Early Stage Of Phase Separation Research Articles

Early stages of phase separation from polydisperse polymer mixtures

We study the early stages of phase separation in a mixture of a polydisperse and a monodisperse polymer within the Cahn-Hilliard framework. We model the polydisperse component using a finite, but arbitrarily large, number of components, and show that the number of components required for convergent behaviour to be achieved is computationally undemanding. We study the growth rate of fluctuations following a quench into the two-phase region of the phase diagram. The q-dependence of the growth rate is shown to be commensurate with the behaviour of a monodisperse-monodisperse mixture, with the major difference being an effective mobility that is dependent on the quench depth. We also study the deviation of the time dependence of the scattering function from single exponential behaviour.

Numerical analysis of InGaN dot-like structure and compositional fluctuation caused by phase separation:: comparison with experiment

We studied numerically the details of In compositional fluctuations and a spontaneous formation of a dot-like structure of InGaN alloy semiconductor due to phase separation by using the cell dynamical system (CDS) approach focusing on the details of the stage of time-evolution of phase separation. The numerical results in this work resemble the experimental results on inhomogeneouos alloying of InGaN reported so far and in addition predict the diffusion which previous experiments could not determine quantitatively. The In-rich regions with a dot-like structure appearing in InGaN-based multi-quantum-well (MQW) laser diodes (LDs) with their emission wavelength below 450 nm are composed of InGaN showing small spatial fluctuations of In composition formed at an early stage of phase separation. The large blueshift of the static electroluminescence (EL) peak observed in blue and green InGaN-based single-quantum-well (SQW) light-emitting diodes (LEDs) above 450 nm also relates to the large spatial fluctuations of In composition grown at an early stage of phase separation. For the higher In composition corresponding to the emission wavelength longer than 450 nm, the time-evolution of phase separation proceeds rapidly, indicating the large In compositional fluctuation and thus the large blueshift. In order to obtain a spatially uniform In composition, we should realize a uniform distribution of In composition during the growth of InGaN layer before phase separation proceeds.

Effect of Hydroxyl-Terminated Polyethersulfone on the Phase Separation of Polyetherimide-Modified Epoxy Resin

Hydroxyl-terminated polyethersulfone (HPES) is added as a second toughener to a polyetherimide (PEI)-modified epoxy resin, and phase separation initiated by curing is studied by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and time-resolved light scattering (TRLS). SEM shows that, by addind HPES with a higher molecular weight, phase inversion can be observed at different temperatures, and the dispersed particles show a bimodal size distribution. THe TRLS experiment reveals that the peak scattering vector q m shifts towards a smaller angle or towards a larger angle, depending on the molecular weight of HPES added. The TEM experiment shows that, at an early stage of phase separation, dissimilar morphologies are observed when HPES of different molecular weights is added. The rheometry and TRLS results indicate that the morphology is pinned up by the low mobility of the two components before gelation or vitrification.

Crystallization and Nonlinear Optical Properties of Potassium Niobium Silicate Glasses

The crystallization of the xK2O · xNb2O5· (1 – 2x)SiO2(x= 0.167–0.250) glasses and glasses close in composition to K2O · Nb2O5· 4SiO2at the ratio K2O : Nb2O5≠ 1 is investigated. In high-silica glasses, the metastable phase separation followed by the bulk multiphase crystallization are observed at temperatures close to the glass transition point Tg. The nanostructured transparent glasses that exhibit the optical second harmonic generation (SHG) effect are formed at the early stages of phase separation. The surface crystallization of glasses with the precipitation of the KNbSi2O7noncentrosymmetric phase occurs at higher temperatures.

Theory and simulation of polymerization-induced phase separation in polymeric media

A rigorous model of polymerization-induced phase separation (PIPS), based on the non-linear Cahn-Hilliard (C-H) and Flory-Huggins (F-H) theories combined with a second-order polymerization reaction equation, has been formulated and its solutions characterized. The model describes phase separation in system consisting of a non-reactive polymer and a monomer that undergoes condensation polymerization. The model consists of a balance equation for the low molecular weight polymerization regime and another balance equation for the high molecular weight entangled regime. The model equations are solved, and the solutions are characterized to identify the dynamical and morphological phenomena of the PIPS process. The extent of phase separation increases significantly with time during the early stage of phase separation, and slows down in the intermediate stage. The various types of phase-separated morphologies are fully characterized using a novel morphological characterization techniques, known as the intensity and scale of segregation. Both the dynamical and morphological features of the PIPS method are sensitive to the magnitudes of the dimensionless diffusion coefficient D* and the dimensionless reaction rate constant K*. The scale of segregation and the droplet size decreases as D* and K* increase. On the other hand, the intensity of segregation increases with K*, but decreases with D*. The present results extend the present knowledge of the PIPS process by taking into account the effects arising from the presence of a non-reactive polymer.

Kinetic studies of thermally induced phase separation in polymer-diluent system

Thermally induced phase separation was studied by the light scattering in polypropylene/methyl salicylate system. Data could be well fitted with the linear Cahn theory for spinodal decomposition (SD) in the early stage of phase separation. Characteristic properties of the early stage of SD, such as an apparent diffusion coefficient and an interphase periodic distance, were obtained. The periodic distance ranged from 3 μm to 4 μm. The growth of the phase-separated structure obeyed power-law scaling in the later stage, and the structure factor could be scaled into a universal time-independent form. Domain sizes obtained from the light-scattering measurements were consistent with the optical microscope measurements. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1028–1036, 2000

Studies on the phase separation of a polyetherimide-modified epoxy resin, 4. Kinetic effect on the phase separation mechanism of a blend at different cure rates

Keeping the same thermodynamics of the blend, the kinetic effect on the pase separation mechanism of polyetherimide modified epoxy resin systems was studied. With the changes of cure rates phase separation in the reacted blends takes place. The process of phase separation is traced by time-resolved light scattering (TRLSand the final morphology is observed by scanning electron microscopy (SEM). The early stage of phase separation is analyzed using Cahn's linearized theory, while the scaling postulate is tested in the late stage. The effect of the competition between thermodynamics and kinetics on phase separation mechanism is discussed.

Studies on the phase separation of a polyetherimide-modified epoxy resin, 4. Kinetic effect on the phase separation mechanism of a blend at different cure rates

Keeping the same thermodynamics of the blend, the kinetic effect on the phase separation mechanism of polyetherimide modified epoxy resin systems was studied. With the changes of cure temperature and amount of cure agent, at different cure rates phase separation in the reacted blends takes place. The process of phase separation is traced by time-resolved light scattering (TRLS) and the final morphology is observed by scanning electron microscopy (SEM). The early stage of phase separation is analyzed using Cahn's linearized theory, while the scaling postulate is tested in the late stage. The effect of the competition between thermodynamics and kinetics on phase separation mechanism is discussed.

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.

Halo formation in asymmetric polyetherimide and polybenzimidazole blend hollow fiber membranes

For the first time, we have reported a halo (ring) formation occurred in the cross-section of integrally skinned asymmetric membranes. These membranes were wet-spun from solutions containing 30 and 33 wt % of 95/5 and 90/10 polyetherimide (PEI)/polybenzimidazole (PBI). Both Imaging X-ray Photoelectron Spectroscopy (XPS) and Dynamic Mechanical Analyzer's (DMA) data suggest PEI and PBI form miscible blends the “halo” is not chemically different from the matrix and is most likely a physical phenomenon of unique pore morphology. In other words, uniform porosity was created in the middle of hollow fiber cross-section area, which performs as a filter for light transmission. We found that the addition of PBI in PEI/DMAc solution not only depresses the macrovoid formation, but also changes the precipitation path: nucleation growth vs. spinodal decomposition. The formation of a halo within a membrane is possibly due to the fact that a uniform nucleation growth occurs in the ring region during the early stage of phase separation because of high solution viscosity and diffusion controlled solvent-exchange process, and then separation grows in the mechanism of spinodal decomposition from small amplitude composition fluctuations. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1575–1585, 1999

Phase-separation kinetics of a multicomponent alloy

Phase separation kinetics of multicomponent 350-grade maraging steel has been investigated on both recrystallized as well as cold-worked specimens by small-angle x-ray scattering, wide angle x-ray scattering, and transmission electron microscopy at two different temperatures, viz. 430 \ifmmode^\circ\else\textdegree\fi{}C and 510 \ifmmode^\circ\else\textdegree\fi{}C, for different aging times. Unlike previous observations, at both the temperatures, dynamical scaling behavior is observed at the early stages of phase separation accompanied by diffuse interface of the secondary phases. Porod exponents have been found to be greater than 4. At late stages, the precipitate-matrix interface becomes sharp --- the Porod exponent is close to 4 but clear deviation from the dynamical scaling behavior is evident. At $430\ifmmode^\circ\else\textdegree\fi{}\mathrm{C},$ the phase separation is attributed to the formation of an ordered $\ensuremath{\omega}$ phase through a mechanism involving chemical ordering and the $\ensuremath{\omega}$-like lattice collapse in the bcc structure. Time (t) dependent population averaged precipitate radius follows ${t}^{1/5}$ power law indicating cluster diffusion mechanism of Binder-Stauffer type for the entire range, 30 min--72 h, of aging time. At $510\ifmmode^\circ\else\textdegree\fi{}\mathrm{C},$the phase separation is attributed to the formation of ${\mathrm{Ni}}_{3}(\mathrm{T}\mathrm{i},\mathrm{M}\mathrm{o})$ with ${\mathrm{DO}}_{24}$ structure through the process of nucleation and growth. Average precipitate radius follows ${t}^{1/3}$ Lifshitz-Slyozov power law for the entire range, 5 min--18 h, of aging time. The system, despite being multicomponent and complex, appears to follow two distinct time-temperature-transformation curves. As far as the effect of cold work on phase-separation behavior is concerned, it has been found that cold work facilitates the growth of the precipitates. Also, it narrows down the size distribution and enforces strong spatial correlation of the precipitates. Cold working the material is found to be detrimental to the dynamical scaling behavior.

Excitation of Surface Deformation Modes of a Phase-Separating Polymer Blend on a Patterned Substrate

The phase separation kinetics of ultrathin deuterated poly(styrene)/poly(butadiene) polymer blend films spun cast onto striped self-assembled monolayer (SAM) substrates is studied by atomic force microscopy (AFM). Fourier transform analysis of the AFM topographic data at various stages of the film pattern development reveals the presence of quantized surface deformation modes. These modes are excited by the phase separation process when the scale of phase separation becomes commensurate with the period of the striped surface pattern. Thus, higher frequency modes become excited at early stages of phase separation, and these excitations decay with time as the phase separation pattern further coarsens. The film ultimately self-organizes into a periodic structure in which the fundamental mode has the largest amplitude. The influence of film thickness on the film morphology in this late stage is also investigated. A decrease in the film thickness leads to surface patterns that match those of the SAM substrates...

Early Stage Kinetics of Phase-Separating Liquid Mixtures

Observation of the very early stage of phase separation is made difficult by the large number of nucleated domains and the polydispersity of the droplet distribution. We investigate this issue using laser waves to locally quench a liquid mixture with two intersecting pump beams whose interference pattern traps the nuclei on the fringes. The time-resolved reflectivity of a third probe wave on the induced droplet grating (i) confirms that nucleation is heterogeneous even in the bulk, and (ii) surprisingly shows that impurities lead to an unexpected reduction of the growth onto a single ``medium-dependent master curve'' when samples are synthesized with the same lots of constituents.

Fundamental understanding of the effect of air-gap distance on the fabrication of hollow fiber membranes

The objectives of this work are, fundamentally, to understand hollow fiber membrane formation from an engineering aspect, to develop the governing equations to describe the velocity profile of nascent hollow fiber during formation in the air gap region, and to predict fiber dimension as a function of air-gap distance. We have derived the basic equations to relate the velocity profile of a nascent hollow fiber in the air-gap region as a function of gravity, mass transfer, surface tension, drag forces, spinning stress, and rheological parameters of spinning solutions. Two simplified equations were also derived to predict the inner and outer diameters of hollow fibers. To prove our hypotheses, hollow fiber membranes were spun from 20 : 80 polybezimidazole/poly- etherimide dopes with 25.6 wt % solid in N,N-dimethylacetamide using water as the external and internal coagulants. We found that inner and outer diameters of as-spun fibers are in agreement with our prediction. The effects of air-gap distance or spin-line stress on nascent fiber morphology, gas performance, and mechanical and thermal properties can be qualitatively explained by our mathematical equations. In short, the spin-line stresses have positive or negative effects on membrane formation and sepa- ration performance. A high elongational stress may pull molecular chains or phase- separated domains apart in the early stage of phase separation and create porosity, whereas a medium stress may induce molecular orientation and reduce membrane porosity or free volume. Scanning electron microscopic photographs, coefficient of thermal expansion, and gas selectivity data confirm these conclusions. Tg of dry-jet wet-spun fibers is lower than that of wet-spun fibers, and Tg decreases with an increase in air-gap distance possibly because of the reduction in free volume induced by gravity and elongational stress. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 72: 379 -395, 1999

Characterization of the Early Stages of Phase Separation by Atom probe Tomography

AbstractAn atom probe tomography characterization of the early stages of phase separation in the FeCu-Ni system has been performed. The development of the copper-enriched regions into copper precipitates has been investigated during isothermal ageing at 573 K and 673 K for times up to 10,000 h. The formation and growth of the secondary precipitates in the nickel based superalloy, Alloy 718, have been determined during isothermal ageing at 873 K. These secondary precipitates were found to be a mixture of the L12-ordered γ' phase and the DO22-ordered γ” phase.

Metastability and Depletion-Driven Aggregation

Depletion-driven self-assembly in binary colloidal mixtures is studied via the time evolution of the cluster-size distribution and structure factor as the mixtures equilibrate after shear melting. The data suggest a two-stage crystallization process governed by an initial collapse into an amorphous metastable state, the growth kinetics of which are interpreted within the context of reversible aggregation and early-stage phase separation.

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

Spinodal decomposition (SD) kinetics in a concentrated polymer solution was investigated with dynamic Monte Carlo simulation. It is found that the positions of scattering peaks are altered during the early stage of phase separation, which cannot be described by the classic Cahn-Hilliard linearized theory quite well, whereas during the late stage SD induced by a deep off-critical quench, the structure factors can be scaled with Furukawa dynamic scaling law associated with a percolation morphology instead of with a non-continuous phase morphology. Our simulation outputs agree basically with the experimental observations in the pertinent literature. It is also revealed that after a deep quench, chain coils shrink strikingly at first and then expand gradually during phase separation. As a consequence, this paper demonstrates that the dynamic Monte Carlo method is unique in detecting both chain configurations and phase separation kinetics and thus very useful for elucidating their relationship in mixtures containing macromolecules.

Dynamics of Spinodal Decomposition in Polymer Solutions near a Glass Transition

A model based on the Cahn−Hilliard formalism is used to simulate structure formation in thermally quenched polymer solutions in the vicinity of a glass transition. Simulation results for the system poly(methyl methacrylate)/cyclohexanol are correlated with light scattering and microscopy measurements recently reported in the literature. Good qualitative and quantitative agreement with experimental observations indicates the applicability of current free-volume and thermodynamic theories to quantify the dynamics near a glass transition. The model accurately predicts late-stage scaling exponents, and results show that the early stage of phase separation occurs on time scales ≪ 1 s. Pore growth rates based on zero-free-parameter calculations agree well with experimental observations. Simulations also show that quenching a phase-separated structure below a glass transition can result in the formation of a secondary droplet structure within the polymer-rich phase, prior to freezing-in of the preexisting morphology. Such secondary structures, which have also been observed experimentally, appear to have little or no effect on the calculated structure factor, which is also consistent with light-scattering measurements.

Viscoelastic Effects on the Early Stages of Phase Separation in Polymer Blends

We modify the Cahn-Hilliard theory of concentration fluctuation dynamics to account for the short-time networklike nature of high molecular weight polymers. We propose an additional term in the free energy, due to elastic energy arising from the finite lifetime of entanglements. If we assume a single-exponential decay time for the entanglements, the equation of motion is governed by two exponential modes. For quenches into the two-phase region, the faster mode always decays with time, and the slower mode grows. The theory successfully accounts for data from spinodal decomposition of polymer blends containing at least one component of very high molecular weight.

Viscoelastic effects in early stage phase separation in polymeric systems

We examine how viscoelasticity affects early stage spinodal decomposition in polymer solutions and blends when fluctuations of the stress and the composition are coupled in dynamics. The coupling is increased with increasing asymmetry between the two components. We introduce a long viscoelastic length ξve within which the stress relaxation governs the composition relaxation. It can be of the order of the tube length in the reptation theory in strongly asymmetric polymer blends. For shallow quenching phase separation proceeds on time scales slower than the stress relaxation time τ and the kinetic coefficient depends on the wave number q as q−2 for qξve>1. On the other hand, for deep quenching phase separation takes place as in gels on time scales faster than τ. We describe the crossover between these two cases by assuming a single stress relaxation time.