Late Stage Of Phase Separation Research Articles

Kinetics of Micellization and Liquid-Liquid Phase Separation in Dilute Block Copolymer Solutions.

A lattice theory for block copolymer solutions near the boundary between the micellization and liquid-liquid phase separation regions proposes a new kinetic process of micellization where small concentrated-phase droplets are first formed and then transformed into micelles in the early stage of micellization. Moreover, the thermodynamically stable concentrated phase formed from metastable micelles by a unique ripening process in the late stage of phase separation, where the growing concentrated-phase droplet size is proportional to the square root of the time.

Phase separation kinetics and rheological behavior of Poly(ethylene oxide)/ionic liquid mixtures with large dynamic asymmetry

Phase separation kinetics of dynamically asymmetric mixtures poly(ethylene oxide)/ionic liquid (PEO/[EMIM][BF4]) was investigated through optical microscopy and rheological measurements. The distinct phase-separating morphologies including network structure at lower PEO concentrations of 10∼30 wt % (P10, P30) driven by viscoelastic phase separation (VPS), co-continuous structure at the moderate concentrations (P40, P50) governed by spinodal decomposition (SD) and droplets-matrix at higher concentrations (P60, P70) driven by either SD or nucleation and growth (NG) are observed under different temperatures. Evident deviation of the storage modulus G′ and gel-like behavior on loss tangent tanδ at low frequencies can be seen upon entering into the two-phase region dependent on different morphologies. During time sweeps, the initial increase of G′ can be ascribed to the growth of concentration fluctuation, and the subsequent decrease possibly due to the phase domain coarsening, breaking up or coalescence. The interfacial tension σ at the late stage of phase separation with droplet-matrix morphologies is estimated by using the Gramespacher-Meissner (G-M) model and Palierne model.

Insights from inside the spinodal: Bridging thermalization time scales with smoothed particle hydrodynamics.

We report the influence of the strength of heat bath coupling on the demixing behavior in spinodal decomposing one component liquid-vapor systems. The smoothed particle hydrodynamics (SPH) method with a van der Waals equation of state is used for the simulation. A thermostat for SPH is introduced that is based on the Berendsen thermostat. It controls the strength of heat bath coupling and allows for quenches with exponential temperature decay at a certain thermalization time scale. The present method allows us to bridge several orders of magnitude in the thermalization time scale. The early stage is highly affected by the choice of time scale. A transition from exponential growth to a 1/2 ordinary power law scaling in the characteristic lengths is observed. At high initial temperatures the growth is logarithmic. The comparison with pure thermal simulations reveals latent heat to raise the mean system temperature. Large thermalization time scales and thermal conductivity are figured out to affect a stagnation of heating, which is explained with convective processes. Furthermore, large thermalization time scales are responsible for a stagnation of growth of domains, which is temporally embedded between early and late stage of phase separation. Therefore, it is considered as an intermediate stage. We present an aspect concerning this stage, namely that choosing larger thermalization time scales increases the duration. Moreover, it is observed that diffuse interfaces are formed during this stage, provided that the stage is apparent. We show that the differences in the evolution between pure thermal simulations and simulations with an instantaneously scaled mean temperature can be explained by the thermalization process, since a variation of the time scale allows for the bridging between these cases of limit.

Rheological behavior of the epoxy/thermoplastic blends during the reaction induced phase separation

The correlation between rheological behavior and time evolution of the phase separation patterns was investigated in the epoxy/thermoplastic blends. Before and during the induction period of phase separation, the storage and loss modulus initially increased with epoxy curing reaction and the concentration fluctuation. At the late stage of phase separation, the modulus values also increased and showed a sharp enhancement around the epoxy gel point. However, the time evolution during the reaction induced phase separation process differed a lot at various thermoplastic (TP) concentrations. At the low TP concentrations, the rheological parameters decreased with the coarsening of sea-island structure. At the high TP concentrations, the TP-rich continuous structures initially formed and maintained until the end, resulting in a continuous increase for the rheological characters. At middle TP concentrations, formation and evolution of the three-layered structure displayed a complicated rheological behavior. It was found that the storage modulus quickly increased, reached a vertex, then rapidly decreased, reached a minimum, and increased again afterwards. Although the rheological behaviors were almost phenomenologically similar as that in the normal dynamically symmetric system, driving force for the variation was fundamentally different. Especially for the case of middle TP concentrations, the behavior of the holistic volume shrinking of the slow dynamic TP-rich network and the flowing out of the fast dynamic epoxy-rich phase from the network during this period, as radically transformed the nature of the matrix from an elastic network to a macro-phase separated layer structure and caused the dramatic change of the rheological behaviors.

Reduced graphene oxide induced phase miscibility in polystyrene–poly(vinyl methyl ether) blends

Graphene oxide and reduced graphene oxide (r-GO) were synthesized by wet chemistry and the effect of r-GO in PS–PVME blends was investigated here with respect to phase miscibility, intermolecular cooperativity in the glass transition region and concentration fluctuation variance by shear rheology and dielectric spectroscopy. The spinodal decomposition temperature (Ts) and correlation length were evaluated from isochronal temperature scans in shear rheology. The r-GO is shown to induce miscibility in the blends, which may lead to increased local heterogeneity in the blends, though the length of cooperatively re-arranged regions (ξ) at Tg is more or less unaltered. The evolution of the phase morphology as a function of temperature was assessed using polarized optical microscopy (POM). In the case of the 60/40 PS–PVME blends with 0.25 wt% r-GO, apart from significant refinement in the morphology, retention of the interconnected ligaments of PVME was observed, even in the late stages of phase separation suggesting that the coarsening of the phase morphology has been slowed down in the presence of r-GO. This phenomenon was also supported by AFM. Surface enrichment of PVME, owing to its lower surface tension, in the demixed samples was supported by XPS scans. The interconnected network of PVME has resulted in significantly higher permittivity in the bi-phasic blends, although the concentration of r-GO is below the percolation threshold.

Fish gelatin/Laponite biohybrid elastic coacervates: A complexation kinetics–structure relationship study

Complex coacervation in exfoliated Laponite nanoplatelets and fish gelatin mixtures was studied as a function of four key parameters: pH, ionic strength, gelatin/Laponite weight ratio, and total weight. The aim was to understand how these parameters influence phase separation kinetics, composition, internal structure, and viscoelastic properties of coacervates. By careful experimental design and turbidity measurements, the optimum conditions for coacervation were obtained. Thermogravimetric analysis revealed an outstanding heat-resistance for gelatin/nanoclay coacervates. Finally, structure of the coacervate phase was characterized by oscillatory shear experiments. The storage modulus data was observed to follow a power-law behavior and it was confirmed that under the optimum conditions, the coacervate phase was dense and structured with a characteristic length scale (ξrheol) of ∼8.25nm. Regardless of the physicochemical condition at which complexation occurred, it was shown that the equilibrium structure of the coacervates is related to the kinetics of intermediate and late stages of phase separation; as the new defined kinetics parameter K was observed to be inversely proportional to ξrheol that quantifies the compactness of the coacervate networks.

Phase morphology evolution upon melt annealing treatment and corresponding mechanical performance of impact-resistant polypropylene copolymer

The evolution of phase morphology upon melt annealing and the corresponding changes in mechanical properties of impact-resistant polypropylene copolymers (IPCs) have been systematically investigated. A distinct coarsening process is observed during melt annealing and the statistical analysis of stereology reveals that the increase of dispersed domain size well follows the Ostwald ripening mechanism. Mechanical tests suggest that the notched impact strength and elongation at break decrease gradually with increasing annealing time, while the tensile strength remains relatively constant. The decrease of toughness is consistent with the size increase of dispersed domains, which may result from the development of late-stage phase separation of IPC. However, the tensile strength, which is mainly dominated by the crystalline phase structure, remains relatively constant during the annealing treatment. On the basis of these results, the probable relationship between the change of mechanical properties and phase morphology evolution has been proposed.

Phase Separation Dynamics for a Polymer Blend Compatibilized by Protein-like Copolymers: A Monte Carlo Simulation

We use Monte Carlo simulation based on the bond fluctuation model to investigate how adding ≈4.92% protein-like copolymer (PLC) to an immiscible binary polymer blend affects the dynamics of phase separation. PLCs slow down effectively the process of phase separation in binary blends by migrating to the biphasic interface between the immiscible homopolymers, thereby reducing the interfacial tension. The ability of PLCs to retard effectively the process of phase separation depends sensitively on the interaction energy between the PLCs and homopolymers and the PLC chain length. PLCs compatibilize the binary blend more effectively with increasing attractive interaction between the PLC blocks and homopolymers. Nominal improvement in compatibilization of the binary blend is achieved with increasing PLC chain length. The growth of phase-separated domains follows a dynamical scaling law for both the binary blend and PLC compatibilized ternary blend in the late stages of phase separation. The universal scaling functions are nearly independent of the interaction energy and PLC chain length. Thus, the phase-separated domains grow with dynamical self-similarity irrespective of the type of PLC added to the binary blend, although the type of PLC significantly alters the growth rate of the phase-separated domains.

Effect of Polydispersity on the Phase Behavior of Polystyrene (PS)/Poly (Vinyl Methyl Ether) (PVME)

The thermodynamics and kinetics of phase separation in partially miscible blends of poly (vinyl methyl ether) (PVME) and two kinds of polystyrene (PS) with the same weight average molecular weight but different polydispersity were studied. The miscibility of PS/PVME with the monodisperse PS was better than that of PS/PVME with the polydisperse PS. Different morphology was observed for the two kinds of PS/PVME (10/90) blends during the nonisothermal phase separation process. The blend with monodisperse PS presented a co-continuous structure while the blend with polydisperse PS presented a viscoelastic phase separated network structure at a quench depth of 29°C. With increase of the heating rate, the increase of cloud point of PS/PVME (30/70) with polydisperse PS was smaller than that of PS/PVME (30/70) with monodisperse PS. During the isothermal phase separation of the critical composition (20/80) of PS/PVME with a quench depth of 30°C, it was found that the phase morphology of the two kinds of blends was nearly the same at the early stage of phase separation. However, as the dispersed phase, an approximately spherical droplet structure was observed in the blend with monodisperse PS at the late stage of phase separation, which did not appear in the blend with polydisperse PS.

Investigation on Phase Separation Kinetics of Polyolefin Blends through Combination of Viscoelasticity and Morphology

Phase separation kinetics of polyethylene copolymer blends polyethylene-co-hexene (PEH)/polyethylene-co-butene (PEB) at a phase separation temperature of 130 degrees C have been investigated through the combination of rheological measurements and optical microscope observation. When the blends are located in the unstable region, i.e., PEH/PEB 40/60 blend (H40), 50/50 blend (H50), and 60/40 blend (H60), due to the coeffect of the fast decay of concentration fluctuations and the reduced interfacial area, the stroage modulus, G', behaves dramatically, decreasing at the early or intermediate stages; while when the blends are located in the metastable region, i.e., PEH/PEB 70/30 blend (H70), G' decreases slightly and slowly during the whole time sweep process. During the cyclic frequency sweeps, G' evolutions of H50 and H70 show similar trends. Obviously different from the strong phase segregation systems, the increase of G' with time in the metastable region has not been observed, possibly due to the entanglement effects and weak interaction between the components of polyethylene blends. The interfacial tension-driven or diffusion-limited morphological evolutions of H50 and H70 during phase separation give direct interpretations to the viscoelastic difference between the two blends, which is dominated by different phase separation kinetics. The relatively low interfacial tensions at the late stage of phase separation for H50 (0.5-0.38 mN/m varying with time) and H70 (1.2 mN/m) can be estimated by using the Gramespacher-Meissner model.

SURFACE-DIRECTED SPINODAL DECOMPOSITION: LATTICE MODEL VERSUS GINZBURG–LANDAU THEORY

When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long-wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. These boundary conditions can be derived from lattice models by suitable continuum approximations. But the lattice models can also be simulated directly, and thus used to clarify the conditions under which the Ginzburg–Landau type theory is valid. This comparison shows that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations can also be neglected (true for the late stages of phase separation). In contrast, a local kinetic molecular field theory can take full account of nonlinearities and of rapid concentration variations, and thus has a much wider validity. This enables the detailed study of phase separation processes in thin films of solid binary alloys. However, the extension to spinodal decomposition in fluid binary systems (which can be simulated by brute force large scale molecular dynamics methods, of course) remains an unsolved challenge.

Lattice Boltzmann study of hydrodynamic effects in lamellar ordering process of two-dimensional quenched block copolymers

By incorporating self-consistent field theory with lattice Boltzmann method, a model for polymer melts is proposed. Compared with models based on Ginzburg-Landau free energy, our model does not employ phenomenological free energies to describe systems and can consider the chain topological details of polymers. We use this model to study the effects of hydrodynamic interactions on the dynamics of microphase separation for block copolymers. In the early stage of phase separation, an exponential growth predicted by Cahn-Hilliard treatment is found. Simulation results also show that the effect of hydrodynamic interactions can be neglected in the early stage. For the late stage of phase separation, it is easy to see the effects of hydrodynamic interactions on the ordering process of lamellae phase. From the analysis of structure factor curves, we find that the growth of domains is faster if hydrodynamic interactions are introduced. Furthermore, the scaling of the pattern dynamics is investigated for the late stage at zero thermal noise. By studying the behavior of scaling exponents of the structure factor and the nematic order-parameter correlation function C(nn), we can see that the effects of hydrodynamic interactions lead to bigger growth exponent for both functions.

Time evolution of phase structure and corresponding mechanical properties of iPP/PEOc blends in the late-stage phase separation and crystallization

A typical toughened polymeric alloy system, isotactic polypropylene (iPP)/poly(ethylene-co-octene) (PEOc) blend, was selected in this study to investigate the influence of phase separation and crystallization on the final mechanical properties of the polyolefin blend. The time dependence of the morphology evolution of this iPP/PEOc blend with different compositions was annealed at both 200 and 170°C and investigated with scanning electron microscopy (SEM) and phase contrast optical microscopy (PCOM). It was found that under the above two phase separation temperatures, the domain size of iPP80/PEOc-20 (PEOc-20) increases only slightly, while the structure evolution of iPP60/PEOc-40 (PEOc-40) is quite prominent. The tensile tests revealed that the mechanical properties of PEOc-20, including break strength and elongation at break decrease only in a very small amount, while those of PEOc-40 are depressed obviously with phase separation time. The decrease of interphase and a sharper boundary resulting from domain coarsening during the late-stage phase separation are responsible for the poor tensile properties. It is believed that the composition, the annealing time and the processing temperatures all contribute to the morphology evolution and the consequent mechanical properties of iPP/PEOc blends, furthermore, the crystallization procedure is another crucial factor influencing the ultimate mechanical properties of the investigated blends.

Dynamic scaling behaviour of late-stage phase separation in Ni 75 Al x V 25− x alloys

The dynamic scaling behaviour of late-stage phase separation and coarsening mechanisms of L12 and D022 in Ni75AlxV25−x (3 ≤x≤10, at.%) alloys are studied using the microscopic phase-field dynamic model. The microelasticity field is incorporated into the diffusion dynamic model. The results show the morphology and coarsening dynamics being greatly changed by the elastic interactions among different precipitates, the particles aligning along the dominant directions, the average domain size (ADS) of L12 and D022 deviating from the exponent of temporal power-law, and the growth slowing down due to the increasing of elastic interactions. The dynamic scaling regime of late-stage coarsening of the precipitates is attained. Thus the scaling behaviour of structure function is also applicable for elastic interaction systems. It is also found that the variations of ADS and scaling function depend on the volume fraction of precipitates.

Structure and phase separation of Ag–Cu alloy thin films

We report an in situ electron diffraction study and microscopy observation of phase separation in Ag–Cu solution alloy thin films of different compositions and film thicknesses. The results show that the as-deposited films consist of nanocrystalline Ag- and Cu-rich phases of a few nanometers in size. Upon annealing, two stages of thin-film transitions are observed. In the first stage, the growth of Cu crystallites is responsible for phase separation in Ag 50Cu 50 or Ag-rich alloy. For the Cu-rich samples, the phase separation process is much slower. The second stage transition involves thin film dewetting. A combination of Z-contrast scanning transmission electron microscopy imaging and electron diffraction reveal grain growth and phase separation between Ag and Cu in both stages. Atomic force microscopy results show the surface morphology of thin films only changes significantly at the late stage of phase separation when the thin film dewets.

Detrended fluctuation analysis in x-ray photon correlation spectroscopy for determining coarsening dynamics in alloys

We study the dynamics of precipitate coarsening in phase-separating alloys at late stages of phase separation by x-ray photon correlation spectroscopy (XPCS). For analyzing time series of fluctuating speckle intensities from small-angle scattering of coherent x rays, the method of detrended fluctuation analysis (DFA), which is ideal for determining power-law correlations, is applied. We discuss the application of DFA with respect to XPCS data by means of simulated time series. In particular, the effects of different signal-to-noise ratios are examined. Results from measurements of the two model systems Al-6 at. % Ag at 140 degrees C and Al-9 at. % Zn at 0 degrees C are presented. Since the DFA effectively removes adulterating trends in the data, quantitative agreement with Monte Carlo simulations is obtained. It is verified that two different coarsening mechanisms are predominant in the two systems--coarsening either by diffusion of single atoms or by movement of whole precipitates.

Kinetics of pressure-induced phase separation in polystyrene + acetone solutions at high pressures

The kinetics of pressure-induced phase separation in solutions of polystyrene ( M w = 129,200; PDI = 1.02) in acetone has been studied using time- and angle-resolved light scattering. A series of controlled pressure quench experiments with different quench depths were conducted at different polymer concentrations (4.0%, 5.0%, 8.2% and 11.4% by mass) to determine the binodal and spinodal boundaries and consequently the polymer critical concentration. The results show that the solution with a polymer concentration 11.4 wt% undergoes phase separation by spinodal decomposition mechanism for both the shallow and deep quenches as characterized by a maximum in the angular distribution of the scattered light intensity profiles. Phase separation in solutions at lower polymer concentrations (4.0, 5.0 and 8.2 wt%) proceeds by nucleation and growth mechanism for shallow quenches, but by spinodal decomposition for deeper quenches. These results have been used to map-out the metastable gap and identify the critical polymer concentration where the spinodal and binodal envelops merge. The time scale of new phase formation and growth as (accessed) from the time evolution of scattered light intensities is observed to be relatively short. The late stage of phase separation is entered within seconds after a pressure quench is applied. For the systems undergoing spinodal decomposition, the characteristic wave number q m corresponding to the scattered light intensity maximum I m was analyzed by power–law scaling according to q m ∼ t − α and I m ∼ t β . The results show β ≈ 2 α . The domain size is observed to grow from 4 μm to 10 μm within 2 s for critical quench, but about 9 s for off-critical quenches. The domain growth displays elements of self-similarity.

Crystallization behavior of PVDF in PVDF‐DMP system via thermally induced phase separation

AbstractThe crystallization behavior of PVDF (poly (vinylidene) fluoride) in PVDF‐dimethylphthalate(DMP) system was investigated in the liquid–liquid (L–L) phase separation region, solid–liquid (S–L) phase separation region and different quenching conditions via thermally induced phase separation (TIPS). Differential scanning calorimetry (DSC) indicated the crystallinity of PVDF in PVDF‐DMP system increased in the early stage of phase separation and polymer‐rich phase crystallized completely in the late stage of phase separation. The scanning electron microscopy (SEM) showed the different quenching temperatures had effects on the spherulite size of polymer rich phase and the ultimate membrane structure in the different phase separation regions. The wide angle X‐ray diffraction (WAXD) was used to quantify the crystal structure of PVDF in PVDF‐DMP system. The α‐phase PVDF was obtained when the system quenched to different temperatures above 40°C, and the area of diffraction peaks changed when quenching temperatures changed. While the β‐phase PVDF was formed when PVDF‐DMP system was quenched form liquid nitrogen and crystallized for 24 h in 25°C water bath. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3714–3719, 2006

Investigating slow dynamics in alloys using X-ray photon correlation spectroscopy

We show that the emerging method of X-ray photon correlation spectroscopy (XPCS) is a promising tool for investigations of slow dynamics in alloys. Examples for such dynamics are precipitate coarsening in phase-separating alloys at late stages of phase separation and movement of antiphase boundaries. For the sake of brevity we concentrate on latest results for the determination of the coarsening mechanism in the phase-separating system Al–12at.%Li at 150°C and compare it with results for Al–9at.%Zn at 0°C. Thereby, XPCS data is evaluated by the so-called fluctuation analysis technique.

An upper bound on the coarsening rate for mushy zones in a phase-field model

We prove an upper bound on the coarsening rate for solutions of a phase field model with arbitrarily complicated patterns of phases. The analysis is performed in a regime corresponding to the late stages of phase separation, in which the ratio between the transition layer thickness and the length scale of the pattern is small, and is also small compared to the square of the ratio between the pattern scale and the system size. The analysis extends the method of Kohn and Otto (Comm.\ Math.\ Phys.\ 229 (2002), 375-395) to deal with both temperature and phase fields.