Early Stage Of Phase Separation Research Articles

Coupled flow-polymer dynamics via statistical field theory: Modeling and computation

Field-theoretic models, which replace interactions between polymers with interactions between polymers and one or more conjugate fields, offer a systematic framework for coarse-graining of complex fluids systems. While this approach has been used successfully to investigate a wide range of polymer formulations at equilibrium, field-theoretic models often fail to accurately capture the non-equilibrium behavior of polymers, especially in the early stages of phase separation. Here the “two-fluid” approach serves as a useful alternative, treating the motions of fluid components separately in order to incorporate asymmetries between polymer molecules. In this work we focus on the connection of these two theories, drawing upon the strengths of each of the approaches in order to couple polymer microstructure with the dynamics of the flow in a systematic way. For illustrative purposes we work with an inhomogeneous melt of elastic dumbbell polymers, though our methodology will apply more generally to a wide variety of inhomogeneous systems. First we derive the model, incorporating thermodynamic forces into a two-fluid model for the flow through the introduction of conjugate chemical potential and elastic strain fields for the polymer density and stress. The resulting equations are composed of a system of fourth order PDEs coupled with a non-linear, non-local optimization problem to determine the conjugate fields. The coupled system is severely stiff and with a high degree of computational complexity. Next, we overcome the formidable numerical challenges posed by the model by designing a robust semi-implicit method based on linear asymptotic behavior of the leading order terms at small scales, by exploiting the exponential structure of global (integral) operators, and by parallelizing the non-linear optimization problem. The semi-implicit method effectively removes the fourth order stability constraint associated with explicit methods and we observe only a first order time-step restriction. The algorithm for solving the non-linear optimization problem, which takes advantage of the form of the operators being optimized, reduces the overall simulation time by several orders of magnitude. We illustrate the methodology with several examples of phase separation in an initially quiescent flow.

Kinetics of phase separation at the early stage of spinodal decomposition in epoxy resin modified with PEI blends

The behavior at the early stage of spinodal decomposition (SD) for polyetherimide (PEI)/epoxy blends was investigated. It was found that the phase separation of PEI/epoxy blends took place by SD mechanism. The development of molar mass in the epoxy resin was gradual and then the three blends could still be considered as concentrated solutions of thermoplastic. The kinetics at the early stage of phase separation for these blends could be described by the Cahn–Hilliard–Cook linearized theory.

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.

Universality in early-stage growth of phase-separating domains near the critical point

We present both the experimental and computational methods and results of phase-separating experiments performed with sulfur hexafluoride (SF6) close to its critical density. These experiments were performed in microgravity to suppress buoyancy and convection-driven effects. Phase separation under reduced gravity is analyzed for both 0.3 mK and 3.6 mK temperature quenches in order to derive the early-stage growth law. We found a 1/3 growth law for early stages of phase separation for a volume fraction of minority domains of 50%. Our findings support the hypothesis of a crossover between Brownian motion and hydrodynamic effects in the early stages of phase separation. The temperature inside the bulk of the pure fluid was estimated using a proposed histogram method. Our histogram method allowed temperature estimation below thermistors' sensitivity and detected small temperature variations inside the bulk of the pure fluid.

An in situ rapid heat–quench cell for small-angle neutron scattering

A dual-temperature sample environment has been developed enabling the rapid heating and quenching of samples in situ for small-angle neutron scattering (SANS). The rapid heat and quench cell (RHQC) allows samples to be rapidly heated up to 600 K and then quenched to 150 K, or vice versa, in a single shot or cycle mode, with the sample in position for data collection. Measured cooling rates of up to 11 K s−1 and heating rates up to 19 K s−1 have been recorded during the testing stages. First results using the RHQC on a hydrogenated/deuterated paraffin blend quenched from the melt illustrate the value of the device in accessing the early stage phase separation kinetics with SANS.

Phase Separation in Poly(tert-butyl acrylate)/Polyhedral Oligomeric Silsesquioxane (POSS) Thin Film Blends

Phase separation in thin film blends of poly(tert-butyl acrylate) (PtBA) and a polyhedral oligomeric silsesquioxane (POSS), trisilanolphenyl-POSS (TPP), is studied as functions of annealing temperature and time, using reflected light optical microscopy, atomic force microscopy, and X-ray photoelectron spectroscopy. The results demonstrate that the PtBA/TPP blend system confined to thin films ( approximately 90 nm) exhibits lower critical solution temperature (LCST) behavior with a critical temperature of approximately 70 degrees C and a critical composition of 60 wt % PtBA with insignificant dewetting at the phase boundary. Off-critical spinodal behavior is observed for 58 and 62 wt % PtBA blend films. Phase separation by nucleation and growth is observed for all compositions outside the window between 58 and 62 wt % PtBA. The temporal evolution of spinodal decomposition in 60 wt % PtBA blend films is explored at annealing temperatures of 75, 85, 95, and 105 degrees C. The morphological evolution in 60 wt % PtBA blend films is similar for all experimental temperatures (75, 85, 95, and 105 degrees C) with the expected shorter time scales for phase evolution at higher annealing temperatures. Fast Fourier transforms of optical micrographs reveal that these blend films immediately undergo phase separation by spinodal decomposition during temperature jump experiments. Power law scaling for the characteristic wavevector with time (q approximately t(n) with n approximately -1/4 to -1/3) for domain growth during the early stages of phase separation yields to domain pinning at the later stages for 60 wt % PtBA blend films annealed at 75, 85, and 95 degrees C. In contrast, domain growth is pinned over the entire experimental time scale for 60 wt % PtBA blend films annealed at 105 degrees C.

Nucleation induced by phase separation in the interface of polyolefin blend

The two-step quenching experiments, which were performed to investigate the interplay between phase separation and crystallization in polyolefin blend system (Zhang XH, Wang ZG, Muthukumar M, Han CC. Macromol Rapid Commun 2005 26:1285 and the following papers.), showed that almost all the nuclei appear in the interfacial regions of phase separation. The nucleation rates in the second step quenching decay with the time of phase separation with simple power law. These novel phenomena are attributed to that the interdiffusion in the spinodal decomposition process makes the polymer chains oriented in the interfacial regions. The orientation of polymer chains decreases the nucleation barriers of crystallization. A reasonable assumption is that the nucleation rate is proportional to the interfacial volume. In the early stage of phase separation, the interface thinning process is faster than the phases coarsening process, and hence the interfacial area is approximately kept the same; the nucleation rate is then proportional to the interfacial thickness. In present work, we explore the interfacial forming of spinodal decomposition in an asymmetric polymer blend through numerical integral of the Cahn–Hilliard equation with Flory–Huggins–de Gennes free energy functional. The numerical results demonstrate that the time-dependent evolutions of the nucleation rate satisfy the power law with the index of −0.47, which is well consistent with the experiments.

Is vorticity-banding due to an elastic instability?

A possible mechanism for the vorticity-banding instability is proposed on the basis of experiments with colloidal rod-like particles that exhibit an isotropic-nematic phase transition. The proposed mechanism is similar to the well-known elastic instability for polymer systems that is due to nonuniform elastic deformation of polymer chains as a result of gradients in the local shear rate (the Weissenberg effect). However, the role of polymer chains is now played by inhomogeneities that exist in systems exhibiting vortic- ity banding. For the rod-like colloidal system investigated here, inhomogeneities are formed during the early stages of phase separation. Nonuniform deformation of these inho- mogeneities are thus proposed to lead to hoop stresses which give rise to banded structures where there is secondary, weakly rolling flow within each of the bands. Many of the features found experimentally for the rod-like colloidal system can be understood on the basis of this proposed mechanism. For different types of systems that also show vorticity banding, inhomogeneities can be identified, which might lead to vorticity banding for the same reasons as for the rod-like colloidal systems studied here.

Phase separation in the polyurethane/poly(2‐hydroxyethyl methacrylate) semi‐interpenetrating polymer networks synthesized by different ways

AbstractThe thermal, dynamic mechanical analysis, morphology and mechanical properties of semi‐interpenetrating polymer networks based on crosslinked polyurethane (PU) and poly(2‐hydroxyethyl methacrylate) (PHEMA) synthesized by photopolymerization and by thermopolymerization have been investigated. The thermal analysis has evidenced the two glass temperature transitions in the semi‐IPNs and this is confirmed by the thermodynamic miscibility investigation of the systems. The Dynamic Mechanical Analysis spectra have shown that the phase separation is more significant in the thermopolymerized semi‐IPNs: the tan δ peaks of constituent polymers are more distinct and the minimum between the two peaks is deeper. The calculated segregation degree values of semi‐IPN's components are significantly higher for thermopolymerized semi‐IPNs, thereby the process of phase separation in the thermopolymerized semi‐IPNs is more developed. The structures of two series of samples investigated by SEM are completely different. The mechanical properties reflect these changes in structure of semi‐IPNs with increasing amount of PHEMA and with the changing of the method of synthesis. The results suggest that the studied semi‐IPNs are two‐phase systems with incomplete phase separation. The semi‐IPN samples with early stage of phase separation demonstrate higher mechanical characteristics. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers

Investigation of Phase Separation in a Partially Miscible Polymer Blend by Rheology

The phase boundary and phase‐separation dynamics of a binary poly(styrene‐co‐maleic anhydride)/poly(methyl methacrylate) blend have been investigated by rheological measurements and light scattering. The phase diagram was experimentally established by rheology, in which the binodal line was obtained by dynamic temperature ramps and the spinodal temperatures were quantitatively estimated on the basis of the theory developed by Ajji et al. The phase‐separation dynamics from rheological viewpoints have been further investigated on the basis of the obtained phase diagram. Rheological measurements can sensitively detect the rather early stages of phase separation compared with light scattering techniques. It was found that the dynamic storage modulus initially increases over time and subsequently decreases during nucleation and growth; on the other hand, it always decreased over time during spinodal decomposition. Compared with light scattering techniques, rheological measurements were found to be relatively reliable for probing phase‐separation mechanisms.

Early stages of phase separation using three‐dimensional atom probe and atomistic modelling

AbstractThe early stages of clustering in Al‐14.8 Mg alloy have been studied using atomistic modelling and 3DAP analysis. Atomistic modelling was based on first‐principles quantum mechanical calculations and Monte Carlo (MC) based techniques. A good agreement between the experimental results and simulated data was obtained showing the appropriateness of the theoretical approach used. It has been shown that after 720 h at 35 °C (308 K) clustering of Mg was clearly detectable in the experimental alloy. The simulated data after 200 MC steps corresponded well to the experimental results obtained after ageing for 720 h. Copyright © 2007 John Wiley & Sons, Ltd.

The Joint Research Program “CPR Precipitation” — Breakthroughs in the Understanding of Kinetic Pathways for the Early Stages of Phase Separation

The CNRS joint research program, “CPR Precipitation”, has been carefully prepared by the industrial initiators. Very significant results were obtained: they are summarized in the following and presented in this meeting. As for the future, the CPR has catalyzed the formation of a community of promising scientific interest: it would be of common benefit to stabilize this community by an appropriate further support.

On relationship of atomic structure, nano-sized inhomogeneities and second-order optical non-linearity of K 2O–TiO 2–P 2O 5 glasses

Glasses at early stages of phase separation, while remaining amorphous, are shown to possess or not to possess second-order optical nonlinearity (SON) depending on specific features of their short-range/medium range order and nanoinhomogeneous structure characterized with IR and Raman spectroscopy, X-ray diffraction, small-angle X-ray and neutron scattering and second harmonic generation (SHG). In the present work it is demonstrated by the example of potassium titanium phosphate glasses of composition near KTiOPO 4 stoichiometry. Formation of nanoinhomogeneities, structure of which is similar to the structural motif of some non-linear optical (NLO) crystal, favors SON. Heat treatment of such glasses at temperatures near glass-transition temperature T g stimulates remarkable SON enhancement keeping transparency and amorphous state. While temperature is increasing SHG grows up to values, comparable with those of NLO crystals with rise of Bragg reflections in the X-ray diffraction pattern of the glass and decrease of its transparency. Revealing correlations between structural peculiarities of glasses and their SON argues preference of description of short- and medium-range order in glasses with composition close to boundaries of glass-forming regions from the position of quasi-crystallite models.

Numerical modeling of the spatial distribution of particles at an early stage of phase separation in glasses

The pairwise correlation function of particles at the nucleation stage is numerically modeled, using the model of diffusion-limited nucleation phase separation. The model takes into account the spatial inhomogeneity of the nucleation intensity, caused by the formation of diffusion zones around the particles. The results of the calculations showed that the spatial distribution of the particles is random at an early stage of the nucleation and is characterized by elements of close-range ordering at the final stage of the nucleation. The ordering elements entail interference effects in the scattering of light by a system of particles and accordingly a reduction of the scattering and extinction coefficients by a factor of 2 by comparison with the case of independent scattering of light by particles. The results of the calculations are in agreement with the results of an experimental study of the structure of a liquating sodium-borosilicate glass.

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

The morphology and dynamics of polymerization-induced phase separation

The morphology and dynamics of polymerization-induced phase separation in the initially homogeneous solution of a non-reactive component in reactive monomers are investigated by incorporating the reaction kinetics into the Cahn–Hilliard equation. Analytical results show that there is a reduction of the initial length scale in the early stage of phase separation. The reason is the increase of the molecule weight of emerging polymer, independent of the fact whether the system goes through the metastable region or not. The numerical results are in good agreement with theoretical prediction quite well.

Computational Modeling of Mineral Unmixing and Growth

A new finite element based simulation technique for mineral growth governed by the classical Cahn–Hilliard equation is presented. The particular format of the underlying Flory–Huggins free energy for non-ideal mixtures is characterized through a double-well potential. It allows for uphill diffusion driven by gradients in the chemical potential and thus provides the appropriate framework to simulate phase separation typically encountered in mineral unmixing and growth. For the finite element discretization, the governing fourth order diffusion equation is reformulated in terms of a system of two coupled second order equations. For the temporal discretization, a heuristic adaptive time stepping scheme is applied in order to simulate not only the early stages of phase separation but also the long term behavior of ageing and grain fusion. The basic features of the Cahn–Hilliard equation are elaborated by means of selected geologically relevant examples. In particular, isotropic and anisotropic mineral growth and symplectite formation are studied and the long term response in the sense of Ostwald ripening is illustrated.

Phase behavior of near-critical PVME/SAN blend in film

The phase behavior of near-critical PVME/SAN blend in thin film was studied by time-resolved small-angle light scattering (SALS) and atomic force microscopy (AFM). The phase diagram showed that PVME/SAN99 blend had the lower critical solution temperature (LCST), the LCST and the critical composition was 119 °C, 74 wt.% PVME, respectively. However, the cloud points of this system were hard to be obtained before the decomposition of PVME when the weight fraction of SAN99 was more than 50 wt.%. Both SALS and AFM results confirmed that, for PVME/SAN99 blend, there was certainly a transition from homogeneous nucleation and growth to nonlinear spinodal decomposition in the two-phase region of 3D Ising regime. For 80 / 20 PVME / SAN99 blend, during the phase separation, the small orientation of SAN99 domains took place at the early stage of phase separation, and finally disappeared when the phase separation finished. But for 70 / 30 PVME / SAN99 blend, the orientation did not appear.

Phase behavior of blends of poly (vinyl methyl ether) with styrene-acrylonitrile in film

The phase behavior of blends of SAN/PVME in film is studied by Time-resolved Small-angle light scattering (SALS) and Atomic force microscopy (AFM). The phase diagram shows that both SAN99 (styrene volume fraction is 0.99)/PVME and SAN97 (styrene volume fraction is 0.97)/PVME have the lower critical solution temperature (LCST), the LCST of SAN97/PVME is (117 °C) lower than that (119 °C) of SAN99/PVME, and the cloud points of these two systems are hard to be obtained before the decomposition of PVME when the weight fraction of SAN (SAN99 or SAN97) is more than 50 wt%. For 20/80 SAN97/PVME and 20/80 SAN99/PVME blends (80 wt% PVME), although the experimental temperature is higher than the phase separation temperature, the phase separation does not take place immediately. It takes a period of time before the phase separation. The AFM phase images of 20/80 SAN99/PVME blend show that, as the phase separation proceeds, very small SAN99-rich droplets appear, the droplets become large step by step, then two large droplets coalesce into one larger droplet, and the obtained droplet size distribution is broader. Both SALS and AFM results show that, during the phase separation, the very small orientation of SAN domains takes place at the early stage of phase separation, and finally disappears when the phase separation finishes.

Early Stage of Phase Separation in Aluminoborosilicate Glass for Liquid Crystal Display Substrate

The early stage of phase separation in aluminoborosilicate glass for liquid crystal display substrates was investigated using a scanning electron microscope (SEM) and small‐angle X‐ray scattering measurement device (SAXS). The phase‐separated particles were detected with SAXS in samples in which no particle was observed with SEM. The particle diameter in an as‐formed sample was 2 nm. The relationship between the diameter and heat‐treatment time indicates that the phase separation proceeds by a diffusion‐controlled process. Based on the results of Fourier‐transform infrared spectroscopy, fast compositional change may occur in the early stage of phase separation.