Prediction of vapor–liquid and liquid–liquid equilibria for polymer systems: Comparison of activity coefficient models

A large number of equations of state and activity coefficient models capable of describing phase equilibria in polymer solutions are available today, but only a few of these models have been applied to different systems. It is therefore useful to investigate the performance of existing thermodynamic models for complex polymer solutions which have not yet been widely studied. The present work studies the application of several activity coefficient models [P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, New York, NY, 1953; T. Oishi, J.M. Prausnitz, Estimation of solvent activities in polymer solutions using a group-contribution method, Ind. Eng. Chem. Process Design Dev. 17 (1978) 333; H.S. Elbro, A. Fredenslund, P. Rasmussen, A new simple equation for the prediction of solvent activities in polymer solutions, Macromolecules 23 (1990) 4707; G.M. Kontogeorgis, A. Fredenslund, D. Tassios, Simple activity coefficient model for the prediction of solvent activities in polymer solutions, Ind. Eng. Chem. Res. 32 (1993) 362; C. Chen, A segment-based local composition model for the Gibbs energy of polymer solutions, Fluid Phase Equilib. 83 (1993) 301; A. Vetere, Rules for predicting vapor–liquid equilibria of amorphous polymer solutions using a modified Flory–Huggins equation, Fluid Phase Equilib. 97 (1994) 43; C. Qian, S.J. Mumby, B.E. Eichinger, Phase diagrams of binary polymer solutions and blends, Macromolecules 24 (1991) 1655; Y.C. Bae, J.J. Shim, D.S. Soane, J.M. Prausnitz, Representation of vapor–liquid and liquid–liquid equilibria for binary systems containing polymers: applicability of an extended Flory–Huggins equation, J. Appl. Polym. Sci. 47 (1993) 1193; G. Bogdanic, J. Vidal, A segmental interaction model for liquid–liquid equilibrium calculations for polymer solutions, Fluid Phase Equilibria 173 (2000) 241] and activity coefficient from equations of state [F. Chen, A. Fredenslund, P. Rasmussen, Group-contribution Flory equation of state for vapor–liquid equilibria en mixtures with polymers, Ind. Eng. Chem. Res. 29 (1990) 875; M.S. High, R.P. Danner, Application of the group contribution lattice—fluids EOS to polymer solutions, AIChE J. 36 (1990) 1625]. The evaluation of these models was carried out both at infinite dilution and at finite concentrations and the results compared to experimental data. Furthermore, liquid–liquid equilibrium predictions for binary polymer solutions using six activity coefficient models are compared in this work. The parameters were estimated for all the models to achieve the best possible representation of the reported experimental equilibrium behavior.     

Liquid-liquid phase equilibria in polymer solutions and polymer mixtures

The pressure dependence of liquid-liquid equilibria in weakly interacting binary macromolecular systems (homopolymer solutions and blends) will be discussed. The common origin of the separate high-temperature/low-temperature and high-pressure/low-pressure branches of demixing curves will be demonstrated by extending the study into the region of metastable liquid states including the undercooled, overheated and stretched states (i.e. states at negative pressures). The seemingly different response of the UCST-branch of solutions and blends when pressurized (pressure induced mixing for most polymer solutions, pressure induced demixing for most blends) will be explained in terms of the location of a hypercritical point found either at positive (most solutions) or negative pressure (most blends). Further, it is shown that the pressure dependence of demixing of homopolymer solutions and blends may be described using a ‘master-curve’ which, however, is sometimes partly masked by degradation or by vapour-liquid and/or solid-liquid phase transitions. Experimental results demonstrating the extension of liquid-liquid phase boundary curves into the metastable regions will be presented, and the existence of solubility islands in the vicinity of the hypercritical points discussed.     

Interaction and Scale of Mixing in Cellulose Acetate/Poly(<Emphasis Type="Italic">N</Emphasis>-vinyl Pyrrolidone-co-vinyl Acetate) Blends

Binary blends and pseudo complexes of cellulose acetate (CA) with vinyl polymers containing N-vinyl pyrrolidone (VP) units, poly(N-vinyl pyrrolidone) (PVP) and poly(N-vinyl pyrrolidone-co-vinyl acetate) [P(VP-co-VAc)], were prepared, respectively, by casting from mixed polymer solutions in N,N-dimethylformamide as good solvent and by spontaneous co-precipitation from solutions in tetrahydrofuran as comparatively poor solvent. The scale of miscibility and intermolecular interaction were examined for the blends and complexes by solid-state ¹³C-NMR spectroscopy. It was revealed that the formation of complexes was due to a higher frequency of hydrogen-bonding interactions between the residual hydroxyl groups of CA and the carbonyl groups of VP residues in the vinyl polymer component. From measurements of CP/MAS spectra and proton spin-lattice relaxation times (T_1ρ^H) in the NMR study, the existence of the hydrogen-bonding interaction was also confirmed for the miscible blends and the homogeneity of the mixing was estimated to be substantially on a scale within a few nanometers.     

Classical and recent free-volume models for polymer solutions: A comparative evaluation

In this work, two “classical” (UNIFAC-FV, Entropic-FV) and two “recent” free-volume (FV) models (Kannan-FV, Freed-FV) are comparatively evaluated for polymer–solvent vapor–liquid equilibria including both aqueous and non-aqueous solutions. Moreover, some further developments are presented here to improve the performance of a recent model, the so-called Freed-FV. First, we propose a modification of the Freed-FV model accounting for the anomalous free-volume behavior of aqueous systems (unlike the other solvents, water has a lower free-volume percentage than polymers). The results predicted by the modified Freed-FV model for athermal and non-athermal polymer systems are compared to other “recent” and “classical” FV models, indicating an improvement for the modified Freed-FV model for aqueous polymer solutions. Second, for the original Freed-FV model, new UNIFAC group energy parameters are regressed for aqueous and alcohol solutions, based on the physical values of the van der Waals volume and surface areas for both FV-combinatorial and residual contributions. The prediction results of both “recent” and “classical” FV models using the new regressed energy parameters are significantly better, compared to using the classical UNIFAC parameters, for VLE of aqueous and alcohol polymer systems.     

Liquid–liquid equilibria of polydisperse polymer systems: applicability of continuous thermodynamics

Continuous thermodynamics is a suitable tool for describing the thermodynamic properties of solutions of polydisperse polymers. To represent liquid–liquid equilibria of polydisperse polymer/solvent systems, a continuous distribution function to represent the composition of polydisperse polymers has to be considered. In this study, we calculate the molar mass distributions of both principal phases and conjugate phases, using the extended Flory–Huggins model. The results for various polydisperse polymer systems are compared with experimental data.     

STUDIES ON STRUCTURE AND PHASE BEHAVIOR OF MULTICOMPONENT POLYMERS THROUGH RHEOLOGICAL TESTS

Rheological measurement has been a preferred approach to the characterization of the structure and phase behaviors for multi-component/multi-phase polymer systems, due to its sensitive response to the changes of structure for these heterogeneous polymers. In the present article, recent progresses in the studies on rheology for heterogeneous polymer systems including phase-separated polymeric blends and block copolymers are reviewed, mainly depending on the results by the authors＇ research group. By means of rheological measurements, not only some new fingerprints responsible for the evolution of morphology and structure concerning these polymer systems are obtained, also the corresponding results are significant for design and preparation of novel polymeric structural materials and functional materials.     

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.     

Effect of crosslinking on intermolecular interactions in thermosetting blends of epoxy resin with poly(ethylene oxide)

The miscibility and intermolecular-specific interactions in thermosetting blends of epoxy resin (ER) with poly(ethylene oxide) (PEO) cured with various amounts of 1,3,5-tridroxybenzene (THB) were investigated by differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopy (FTIR). The glass-transition behavior indicated that all the blends were miscible and had homogeneous amorphous phases; FTIR showed that there were the intermolecular hydrogen-bonding interactions between crosslinked ER and PEO. However, both the glass-transition behavior and infrared spectroscopy also indicated that the intermolecular interactions were significantly reduced by the formation of crosslinked structures, which was shown by comparing the experimental results of poly(hydroxyether of bisphenol A) (PH)/PEO and ER/PEO blends cured with various amounts of the curing agent. In ER/PEO blends the intermolecular hydrogen-bonding interactions were much weaker than the self-association of hydroxyls of ER, which was in marked contrast to the interactions in PH/PEO blends. In ER/PEO blends with various amounts of the curing agent, the intermolecular interactions between epoxy polymers and PEO were reduced with an increasing degree of crosslinking. The results were interpreted in terms of the effect of crosslinking on the intermolecular interactions, such as steric shielding, the screening effect, and chain connectivity resulting from the formation of the three-dimensional crosslinked network, which could reduce the intermolecular hydrogen-bonding interactions among hydroxyls of ER versus ether oxygen atoms of PEO. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2567–2575, 2004     

Interfacial tension in polymer blends

Theoretical models of the interfacial tension coefficient in polymer blends, v₁₂, were evaluated. A new working relation was derived that makes it possible to compute v₁₂ from the chemical structure of two polymers. The calculations involve determination of the dispersive, polar and hydrogen-bonding parts of the solubility parameter from the tabulated group and bond contributions. The computed values of v₁₂ for 46 blends were found to follow the experimental ones with a reasonable scatter of ± 36%. Next, the experimental methods of v₁₂-measurements were critically examined. Although many have been developed for low viscosity Newtonian fluids, most are irrelevant to industrial polymeric systems. For the present studies two were selected. Values of v₁₂ were measured using the so-called “capillary breakup method,” and a newly developed method based on the retraction rate of deformed drop.     

An extension of cubic equations of state to vapor-liquid equilibria in polymer-solvent mixtures

Cubic equations of state (EOS) are extended to describe polymer-solvent vapor-liquid equilibria (VLE). The solvents are described the conventional way using critical parameters. To describe the pure polymers, only the weight-average molecular weight is necessary, though number-average molecular weight, polydispersity and melt density can be incorporated if desired. To extend the model to mixtures, a mixing rule that combines EOS with excess energy models is used. In this formulation, the excess Gibbs energy term is considered in two parts: the classical Flory term for the entropic contributions and a residual term that takes care of specific interactions between the solvent and the polymer. For athermal mixtures that exhibit no such interactions, the residual term drops out and the model becomes completely predictive. Otherwise, for residual contributions, depending upon the complexity of specific molecular interactions anticipated in the mixture, either a single parameter Flory expression or a two-parameter NRTL equation can be used. We conclude that the simple cubic EOS approach presented here is easy to use, yet competes successfully with more sophisticated EOS models developed particularly for polymer solutions. Moreover, it offers more flexibility if one or more parameters are to be tuned to the process data.     

Mechanical and Morphological Properties of Bio-Phenolic/Epoxy Polymer Blends

Polymer blends is a well-established and suitable method to produced new polymeric materials as compared to synthesis of a new polymer. The combination of two different types of polymers will produce a new and unique material, which has the attribute of both polymers. The aim of this work is to analyze mechanical and morphological properties of bio-phenolic/epoxy polymer blends to find the best formulation for future study. Bio-phenolic/epoxy polymer blends were fabricated using the hand lay-up method at different loading of bio-phenolic (5 wt%, 10 wt%, 15 wt%, 20 wt%, and 25 wt%) in the epoxy matrix whereas neat bio-phenolic and epoxy samples were also fabricated for comparison. Results indicated that mechanical properties were improved for bio-phenolic/epoxy polymer blends compared to neat epoxy and phenolic. In addition, there is no sign of phase separation in polymer blends. The highest tensile, flexural, and impact strength was shown by P-20(biophenolic-20 wt% and Epoxy-80 wt%) whereas P-25 (biophenolic-25 wt% and Epoxy-75 wt%) has the highest tensile and flexural modulus. Based on the finding, it is concluded that P-20 shows better overall mechanical properties among the polymer blends. Based on this finding, the bio-phenolic/epoxy blend with 20 wt% will be used for further study on flax-reinforced bio-phenolic/epoxy polymer blends.     

Ionic miscibility enhancement via microion elimination in sulfonated polystyrene/poly(ethyl-acrylate-co-4-vinyl pyridine) ionomer blends

Miscibility enhancement of ionomer/ionomer and ionomer/polymeric acid systems is studied on the polymer pairs of poly(styrene-co-tetramethyl ammonium styrenesulfonate)/poly(ethyl acrylate-co-N-methyl-4-vinylpyridinium iodide) and poly(styrene-co-styrenesulfonic acid)/poly(ethyl acrylate-co-N-methyl-4-vinylpyridinium iodide). NMR and dynamic mechanical results show that in these blends direct macroion–macroion interaction can be achieved with the elimination of microcounterions from the polymer chains. Ion-ion attraction leads to a miscibility enhancement comparable to that of the previously reported proton transfer blends; a miscible blend is obtained with ca. 5 mol% of ions in the polymers.     

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.     

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     

Design and characterization of polymers and polymer blends for high temperature structural applications

Reviewing the development of new polymeric materials for high temperature structural applications (T > 200°C) over the past several decades, reveals a paradox which, to date, has not been completely resolved. Polymers which exhibit very high temperature stability tend to be either intractable or brittle, whereas, easily processible polymers tend to fall short of property targets. Approaches to resolving this paradox include modification of the chain backbone chemistry and polymer blending (especially to form miscible systems). Recent research has shown that, in contrast to low temperature flexible polymers, many high temperature aromatic heterocyclic polymers form miscible systems which permit the design of the desired processibility and performance into the blend. An example of such a system is the blend of Poly(2,2′-(meta-phenylene-5,5′-bibenzimidazole) (PBI) with a series of polyamides, including commercially available polyether imide (PEI) and imide copolymers containing sulfone and fluorinated isopropylidene (6F) units. Other examples include all polyimide blends and blends of polyimides with polyethersulfone.     

Thermodynamic study of poly(vinyl chloride)/polyester blends by inverse-phase gas chromatography at 120°C

Polymer/polymer interaction parameters χ′₂₃ have been measured at 120°C as a function of polymer concentration for six different poly(vinyl chloride)/linear aliphatic polyester blends. The technique used is inverse-phase gas chromatography with several molecular probes. The polymers investigated are poly(DL-lactide), poly(ethylene succinate), poly(ethylene adipate), poly(butylene adipate), poly(δ-valerolactone), poly(ε-caprolactone) and poly(hexamethylene sebacate). Probe/polymer interaction parameters χ₁₂ and polymer/polymer interaction parameters χ′₂₃ values are dependent upon the methylene to carbonyl ratio of the polyester, reaching a minimum for a value of 5, this ratio corresponding to poly(ε-caprolactone) blends. Results are interpreted in terms of pairwise interactions between carbonyl, methylene, and [CHCl] groups.     

Structure and interactions in homopolymers and blends as studied by the methods of vibrational and nmr spectroscopy

The combination of IR, Raman and NMR spectroscopy was used in the study of the blends of semicrystalline and amorphous polymers with considerably different strength of intermolecular interactions: poly(ϵ-caprolactam)/polystyrene (PCL/PS), poly(ethylene oxide)/poly(methyl methacrylate) (PEO/PMMA) and poly(N-methyllaurolactam)/poly(4-vinylphenol) (PNMLL/PVPh). In the vibrational and NMR spectra of the blends composed of non-interacting polymers (PCL/PS) and weakly interacting polymers (PEO/PMMA), no band changes were observed which would indicate changes of the conformational structures. ¹H NMR relaxation of the PCL and PS components in the blends is the same as in the respective homopolymers similarly treated. In the blends of weakly interacting polymers (PEO/PMMA), the crystallinity of PEO is influenced by the presence of PMMA and is negligible in the blends with less than 30 wt.-% of PEO. The rotating-frame spin-lattice relaxation time for protons T^H_1p of PMMA indicates close contact of the PMMA and PEO chains. In the blends PNMLL/PVPh with strong hydrogen-bonding interactions, both components are intimately mixed on a scale of 3–4 nm and significant shifts of some bands both in vibrational and in NMR spectra reveal changes of structure.     

Formation of a True Molecular Composite using Optimal Hydrogen Bonding

Guidelines for creating miscible blends containing a liquid crystalline polymer and an amorphous polymer by optimizing intermolecular interactions between the two polymers are presented. It is shown that by controlling the spacing between the functional groups that participate in hydrogen bonding along the amorphous polymer chain, the extent of intermolecular interactions between the two polymers is optimized, and this induces miscibility in the systems studied.     

Spectroscopic Ellipsometry for Characterization of Thin Films of Polymer Blends

Morphology, composition, miscibility, interdiffusion, and interactions at interfaces are important quantities of polymer blends. Many of these parameters can be probed with spectroscopic ellipsometry. Ellipsometry in the visible spectral range is very suitable for determination of thicknesses and the high frequency refractive indices of thin organic films. However the spectral contrast is low for many polymers in comparison to infrared spectroscopic ellipsometry (IRSE) where specific contributions of the molecular vibrations are probed. In the presented study the infrared optical constants of a double layer (206.6 nm in total) of poly(n-butyl methacrylate) (PnBMA) and poly(vinyl chloride) (PVC) and of the films of the single compounds have been determined with optical simulations using layer models. The multiple layer model served for simulation of the ellipsometric spectra taken after an annealing induced mixing process in a polymeric double layer. The ellipsometric spectra of a not completely mixed sample could be fitted in a three-layer model, in which a mixed interphase in between the two layers of the polymers is formed due to interdiffusion.     

Calculation of phase equilibria in random copolymer systems

Synthesis and application of copolymers are not seldom connected with different phase equilibria. Their precise knowledge is of importance for industrial processing as well as it is a profound basis for a better understanding of the nature and thermodynamics of such systems. As a common situation today, enough experimental information is seldom available in the necessary or desired amount, and a lot of model calculation is, therefore, more or less unavoidable to cover the desired ranges of application. Different equations-of-state as well as lattice models are discussed with respect to their applicability for calculating liquid-liquid and gas-liquid phase equilibria in copolymer solutions and blends. Examples for high-pressure phase equilibria in monomer/copolymer mixtures, liquid-liquid demixing in copolymer blends and for the isotropicnematic phase equilibrium in systems with rigid rod-like copolymers characterized by distributions of rigid and flexible chain parts are given. The effects of copolymer polydispersity are included by means of continuous thermodynamics. Literature references for original sources, earlier reviews and further applications round up this paper.