Flory状态方程理论与聚合物混合物的热力学

由Flory状态方程理论的化学位公式推导了二元混合物的亚稳单相极限线,同时导出了状态方程参数的温度、压力依赖性,计算表明Flory理论是可以像McMaster修正理论一样描述聚合物的相溶性行为的。 指出前人的工作由于假定相互作用能和熵参数均为0,分子量和状态方程参数对相界的影响被誇大了,相分离也只发生在很窄的浓度范围内。如果考虑了实际体系中相互作用能和熵参数均不为0,上述因素对相界的影响以及相界的形状将趋于合理。     

Miscibility and volume changes of mixing in the polystyrene/poly(2-chlorostyrene) blend system

The specific volume-temperature relationships of polystyrene, poly(2-chlorostyrene), and their polymer blends as well as the volume change of mixing Δv_m of the blends were obtained in the liquid state by dilatometry. The equation of state parameter and the molecular parameter of each homopolymer and blends were determined according to the lattice fluid theory of Sanchez and Lacombe. The experimental Δv_m obtained agreed quite well with that predicted from theory, and the enthalpy of mixing ΔH_m was also predicted using the pair molecular parameter. These two values were negative, indicative of miscibility of polystyrene and poly(2-chlorostyrene) in the liquid state. The absolute values of Δv_m and ΔH_m were about twice those for polystyrene and poly(phenylene oxide) blend, suggesting a specific interaction between the two polymers.     

Phase diagrams of poly(siloxane)/liquid crystal blends

Phase diagrams of blends of poly(methylphenylsiloxane) in short PMPS and two low molecular weight liquid crystals (4‐cyano‐4′‐n‐pentyl‐biphenyl and an eutectic mixture of paraphenylenes) are reported. Two polymers with very different weight‐average molar masses are considered in an evaluation of the loss of miscibility resulting from a known increase in the weight‐average molar mass. The experimental diagrams have been constructed via polarized optical microscopy and are rationalized in terms of the Flory–Huggins theory of isotropic mixtures and the Maier–Saupe theory of nematic order. The results show a good agreement between the theory and experiments and reveal a remarkable enhancement of miscibility with respect to similar systems involving poly(dimethylsiloxane). Variations of the interaction parameter with the temperature are compared for different systems of polysiloxanes. The effects of the nature of the liquid crystal and the polymer molar mass on the χ parameter are evaluated. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 39–43, 2003     

An improvement in the flory corresponding-states theory of polymer solutions

The original Flory corresponding-states theory of polymer solutions requires an entropic correction parameter Q₁₂, the sign and value of which seem to be arbitrary, and the physical meaning of which is obscure. Moreover, calculated excess volumes of mixing for many polymer solutions are often in significant disagreement with experimental data. In order to eliminate these problems, we have modified the kinetic part of the partition function, introduced an effective mass for the mixture segment, and adopted the nonlinearity of the number of degrees of freedom with respect to the composition for the mixture segment. In addition, the effect of nonrandom configurations of the segments in the mixture has been included. In the improved equations, derived in this work, the Flory interaction parameter χ can be considered to comprise three parts: (a) a kinetic part due to the contribution of the average number of degrees of freedom and the effective mass of the mixture; (b) a free volume part; and (c) an interaction part including the contributions due to the contact interaction and the nonrandom configuration of the segments in the mixture, caused by the interaction. The improved theory is in good agreement with literature data on polystyrene solutions and poly (dimethyl siloxane) solutions.     

Relaxation and Miscibility of the Blends of a Poly (Ether Imide) (Ultem™) and a Phenol-A-Based Copolyester (Ardel™) by Inverse Gas Chromatography

Inverse gas chromatography (IGC) was used to analyze the secondary transition temperatures and the miscibility of binary mixtures of poly (ether imide) (Ultem™) and a copolyester of bisphenol-A with terephthalic and isophthalic acids (50/50) (Ardel™) in three compositions (25/50, 50/50 and 75/25). Retention diagrams of the mixtures of Ultem™ and Ardel™ for n-nonane, n-decane, n-butyl acetate and isoamyl acetate were obtained at temperatures between 60 and 285 °C. Second-order transition temperatures of the mixtures were determined according to the slope change in retention diagrams of the solvents. The glass transition temperatures of the mixtures suggested the miscibility of the polymers. Polymer–polymer interaction parameters of binary mixtures of the polymers were determined at temperatures between 260 and 285 °C by Flory–Huggins theory. The polymer–polymer interaction parameters were dependent on the solvent used. The small values of polymer–polymer interaction parameters close to zero suggest some weak interactions between the polymers in the mixture. It was concluded that it was possible to obtain more meaningful information related to the interactions of polymers in a mixture from IGC measurements, if binary polymer–solvent interaction parameters of the used solvent probes were around 0.5.

     

Statistical thermodynamics in the framework of the lattice fluid model, 2. Binary mixture of polydisperse polymers of special distribution

In this paper, the Gibbs free energy, the equation of state and the chemical potentials of polydisperse multicomponent polymer mixtures are derived. For general binary mixtures of polydisperse polymers, we also give the Gibbs free energy, the equation of state and the chemical potentials and derive the stability criteria and spinodal. Furthermore, binary polydisperse polymer mixtures of special distribution, i.e., Flory distribution, uniform distribution and Schulz distribution, are discussed and the influence of polydispersity on the interaction energy parameter is considered. For these special-distribution systems, the spinodal curves are simulated and the influence of chain length and polydispersity on the spinodal curves is discussed. The results suggest that the spinodal temperature of the mixture with a given volume fraction of one component decreases with increasing polydispersity and the extent of the shift decreases with increasing degree of polymerization when η = M̄_w/M̄_n is given. In addition, the variations of the spinodal curves with polydispersity and chain length are shown and they are qualitatively compared with the experimental results.     

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     

Viscometric Studies in Dilute Solution Mixtures of Chitosan and Microcrystalline Chitosan with Poly(vinyl alcohol)

The viscosity behavior of aqueous mixtures formed by a polyelectrolyte (A) and a neutral polymer (B), such as chitosan/poly(vinyl alcohol) (Ch/PVA) and microcrystalline chitosan/poly(vinyl alcohol) (MCCh/PVA), have been investigated at 25 °C. The intrinsic viscosity and the viscosity interaction parameter of each polymer in 0.1 mol·dm^?3 CH₃COOH/0.2 mol·dm^?3 NaCl solution as well as the ternary systems (polymer A/polymer B/solvent) have been determined and have served for estimation of the miscibility of different polymer mixtures by means of the method of classical dilution. By comparing the experimental and ideal viscosity data it is clearly seen that the satisfaction of the miscibility criterion depends on the definition of the ideal parameter $ b_{\text{m}}^{\text{id}} $ b m id . If the $ b_{\text{m}}^{\text{id}} $ b m id parameter is defined according to the Krigbaum–Wall criterion and Garcia criterion, the investigated blends of Ch/PVA satisfy the miscibility criterion. In the case of MCCh/PVA blends, the polymeric components show poor miscibility. Additionally, the viscosity results show that the degree of miscibility depends on the molecular weight of chitosan and on the degree of PVA hydrolysis.     

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.     

Depolarized light scattering studies on single-phase mixtures of dissimilar polymers: Evidence for local ordering

Depolarized light scattering measurements on single-phase mixtures of dissimilar polymers, poly(methyl methacrylate) (PMMA)/poly (acrylonitrile-co-styrene) (SAN, AN content = 15 wt %) and PMMA/poly (vinylidene fluoride) (PVDF) were carried out. The effective mean-square optical anisotropy γ² of the mixtures was found to be much higher than that estimated by the simple additivity of γ² of component polymers. From the deviation, the order parameter (1 + J₁₂) was estimated to be in a range of 2–13, depending on the blend composition. This suggests local ordering in the single-phase mixtures, i.e., nematic alignment of the locally stretched dissimilar chains. In contrast, the deviation was slight in the polymer/solvent systems, SAN/MMA (monomer) and PVDF/butanone. The degree of ordering decreased with increasing temperature. T. The Specific interaction evidenced by FTIR spectroscopy exhibited a similar temperature dependence. Thus, local ordering seems to be induced by specific interactions and chain connectivity. The temperature dependence of J₁₂ was successfully described by the Landau-de Gennes theory; J ∞ (T + T₀)/ T, T₀ being the isotropic-nematic transition temperature, as in the case of liquid crystals.     

Studies on the miscibility and effect of the addition of urea to poly(acrylic acid) and poly(sodium styrene sulfonate) blends by dilute solution viscometry method

The miscibility of poly(acrylic acid) (PAA) and poly(sodium styrene sulfonate) (PSSNa), in H₂O was investigated by a dilute solution viscometry method (DSV). The miscibility of the polymer blend was investigated on the basis of the signs of the interaction parameters Δ[b]_m, Δ[η]_m, ΔB and μ. The results from the viscosity method were correlated with the miscibility data obtained for the same blend by Fourier transform infrared and differential scanning calorimetry. These investigation indicated that the examined blend was miscible for all composition ratios examined (w₂ = 0.10, 0.25, 0.50, 0.75, and 0.90).The addition of urea to the polymer mixture H₂O (1)/PAA (2)/PSSNa (3) decreased the miscibility.     

Melting behavior,miscibility, and hydrogen-bonded interactions of poly(ε-caprolactone)/poly(4-hydroxystyrene-co-methoxystyrene) blends

The miscibility of poly(4-hydroxystyrene-co-methoxystyrene) (HSMS) and poly(ε-caprolactone) (PCL) was investigated by differential scanning calorimetry and Fourier transform infrared spectroscopy (FTIR). HSMS/PCL blends were found to be miscible in the whole composition range by detecting only a glass transition temperature (T_g), for each composition, which could be closely described by the Fox rule. The crystallinity of PCL in the blends was dependent on the T_g of the amorphous phase. The greater the HSMS content in the blends, the lower the crystallinity. The polymer–polymer interaction parameter, χ₃₂, was calculated from melting point depression of PCL using the Nishi-Wang equation. The negative value of χ₃₂ obtained for HSMS/PCL blends has been compared with the value of χ₃₂ for poly(4-hydroxystyrene) (P4HS)/PCL blends. The specific nature, quantitative analysis, and average strength of the intermolecular interactions in HSMS/PCL and P4HS/PCL blends have been determined at room temperature and in the molten state by means of Fourier transform infrared spectroscopy (FTIR) measurements. The FTIR results have been in good correlation with the thermal behavior of the blends. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 95–104, 1998     

Phase Behavior of Polymer Blends

The present report deals with some results on phase behavior, miscibility and phase separation for several polymer blends casting from solutions. These blends are grouped as the amorphous polymer blends, blends containing a crystalline polymer or two crystalline polymers. The blends of PMMA/PVAc were miscible and underwent phase separation at elevated temperature, exhibited LCST behavior. The benzoylated PPO has both UCST and LCST nature. For the systems composed of crystalline polymer poly(ethylene oxide) and amorphous polyurethane, of two crystalline polymers poly(-caprolactone) and poly[3,3,-bis-(chloromethyl) oxetane], appear a single T_g, indicating these blends are miscible. The interaction parameter B's were determined to be –14 J cm^–3, –15 J cm^–3 respectively. Phase separation of phenolphthalein poly(ether ether sulfone)/PEO blends were discussed in terms of thermal properties, such as their melting and crystallization behavior.This revised version was published online in November 2005 with corrections to the Cover Date.     

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.     

Investigation of polymer–solvent interactions in poly(styrene sulfonate) thin films

The swelling behavior of acid form poly(styrene sulfonate) (PSS‐H) thin films were investigated using in situ spectroscopic ellipsometry (SE) to probe the polymer–solvent interactions of ion‐containing polymers under interfacial confinement. The interaction parameter (χ), related to the polymer and solvent solubility parameters in the Flory–Huggins theory, describes the polymer‐solvent compatibility. In situ SE was used to measure the degree of polymer swelling in various solvent vapor environments, to determine χ for the solvent‐PSS‐H system. The calculated solubility parameter of 40–44 MPa^1/2 for PSS‐H was determined through measured χ values in water, methanol, and formamide environments at a solvent vapor activity of 0.95. Flory–Huggins theory was applied to describe the thickness‐dependent swelling of PSS‐H and to quantify the water‐PSS‐H interactions. Confinement had a significant influence on polymer swelling at low water vapor activities expressed as an increased χ between the water and polymer with decreasing film thickness. As the volume fraction of water approached ～0.3, the measured χ value was ～0.65, indicating the water interacted with the polymer in a similar manner, regardless of thicknesses. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1365–1372     

Theoretical Calculation of Flory‐Huggins and Scattering Interaction Parameters by Means of the Lattice Fluid Theory for PVME/PSD Blends

By fitting the spinodals of poly(vinyl methyl ether)/deuterated polystyrene (PVME/PSD) systems, the adjustable parameters ε*₁₂ and δε* in the Sanchez‐Balasz lattice fluid (SBLF) theory could be determined for different molecular weights. According to these parameters, Flory‐Huggins and scattering interaction parameters were calculated for PVME/PSD with different molecular weights by means of the SBLF theory. From our calculation, Flory‐Huggins and scattering interaction parameters are both linearly dependent on the reciprocal of the temperature, and almost linearly on the concentration of PSD. Compared with the scattering interaction parameters, the Flory‐Huggins interaction parameters decreased more slowly with an increase in the concentration for all three series of blends.     

Miscibility in crystalline/amorphous blends of poly(3-hydroxybutyrate)/DGEBA

A differential scanning calorimetry (DSC) and small-angle X-ray scattering (SAXS) study of miscibility in blends of the semicrystalline polyester poly(3-hydroxybutyrate) (PHB) and amorphous monomer epoxy DGEBA (diglycidyl ether of bisphenol A) was performed. Evidence of the miscibility of PHB/DGEBA in the molten state was found from a DSC study of the dependence of glass transition temperature (T_g) as a function of the blend composition and isothermal crystallization, analyzing the melting point (T_m) as a function of blend composition. A negative value of Flory–Huggins interaction parameter χ_PD was obtained. Furthermore, the lamellar crystallinity in the blend was studied by SAXS as a function of the PHB content. Evidence of the segregation of the amorphous material out of the lamellar structure was obtained. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Characterization of the interactions in polymer/silica systems by inverse gas chromatography

Authors propose to express the magnitude of modified filler/polymer interactions by Flory ‐ Huggins χ₂₃ parameter. We investigated polyether‐urethane/modified silica systems containing different amounts of filler (5, 10,20%wt). Moreover, information on the physicochemical properties of oligomer and modified silicas were presented with the use of the following parameters: • solubility parameter δ₂, describing properties of the polymer layer; • Flory‐Huggins parameter χ₁₂^∞ which describes polymer‐solute or mixture polymer/silica‐solute interactions. These parameters δ₂ and χ₁₂^∞ are obtained from Inverse Gas Chromatography experiments. The influence of the IGC experiment temperature, the content of modified silica, the nature of test solute on the evaluated parameters are presented and discussed.     

Water sorption in poly(ammonium sulfopropylbetaines). II. Sorption isotherms

Water sorption by four amorphous acrylic and methacrylic poly(zwitterions) bearing ammonium sulfopropylbetaine side groups () was studied at a constant temperature of 23°C and over a broad range of water activity (0.14-0.90). Whatever the physical state of the hydrated polymer, glassy or viscoelastic, water diffusion is Fickian (average diffusion coefficient D?_s in the range 2-16 × 10^?8 cm² s^?1), and the sorption isotherms may be quantitatively analyzed according to the Guggenheim-Anderson-De Boer amended BET equation for multilayer sorption processes. The number of sitebound water molecules per monomeric unit is in the range 1.5–2.0, and apparently there is no great energy difference between direct site binding and indirect binding in the successive solvation layers. The polymer-water interaction parameter (?0.6 < χ Flory < 0.6) is an increasing function of the water content of the hydrated poly(zwitterions) over the whole composition range (water volume fraction < 0.5), without any clear transition from the glassy to the viscoelastic state. Clustering of water molecules (Zimm-Lundberg theory) is never observed, even at high water content. Because of the charged structure of their dipolar units, the poly(zwitterions) show a water sorption process similar to that of the corresponding poly(electrolytes) of the tetra-alkylammonium sulfonate type. © 1992 John Wiley & Sons, Inc.