited more similar viscoelastic behavior and gel microstructures; D ∼ 1.97 ± 0.02 for all three dihydric alcohol systems.

Multilamellar Structures Induced by Hydrophilic and Hydrophobic Ions Added to a Binary Mixture ofD2Oand 3-Methylpyridine

A phase transition is observed between a one-phase disordered phase and an ordered phase with multilamellar (onion) structures in an off-critical mixture of D2O and 3-methylpyridine (3MP) containing 85 mM of a salt in the absence of a surfactant. The salt consists of hydrophilic cations and hydrophobic anions that interact asymmetrically with the solvent composition fluctuations inducing mesophases. The structure factor of the composition distribution obtained from small-angle neutron scattering has a peak at an intermediate wave number in the disordered phase and multiple peaks in the ordered phase. Lamellar layers forming onions are composed of solvation-induced charged membranes swollen by D2O. The onion phase is realized only for small volume fractions of 3MP (in D2O-rich solvent).

Diffuse-interface modeling of phase segregation in liquid mixtures

We simulate the phase separation of a binary mixture that is deeply quenched into the unstable range of its phase diagram. The mixture is described through the diffuse-interface model and the governing equations are integrated in 2D and 3D in a periodic box and in a channel using a pseudo-spectral method. Spinodal decomposition patterns for critical and off-critical mixtures are studied, revealing the scaling laws of the characteristic lengthscale and composition of single-phase microdomains, together with their dependence on the Peclet number. Comparison between 2D and 3D results reveals that 2D simulations capture, even quantitatively, the main features of the phenomenon. However, while the agreement between 2D and 3D simulations is excellent when the mixture is confined in a periodic box, it appears to be less pronounced in a channel-like geometry.

Coarsening Rates in Off-Critical Mixtures

We study coarsening of a binary mixture within the Mullins--Sekerka evolution in the regime where one phase has small volume fraction $\phi \ll1$. Heuristic arguments suggest that the energy density, which represents the inverse of a typical length scale, decreases as $\phi t^{-1/3}$ as $t \to \infty$. We prove rigorously a corresponding weak lower bound. Moreover, we establish a stronger result for the two-dimensional case, where we find a lower bound of the form $ \phi(\ln \phi^{-1})^{1/3}t^{-1/3}$. Our approach follows closely the analysis in [R. V. Kohn and F. Otto, Comm. Math. Phys., 229 (2002), pp. 375-395], which exploits the relation between two suitable length scales. Our main contribution is an isoperimetric inequality in the two-dimensional case.

Adsorption at the liquid-vapor surface of a binary liquid mixture

In a binary liquid mixture, the component possessing the lowest surface tension preferentially adsorbs at the liquid-vapor surface. In the past this adsorption behavior has been extensively investigated for critical binary liquid mixtures near the mixture's critical temperature T(c). In this fluctuation-dominated regime the adsorption is described by a universal function of the dimensionless depth zxi where xi is the bulk correlation length. Fewer studies have quantitatively examined adsorption for off-critical mixtures because, in this case, one must carefully account for both the bulk and surface crossover from the fluctuation-dominated regime (close to T(c)) to the mean-field dominated regime (far from T(c)). In this paper we compare extensive liquid-vapor ellipsometric adsorption measurements for the mixture aniline+cyclohexane at a variety of critical and noncritical compositions with the crossover theory of Kiselev and co-workers [J. Chem. Phys. 112, 3370 (2000)].

Kinetics of Phase Separation in Poly(ɛ-caprolactone)/Poly(ethylene glycol) Blends

The poly(ɛ-caprolactone)/poly(ethylene glycol) (PCL/PEG) blends reveal a miscibility window of upper critical solution temperature (UCST) character. The kinetics of liquid–liquid phase separation (LLPS) for the blends of PCL/PEG is investigated by time-resolved small angle light scattering (TRSALS). The time evolution of scattering profile is analyzed by linear Cahn–Hilliard theory for early stage of spinodal decomposition (SD). The evolution of the maximum intensity Im(t) and the corresponding wavenumber qm(t) obey the power-law scheme (Im(t)∼tβ and qm(t)∼t−α). A relation of β=3α in late stage is obtained almost the same scaling exponents with β≅1 and α≅1/3 for various quenching depths. The α≅1/3 implied that a coarsening mechanism at the late stage of phase separation may proceed with Ostwald ripening or Brownian coalescence process. Besides, the intermediate and late stages of SD can be scaled into a universal from represented well by Furukawa’s structure factor. The percolation to cluster transition is accompanied with α∼0.13→1/3 from intermediate to late stage of SD for the off-critical mixture of PCL/PEG (4/6) blend. In this study, the experimental result demonstrates that the crystallization is a viable mechanism to lock phase-separated structure of the blends. The competition between phase separation and crystallization has been suggested to determine the final morphology.

Thermal phase behavior of triethylamine–water mixtures studied by near-infrared spectroscopy: band shift of the first overtone of the C–H stretching modes and the phase diagram

Thermal phase behavior of triethylamine (TEA)–water mixtures with various concentrations has been studied by use of near-infrared (NIR) spectroscopy. Bands due to the first overtones of C–H stretching bands (6000–5500 cm −1) of TEA in the NIR spectra of one-phase region of the mixtures show significant shifts to a lower wavenumbers during heating process. It has been revealed that the magnitude of the band shift for the critical mixture (32.1 wt%) is markedly prominent in comparison with that of the off-critical mixtures. Since the C–H band shifts to the lower wavenumber are accompanied by the condensation of TEA, these results suggest that the microscopic association of non-polar moieties acts as a trigger for the LCST-type phase separation.

Percolation-to-droplets transition during spinodal decomposition in polymer blends, morphology analysis.

Phase separation kinetics of the off-critical mixture of polystyrene and poly(methylphenylsiloxane) is studied by the time-resolved light scattering and optical microscopy. The results from the light scattering experiments are correlated with the images obtained by the optical microscopic observation in order to find characteristic features of the scattering intensity during the percolation-to-droplets morphology transition. At the beginning of the spinodal decomposition process only a bicontinuous network is present in the system and the light scattering intensity has only one peak. The network coarsens and at the same time small droplets appear in the system resulting in a growth of the scattering intensity at very small wave vectors. When the large network starts to break up into disjoint elongated domains a second peak in the scattering intensity appears. Finally, both peaks merge into a single peak at zero wave vector, indicating a complete transformation of elongated domains into spherical droplets of variable sizes. The comparison of the direct microscopic observations with the light scattering spectra shows that the process of breaking up of the bicontinuous network starts when the growth of the first peak, corresponding to the bicontinuous pattern, becomes very slow (essentially pinned down).

Inhibition of thin polystyrene film dewetting via phase separation

By addition of a small amount of poly(methyl methacrylate) (PMMA) into polystyrene (PS), we present a novel approach to inhibit the dewetting process of thin PS film through phase separation of the off-critical polymer mixture (PS/PMMA). Owing to the preferential segregation of PMMA to the solid SiOx substrate, a nanometer thick layer, rich in PMMA phase, is formed. It is this diffusive PMMA-rich phase layer near the substrate that alters the dewetting behavior of the PS film. The degree of inhibition of dewetting depends on the concentration and molecular weight of PMMA component. PMMA with low (15.9k) and intermediate (102.7k) molecular weight stabilizes the films more effectively than that with a higher molecular weight (387k).

Convection-driven phase segregation of deeply quenched liquid mixtures

Observing the phase separation of deeply quenched, low viscosity liquid mixtures we inferred that the process is driven by the convection due to capillary forces, and not by molecular diffusion neither by gravity, heat or surface effects. After quenching a partially miscible, initially homogeneous, off-critical liquid mixture to a temperature T deeply below its critical point of miscibility Tc, with |T−Tc|/Tc≈0.1, we observed the formation of rapidly coalescing droplets of the minority phase, whose size grows linearly with time. Following the motion of isolated 10 μm droplets, we saw that they move in random directions at speeds exceeding 100 μm/s, showing that during most of the process the system is far from local equilibrium. Eventually, when their size reaches the capillary length, the nucleating drops start sedimenting as gravity becomes the dominant force. This behavior was observed for both density-segregated and density-matched systems, irrespectively whether they were kept in horizontal or vertical cells. The experiments were repeated using both untreated (i.e., hydrophilic) and modified (i.e., hydrophobic) cell walls, with identical results and, in addition, no bulk motion was observed when the mixture was replaced with water, showing that the observed convection is not induced by gravity, neither by surface or temperature effects. Using a simple dimensional analysis of the governing equations based on the diffuse interface model, we showed that convection is induced by the coalescence among drops which, in turn, is the result of a nonequilibrium capillary force that indeed dominates both diffusion and gravity forces.

Topography of Phase-Separated Critical and Off-Critical Polymer Mixtures

We investigate the spinodal decomposition of a polymer mixture, at both critical and off-critical compositions, using atomic force microscopy. Phase separation in the bulk is imaged using tapping mode on the surface of microtomed samples. The generated surface profiles, revealed in height images, are analyzed according to their in-plane spinodal morphology and their (perpendicular) height distribution. The former is characterized in terms of the periodicity of the structure and volume fraction of coexisting phases, both in the percolation and cluster regimes. The average height profiles are shown to be bimodal with a height step, Δh, ranging from 1 to 7 nm, for the temperature quench depths spanned. Δh is time-independent but depends linearly on annealing temperature and therefore on the composition difference between coexisting phases. This temperature dependence allows us to extrapolate to the mixture's critical temperature. A blend of tetramethyl bisphenol A polycarbonate and polystyrene was employed for this demonstration.

Effects of a fumed silica network on kinetics of phase separation in polymer blends

We have carried out a systematic investigation of the kinetics of domain growth of a model binary mixture in contact with a fractal network similar to the fumed silica network used in recent experiments with polymer blends. This network has selective affinity for one component of the blend. We study the morphology of the growing domains and the wetting layer, the growth exponent, and dynamical scaling behavior for a critical composition of the mixture. We find that the characteristic size of domains grows as t1/3 for deep quenches, as long as the average domain size is small compared to the average “pore” radius of the unoccupied region. This suggests that the kinetics of domain growth at intermediate times is not appreciably perturbed by the presence of the network. For off-critical compositions, we study domain growth in two different situations where either the majority or the minority component of the blend wets the network. When the majority component wets the network, a network-induced nucleation is possible for sufficiently off-critical mixtures due to the reduction or elimination of the local nucleation barrier for the minority phase near the network. For this reason, minority droplets nucleate predominantly near the network before they appear in the bulk. When the minority phase wets the network, a slowdown in wetting layer growth is found to occur at late times due to a depletion of the system of its minority component.

Spinodal Decomposition in a Subsurface Layer of a Polymer Blend Film

We have studied phase separation in off-critical mixtures of poly(ethylene propylene) (hPEP) and perdeuterated poly(ethylene propylene) (dPEP) inside the metastable and unstable region of the phase diagram but under the influence of a surface that attracts the majority component (dPEP). In the adjacent depletion region nucleation barriers are eliminated, and the film starts to phase separate long before phase separation occurs in the bulk. The hPEP-rich domains are confined to grow anisotropically within the unstable region. The growth gives rise to the formation of a regular roughness pattern on the surface when the domains relax into a more circular shape driven by interfacial tension. The volume fraction versus depth profiles are obtained using time-of-flight forward recoil spectrometry (TOF-FRES) while the roughness pattern that mirrors the phase morphology in the depletion layer can be monitored by scanning force microscopy (SFM). Depending on initial dPEP volume fraction the lateral bicontinuous pha...

Heterogeneous percolation-to-cluster transition in phase separation of an off-critical polymer mixture

Phase separation kinetics of an off-critical polymer mixture involving percolation-to-cluster transition (PCT) was investigated by time-resolved light scattering and by transmission optical and electron microscopies. The process involving a splitting of a single peak in the light scattering profile into a double peak was observed for the first time after the onset of PCT. Each peak changes with time (t) according to different evolution modes, e.g., the first peak wave number qm,1 evolved according to the power law of percolated structures (qm∼t−α; α=0.9), while the time evolution of the second peak wave number qm,2 is very slow, which corresponds to the growth of cluster of the droplets after PCT. Furthermore, the real space pictures and the light scattering analysis reveal that a cluster of the small spherical droplets and the locally percolating domains coexist for a very long time. The percolating domains are larger than the small droplets, minor in volume fraction, and formed in bulk and they are developed into sheet-like grains with their surfaces parallel to the glass surface.

Formation of droplets with a very narrow size distribution in mixtures subjected to shear flow. I. Shear rate dependence

The phase-separated structures of a semidilute solution of off-critical polymer mixtures composed of polystyrene (PS) and polybutadiene (PB) in a common solvent of dioctylphthalate (DOP) under steady shear flow are investigated by light scattering as a function of shear rate γ̇. Light scattering patterns show multiple-order scattering maxima up to the 13th order or more in a weak shear regime, revealing formation of droplets with surprisingly uniform size having a relative standard deviation of droplet radius σR∼0.03. The average droplet radii R̄x parallel and R̄z perpendicular to the flow direction are proportional to γ̇−1, with an average aspect ratio v̄R≡R̄x/R̄z of 2 independent of γ̇ in the weak shear regime. The result obtained in the average particle size is in good agreement with that predicted by Taylor’s theory for a single droplet case, but the extreme uniformity in size distribution would not be trivial and be worth it for future theoretical considerations.

Hydrodynamic effects on domain growth in off-critical polymer blends

Starting from a coarse-grained model, which includes hydrodynamic interactions, we numerically study kinetics of phase separation in a two-dimensional model of a polymer blend. In the absence of hydrodynamics, domains grow according to the Lifshitz–Slyozov power law without any evidence of pinning, regardless of the relative concentration of the blend components. In the presence of hydrodynamics, our results suggest that critical and off-critical mixtures are characterized by different growth laws. For the critical composition of the blend, hydrodynamic effects are found to be important during the entire growth process and this leads to a larger growth exponent. On the other hand, for off-critical blends, hydrodynamic effects are important only for blends with volume fraction not far away from the critical value. Even in these cases, domains show a faster growth only at intermediate times under the influence of hydrodynamics; subsequently the growth exponent crosses over to a Lifshitz–Slyozov value at late times. This gives strong support to the argument that the apparent pinning of domain growth observed in experiments on off-critical polymer blends may be due to this crossover phenomenon.