Density functional theory of polymer-polymer phase separation behavior

Polyatomic density functional theory is applied to a binary polymer blend. The polymer reference interaction site model (PRISM) liquid state theory provides the homogeneous state correlation functions necessary for the application of density functional theory. An effective chi parameter can be recognized from the density functional expression; however, the phase separation criteria does not depend solely upon the chi parameter, rather it depends upon various combinations of the species-dependent direct correlation functions of the blend. The Flory-Huggins chi parameter along with the associated phase diagram is obtained when the monomer volumes of the blend species are equal and for a range of monomer-monomer attractive interactions. Calculations are performed both with and without the assumption of incompressibility. The density functional theory along with the PRISM determined “input” predict that an isotopic polymer blend shows an upper critical solution temperature (UCST) phenomena. © 1995 John Wiley & Sons, Inc.     

MECHANICAL MODEL FOR TWO-PHASE POLYMER BLEND SYSTEMS WITH THE CHARACTERISTICS OF PHASE INVERSION

For two-phase polymer blend systems, the phase inversion will take place as the blendcomposition is changed. In this paper a mechanical model has been proposed to describe themodulus-composition relation in the phase inversion region. The application of the mechanicalmodel to two polyurethane blend systems has been studied. It was found that the theoreticalprediction for the modulus-composition relation is quite consistent with the experimentalresults. Furthermore, the characteristics of the phase inversion can be determined uniquelyby the parameters involved in the mechanical model.     

Structure and dielectric properties of a thermoplastic blend containing dispersed metal

In the present work broadband dielectric relaxation spectroscopy measurements were employed to investigate the dielectric properties of polymer composites. A polyethylene/polyoxymethylene (PE/POM) thermoplastic blend was used as a matrix, while the inclusions were iron (Fe) particles. For comparison, the two pure polymers- PE and POM- were used as a matrix, too. In the PE/POM-Fe composites, the polymer matrix is two-phase and the filler particles are localized only in the POM phase, resulting in an ordered distribution of the dispersed filler particles within the blend. In PE-Fe and POM-Fe composites, the filler spatial distribution is random. The behaviour of all the composites studied is described in terms of the percolation theory. The PE/POM-Fe composites, based on the PE/POM blend, demonstrate different electrical behaviour compared to that of POM-Fe and PE-Fe systems. The percolation threshold value of the PE/POM-Fe composites was found much lower than that of the other two systems. The results were related to the microstructure of the composites. A schematic model for the morphology of the composites studied has been proposed. This model explains the peculiar behaviour of the PE/POM-Fe composites by taking into account the ordered distribution of the filler particles in a binary polymer matrix. Optical microscopy photographs confirm this model.     

Miscibility of poly(vinyl chloride) with poly(methyl-co-hexyl acrylate) and poly(methyl-co-2 ethyl hexyl acrylate)

The miscibility and phase behavior in blends of PVC with poly(methyl-co-hexyl acrylate)[MHA] and poly(methyl-co-2 ethyl hexyl acrylate)[MEH] were studied. It was found that PVC is miscible with MHA copolymers having a HA volume fraction from 0.30 to 0.92 and MEH copolymers having an EH volume fraction from 0.30 to 0.83 at 100°C. By applying the mean field theory to the phase diagrams of these blend systems, segmental interaction parameters which represent the binary interaction between different monomer units were estimated. The calculated values reflect the fact that the miscibility window observed for PVC/MHA and PVC/MEH blend systems was attributed to the effect of repulsion between different monomer units within the copolymer. To investigate the effect of specific interaction on the miscibility for these blend systems, an attempt was also made to describe the blend interaction parameter as a function of polar group concentration in the acrylate copolymer. The blend interaction parameter values exhibit a u-shaped curve as a function of the weight fraction of C?O group in the copolymer, and the lowest blend interaction parameter value appears at about 0.24 C?O weight fraction.     

UCST behavior in blend systems of isotactic polystyrene/poly(4-methyl styrene) in comparison with atactic polystyrene/poly(4-methyl styrene)

Blends of poly(4-methylstyrene) (P4MS) with polystyrene (iPS) exhibit an upper critical solution temperature (UCST) at ca. 270 °C. The overall phase behavior and trend of variation in the phase diagrams for the iPS/P4MS blend system with respect to molecular weights of iPS is similar to an earlier studied blend system of atactic PS with P4MS. This suggests that the crystal phase-related tacticity and crystallinity in iPS does not influence the amorphous phase behavior and UCST behavior of the polymer mixtures. A model based on a modified Flory-Huggins expression for binary interactions was constructed to describe the UCST-type behavior of the iPS/P4MS blend and to compare the qualitative effects of molecular weights on iPS/P4MS blend vs. atactic PS/P4MS systems.     

Viscoelastic behavior of polypropylene/nitrile rubber thermoplastic elastomer blends: Application of Kerner's models for reactively compatibilized and dynamically vulcanized systems

The viscoelastic properties of binary blends of nitrile rubber (NBR) and isotactic polypropylene (PP) of different compositions have been calculated with mean‐field theories developed by Kerner. The phase morphology and geometry have been assumed, and experimental data for the component polymers over a wide temperature range have been used. Hashin's elastic–viscoelastic analogy principle is used in applying Kerner's theory of elastic systems for viscoelastic materials, namely, polymer blends. The two theoretical models used are the discrete particle model (which assumes one component as dispersed inclusions in the matrix of the other) and the polyaggregate model (in which no matrix phase but a cocontinuous structure of the two is postulated). A solution method for the coupled equations of the polyaggregate model, considering Poisson's ratio as a complex parameter, is deduced. The viscoelastic properties are determined in terms of the small‐strain dynamic storage modulus and loss tangent with a Rheovibron DDV viscoelastometer for the blends and the component polymers. Theoretical calculations are compared with the experimental small‐strain dynamic mechanical properties of the blends and their morphological characterizations. Predictions are also compared with the experimental mechanical properties of compatibilized and dynamically cured 70/30 PP/NBR blends. The results computed with the discrete particle model with PP as the matrix compare well with the experimental results for 30/70, 70/30, and 50/50 PP/NBR blends. For 70/30 and 50/50 blends, these predictions are supported by scanning electron microscopy (SEM) investigations. However, for 30/70 blends, the predictions are not in agreement with SEM results, which reveal a cocontinuous blend of the two. Predictions of the discrete particle model are poor with NBR as the matrix for all three volume fractions. A closer agreement of the predicted results for a 70/30 PP/NBR blend and the properties of a 1% maleic anhydride modified PP or 3% phenolic‐modified PP compatibilized 70/30 PP/NBR blend in the lower temperature zone has been observed. This may be explained by improved interfacial adhesion and stable phase morphology. A mixed‐cure dynamically vulcanized system gave a better agreement with the predictions with PP as the matrix than the peroxide, sulfur, and unvulcanized systems. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1417–1432, 2004     

Chemically induced phase separated morphologies in epoxy resin‐hyperbranched polymer blends

The morphology build‐up in toughened epoxy blends using reactive hyperbranched dendritic polymers (HBP) and amine‐cured epoxy resins has been investigated in the present work. By changing the processing conditions or the surface chemistry of the modifier, very different morphologies can be obtained, ranging from homogeneous blends to coarse two‐phase systems. The morphology characterised by electron and optical microscopy has been interpreted combining constitutive equations for phase separation and thermodynamic modelling of phase interactions. The latter model, based on the Flory‐Huggins lattice theory, was modified in order to take into account the addition reactivity of the HBP modifiers. This approach proved successful and can be used as a tool for final morphology prediction in any reactive blend formulation.     

Phase behavior of polymer/diluent/diluent mixtures and their application to control microporous membrane structure

Rechargeable battery separators containing controlled pores were fabricated via the thermally-induced phase separation (TIPS) process. Based on the idea that pores could be manipulated by controlling the liquid–liquid phase separation temperature in the TIPS process, phase boundaries of the polymer–diluent systems were controlled by using diluent mixtures. Phase behaviors of the polymer/diluent/diluent ternary blends consisting of polyethylene (PE) as polymer, and soybean oil (SBO) and dioctyl phthalate (DOP) as diluents were explored. PE/SBO and PE/DOP binary blends, and PE/SOB/DOP ternary blends exhibited typical upper critical solution temperature (UCST) type phase behaviors, and the phase separation temperatures of the PE/SBO blends were higher than those of the PE/DOP blends. When the mixing ratio of the polymer and diluent-mixture was fixed, the phase separation temperature of the PE/SBO/DOP blend initially increased with increasing SBO content in the diluent-mixture passing through a maximum centered at about 80 wt% SBO and decreased beyond this point. Furthermore, the phase separation temperature of the PE/diluent-mixture blend was always higher than that of the PE/SBO blend when the diluent-mixture contained more than or equal to 50 wt% SBO. To understand the observed phase behavior of the blends, thermodynamic analyses based on the lattice-fluid theory were performed. Larger pore membranes were fabricated from the blend when higher phase separation temperatures of the blend were exhibited.     

Shear influences on polymer blends: experimental,theoretical approaches and technical implications

We examine the effects of shear on polymer blends consisting of partially miscible components, i.e. systems close to the phase boundary. The eminent phenomenon is the shift of the phase boundary, either extending the homogeneous area (flow‐induced mixing) or the opposite effect (flow‐induced demixing). The kinetics of the demixing process and concentration fluctuations are also influenced by flow fields, inducing anisotropy due to the flow direction. Experiments (scattering, rheology, in‐situ flow‐scattering, microscopy, DSC) are carried out with the academic model blend polystyrene/poly(vinyl methyl ether) and the industrial poly(styrene‐co‐maleic anhydride)/poly (methyl methacrylate) blend. The experimental results are rationalised in terms of a generalised Gibbs energy of mixing by including the energy which is stored in the sheared fluids.     

高分子相分离的分子动力学模拟

用粗粒化分子动力学(MD)模拟方法从分子层次研究两组分聚合物共混体系相分离过程中的动力学. 在相分离初期, 相区尺寸不随时间增加而变化; 在相分离中期, 相区尺寸与时间有很好的标度关系, 标度指数(α=1/3)符合Lifshiz-Slyozov提出的以扩散为主导的蒸发-凝聚机理的标度预测; 在相分离后期, 体系实现宏观相分离, 相区尺寸不再随时间改变而变化. 体积分数小的高分子链尺寸在相分离过程中先收缩再扩张, 在实现宏观相分离后, 高分子链尺寸又回到本体状态尺寸.     

Phase behavior and structure formation in ternary blends: studies on blends of PVDF/PMMA/PVAC

The phase behavior of ternary blends was analyzed on the basis of the lattice approach. Both compatibilization and incompatibilization effects are predicted to occur depending on the relative magnitudes and the sign of the interaction parameters of the binary subsystems. Thermodynamic, structural and kinetic properties were investigated for a ternary model blend composed of poly(vinylidene fluoride), poly(methyl methacrylate) and poly(vinyl acetate). This particular ternary system is characterized by a specific symmertry with respect to the interactions in the binary subsystems. This symmetry affects both thermodynamic and structural properties. The experimentally determined interaction parameters were used to model the phase diagram on the basis of the lattice model: the theoretical phase diagram was found to be close to the experimental one. The crystallization processes were analyzed both for the binary and the ternary systems on the basis of a modified Turnbull–Fisher equation. The conclusions are that the properties of the ternary systems can be understood to a first approximation on the basis of those of the corresponding binary systems and the symmetry of the interactions.     

Effect of random and block copolymer additives on a homopolymer blend studied by small-angle neutron scattering

Small-angle neutron scattering (SANS) has been employed to study a blend of polystyrene and polybutadiene modified by copolymer additives. SANS data from the one-phase region approaching the phase boundary has been acquired for blends modified by random and diblock copolymers that have equal amounts of styrene and butadiene monomers as well as a random copolymer with an unequal monomer composition. The binary blend is near the critical composition, and the copolymer concentrations are low at 2.5% (w/w). The data have been fitted with the random-phase approximation model (binary and multicomponent versions) to obtain Flory–Huggins interaction parameters (χ) for the various monomer interactions. These results are considered in the context of previous light scattering data for the same blend systems. The SANS cloud points are in good agreement with previous results from light scattering. The shifts in the phase boundary are due to the effects of the additives on the χ parameter at the spinodal. All the additives appear to lower the χ parameter between the homopolymers; this is in conflict with the predicted Flory–Huggins behavior. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3191–3203, 2004     

Phase behavior and its viscoelastic response of polylactide/poly(ε-caprolactone) blend

Polylactide (PLA)/polycaprolactone (PCL) blends with various blend ratios were prepared via melt mixing. The morphology, linear and non-linear viscoelastic properties of the blend were studied using scanning electron microscope (SEM) and cone-plate rheometer. Three typical immiscible morphologies, i.e., spherical droplet, fibrous and co-continuous structure can be observed at various compositions. The elasticity ratio was proposed to play an important role together with the viscosity on the phase inversion because PLA/PCL blend presents a high viscosity ratio between two components. Two emulsion models were used to predict the linear viscoelastic properties of the blend with various morphologies. The Palierne model gives better fit compared with the G–M model, but both fail to predict the viscoelastic properties of the co-continuous blend. The viscoelastic behavior of those blends shows different temperature dependence due to their different morphologies. The principle of time–temperature superposition (TTS) is only valid for the co-continuous blend while fails with the rheological data of those blends with discrete spherical and fibrous domain structure. Moreover, although the discrete phase is difficult to be broken up due to the high viscosity ratio of the systems, the change of viscoelastic responses of those blends before and after preshear shows large difference, indicating that different morphologies have different sensitivity to the steady shear flow.     

Phase behavior in mixtures of a homopolymer and a block copolymer. 4. SALS and SAXS studies

Phase behavior of blends of poly(vinyl methyl ether) (PVME) with four styrene-butadiene-styrene (SBS) triblock copolymers, being of various molecular weights, architecture, and compositions, was investigated by small-angle light scattering. Small-angle X-ray scattering investigation was accomplished for one blend. Low critical solution temperature (LCST) and a unique phase behavior, resembling upper critical solution temperature (UCST), were observed. It was found that the architecture of the copolymer greatly influenced the phase behavior of the blends. Random phase approximation theory was used to calculate the spinodal phase transition curves of the ABA/C and BAB/C systems; LCST and resembling UCST phase behavior were observed as the parameters of the system changed. Qualitatively, the experimental and the theoretical results are consistent with each other. © 1996 John Wiley & Sons, Inc.     

聚合物二元体系动态力学性能的估算

动态热机械分析是多相聚合物体系的一个重要研究手段.分析动态力学性能可以研究共混高聚物的相容性、复合材料的界面特性以及高分子运动机理等.本文综述了聚合物二元体系,即填充、纤维增强、共混体系动态力学性能的估算方法.在填充体系中,分别概述有无界面作用两种情况,当存在界面作用时,界面作用越强,模量越大,阻尼越小.对纤维增强体系,讨论了玻璃纤维有无取向的情况下模量和阻尼的估算.特别对于聚合物二元共混体系,分"海-岛"结构和双连续相两种情况,分别讨论了模量与阻尼的估算.     

Thermodynamic characterization of polymer‐polymer interfaces

The properties of multiphase polymer blends are determined in part by the nature of the polymer‐polymer interface. The interfacial tension, γ, influences morphology development during melt mixing while interfacial thickness, λ, is related to the adhesion between the phases in the solid blend. A quantitative relation between the thermodynamic interaction energy and these interfacial properties was first proposed in the theory of Helfand and Tagami and has since been correlated with experimental measurements with varying degrees of success. This paper demonstrates that the theory and experiment can be unified for polymer pairs of some technological importance: copolymers of styrene and acrylonitrile (SAN) with poly (2, 6‐dimethyl‐1, 4‐phenylene oxide) (PPO) and with bisphenol‐A polycarbonate (PC). For each pair, the overall interaction energy was calculated using a mean‐field binary interaction model expressed in terms of the interactions between repeat unit pairs extracted from blend phase behavior. Predictions of γ and λ as a function of copolymer composition made by combining the binary interaction model with the Helfand‐Tagami theory compare favorably with experimental measurements.     

Correlations between the free-volume properties and the miscibility of chitosan/polar polymers blend membranes

The miscibility of chitosan (CS)/polar polymer blend membranes has been studied by positron annihilation and other methods. The miscibility of these two blend systems (CS/polyvinyl pyrrolidone (PVP) and CS/polyethylene glycol (PEG)) is good in the solution state due to the hydrogen interaction between the functional groups of the studied polymers. However, the miscibility of these two blend systems in the solid state is better in the CS/PVP system than in the CS/PEG system. The differences in miscibility of such two blend systems in the solid state were powerfully demonstrated with positron annihilation lifetime spectroscopy (PALS) methods. The CS/PEG blend system had much larger free-volume size and lower free-volume concentration. For their poorer interaction and phase separation fact, the molecules in the interfacial zone of the CS/PEG blend are less compact than the CS matrix. Therefore, the free-volume size in the interfacial zone was much larger than it in the CS matrix.     

Surface tension of polystyrene blends: Theory and experiment

Surface tension of linear–linear and star/linear polystyrene blends were measured using a modified Wilhelmy method. Our results show that for both polystyrene blend systems, the surface tension‐composition profile is convex, indicating a strong surface excess of the component with lower surface energy. Star/linear blends display more convex surface tension profiles than their linear–linear counterparts, indicative of stronger surface segregation of the branched‐component relative to linear chains. As a first step toward understanding the physical origin of enhanced‐surface segregation of star polymers, self‐consistent field (SCF) lattice simulations (both incompressible and compressible models) and Cahn‐Hilliard theory were used to predict surface tension‐composition profiles. Results from the lattice simulations indicate that the highly convex surface tension profiles observed in the star/linear blend systems are only possible if an architecture‐dependent, Flory interaction parameter (χ = 0.004) is assumed. This conclusion is inconsistent with results from bulk differential scanning calorimetry (DSC) measurements, which indicate sharp glass transitions in both the star/linear and linear/linear homopolymer blends and a simple linear relationship between the bulk glass transition temperature and blend composition. To implement the Cahn‐Hilliard theory, pressure‐volume‐temperature (PVT) data for each of the pure components in the blends were first measured and the data used as input for the theory. Consistent with the experimental data, Cahn‐Hilliard theory predicts a larger surface excess of star molecules in linear hosts over a wide composition range. Significantly, this result is obtained assuming a nearly neutral interaction parameter between the linear and star components, indicating that the surface enrichment of the stars is not a consequence of complex phase behavior in the bulk. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1666–1685, 2009     

Phase ordering in blend films of semi‐crystalline and amorphous polymers

A combination of optical and atomic force microscopy (AFM) is used for probing changes in the morphology of polymer blend films that accompany phase ordering processes (phase separation and crystallization). The phase separation morphology of a “model” semi‐crystalline (polyethyleneoxide or PEO) and amorphous (polymethylmethacrylate or PMMA) polymer blend film is compared to previous observations on binary amorphous polymer blend films of polystyrene (PS) and polyvinylmethylether (PVME). The phase separation patterns are found to be similar except that crystallization of the film at high PEO concentrations obscures the observation of phase separation. The influence of film defects (e.g., scratches) and clay filler particles on the structure of the semi‐crystalline and amorphous polymer films is also investigated.     

Control of phase separation behavior of PC/PMMA blends and their application to the gas separation membranes

Gas transport and thermodynamic properties for the blends of polycarbonate (PC) and polymethylmethacrylate (PMMA) were studied. To explore glass transition temperatures of blends and their phase separation temperatures due to a lower critical solution temperature, LCST, a type of phase boundary, transparent blend films that are miscible and do not contain solvent-induced PC crystals were prepared by controlling molecular weights of each component. The average value of interaction energy densities between PC and PMMA obtained from the phase boundaries and the equation of a state theory based on the lattice fluid model was 0.04 cal/cm³. This result confirmed that miscibility of PC and PMMA blends at equilibrium depends upon the molecular weights of components. Gas transport properties of miscible blends and immiscible blends having the same chemical components and composition but a difference in morphology were examined at 35°C and 1 atm for the gases N₂ and O₂. Permeability and apparent diffusion coefficients were ranked in the order of the immiscible blend having a domain–matrix structure > the immiscible blend having an interconnected structure > the miscible blend. These results might be related to the differences in the local chain motions that depend on the intermolecular mixing level. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2950–2959, 1999