Refined Continuous Thermodynamic Treatment for the Liquid-Liquid Equilibrium of Copolymer Solutions

Based on an improved calculation of activity coefficients, continuous thermodynamics using a generalized divariate Stockmayer distribution is applied to the liquid-liquid equilibrium of random copolymer solutions. The effects of the chemical polydispersity on the cloud-point curve, the shadow curve, the spinodal, and the critical point are discussed. The theory can account for the occurrence of three-phase equilibria as well as for the phase separation in pure copolymers.     

Liquid-Liquid Equilibrium of Polydisperse Copolymer Solutions. Multivariate Distribution Functions in Continuous Thermodynamics

In addition to the usual polydispersity with respect to molar mass, copolymers show chemical polydispersity. Thus, the species present may not be adequately characterized by a single variable, and a divariate distribution function has to be applied for describing the composition of the copolymer. In continuous thermodynamics, such continuous distribution functions are used directly (without splitting into pseudocomponents) for describing the composition of complex multicomponent systems. Whereas until now usually only one distribution variable has been used in continuous thermodynamics, consideration of copolymers requires an extension to divariate distribution functions. Continuous thermodynamics is generalized to divariate distribution functions in this paper. The liquid-liquid equilibrium of copolymer solutions is considered as a specific example.     

The structure and phase transitions in polymer blends,diblock copolymers and liquid crystalline polymers: The Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.     

Liquid—Liquid Equilibrium in Polydisperse Random Copolymer Blends

Continuous thermodynamics is applied to the liquid‐liquid equilibrium in random copolymer blends. Two copolymers are mixed, each consisting of two different monomer units. Hence, up to four monomer units may be present in the system. Both copolymers are characterized by divariate distribution functions with respect to molecular weight (chain length) and chemical composition. The basic relations necessary for phase equilibrium calculations are derived. The influences of both polydispersities and of the different parameters included in the model for the excess Gibbs free energy are discussed by calculating cloud‐point curves and shadow curves. Applications to practical systems are given.     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

Influence of copolymer configuration on the phase behavior of ternary blends

The influence of copolymer configuration on the phase behavior of various ternary polymer blends containing a crystallizable polyester, a noncrystallizable polyether, and an acrylic random copolymer of different chain configuration was investigated. In these ternary blends, the acrylic random copolymer is typically added to control rheological properties at elevated temperatures. In fact, the acrylic random copolymers composed of various compositions of MMA and nBMA were found to have different miscibility with polyester as well as polyether, leading to substantially different phase behavior of ternary blends. Remarkable temperature dependence was also found. The mean-field Flory-Huggins theory for the free energy of mixing, extended to ternary polymer blends, was adopted for predicting phase diagrams where the exact spinodal and binodal boundaries could be calculated. Phase diagrams of ternary blends, predicted by the Flory-Huggins formulations and related calculations, were in good agreement with experimental phase diagrams. The differences observed in the rheological processes of various ternary blends with different acrylic copolymers were directly related to changes in miscibility, associated phase behavior, and chain configuration.     

对称长链和近对称短链两嵌段聚合物混合体系相行为研究

利用自洽平均场理论(SCMFT)系统地研究了对称长链和近对称短链两嵌段聚合物混合体系在纳米尺度下的自组装行为.体系中具有较高聚合度的对称长链熔体处于层状相,聚合度较低的近对称短链熔体处于无序相,而其混合体系却随着两种成分的不同比例呈现出有序-无序相转变、有序-有序相转变及有序-无序两相共存等复杂的相行为,计算结果与近期类似体系的实验有着较好的吻合.同时与两种对称的两嵌段聚合物混合体系的计算结果进行了比较,得出这两种体系的异同之处.     

Ftir study of hydrogen bonding and phase behaviour in poly(vinylpyridines)/poly(ethylene-CO-vinyl alcohol) blends

The specific interactions between polyvinylpyridines and ethylene-vinyl alcohol copolymers of different compositions have been studied by Fourier transform infrared spectroscopy (FTIR). Hydrogen bonding between both polymer components leads to significant spectral modification in pyridine rings spectral bands. Minor modifications in other spectral modes have been also detected. The spectral results indicate at least three competing equilibria processes in the blends: hydroxyl-hydroxyl copolymer self-association and hydroxyl-pyridine interassociation. Painter-Coleman association model was successfully applied and the phase diagram for these systems has been predicted.     

Recent developments in phase separation of polyolefin melt blends

Saturated hydrocarbon polymers may be differentiated by the relative amount and placement of methylene, methyl, methine, and quaternary carbon moieties. While it has been known or suspected for some time that polyolefins of conventional molecular weight (M_w ≈ 100 kg/mol) with dissimilar chemical microstructures are most often immiscible in the liquid state, recent experiments with binary blends of model polyolefins have increased greatly our understanding of thermodynamic interactions between unlike chains. Model systems with methyl (−CH₃) and ethyl (−C₂H₅) short-chain branches give results, expressed as the Flory-Huggins interaction parameter χ, that are nearly universal; repulsive interactions (χ > 0) are more pronounced at low temperatures, leading to liquid-liquid phase separation at an upper critical solution temperature. Phase behavior of more complex systems (with distributions of chain microstructures and/or molecular weight) is generally consistent with predictions from model systems. An interesting exception is from work at Bristol on blends of lightly branched ethylene − α-olefin copolymers with unbranched polyethylene as the minority species. Here the presence of two liquid phases is inferred under conditions not expected from model studies; effects of copolymer composition and molecular weight are also unusual. Recent theoretical work points to the importance of chain stiffness (established by short-chain branching) in determining the thermodynamics of model blends. Nonrandom mixing of chains with different stiffness gives rise to an enthalpic χ, which may be negative under certain conditions. Other limitations of the Flory-Huggins approach to describing blend energetics are considered. At present there is no theoretical basis for liquid-liquid phase separation reported by the Bristol group. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2329–2353, 1997     

SAN共聚物组成对PVC/ABS共混物相容性的影响

采用乳液聚合技术通过改变共聚单体的投料比(St/AN)合成了一系列不同AN结合量的ABS接枝共聚物粉料和SAN共聚物.将其与聚氯乙烯(PVC)和邻苯二甲酸二辛酯(DOP)熔融共混分别制得了PVC/ABS、PVC/SAN、PVC/ABS/DOP和PVC/SAN/DOP共混物,利用SEM、TEM和动态力学粘弹谱仪(DMA)对共混物的相容性和相结构进行了表征.结果发现,在PVC/ABS共混体系中,尽管改变接枝SAN共聚物的AN结合量,PVC和SAN共聚物均为不相容体系;在该共混物中引入增塑剂DOP后,虽然当SAN共聚物AN结合量小于23.4 wt%时,共混物在室温以上只存在一个tanδ峰,但形态结构研究结果表明共混物仍为不相容体系,共混物的相区尺寸明显地依赖于SAN共聚物中的AN结合量,当AN结合量为23.4 wt%时相区尺寸最小.     

Liquid–liquid equilibrium calculations for methanol–gasoline blends using continuous thermodynamics

This work presents the application of continuous thermodynamics to investigate the limited miscibility of methanol–gasoline blends. To predict the liquid–liquid equilibrium of these systems, the Gaussian distribution function was used to represent the composition of paraffins in the gasoline. The naphthenes and aromatics were represented by model compounds. A model has been developed using three different continuous versions of the UNIFAC model. Methanol is an associating component, and association affects phase equilibria. Therefore, the CONTAS (continuous thermodynamics of associating systems) model based on the Flory–Huggins equation, for multicomponent methanol–gasoline blends has also been investigated. The predicted results including the cloud point curve, shadow curve and phase separation data have been compared with experimental data and good agreement was found for the two UNIFAC and CONTAS models.     

Random and block copolymers as compatibilizers,directly compared

Most blends are two‐phase systems that exhibit coarse morphologies with weak interfaces between the phases. It is well known that these blends can be compatibilized by suitably adapted block copolymers is known. Less known is that random copolymers can compatibilize blends as well, forming interphases. In this study, block and random copolymers of styrene and methylmethacrylate were tested in direct comparison, in a blend of polystyrene and polyvinylchloride. The random copolymers are inferior, as regards the phase morphologies, but competitive, as far as the tensile strength is concerned.     

The influence of polymer structure and component ratios on blend miscibility

The mean field, rigid lattice treatment as applied to polymer mixtures has been used to estimate segment-segment interaction parameters for a wide range of polymers. These parameters incorporate, without distinction, contributions from non-combinatorial entropy effects, dispersion forces and any specific interactions that operate in the polymer blend. Thus while these parameters can be used to predict successfully the nature of the phases in untested polymer blends, structural effects may also play a role in determining miscibility, and these may have to be assessed individually. Examples of structural effects are described using chlorine-containing polymers and blends of copolymers with an anhydride ring attached in two different ways to the polymer chain. The extension of binary interaction parameters to the prediction of phase behaviour in complex ternary copolymer blends and the effect on the phase behaviour of changing the component ratios in the blends, is also illustrated.     

接枝共聚物EPR-g-PS作PS/EPDM共混体系增容剂的探讨

使用了由大分子单体共聚合制备的以乙丙橡胶(EPR)为主干、聚苯乙烯(PS)为支链的接枝共聚物EPR-g-PS作为PS/EPDM共混体系的增容剂。实验结果表明,共混体系的组成、增容剂加入量以及增容剂分子结构对共混体系冲击强度有很大影响。将这些因素与相差显微镜及扫描电镜研究所揭示的共混物形态的变化相联系,对此类接校共聚物作为不相容体系增容剂的机理作了探讨。     

In-situ preparation of graft copolymers

Graft copolymers are closer to supermolecular structures than any other class of polymers. Most grafting reactions proceed in demixed blends or lead in situ to such blends The competition of chemical chain coupling and physical phase separation generates complex phase morphologies that cannot (or not so directly) be produced otherwise. To demonstrate potential and problems of graft copolymer systems, high-impact thermoplastics, block-graft copolymers and reactive blending are discussed.     

最有效的相容剂是两嵌段还是多嵌段聚合物?

Monte Carlo simulations were used to investigate the compatibilizing behaviors of multi-block copolymers with different architectures in A/B/(block copolymer) ternary blends. The volume fraction of homopolymer A, employed as the dispersed phase, was 19%. The simulations illustrate how a di- or multi-block copolymer aggregates at the interfaces and influences the phase behaviour of such incompatible polymer blends. The di-block copolymer chains tend to "stand" on the interface whereas the multi-block chains lie on the interface.In comparison with the dj-block copolymer, the block copolymers with 4, or 10 blocks can occupy more areas on the interface, and thus the multi-block copolymers have higher efficiency for the retardation of the phase separation.     

Interfacial tension of evaporating emulsion droplets containing amphiphilic block copolymers: effects of solvent and polymer composition

Evaporating droplets of volatile organic solvent containing amphiphilic block copolymers may undergo hydrodynamic instabilities that lead to dispersal of copolymer micelles into the surrounding aqueous phase. As for related phenomena in reactive polymer blends and oil/water/surfactant systems, this process has been ascribed to a nearly vanishing or transiently negative interfacial tension between the water and solvent phases induced by adsorption of copolymer to the interface. In this report, we investigate the influence of the choice of organic solvent and polymer composition for a series of polystyrene-b-poly(ethylene oxide) (PS-PEO) diblock copolymers, by in situ micropipette tensiometry on evaporating emulsion drops. These measurements suggest that the sensitivity to the organic solvent chosen reflects both differences in the bare solvent/water interfacial tension as well as the propensity of the copolymer to aggregate within the organic phase. While instabilities coincident with an approach of the interfacial tension nearly to zero were observed only for copolymers with PEO content greater than 15 wt.%, beyond this point the interfacial behavior and critical concentration needed to trigger surface instability were found to depend only weakly on copolymer composition.     

Organizing thermodynamic data obtained from multicomponent polymer electrolytes: Salt‐containing polymer blends and block copolymers

The objective of this review is to organize literature data on the thermodynamic properties of salt‐containing polystyrene/poly(ethylene oxide) (PS/PEO) blends and polystyrene‐b‐poly(ethylene oxide) (SEO) diblock copolymers. These systems are of interest due to their potential to serve as electrolytes in all‐solid rechargeable lithium batteries. Mean‐field theories, developed for pure polymer blends and block copolymers, are used to describe phenomenon seen in salt‐containing systems. An effective Flory–Huggins interaction parameter, χ_eff , that increases linearly with salt concentration is used to describe the effect of salt addition for both blends and block copolymers. Segregation strength, χ_effN , where N is the chain length of the homopolymers or block copolymers, is used to map phase behavior of salty systems as a function of composition. Domain spacing of salt‐containing block copolymers is normalized to account for the effect of copolymer composition using an expression obtained in the weak segregation limit. The phase behavior of salty blends, salty block copolymers, and domain spacings of the latter systems, are presented as a function of chain length, composition and salt concentration on universal plots. While the proposed framework has limitations, the universal plots should serve as a starting point for organizing data from other salt‐containing polymer mixtures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1177–1187     

Interfaces in polymer blends

We investigate the structure and thermodynamics of interfaces in dense polymer blends using Monte Carlo (MC) simulations and self‐consistent field (SCF) calculations. For structurally symmetric blends we find quantitative agreement between the MC simulations and the SCF calculations for excess quantities of the interface (e.g., interfacial tension or enrichment of copolymers at the interface). However, a quantitative comparison between profiles across the interface in the MC simulations and the SCF calculations has to take due account of capillary waves. While the profiles in the SCF calculations correspond to intrinsic profiles of a perfectly flat interface the local interfacial position fluctuates in the MC simulations. We test this concept by extensive Monte Carlo simulations and study the cross‐over between “intrinsic” fluctuations which build up the local profile and capillary waves on long (lateral) length scales. Properties of structurally asymmetric blends are exemplified by investigating polymers of different stiffness. At high incompatibilities the interfacial width is not much larger than the persistence length of the stiffer component. In this limit we find deviations from the predictions of the Gaussian chain model: while the Gaussian chain model yields an increase of the interfacial width upon increasing the persistence length, no such increase is found in the MC simulations. Using a partial enumeration technique, however, we can account for the details of the chain architecture on all length scales in the SCF calculations and achieve good agreement with the MC simulations. In blends containing diblock copolymers we investigate the enrichment of copolymers at the interface and the concomitant reduction of the interfacial tension. At weak segregation the addition of copolymers leads to compatibilization. At high incompatibilities, the homopolymer‐rich phase can accommodate only a small fraction of copolymer before the copolymer forms a lamellar phase. The analysis of interfacial fluctuations yields an estimate for the bending rigidity of the interface. The latter quantity is important for the formation of a polymeric microemulsion at intermediate segregation and the consequences for the phase diagram are discussed.     

Reactively and physically compatibilized immiscible polymer blends: stability of the copolymer at the interface

This paper reports on the interfacial behaviour of block and graft copolymers used as compatibilizers in immiscible polymer blends. A limited residence time of the copolymer at the interface has been shown in both reactive blending and blend compatibilization by preformed copolymers. Polystyrene (PS)/polyamide6 (PA6), polyphenylene oxide (PPO)/PA6 and polymethylmethacrylate (PMMA)/PA6 blends have been reactively compatibilized by a styrene-maleic anhydride copolymer SMA. The extent of miscibility of SMA with PS, PPO and PMMA is a key criterion for the stability of the graft copolymer at the interface. For the first 10 to 15 minutes of mixing, the in situ formed copolymer is able to decrease the particle size of the dispersed phase and to prevent it from coalescencing. However, upon increasing mixing time, the copolymer leaves the interface which results in phase coalescence. In PS/LDPE blends compatibilized by preformed PS/hydrogenated polybutadiene (hPB) block copolymers, a tapered diblock stabilizes efficiently a co-continuous two-phase morphology, in contrast to a triblock copolymer that was unable to prevent phase coarsening during annealing at 180°C for 150 minutes.