A continuous polydisperse thermodynamic algorithm for a modified flory–Huggins model: The (polystyrene + nitroethane) example

A modified Flory–Huggins model is presented, considering a concentration‐ and temperature‐dependent interaction parameter, and using the methodology of Continuous Thermodynamics to take into account both polydispersity and its effect on phase equilibrium of polymeric systems. This model describes all commonly found, as well as other unusual polymer + solvent and polymer + polymer, liquid–liquid phase diagrams and is easily extended to take all possible pressure effects into consideration. Modeling and least‐squares fit of polystyrene + nitroethane liquid–liquid cloud‐point data have produced results in good accord with the experimental ones by using meaningfully physical parameters. These results have been used to discuss polystyrene molecular weight, pressure, and isotopic substitution effects on polystyrene + nitroethane systems. A first‐order interpretation of phase equilibrium isotopic substitution effect has also been applied. It combines the simplest form of the Flory–Huggins model with the statistical theory of condensed phase isotope effects. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 632–651, 2000     

Nematic–isotropic phase behaviors of polydisperse polymer/liquid‐crystal systems: Chain‐length‐dependent interaction parameter

Phase behaviors of polydisperse polystyrene (PS)/nematic liquid‐crystal systems [P‐ethoxy ‐ benzylidene ‐ p ‐ n‐butylaniline (EBBA)] are investigated with a thermo‐optical analysis technique. We also develop a thermodynamic framework to describe the phase behaviors of polydisperse PS/EBBA systems. The proposed model is based on a modified double‐lattice model to describe isotropic mixing and Maier–Saupe theory for anisotropic ordering. To correlate the polymer chain length and energy parameters in a nematic–isotropic biphasic region and to apply the primary interaction parameter in an isotropic–isotropic phase‐transition behaviors of polydisperse PS/EBBA systems. The proposed model shows remarkable agreement with experimental data for the model systems in comparison with an existing model. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1031–1039, 2006     

Thermodynamics of solutions of cyclic polymethylene ester oligomers in p‐dioxane and chloroform

Differential vapor pressures were measured for mixtures of two cyclic polymethylene ester oligomers in p‐dioxane and chloroform at 25, 30, 35, and 40 °C at five different concentrations ranging from 1 to 20 wt %. The Flory–Huggins interaction parameter (χ) as well as Leonard's interaction parameter (χ′) for flexible and semiflexible rings were calculated and compared to one another. A new method for the estimation of the number of segments of a cyclic polymer is proposed that allows Leonard's equations to be applied correctly to a particular cyclic compound. Consistent differences between χ and χ′ were observed for all studied mixtures, and the differences became smaller if the cyclic oligomers were considered semiflexible. Interestingly, the enthalpic parameter (κ) deduced from values of χ and χ′ did not differ within their uncertainties. This supports the prediction that mixing cyclic polymer compared to its linear counterpart is mainly due to a molecular configurational entropy difference and that this difference should become less pronounced as the cyclic compound becomes larger. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 443–455, 2000     

Liquid–liquid equilibria of polymer solutions: Flory‐huggins with specific interaction

We have developed a new Flory‐Huggins model by adding a specific interaction parameter derived from a modified double‐lattice model for the Helmholtz energy of mixing for binary liquid mixtures. This model is very simple and could be easily integrated into engineering applications. Using this revised model, we can successfully describe the phase behavior of polymer solutions with an upper critical solution temperature (UCST), a lower critical solution temperature (LCST), both UCST and LCST, and a closed miscibility loop. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 162–167, 2010     

Evaluation of solubility parameters during polymerisation of amine‐cured epoxy resins

A new procedure for the calculation of solubility parameter evolution during polymerisation has been developed for amine‐cured epoxy systems, which allows quantitative thermodynamic modelling of chemically induced phase separation (CIPS). Solubility parameters calculation, chemical analysis based on near infrared spectroscopy and curing kinetics results obtained by differential scanning calorimetry will allow to model the evolution of the Flory–Huggins interaction parameter in amine‐cured epoxy blends. The resin system investigated was based on a diglycidyl ether bisphenol A (DGEBA) epoxy resin cured with isophorone diamine (IPD) blended with various reactive epoxydised dendritic hyperbranched polymer modifiers (HBP), yielding a CIPS‐controlled morphology. The analysis showed the evolution of the different contributions to the solubility parameters to follow the polymerisation kinetics. The dispersive contribution had the highest value at all stages of polymerisation, but the hydrogen and polar contributions showed the largest variation. By evaluating the dynamic evolution of the solubility parameter components, the Flory–Huggins interaction parameter in the epoxy resin‐hyperbranched polymer blends has been modelled as a function of time. This procedure, combined with thermodynamic modelling, will enable to predict phase diagrams in CIPS thermosetting blends quantitatively. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1883–1892, 2000     

Phase equilibria of polymer dispersed liquid crystal systems in the presence of an external electrical field

The effect of an external electrical field on phase behaviors is reported for polymer dispersed liquid crystal films of 4′‐pentyl‐4‐biphenylcarbonitrile/poly(methyl methacrylate) binary mixtures with various polymer molecular weights. The experimental results show that increasing the molecular weight of the polymer or the electrical field intensity can give rise to an increase in the phase‐transition temperature and a widening of the binary phase region. The lattice theory, regarding a binary system consisting of a rigid nematic liquid crystal and a random polymer, has been extended to the case in which an external electrical field is present. A comparison of the theoretical predictions with the experimental results has been carried out, and satisfactory agreement has been found. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1898–1906, 2007     

Evaluation of gas sorption parameters and prediction of sorption isotherms in glassy polymers

A model of continuous‐site distribution for gas sorption in glassy polymers is examined with sorption data of CO₂ and Ar in polycarbonate. A procedure is presented for determining from a measured isotherm the number of sorption sites in a polymer, an important parameter that previously had to be assumed. With this parameter value and solubility data obtained at zero pressure, the model can reasonably predict sorption isotherms of CO₂ in glassy polycarbonate for a wide temperature range. The number of sorption sites and the average site volume evaluated from CO₂ sorption isotherms are employed for the prediction of Ar sorption isotherms with zero‐pressure solubility data and the independently measured partial molar volume of Ar. A reasonable fit to the measured isotherms of Ar is achieved. With the proposed procedure, the continuous‐site model shows several advantages over the conventional dual‐mode sorption model. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 883–888, 2000     

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     

Phase behavior of a water/2‐propanol/poly(methyl methacrylate) cosolvent system

A phase diagram of poly(methyl methacrylate) in mixtures of water and 2‐propanol, individually nonsolvents for the polymer, was studied at 25 °C. For this system, there were two liquid–liquid demixing regions separated by a miscible region. This cosolvent phenomenon was thought to be a joint effect of the nonsolvents. The phase behavior was modeled according to modified Flory–Huggins chemical‐potential equations, which accounted for the possible contribution from a ternary interaction in terms of a lumped parameter, χ₁₂₃. The calculated phase‐equilibrium curves (binodals) agreed well with the measured results. By contrast, if only binary interaction parameters were considered, computations yielded binodals whose compositions departed significantly from the measured data. Using the wet phase inversion method with casting dopes selected on the basis of the phase diagram, we prepared membranes with microporous structures in various coagulation baths. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 747–754, 2000     

Separation studies of hydrazine from aqueous solutions by pervaporation

Separation of hydrazine from aqueous solutions with ethylcellulose membranes has been investigated by using the pervaporation technique. The effect of membrane thickness, concentration polarization, and feed concentration on flux and selectivity were evaluated. A separation mechanism is proposed based on the measurements of sorption, and diffusion coefficients, and estimations of Flory–Huggins interaction parameters and Hansen's solubility parameter. States of water, hydrazine, and hydrazine hydrate are explained with DSC spectra. The specific interaction sites in ethylcellulose matrix where the solvent interacts extensively with the polymer have been identified by FTIR analysis. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1969–1980, 1999     

Effect of specific rotation of chiral dopant and polymerization temperature on reflectance properties of polymer stabilized cholesteric liquid crystal cells

A series of polymer stabilized cholesteric liquid crystal (PSCLC) cells were prepared by photo‐polymerization of a cholesteric liquid crystal (Ch‐LC) mixture containing a nonreactive LC, a nematic diacrylate and a novel cholesteryl monomer. The influence of the specific rotation and concentration of the chiral dopants, and the polymerization temperature on reflection properties was investigated. The results demonstrate that the reflection band was broadened after polymerization for all the systems both left‐handed S811 and right‐handed R1011 as the chiral dopant, which is speculated to be a result of an inhomogeneous consumption of the chiral monomer within the system. Additionally, the polymer temperature plays an integral role in the observed reflection spectra, and at optimum polymerization temperature the broadband reflection effect becomes much more pronounced. Scanning electron microscopy (SEM) was used to examine the role of microscopic changes of the polymer network induced by polymerization temperature. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1562–1570, 2008     

Structure of a self-assembled hydrogen-bonded ‘living’ main chain liquid crystalline polymer

A main chain hydrogen-bonded liquid crystalline polymer was formed by melt mixing two complementary components, A and B, which in their individual states do not exhibit liquid crystallinity. The structure of the polymer and the thermal stability of its mesophase were studied using synchrotron radiation SAXS/WAXS/DSC at Daresbury (UK) and by variable temperature Fourier transform infrared. The chain extension, or “polymerization” process, was accelerated at the point when the polymer formed a liquid crystalline phase upon cooling from the isotropic melt. The polymer has an aabb chain structure and forms a smectic layer with a length of the A-B repeating unit. The hydrogen-bonded main chain polymer studied here is a monotropic liquid crystal. Above 150°C, it exhibits kinetic stabilization of its monotropic smectic phase. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1617–1624, 1998     

Thermodynamic model of gas permeability in polymer membranes

A new molecular thermodynamic model is developed of the gas permeability in polymer membranes on the basis of configurational entropy and Flory‐Huggins theory to predict permeability dependence on the concentration of penetrant. Three kinds of configurational entropy are taken into account by this model; that is, the disorientation entropy of polymer, the mixing entropy, and specific interaction entropy of polymer/gas. The validity of the mathematical model is examined against experimental gas permeability for polymer membranes. Agreement between experimental and predicted permeability is satisfactory. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 661–665, 2007     

Effects of formulation variables on liquid‐crystal droplet size distributions in ultraviolet‐cured polymer‐dispersed liquid‐crystal cells

The size distributions of liquid‐crystal droplets in ultraviolet‐cured polymer‐dispersed liquid‐crystal cells have been studied with optical microscopy. It has been observed that (1) the relative masses of the liquid crystal and crosslinking agent determine the droplet size distribution for submicrometer droplet diameters and (2) only the liquid‐crystal mass fraction affects the droplet size distribution for diameters ranging from 1 to 4 μm. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1842–1848, 2005     

Stereoselective ring‐opening polymerization of rac‐lactide with a single‐site,racemic aluminum alkoxide catalyst: Synthesis of stereoblock poly(lactic acid)

The polymerization of racemic lactide with a racemic aluminum alkoxide catalyst is reported. Microstructural analysis of the polymer produced with ¹H NMR spectroscopy revealed that an isotactic stereoblock poly(lactic acid) formed, where each enantiomerically pure block contained an average of 11 lactide monomer units. The melting point of this polymer, 179 °C, was higher than that of the enantiomerically pure polymer, consistent with the cocrystallization of the enantiomeric blocks of the polymer. The mechanism of the polymer formation is currently unknown, although a polymer exchange pathway, where living chain ends switch between metal centers to produce diastereomeric active species, is proposed. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4686–4692, 2000     

Orientation of semiflexible biopolymers in a magnetic field

A theory is presented to explain the stretching and orientation of a semiflexible chain such as the biopolymeric filamentous actin and deoxyribonucleic acid in a magnetic field. Both dilute and concentrated solutions are considered. The theory predicts the requirement of a high magnetic field to achieve a high degree of orientation in a dilute solution. The experimental value of the order parameter for a dilute, polydisperse F‐actin solution has been compared with the theoretical value. On the other hand, a molecular field (nematic liquid crystal) which exists in a concentrated solution can achieve the same effects of stretching and orientation and can be assisted by a magnetic field. Sources of diamagnetic anisotropy in biopolymers have been cited. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3256–3270, 2000     

Phase behavior predictions for polymer blends containing reversibly associating endgroups

A mean field model is developed to predict how polymer–polymer miscibility changes if polymers are functionalized with noncovalent, reversibly binding endgroups. The free-energy model is based on the Flory–Huggins mixing theory and has been modified using Painter's association model to account for equilibrium self-association of endgroups. Model input parameters include the length of polymer chains, a temperature-dependent interaction parameter, and a temperature-dependent equilibrium constant for each type of associating endgroup. The analysis is applied to 12 possible blend combinations involving self-complementary interactions and seven combinations involving hetero-complementary [i.e. donor–acceptor (DA)] interactions. Combinations involve both monofunctional and telechelic associating chains. Predicted phase diagrams illustrate how self-complementary interactions can stabilize two-phase regions and how DA interactions can stabilize single phase regions. The model is a useful tool in understanding the delicate balance between the combinatorial entropy of mixing polymer chains, the repulsive interactions between dissimilar polymers, and the additional enthalpic and entropic changes due to end-group association of chain ends. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3285–3299, 2007     

Solvent sorption effects on the structure and properties of PP/Rodrun blends

Toluene, carbon tetrachloride, and tetrahydrofuran sorption and desorption by polypropylene (PP) and PP/thermotropic liquid crystal polymer (Rodrun) blends with 20 and 40% Rodrun contents were studied as well as the effects of the solvent presence on the structure and mechanical properties. The rate of sorption and desorption and the solvent content at the equilibrium were higher in the blends than in pure PP. This was attributed to microcracking in the PP matrix induced by the presence of Rodrun. Taking into account the very low permeability of Rodrun to the solvents of this work, and the increase in specific volume of the blends as a result of sorption, sorption‐induced additional microcracking, partially in the form of debonding of the dispersed Rodrun phase, is also believed to occur. Plasticization was the main effect on mechanical properties. The partially irreversible effect of sorption on the mechanical properties agrees with the proposed partial debonding and weak solvent resistance of these blends. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1090–1100, 2000     

Metastable liquid–liquid and solid–liquid phase boundaries in polymer–solvent–nonsolvent systems

In general liquid–liquid demixing processes are responsible for the porous morphology of membranes obtained by immersion precipitation. For rapidly crystallizing polymers, solid–liquid demixing processes also generate porous morphologies. In this study, the interference of both phase transitions has been analyzed theoretically using the Flory–Huggins theory for ternary polymer solutions. It is demonstrated that four main thermodynamic and kinetic parameters are important for the structure formation in solution: the thermodynamic driving force for crystallization, the ratio of the molar volumes of the solvent and the nonsolvent, the polymer–solvent interaction parameter, and the rate of crystallization of the polymer compared to the rate of solvent-nonsolvent exchange. An analysis of the relevance of each of these parameters for the membrane morphology is presented. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 763–770, 1997