Role of crystal-amorphous interaction in phase equilibria of crystal-amorphous polymer blends

A self-consistent theory has been developed for determination of phase diagrams of a crystalline polymer solution. Although the original Flory diluent theory captures the liquidus line, the theory is incapable of accounting for the solidus line due to the inherent assumption of complete immiscibility of solvent in the solid crystal. The present theory considers all possible interactions involving amorphous-amorphous and crystal-amorphous interactions. The self-consistent solutions predict various phase diagrams involving liquid-liquid, pure solid, and liquid-solid coexistence regions bound by liquidus and solidus lines. In the limit of complete insolubility of solvent in neat solid crystal, the original Flory diluent theory is recovered.     

Phase equilibria and phase separation dynamics in a polymer composite containing a main-chain liquid crystalline polymer

Various topological phase diagrams of blends of main-chain liquid crystalline polymer (MCLCP) and flexible polymer have been established theoretically in the framework of Matsuyama–Kato theory by combining Flory–Huggins (FH) free energy for isotropic mixing, Maier–Saupe (MS) free energy for nematic ordering in the constituent MCLCP, and free energy pertaining to polymer chain-rigidity. As a scouting study, various phase diagrams of binary flexible polymer blends have been solved self-consistently that reveal a combined lower critical solution temperature (LCST) and upper critical solution temperature (UCST), including an hourglass phase diagram. The calculated phase diagrams exhibit liquidus and solidus lines along with a nematic–isotropic (NI) transition of the constituent MCLCP. Depending on the strengths of the FH interaction parameters and the anisotropic (nematic–nematic) interaction parameters, the self-consistent solution reveals an hourglass type phase diagram overlapping with the NI transition of the constituent MCLCP. Subsequently, thermodynamic parameters estimated from the phase diagrams hitherto established have been employed in the numerical computation to elucidate phase separation dynamics and morphology evolution accompanying thermal-quench induced phase separation of the MCLCP/polymer mixture. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3621-3630, 2006     

Influence of acrylate arm topology on phase diagrams of mixtures of multiarm acrylate photocurative monomers and nematic liquid crystals

Phase equilibria of binary mixtures of liquid crystal and multiarm star acrylate derivatives have been established as a function of the number of acrylate arms by means of cloud point determination. Equilibrium phase diagrams of liquid crystal/multiarm acrylate derivatives have been calculated self-consistently in the framework of combined Flory-Huggins free energy of liquid-liquid demixing and Maier-Saupe free energy of nematic ordering. It was found experimentally that the phase diagram of the branched/star molecule/solvent shifts to elevated temperatures with an increasing number of acrylate arms. This movement of the coexistence line is attributed to the architectural effect contributing to the athermal entropic part of the chi interaction parameter. The present self-consistent solution has been tested satisfactorily with the observed phase diagrams of liquid crystal/acrylate systems.     

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.     

Toward a prediction of the phase behavior of polyamide blends

As we have reported recently, the application of association models has provided a theoretical basis for the calculation of the free energy changes and phase diagrams of binary polymer blends in which hydrogen bonding plays a significant role. Here we report theoretical calculations of spinodal phase diagrams of a series of polyisophthalamide-polyether blends and compare the predictions with experimental observations of the miscibility of these polymer blend systems. The general agreement between theory and experiment is very encouraging and has important ramifications to discussions of polymer-induced crystallnity, the minimum number of hydrogen bonding sites necessary to ensure significant molecular mixing, and the effect of hydrogen bonding on the breadth of “miscibility windows.”     

Phase transitions in mixtures of a side-on-side chain liquid crystalline polymer and low molar mass nematic liquid crystals

Miscibility phase diagrams of mixtures of side-on side chain liquid crystalline polymers (s-SCLCP) and low molar mass liquid crystals (E48 and E44) have been established by means of polarized optical microscopy and light scattering. E48 and E44 are cyanobiphenyl-based eutectic nematic liquid crystal (LC) mixtures with nematic-isotropic transition temperatures of 93 and 105 C, respectively. The phase diagram of the s-SCLCP/E48 system reveals the coexistence of an isotropic nematic region and a single nematic phase in order of descending temperature. The single nematic phase suggests that the pair is miscible in the nematic region. On the other hand, the s-SCLCP/E44 mixture shows liquid liquid and nematic nematic coexistence phases, suggestive of the immiscibility character of the pair. These nematic phase diagrams of the s-SCLCP/E48 and s-SCLCP/E44 have been analysed in the context of the combined Flory-Huggins (FH) free energy for isotropic mixing and the Maier-Saupe (MS) free energy for nematic ordering of the mesogens. This combined FH/MS theory is capable of predicting the observed nematic phase diagrams consisting of liquid liquid, liquid nematic, nematic nematic, and the pure nematic regions. The change of colour accompanying the appearance and disappearance of the inversion walls may be attributed to the temperature dependence of birefringence.     

Nucleation in binary polymer blends: effects of foreign mesoscopic spherical particles

We study nucleation in binary polymer blends in the presence of mesoscopic spherical particles using self-consistent field theory, considering both heterogeneous and homogeneous nucleation mechanisms. Heterogeneous nucleation is found to be highly sensitive to surface selectivity and particle size, with rather subtle dependence on the particle size. Particles that preferentially adsorb the nucleating species generally favor heterogeneous nucleation. For sufficiently strong adsorption, barrierless nucleation is possible. By comparing the free energy barrier for homogeneous and heterogeneous nucleation, we construct a kinetic phase diagram.     

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.     

Phase behavior of polystyrene acrylonitril copolymer and polymethylmethacrylate blends under shear

Polymer blends undergo external stresses such as pressure and shear in course of processing cycles. The knowledge of their phase behavior at each step of these cycles is crucial for understanding their physical properties and eventually improves their performance in practical applications. The effects of shear on the phase diagram of binary polymer blends are considered. A theoretical formulism is used upon which the free energy is the sum of two terms. The first term is modeled with the Flory–Huggins free energy of mixing and describes the thermodynamic behavior of the system in the quiescent state. The second term represents the excess free energy stored during flow. In the presence of shear flow, the excess free energy is expressed in terms of the viscosity and the shear modulus. Both quantities depend on composition and shear rate. The curvature of the variation of viscosity versus composition has a tremendous impact upon the nature of phase separation. Phase diagrams are described by the spinodal curves and show for the case considered here miscibility enhancement with increasing shear rate. A good correlation is found with experimental data of the literature on blends of polystyrene acrylonitril copolymer and polymethylmethacrylate. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Crystalline-amorphous interaction in relation to the phase diagrams of binary polymer blends containing a crystalline constituent

The present article describes an equilibrium theory for determining binary phase diagrams of various crystalline-amorphous polymer blends by taking into account the contributions from both liquid-liquid phase separation between the constituents and solid-liquid phase transition of the crystalline component. An analytical expression for determining a crystal-amorphous interaction parameter is deduced based on the solid-liquid transition, involving the solidus and liquidus lines in conjunction with the coexistence curve of an upper critical solution temperature type. Of particular importance is that the crystalline-amorphous interaction parameter can be determined directly from the melting point depression data. The present analysis is therefore different from the conventional Flory-Huggins interaction parameter, which is associated with the liquid-liquid phase separation. The validity of the present theory is tested with the experimental phase diagrams of blends of poly(ethylene oxide)/diacrylate and poly(vinyl alcohol)/cellulose.     

Induced smectic phases in phase diagrams of binary nematic liquid crystal mixtures

To elucidate induced smectic A and smectic B phases in binary nematic liquid crystal mixtures, a generalized thermodynamic model has been developed in the framework of a combined Flory-Huggins free energy for isotropic mixing, Maier-Saupe free energy for orientational ordering, McMillan free energy for smectic ordering, Chandrasekhar-Clark free energy for hexagonal ordering, and phase field free energy for crystal solidification. Although nematic constituents have no smectic phase, the complexation between these constituent liquid crystal molecules in their mixture resulted in a more stable ordered phase such as smectic A or B phases. Various phase transitions of crystal-smectic, smectic-nematic, and nematic-isotropic phases have been determined by minimizing the above combined free energies with respect to each order parameter of these mesophases. By changing the strengths of anisotropic interaction and hexagonal interaction parameters, the present model captures the induced smectic A or smectic B phases of the binary nematic mixtures. Of particular importance is the fact that the calculated phase diagrams show remarkable agreement with the experimental phase diagrams of binary nematic liquid crystal mixtures involving induced smectic A or induced smectic B phase.     

含无规共聚物三元共混体系SMMA-PMMA-SAN相行为

含无规共聚物共混体系的相容性研究正在成为近年来的研究热点 ,因为相容的驱动力来自共聚物分子内不同单体链段间的排斥性相互作用 [1～ 3] .目前研究这类体系还主要采用过份简化的 F- H平均场理论 ,用旨在克服平均场理论缺陷的 Flory状态方程 ( EOS)理论仅局限于研究二元共聚物共混体系[4～ 8] .与三元共混体系相比 ,用 EOS理论预测含两个无规共聚物三元体系相行为尚需确定共聚物 -共聚物间的二元参数 sj/si,Xij和 Qij.若用 Ax B1- x和 Cy D1- y分别代表共聚物 1和 2 ,则 A,B,C,D代表相应共聚物中的单体单元 ,x,y分别是 1和 2的共…     

Free energy of mixing of cross-linked polymer blends

Free energy of mixing of cross-linked polymer blends is derived, as a modification to the Flory-Huggins-de Gennes free energy functional for linear polymer blends. The latter arrives from the assumption of mean-field, short-range thermal interactions among ideal Gaussian chains. However, upon cross-linking a linear chain, the chain no longer remains Gaussian; new chain architectures belying the threadlike image of linear chains emerge. Fractal dimensions of these nonlinear chain clusters convene and command new entropic interactions. Topological constraints by cross-links introduce long-range nonequilibrium elastic forces. Relatively shorter range steric repulsions between fractal network surfaces may arrive if cross-linking is carried out inside the blend's thermodynamically unstable region. Modified free energy has been used to highlight experiments on phase instability of cross-linked polymer blends.     

Diagramme d’equilibre liquide-solide de systemes binaires pyridine+n-alcanes

Solid-liquid phase diagrams have been determined for binary systems of pyridine withn-alkanes. These diagrams show the existence of large regions of partial miscibility. A general quasi chemical theory in terms of group surface interactions [1] has been applied to compute these solid-liquid phase diagrams.     

The case of missing incommensurate smectic A phases

Two binary mixtures of polar liquid crystal materials were previously reported to exhibit three incommensurate smectic A phases predicted for such materials on the basis of phenomenological theory. Results of our recent high-resolution X-ray scattering experiments show that no incommensurate phases exist in the two systems. Wide coexistence regions are found at first order transitions between various frustrated smectic phases of these mixtures. These regions were previously identified as the incommensurate smectic A phases. The phase diagrams of the two systems determined with high-resolution X-ray technique are shown to be in excellent agreement with Baroisa-Prost-Lubensky theory.     

Applications of polymer rism theory to blends

Polymer RISM (reference interaction site model) theory is a theory of polymer systems in the liquid phase in which account for chemical realism can be made. Results are reported here of phase diagrams (spinodals) for blend systems calculated by means of this theory, using the mean spherical approximation as a closure. The systems investigated are an isotopic blend, a set of homopolymer/copolymer blends, and a model blend containing specific interactions.     

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.     

Miscibility and morphology of poly(ethylhexylacrylate)/liquid crystal blends prepared under different conditions

A comparative study of the phase diagrams and morphology of blends of poly(2‐ethylhexylacrylate) and low molecular weight liquid crystals (LCs) prepared under different conditions is presented. Two LCs are used; one is the 4‐cyano‐4′‐n‐pentyl‐biphenyl and the other is the eutectic mixture of cyanoparaphenylenes known as E7. Two series of blends are prepared under different conditions. The first series is obtained by the polymerization induced phase separation (PIPS) process under UV‐curing starting from a monomeric mixture, while the second series is prepared by a combination of the solvent induced phase separation and the thermally induced phase separation process starting from a mixture containing a commercial polymer with known molecular weight. Using gel permeation chromatography, it is found that the polymer molecular weight of the UV‐cured systems decreases with the concentration of LC in the precursor mixture. The experimentally obtained phase diagrams of these two series of systems show a miscibility shift at the composition where the molar mass of the polymer in the PIPS/UV blend exceeds that of the commercial polymer. Data are rationalized in terms of the Flory‐Huggins theory of isotropic mixing and the Maier‐Saupe theory of nematic order. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 18–27, 2007     

聚合物体系散射函数的热力学基础

利用链段浓度和链头浓度的概念，根据热力学涨落理论，给出了聚合物二元共混体系ｄｅＧｅｎｎｅｓ散射函数的一个普遍的热力学证明，指出了这个函数和Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ共混自由能公式一样，也依赖于忽略构象涨落的假设．