Morphology development and characterization of the phase-separated structure resulting from the thermal-induced phase separation phenomenon in polymer solutions under a temperature gradient

This paper studied the morphological development during the fabrication of anisotropic polymeric materials using the thermal-induced phase separation phenomenon (spinodal decomposition) in a model binary polymer solution under a linear spatial temperature gradient using mathematical modeling and computer simulation. The model incorporated the non-linear Cahn-Hilliard theory for spinodal decomposition and the Flory-Huggins theory for polymer solution thermodynamics. Moreover, the slow mode theory and Rouse law were used to account for polymer diffusion. The two-dimensional numerical results showed that an anisotropic morphology was developed when a temperature gradient was imposed along the polymer solution sample. The droplet size and droplet density decrease as temperature increases during the intermediate stage of spinodal decomposition. The spatial temperature gradient, however, had insignificant effect on the droplet shape.     

Multicomponent diffusion in phase-separating polymer blends with different frictional interactions: a mean-friction model

We present a compact formula for describing the mean frictional forces acting on a molecule in multicomponent systems. The friction-based diffusion theory of Zielinski and Hanley was extended to newly include the friction-average molar velocity as a reference frame. The results showed that the previous diffusion theories are unified by the friction-average concept by properly choosing the average velocity. The present model based on the diffusivity-related molar average velocity provides better predictions for the diffusive flux in a ternary miscible liquid compared to the other existing theories. The application of the model in phase-separating ternary systems revealed that the introduction of a highly diffusive third component into demixing polymer blends promotes a particular enhancement of the spinodal decomposition due to the difference in the frictional interactions between polymers.     

Studies of spinodal decomposition in a ternary polymer‐solvent‐nonsolvent system

Much of the work in modeling and computer simulation of spinodal decomposition has been done for binary systems. This work attempts to carry out the analysis of spinodal decomposition in ternary polymer‐solvent‐nonsolvent systems, where the solvent is the monomer used to produce the polymer and the nonsolvent is the major component. Various experimental methods are used to determine values of the parameters of the ternary version of the Cahn‐Hilliard equation of spinodal decomposition, such as cloudpoint experiments, time‐resolved light scattering in the ternary system, and morphological development of polymer membranes formed during the early stages spinodal decomposition. The combination of these experimental methods and computer simulation work shows the validity of the assumptions made in characterizing spinodal decomposition in ternary polymer systems of interest.     

Analysis of polymer membrane formation through spinodal decomposition. III: Two-dimensional simulations of early-stage behavior

A nonlinear diffusion equation is used to study early-stage spinodal decomposition of polymer solutions, in relation to the membrane formation, in two dimensions. The effects of overall polymer composition and composition-dependent mobility and diffusivity are included in our simulations. Our results show a kinetically stable structure is established during the early stages, which corresponds to a circular range of peaks in the two-dimensional frequency spectrum. Such a spectrum is found to result in an interconnected cell structure in the two-dimensional real space. A decrease in the level of polymer interdomain interconnectedness is obtained as time increases, which indicates the influence of interfacial tension. As the overall polymer composition is increased, an increase in interdomain distances is observed, although the same early stage morphological structure is obtained. Finally, calculated interdomain distances from the two-dimensional simulation are larger than those obtained in equivalent one-dimensional model systems.     

Analysis of polymer membrane formation through spinodal decomposition

A phenomenological model used in a previous work for spinodal decomposition of polymer-solvent systems is further analyzed. From the dimensionless form of the nonlinear Cahn-Hilliard equation, the dimensionless induction time is found to be a constant number for suddenly quenched systems. Computer simulation is carried out for prediction of early stage behavior with thermal history corresponding to a linear temperature drop followed by a constant temperature vs. time. In the areas of polymer membrane formation and phase separation studies, the universality of the constant dimensionless Induction time for suddenly quenched systems allows the determination of the minimum time needed for phase separation via spinodal decomposition. Also, simulation results for the double linear temperature history allows the convenient prediction of early stage spinodal decomposition behavior at every point of a membrane cross section undergoing thermal inversion phase separation.     

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.     

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 qm corresponding to the scattered light intensity maximum Im was analyzed by power-law scaling according to qm∼t−α and Im∼tβ. The results show β≈2α. 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.     

Phase Diagram for Liquid Crystalline Polymer/ Polycarbonate Blends

A novel mechanism to form binary polymer blends is through phase separation by spinodal decomposition in the unstable region of the phase diagram. The present work investigates the effects of thermally‐induced phase separation by spinodal decomposition on the morphology development of liquid crystalline polymer/polycarbonate blends. Moreover, a thermodynamic binary phase diagram is obtained using a twin‐screw extruder at various processing melt temperatures. Differential scanning calorimetry and scanning electron microscopy were used to study the miscibility of the blends and the resulting morphology. A thermodynamic binary phase diagram exhibiting a lower critical solution temperature was obtained. The droplet size distribution of the blend was also obtained and discussed in light of the Cahn‐Hilliard theory.     

Interdiffusion in blends of polystyrene and polymethylstyrene studied by light scattering after temperature jumps across the phase boundary

We describe a simple light scattering set-up for measuring interdiffusion coefficients D in polymer blends by generating spinodal decomposition and subsequent dissolution after temperature jumps across the phase boundary. In blends of polystyrene and polymethylstyrene (random copolymer of 60% m-methylstyrene and 40% p-methylstyrene) D values were obtained between 10⁻¹¹ and 10⁻¹⁵ cm²s⁻¹ at temperatures up to 50 K above the upper critical solution temperature. The results are discussed in relation to tracer diffusion in the same system.     

HYDRODYNAMIC EFFECTS IN THE PHASE SEPARATION OF BINARY POLYMER MIXTURES

The phenomenon of phase separation by spinodal decomposition was studied for polymer blends made by compositional quenching. The modified Cahn-Hilliard theory of phase separation was extended to include hydrodynamics, with a volumetric body force, due to concentration gradients, that induced convective flows. This force influenced the morphology and the growth rate of the average domain size. Unlike the conventional treatment of flows driven by surface tension, the velocity and pressure fields were treated as continuous functions of spatial position.

Numerical solutions for the phase separation in a binary mixture were obtained for a three-dimensional system with periodic boundary conditions. For near critical quenches with similar volume fractions for the two components, cocontinuity was destroyed by the hydrodynamics, giving discrete domains. The breakup in interconnectivity is believed to be a universal phenomenon. The domain growth rate followed a power law, r → τⁿ. The growth exponent depended on the dimensionless viscosity group, ξ = (R_g T/v_s) (Km/μD_AB) and ranged from n = 0.32 ± 0.006 for ξ J = 0 (no hydrodynamic effects) to n ∼ 1 for ξ = 1. For off-critical quenches in which a dispersed phase would be formed by diffusion alone, the scaling exponent showed little enhancement. The simulations accurately predicted the particle size formed in the early stages of spinodal decomposition.     

Controlling morphology of polystyrene/poly(vinyl methyl ether) blends undergoing spinodal decomposition process by photo-crosslinks

The morphology developing during the spinodal decomposition process of polystyrene (PS)/poly(vinyl methyl ether) (PVME) blends was successfully controlled by photo-crosslink reactions between PS chains. The crosslink reaction was carried out by taking advantage of the photodimerization of anthracene moieties that are labeled on PS chains. Effects of photo-crosslinks on the morphology induced by temperature jumps (T-jump) from the one-phase region into the spinodal region were examined under several experimental conditions such as T-jump depths and irradiation times. It was found that the concentration fluctuations developing during the spinodal decomposition process were efficiently frozen upon irradiation using a XeF excimer laser as well as a mercury (Hg) lamp. Furthermore, these ordered structures are quite stable upon annealing. These results demonstrate that the morphology developing during the spinodal decomposition process can be well controlled by easily accessible light sources such as high pressure mercury lamps. Thus the photo-crosslink reaction described in this work can provide the basis for a potential technique to design multiphase polymer materials with controllable ordered structures.     

Binodal and spinodal curves: a simulation for various high polymer mixtures

Flory's equation-of-state theory has been used to predict the lower critical solution temperature behaviour of polymer—polymer mixtures. The spinodal phase boundary of numbers of high molecular weight polymer mixtures have been previously simulated using this theory. In this paper a procedure for simultaneous predictions of the binodal and the spinodal curves by equating the chemical potential of each component in the mixture is presented. The method is tested for five different mixtures. The effects of the binary and pure component state parameters on the simulated curves are discussed and the simulated phase diagrams are compared with the experimental cloud point curves. It is found that in most cases the results are more consistent with the cloud point curve being closer to the spinodal curve than the binodal.     

Light scattering behavior and the kinetics of pressure-induced phase separation in solutions of poly(ε-caprolactone) in acetone + CO2 binary fluid mixtures

The miscibility and the kinetics of pressure-induced phase separation in solutions of poly(ε-caprolactone) (PCL) in acetone + CO₂ binary fluid mixtures have been studied at pressures up to 28 MPa and temperatures up to 410 K using a unique high pressure view-cell equipped with a dual set of pistons and dual set of sapphire windows. One set of the windows separated by 25.4 mm allows the assessment of the phase state and is used to monitor the transmitted light intensities. The second set of windows separated by 50 μm is used to monitor the scattered light intensities over a wide range of scattering vector q (from 0.35 to 4 μm⁻¹) which allows the assessment of the mechanism of phase separation. Investigations have been carried out for a wide range of polymer concentrations, from 2.0 to 34.9 wt%, while holding the acetone-to-CO₂ (wt:wt) ratio in each solution at a constant value of 2:1. The dual set of pistons that are employed which are synchronized and motorized create a churn-like action in the cell insuring effective mixing, even at the high polymer concentrations by translating the cell content across a magnetically-coupled rotating mixer impeller. The piston actions assure also that the solution is effectively introduced into the narrow gap between the scattering windows, and refreshed. The solutions at off-critical concentrations undergo pressure-induced phase separation via nucleation and growth mechanism which shows circular symmetric patterns in their light scattering patterns. For these solutions, the Debye–Bueche type scattering function was used to analyze the domain size of the new phase that forms and develops after a pressure quench. The phase separation in solutions at or near the critical polymer concentrations (9.0–15.0 wt%) proceeds via spinodal decomposition which is characterized by the formation and evolution of the spinodal ring patterns corresponding to a maximum in the angular variation of the scattered light intensities. The results in early stage of the spinodal decomposition were described by the linearized Cahn theory. The variation of the scattered light intensity maximum I_m and its location in scattering vectors q_m with time in the later stage of the spinodal decomposition obey power-law scaling according to I_m ∼ t^β and q_m ∼ t^−α. The results for the 9.0 and 12.0 wt% solutions show that β/α changes its value from β/α > 3 to β/α ≈ 3 with time, indicating the progression of the spinodal decomposition from intermediate to late stage.     

Crystallization of polycarbonate induced by spinodal decomposition in polymer blends

We found that amorphous polycarbonate (PC) can be crystallized in several minutes by blending poly(ethylene oxide) (PEO). When the blends were annealed in the two-phase region below the upper critical solution temperature, highly interconnected two-phase structure characteristic of the spinodal decomposition was developed and then the crystallization occurred in the PC-rich phase during the spinodal decomposition. As the molecular weight of PEO decreased, the crystallization rate decreased and the crystallizable temperature became narrower in spite of the acceleration of the polymeric segmental motion. These results suggest that the crystallization of the PC is not induced by the acceleration of the polymeric segmental motion, but by the up-hill diffusion of the liquid-liquid phase separation via spinodal decomposition. Owing to the competitive progress of the crystallization and the spinodal decomposition, the melting peak of the PC crystallites shifted to lower temperature with increasing annealing temperature.     

Molecular Weight Polydispersity Effects on Diffusion at Polymer/Polymer Interfaces

The effect of molecular weight distribution (MWD) on diffusion at symmetric polymer/polymer interfaces is investigated by rheological tools. A new model allowing the determination of a self‐diffusion coefficient of polydisperse polymer systems is presented. The model is based on the double reptation theory and Doi and Edwards' molecular dynamics applied to A/A polymers brought into intimate contact in the molten state. The material parameters for the model are obtained from linear oscillatory shear experiments, in which the dynamic shear modulus is measured in parallel plate geometry under a small amplitude of deformation as a function of time and frequency for a sandwich‐like assembly. The experiments were conducted on polystyrene (PS) blends with constant weight average molecular weight (M_w) but with variable number average molecular weights (M_n). The measured self‐diffusion coefficients showed that the presence of short molecules in the blend increases the mean value of the self‐diffusion coefficient and the magnitude of such increase can be quantitatively evaluated by the proposed model.     

Phase separation of poly (methyl methacrylate) / poly (styrene-co-acrylonitrile) blends in the presence of silica nanoparticles

The effects of silica nanoparticles on the phase separation of poly (methyl methacrylate)/poly (styrene-co-acrylonitrile) (PMMA/SAN) blends are studied by the rheological method. The binodal temperatures of near-critical compositions were obtained by the gel-like behavior during spinodal decomposition, which is a character of polymer blends with co-continuous morphology. The shifted Cole–Cole plot method was introduced to determine the binodal temperatures of off-critical compositions based on the appearance of shoulder-like transition in the terminal regime of blends with droplet morphology. Such method is found also applicable in nanoparticle filled polymer blends. Moreover, a new method to determine the spinodal temperature from Fredrickson-Larson mean field theory was suggested, where the concentration fluctuation's contribution to the storage modulus is used instead of the whole dynamic moduli. This method was also successfully extended to nanoparticle filled polymer blend. The influences of the concentration and the average diameter of silica particles on the phase separation temperature were studied. It was found that the small amount of the silica nanoparticles in PMMA/SAN blends will significantly change the phase diagram, which is related to the selective location of silica in PMMA. The comparisons with thermodynamic theory of particle-filled polymer blends are also discussed.     

Computer vision methods for the study of spinodal decomposition in polymer blends

We demonstrate the use of computer vision techniques and optical microscopy to follow the kinetics and microstructure during spinodal decomposition of a polymer blend. Among other features, the mean of the population of the local maxima of the gradients in each image is computed; this global feature is shown to co-develop with the phase separation of the blend. An algorithm is presented which employs the gradient magnitude technique to analyze optical images of spinodally decomposing polymer blends. This algorithm has been used to extract the Cahn-Hilliard spinodal growth rates for a binary blend of polystyrene with poly(vinyl methyl ether). We show that the spinodal temperature can be found from the temperature dependence of this growth rate. We also show how additional shape features such as compactness might be used to study, the same binary blend.     

Numerical simulation of the self‐assembly of a polymer–polymer–solvent ternary system on a heterogeneously functionalized substrate

The spinodal decomposition of a polymer–polymer–solvent ternary blend spin coated on heterogeneously functionalized substrate is studied in a three‐dimensional numerical model. The Cahn‐Hilliard equation was used to describe the free energy profile of the domain. The mechanism of the morphology evolution was studied quantitatively. The well‐established linear relationship of the characteristic length, R(t), with t^1/3 can be observed in the simulation results. The functionalized substrate greatly affected the morphology evolution of blends with different solvent concentrations. The results indicated that a critical time can be observed, at which the evolution rate changes abruptly, also after which the compatibility of the surface morphology to the functionalized substrate pattern increases at a much lower pace in the diluted solution. In the condensed solution, the compatibility actually decreases beyond the critical time. The influence of solvent evaporation is investigated and a sharper interface was observed in the case with solvent evaporation and film thickness reduction. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Mass transfer dynamics of the evaporation step in membrane formation by phase inversion

A ternary diffusion model has been developed for the evaporation step of the phase inversion process. The model is applied to the analysis of mass transfer dynamics of the evaporation step for the methanol–acetone–cellulose acetate (CA) ternary casting system. The combined analysis of quantitatively computational results from the ternary evaporation model and qualitative dynamic results during the quench process has shown that the evaporation step is essentially necessary to prepare the defect‐free, ultrathin skinned asymmetric CA membrane for the separation of CO₂/CH₄. The skin layer of high CA concentration obtained by evaporation has an ability to suppress liquid–liquid phase separation. And the skin layer with high tensile strength can resist the interfacial tension caused by spinodal decomposition from the substructure. Although the CA concentration in the skin layer increases considerably because of the evaporation step and the following delay time during the quench process, the substructure can still induce the spinodal decomposition because the strong coagulant, methanol, can diffuse rapidly across the ultrathin skin layer. Hence the defect‐free, ultrathin‐skinned asymmetric membrane for gas separation can be prepared from methanol–acetone–CA casting system by evaporation step and the wet phase inversion. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 1564–1571, 2002     

Time-resolved light scattering of the phase separation in polymer-dispersed liquid crystals formed by photo-polymerization induced phase separation

Time-resolved light scattering is utilized to monitor the phase separation of photo-initiated polymer-dispersed liquid crystals. At the lowest cure intensities studied, the system undergoes spinodal decomposition and the results are analyzed with Cahn-Hilliard theory. As the cure intensity increases, the rate of phase separation increases such that the early stages of spinodal decomposition are no longer observable. These systems are analyzed using the Debye-Bueche model, which provides the time evolution of the number and size of LC domains. These results indicate that an increase in cure beam intensity initially increases the rate of domain growth, but this effect is overwhelmed by the fast vitrification and cross-linking that can occur at highest cure beam intensities.