Solvent quality as reflected in concentration‐ and temperature‐dependent Flory–Huggins interaction parameters

Flory–Huggins interaction parameters (χ) between poly(dimethylsiloxane) (weight‐average molecular weight = 152 kg/mol) and various solvents (methyl ethyl ketone, toluene and n‐octane) were determined as a function of composition and temperature with vapor‐pressure measurements. These data, complemented by independent information for dilute and very concentrated solutions, serve as the basis for a discussion of solvent quality via different theoretical relations. Regardless of polymer concentration, the χ values fall from methyl ethyl ketone via toluene to n‐octane, the ketone being the worst solvent and the hydrocarbon being the best solvent. The variation of χ with composition and temperature is complex. Within the range of moderate polymer concentrations, the influences of composition decrease with increasing solvent quality. Additional effects become noticeable at the ends of the composition scale. The enthalpy parts (χ_H) and entropy parts (χ_S) of the Flory–Huggins interaction parameter, obtained from χ(T), vary considerably with composition and change their sign in some cases; these constituents of the Flory–Huggins interaction parameter do not permit a direct assessment of solvent quality. A clear‐cut picture is, however, regained with a comparison of the interdependence of χ_S and χ_H. The elimination of explicit concentration influences re‐establishes the order in the solvent quality setup via χ. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 651–662, 2001     

The miscibility of poly(vinyl alcohol)/poly(N-vinylpyrrolidone) blends investigated in dilute solutions and solids

Poly(vinyl alcohol) (PVA) (polymer A) and poly(N-vinylpyrrolidone) (PVP) (polymer B) are known to form a thermodynamically miscible pair. In the present study the conclusion on miscibility of PVA/PVP solid blends, confirmed qualitatively (DMTA, FTIR) and quantitatively (DSC, χ_AB = − 0.69 at 503 K) is compared with the miscibility investigations of PVA/PVP solution blends by the technique of dilute solution viscometry. The miscibility of the ternary (polymer A/ polymer B/ solvent) system is estimated on the basis of experimental and ideal values of the viscosity parameters k, b and [η]. It is found that the conclusions on miscibility or nonmiscibility drawn from viscosity measurements in dilute solution blends depend: (i) on the applied extrapolation method used for the determination of the viscosity interaction parameters, (ii) on the assumed definition of the ideal values and (iii) on the thermodynamic quality of the solvent, which in the case of PVA depends on its degree of hydrolysis. Hence, viscometric investigations of dilute PVA/PVP solution blends have revealed that viscometry, widely used in the literature for estimation of polymer-polymer miscibility can not be recommended as a sole method to presume the miscibility of a polymer pair.     

Prediction of miscibility regions in ternary blends of poly(styrene-stat-acrylonitrile), poly(acrylonitrile-stat-methyl methacrylate), and poly(styrene-stat-methyl methacrylate)

The miscibilities of ternary copolymer blends prepared from poly(styrene-stat-acrylonitrile), poly(styrene-stat-methyl methacrylate), and poly(methyl methacrylate-stat-acrylonitrile) were predicted by calculating the interaction parameter, χ_blend, for various blend combinations, from the corresponding binary segmental interaction parameters estimated from previous work. Binodal and spinodal curves were calculated using the Flory-Huggins theory and it was observed that the most accurate estimate of the boundary between miscible and immiscible blends was given by the spinodal. It has also been demonstrated that in some of the ternary blends with fixed copolymer compositions the miscibility of the blend can be altered by changing the ratio of the three components in the mixture. Conditions for miscibility in this ternary system, and possibly a general feature of all such systems, are (a) that at least two of the binary interaction parameters χ_ij are less than the critical value χ_crit, while the third should not be too much larger, that is, one of the copolymers may act as a compatibilizer for the other two copolymers, (b) that the difference Δχ = /χ₁₂ ? χ₁₃/ is small. © 1992 John Wiley & Sons, Inc.     

Compatibility of poly(vinyl chloride) with polyalkyleneoxides. II. Poly(propylene oxide) and poly(tetramethylene oxide)

This study [Part II of a series dealing with the compatibility of polyalkyleneoxides with poly(vinyl chloride)] examines blends of PVC with poly(propylene oxide) (PPrO) and poly(tetra-methylene oxide) (PTMO), covering the entire composition range. Morphological, dynamic mechanical and thermal properties investigated indicate that PVC/PPrO blends are incompatible, whereas the PVC/PTMO system shows miscibility in the melt. For this polyblend and at high polyether compositions where the Hoffman–Weeks analysis can be applied, T_m equilibrium data allow the determination of the thermodynamic interaction parameter, χ₁₂ = ?0.15. Experimental compatibility data of all polyether-PVC pairs investigated in Parts I and II are also used to test various blend miscibility prediction schemes, using solubility parameter theory and recent theory on copolymer-copolymer miscibility.     

The assessment of miscibility and morphology of poly(ε-caprolactone) and poly(para-chlorostyrene) blends

The miscibility and morphology of poly(ε-caprolactone) (PCl) and poly(para-chlorostyrene) (PpClS) blend were investigated by using thermal analysis, morphological analysis, viscometry, and the study of melting point depression. A single glass transition temperature was observed by differential scanning calorimetry (DSC) for PCl/PpClS blends in the whole compositional range (0/100, 25/75, 50/50, 62.5/37.5, 75/25, 90/10). Morphology of the polymers and their blends was studied by scanning electron microscopy (SEM). The Fourier transform infrared spectra of the samples were obtained by spectrometer. Up to 12 cm⁻¹ shifts in carbonyl stretching band of PCl was detected in the spectra of PpClS rich blends. The viscosity of PCl, PpClS and their blends has also been studied to investigate the miscibility according the miscibility criteria Δb, and Δ[η]. Using this data, the interaction parameters α and μ, based on the Chee and Sun et al. approaches were determined. These criteria indicated that the blend is miscible in all proportions up to 90% of PCl content in the blends. The melting point depression of PCl in the blends was examined to obtain the interaction parameter, χ₁₂ for this system. The parameter, χ₁₂ was found to be composition dependent. Negative values of the obtained interaction parameter also support the miscibility of this system up to the 90% PCl in the blend.     

Blends of polycarbonate and poly(ϵ‐caprolactone) and the determination of the polymer–polymer interaction parameter of the two polymers

The thermal properties of blends of polycarbonate (PC) and poly(ε‐caprolactone) (PCL) were investigated by differential scanning calorimetry (DSC). From the thermal analysis of PC‐PCL blends, a single glass‐transition temperature (T_g) was observed for all the blend compositions. These results indicate that there is miscibility between the two components. From the modified Lu and Weiss equation, the polymer–polymer interaction parameter (χ₁₂) of the PC‐PCL blends was calculated and found to range from −0.012 to −0.040 with the compositions. The χ₁₂ values calculated from the T_g method decreased with the increase of PC weight fraction. By taking PC‐PCL blend as a model system, the values of χ₁₂ were compared with two different methods, the T_g method and melting point depression method. The two methods are in reasonably good agreement for the χ₁₂ values of the PC‐PCL blends. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2072–2076, 2000     

Thermodynamic Analysis of Phase Separation of a Thermoplastic in the Precursors of Different Epoxy-Amine Systems

The miscibility of a thermoplastic, polystyrene (PS), with the precursors of several epoxy-amine systems has been studied thermodynamically and experimentally. The epoxy-amine systems were different only in the origin of amino groups, which were provided by a monoamine (MA) and a diamine (DA) in different proportions. Cloud-point curves (CPC) at conversion zero were reported for five modified systems with different MA-DA proportion. All CPCs showed an UCST behaviour. CPC shifted to lower temperatures when the ratio of MA/DA in the system increased, meaning that the MA produces an increase in the miscibility of the system. A model based on the Flory-Huggins theory was used for the thermodynamic analysis, in which the dependence of interaction parameter on temperature and composition, χ(T,ϕ), and the polydispersity of components were considered. A general equation for χ(T,ϕ) also depending on the MA-DA proportion was reached and used to obtain the phase diagram of the different systems. A high level of agreement between theoretical and experimental CPCs was obtained.     

Amphiphilic polymer brush in a mixture of incompatible liquids

An analogue of the Alexander‐DeGennes box model is used for theoretical investigation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory‐Huggins parameter χ_AB = 3.5). Thermodynamics of a polymer in the solvents A and B are described by parameters χ_B < χ_A ≤ 1/2. The equilibrium behavior of a brush is investigated in dependence on solvent composition, grafting density, polymer‐solvents and solvent‐solvent interactions. The possibility of a phase transition related with a strong preferential solvation of a brush by a minor solvent component with higher affinity to polymer is shown and examined. Microphase segregation inside a brush is also demonstrated despite overestimating of the brush homogeneity given by the box model. A further simplification of the model permits to obtain scaling formulas and to investigate main regularities in the brush behavior. This offers a clear physical picture of the phase segregation inside a brush in correlation with the phase state of a bulk solvent.     

Novel phosphate glass/polyamide 6 hybrids: Miscibility,crystallization kinetics,and mechanical properties

The miscibility, crystallization kinetics, and mechanical properties of a novel low T_g phosphate glass (Pglass)/polyamide 6 hybrid material were investigated. Here, we report the first evidence for miscibility of inorganic phosphate glass and organic polymer prepared by blending both components in the liquid phase using conventional polymer processing methods. From classical melting point depression measurements, we obtained a chi interaction parameter (χ) of −0.067 for the Pglass/polyamide 6 hybrid, indicating that the inorganic glass and polyamide 6 are miscible. The crystallization kinetic parameters for the hybrids were determined using the Avrami approach and found to depend on the volume fraction of Pglass present in the system. In addition, we studied both the dynamic and static mechanical behavior of the hybrids. The results showed a single T_g that decreased by up to 10 °C with increasing phosphate glass volume percent for the hybrids, giving further evidence for the hybrid component miscibility and plasticizing action of the phosphate glass in the pure polyamide 6, respectively. The tensile (static) mechanical properties of the hybrids were found to be remarkably similar to those obtained from typical polymers plasticized with relatively low molecular weight compounds. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 441–450, 2006     

Evaluation of the interaction parameter for poly(ε‐caprolactone)/poly(styrene‐co‐acrylonitrile) blends

In this article, the miscibility of poly(ε‐caprolactone) (PCL) with poly(styrene‐co‐acrylonitrile) (SAN) containing 25 wt % of acrylonitrile is studied from both a qualitative and a quantitative point of view. The evidences coming from thermal analysis (differential scanning calorimetry) demonstrate that PCL and SAN are miscible in the whole range of composition. The Flory interaction parameter χ_1,2 was calculated by the Patterson approximation and the melting point depression of the crystalline phase in the blends; in both cases, negative values of χ_1,2 were found, confirming that the system is miscible. The interaction parameter evaluated within the framework of the mean field theory demonstrates that the miscibility of PCL/SAN blends is due to the repulsive interaction between the styrene and acrylonitrile segments in SAN. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Systematic comparison study on determination of small organics/polymer miscibility

A mixture system of small molecular organics/polymer is widely applied in various industries. A relatively accurate determination of their miscibility is crucial for well understanding and predicting their phase behaviors and material properties. However, miscibility results from different literature could vary much. This study systematically compares various approaches to determine the mixture miscibility, e.g., the interaction parameter (χ), solubility, observations of the phase separation, and a deviation of glass transition temperature (T_g) or melting temperature (T_m), and demonstrates the advantages, disadvantages, general suitability of each method. Four botanical organics, i.e., β-carotene, betulinic acid, astaxanthin, and curcumin, are used as model small molecular compounds. A widely-used, noncrystallizable, hydrophobic polymer of poly (lactic-co-glycolic acid) (PLGA, LA:GA = 55:45) is employed as a model polymer. This systematic comparison is expected to provide a guide to selecting a suitable determination of small organics/polymer miscibility, beneficial for better predicting the phase stability of an amorphous mixture in applications.     

PA66/PA12/clay based nanocomposites: structure and thermal properties

In a previous paper the structure and the physical properties of melt mixed polyamide 66 (PA66)/polyamide 12 (PA12) blends characterized by different compositions have been investigated by means of morphological and physical analyses. A low amount of organically‐modified layered silicate (OMLS, 4 wt%) was introduced in order to evaluate its effect on blends structure and components miscibility. This paper completes the characterization of these materials investigating their thermal properties by means of standard and modulated differential scanning calorimetry (DSC, MDSC), dynamic‐mechanical analysis (DMA), and thermogravimetric analysis (TGA). The partial miscibility of PA66 and PA12, with phase separation depending on blend composition, has been confirmed by analyzing the glass transition temperature (T_g) dependence on composition as well as the existence of strong segmental interactions between polymer components. A compatibilizing action of OMLS has been observed because of a lowering of interfacial tension avoiding coalescence phenomena between particles during melt mixing process. Copyright © 2010 John Wiley & Sons, Ltd.     

Miscible blends prepared from two crystalline polymers

Differential scanning calorimetry was used to determine the miscibility behavior of several polyester/Saran blends, the two polymers forming these blends being semicrystalline. It was found that Saran is miscible with polycaprolactone (PCL), polyvalerolactone, poly(butylene adipate), and poly(hexamethylene sebacate) since a single glass transition temperature T_g was observed at each composition. However, immiscibility was found between Saran and poly(ethylene adipate), poly-(ethylene succinate), poly(β-propiolactone), and poly(α-methyl-α-n-propyl-β-propiolactone) since two T_g's were recorded at several compositions. Blends were then obtained containing, over a wide range of composition, a miscible amorphous phase and two different types of crystals. From melting-point depression data on PCL and Saran crystals, thermodynamic interaction parameters χ were calculated and found to be different for PCL-rich blends and for Saran-rich blends. This result suggests a variation of χ with composition. Saran is a polymer which does not contain α-hydrogens and its miscibility with polyesters may result from a β-hydrogen bonding interaction or a C?O/C? Cl dipole-dipole interaction.     

Theoretical Phase Behavior of Crosslinked Polymers and Liquid Crystals

Equilibrium phase properties of mixtures of crosslinked polymers and nematic liquid crystals (LCs) are investigated. Effects of the volume fraction of polymer at crosslinking φ₀ , the number of monomers between consecutive crosslinks N_c and the Flory‐Huggins interaction parameter χ on these properties are discussed. Two models for the elastic free energy are used to describe the effects of φ₀ Three cases are considered depending upon polymer volume fraction at crosslinking. If crosslinking takes place in the bulk, the elastic free energy is the same and the two models are identical. Otherwise, either φ₀ is constant or equal to φ₂ , the two models may lead to completely different results depending upon crosslinking density. Strong correlations are found between the effects of φ₀ and N_c on the phase behavior of crosslinked polymers and nematic liquid crystal mixtures. These diagrams are also strongly dependent upon the Flory‐Huggins interaction parameter for isotropic mixing χ. This dependence is illustrated through three models for the variation of χ with temperature and composition.     

Thermal transitions and polymer/polymer miscibility

Poly(vinyl chloride) was blended with ethylene-vinyl acetate copolymer containing 70 wt% of vinyl acetate. The system shows a single glass transition temperature for all compositions, indicating their miscibility. TheT _g vs. composition curves display an inflection, which changes with the chemical environment of the initial solution. The best fit to the shape of the curve was well reproduced by the Kovacs-Braun equation. The T _g values reveal local heterogeneity, which means no total miscibility at a molecular level. Negative values of the Flory-Huggins interaction parameter were obtained from the calorimetric data.Support for this research by CNP_q, FINEP and CAPES is appreciated.     

Deformation of a Polymer Brush Immersed in a Binary Solvent

An analog of the Alexander‐De Gennes box model is used for the theoretical investigation of an external deformation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory‐Huggins parameter χ_AB = 3.5). The thermodynamics of a polymer in the solvents A and B is described by parameters χ_A and χ_B, χ_A > χ_B. The brush behavior under deformation is investigated with regard to solvent composition and polymer‐solvent interactions. It is shown that in a pre‐binodal range of the solvent composition Φ_B < Φ_B⁰ in the bulk (here Φ_B⁰ is a binodal value) there is such a value of Φ_B = Φ _B* that deformation does not affect solvent composition inside the brush. This invariant quantity Φ _B*, being a function of only thermodynamic parameters, is independent of the brush characteristics, such as grafting density. It is shown that two types of the first‐order phase transitions can arise in the system considered: a compositional phase transition induced by a change in the solvent composition in the bulk, and a deformational phase transition caused by an external deformation of the brush. The value of Φ _B* defines a borderline concentration of the admixture in the bulk; the brush behavior in the ranges 00 ⪇ Φ_B ⪇ Φ _B* and Φ _B* ⪇ Φ_B < Φ_B⁰ are different. If no compositional phase transition occurs in the system, the deformational phase transition should arise under stretching at Φ _B* ⪇ Φ_B. If the compositional phase transition exists, it is realized in the range Φ_B < Φ _B* and causes the deformational phase transition in this concentration range, not only under stretching, but also under compression. Microphase segregation inside the brush is demonstrated for both phase transitions despite overestimation of the brush homogeneity in the box model.     

Phase diagram and entropic interaction parameter of athermal all‐polymer nanocomposites

An entropic model is introduced for the prediction of the χ interaction parameter and phase diagram of athermal all‐polymer nanocomposites (chemically identical polymer‐nanoparticle/linear‐polymer blends). According to this model, dilution of contact (hard sphere‐like) nanoparticle/nanoparticle interactions upon mixing plays a key role in explaining the miscibility behavior of athermal all‐polymer nanocomposites in the presence of unfavorable chain expansion (or contraction) effects. The new model is valid both for the cases of chain stretching and chain contraction and provides an appropriate capture of entropy changes accompanying the mixing of chemically identical nanoparticles and polymers. A good agreement was found between predicted χ interaction parameter (χ_cal = ?2.3 × 10^?3) and reported small angle neutron scattering (SANS) experimental data ( ～ ?2 × 10^?3) for 211 kDa cross‐linked poly(styrene) (PS)‐nanoparticles dissolved in 473 kDa deuterated linear‐PS. In addition, the miscibility boundary calculated from the model for PS‐nanoparticle/linear‐PS nanocomposites (?₁ = 0.02) compared very favorably to that experimentally found. For this system, the spinodal line in the polymer radius of gyration (R_g) versus nanoparticle radius (a) phase diagram was found to follow the simple scaling law: , being the polymer radius of gyration at which the second derivative of the free energy of mixing vanishes. Finally, the model has been employed for the prediction of the entropic χ interaction parameter, the miscibility behavior, and the melting point depression of athermal poly(ethylene) (PE)‐nanoparticle/linear‐PE nanocomposites using recent chain dimension data from Monte Carlo (MC) simulations, where chain stretching or chain contraction effects were observed depending on nanoparticle size. Copyright © 2007 John Wiley & Sons, Ltd.     

Adsorption preferentielle dans le systeme: Polystyrene-acetone-cyclohexane

The co-solvent system polystyrene-cyclohexane-acetone has been studied by the light-scattering technique. The selective adsorption parameter exhibits a dependence on solvent composition with the inversion point at u₂ = 0.470. The co-solvent behaviour is discussed in relation to the binary liquid interaction parameters χ_ij the ternary interaction parameter being negligible for this system.     

Thermosetting polymer blends of unsaturated polyester resin and poly(ethylene oxide). I. Miscibility and thermal properties

The miscibility and thermal properties of polyethylene oxide(PEO)/oligoester resin (OER) blends and PEO/crosslinked polyester (PER) blends were studied by differential scanning calorimetry (DSC). The effect of quenching process on the crystallization behavior of PEO for these two systems were investigated and discussed in details. It has been found that a single, composition dependent glass transition temperature (T_g) was observed for all the blends, indicating that the two systems are miscible in the amorphous state at overall compositions. From the melting point depression of PEO, the interaction parameter χ₁₂ for PEO/OER blends and that for PEO/PER blends were found to be −1.29 and −2.01, respectively. The negative values of χ₁₂ confirmed that both PEO/OER blends and PEO/PER blends are miscible in the molten state. Quenching process has a greater hindrance on the crystallization of PEO/OER blends than on that of PEO/PER blends. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3161–3168, 1997     

Heterogeneous polycondensation for composition control of poly(p‐mercaptobenzoyl‐co‐p‐benzamide) by shearing

Composition control of aromatic poly(thioester‐amide) was examined by the reaction‐induced phase separation during polymerization of S‐acetyl‐4‐mercaptobenzoic acid (AMBA) and p‐acetylaminobenzoic acid (AABA) in aromatic solvent. The poly(thioester‐amide)s were obtained as precipitates and their yields became lower at the middle range of the content of AMBA in feed (χ_f). The contents of p‐mercaptobenzoyl (MB) moiety (χ_p) in the precipitates prepared without shearing were in good agreement with the χ_f values. In contrast to this, the χ_p values of the precipitates prepared at χ_f of 50–70 mol % under shearing were much lower than the χ_f values. The reaction rate of AMBA increased with shearing, whereas that of AABA was unchanged by shearing. This shearing effect on the reaction rates accelerated to form the homo‐oligomers. The solubility of MB oligomers enhanced by shearing, whereas that of p‐benzamide oligomers did not enhance owing to the strong interaction through hydrogen bonding. The MB oligomers were inhibited to be precipitated, resulting in the lower χ_p values than the χ_f values. The composition could be controlled by the application of the shearing to the heterogeneous polymerization. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 4301–4308