Organizing thermodynamic data obtained from multicomponent polymer electrolytes: Salt‐containing polymer blends and block copolymers

The objective of this review is to organize literature data on the thermodynamic properties of salt‐containing polystyrene/poly(ethylene oxide) (PS/PEO) blends and polystyrene‐b‐poly(ethylene oxide) (SEO) diblock copolymers. These systems are of interest due to their potential to serve as electrolytes in all‐solid rechargeable lithium batteries. Mean‐field theories, developed for pure polymer blends and block copolymers, are used to describe phenomenon seen in salt‐containing systems. An effective Flory–Huggins interaction parameter, χ_eff , that increases linearly with salt concentration is used to describe the effect of salt addition for both blends and block copolymers. Segregation strength, χ_effN , where N is the chain length of the homopolymers or block copolymers, is used to map phase behavior of salty systems as a function of composition. Domain spacing of salt‐containing block copolymers is normalized to account for the effect of copolymer composition using an expression obtained in the weak segregation limit. The phase behavior of salty blends, salty block copolymers, and domain spacings of the latter systems, are presented as a function of chain length, composition and salt concentration on universal plots. While the proposed framework has limitations, the universal plots should serve as a starting point for organizing data from other salt‐containing polymer mixtures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1177–1187     

Construction of ternary phase diagrams in nonsolvent/solvent/PMMA systems

In this work, the ternary phase diagrams in three nonsolvent/solvent/PMMA systems (n-hexane/n-butyl acetate/PMMA, water/acetone/PMMA, and n-hexane/acetone/PMMA) were constructed by theoretical calculation and experimental measurement. Binodal curves were calculated by using the Flory–Huggins theory for three-component systems and measured by titrating the PMMA solution with nonsolvent until the onset of turbidity. By using concentration-dependent nonsolvent/solvent and solvent/PMMA interaction parameters and constant nonsolvent/PMMA interaction parameters, good agreement has been obtained between the calculation and the measurement. The values of nonsolvent/solvent interaction parameters were taken from the literature sources, and the values of solvent/PMMA and nonsolvent/PMMA interaction parameters were measured by vapor sorption and swelling equilibrium, respectively. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 607–615, 1998     

The use of Flory–Huggins parameters as a measure of interactions in polymer‐filler systems

Any quantitative information on the strength of interactions between inorganic filler and polymer is substantial for the future application of the composite. The magnitude of adhesion of two phases may be deduced from results collected by various experimental techniques. Polyether‐urethane/modified carbonate‐silicate fillers systems containing different amount of filler (5, 10, and 20 wt %) were the materials investigated. We propose to express the magnitude of modified filler/polymer interactions by Flory–Huggins χ parameter. It may be deduced from the results collected by inverse gas chromatographic (IGC) experiment. We have also tried to explain the influence of the solvent on values of the evaluated parameters and to check the usefulness of some of presented methods to minimize Δχ effect. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1853–1862, 2006     

Improvement to the lattice-fluid prediction of gas solubilities in polymer liquids

Previously we have shown that the Lattice Fluid (LF) model can quantitatively predict, without adjustable parameters, gas solubilities for hydrocarbon and chlorinated hydrocarbon vapors in nonpolar polymers. For polar polymers, the model can also predict, with reasonable success, the solubilities of polar and aromatic vapors. However, the solubilities in polar/nonpolar combinations of gas and polymer are systematically overestimated. These are cases in which the geometric mean approximation for the interaction parameter is not expected to be valid. This paper demonstrates that with the addition of a simple empirical correlation for the interaction parameter based on Hansen's three-dimensional solubility parameters, the LF model is then able to quantitatively predict solubilities in all types of gas/polymer systems (excluding strongly self-associating systems, such as alcohols). No adjustable parameters are used; only the pure component equation-of-state and solubility parameters are required. © 1993 John Wiley & Sons, Inc.     

Sorption and partial molar volumes of C2 and C3 hydrocarbons in polypropylene copolymers

The sorption of C₂ and C₃ hydrocarbons in two ethylene–propylene copolymers and a propylene homopolymer and the simultaneous dilation of the polymers were measured at temperatures of 287–363 K and pressures up to 4 MPa. The sorption isotherms were well described by the Flory–Huggins theory of dissolution. Dilation isotherms in the form of elongation versus pressure were similar in shape to the corresponding sorption isotherms. Solubility coefficients, partial molar volumes, and Flory–Huggins interaction parameters were determined from these isotherms. The thermal expansivities of the hydrocarbons dissolved in the polymers were 0.002–0.005 K^?1, and the Flory–Huggins interaction parameters depended not only on temperature but also on concentration. At 323 K, the calculated solubilities of propylene in the ethylene–propylene‐rubber regions of the copolymers were 1.8 times higher than in the amorphous regions of the propylene homopolymer. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1255–1262, 2001     

Influence of binary interactions on phase behavior of water/ dimethylsulfoxide/ polyethersulfone casting solution: Thermodynamic modeling

Prediction and control of membrane morphology using multi‐phase thermodynamic knowledge are of growing interest. The water/dimethylsulfoxide/polyethersulfone ternary system is a widely used casting dope for the preparation of MF, UF, and NF membranes. In the current study, Flory–Huggins (F–H) model was applied to predict the behavior of this ternary system during phase inversion. Titration method was applied to generate cloud point data. The prediction accuracy of the F–H model was directly dependent on the binary interactions of the system components. The compressible regular solution (CRS) model predicts the binodal location using only the pure component properties as the input parameters. Accordingly, the influence of binary parameters on the location of the binodal curves was investigated. The predicted binodal points showed superior accordance with the experimental data, where the binary interaction between nonsolvent (water) and solvent (DMSO) was overlooked. In addition, the modelling results emphasized on the pivotal importance of the interactions between polymer (PES) and nonsolvent (water) on the phase inversion and thus, on the control of the membrane morphology. The CRS model offered a greater conformity with the experimental results in comparison with the F–H theory. Copyright © 2013 John Wiley & Sons, Ltd.     

On what terms and why the thermodynamic properties of polymer solutions depend on chain length up to the melt

Theoretical considerations based on chain connectivity and conformational variability of polymers have led to an uncomplicated relation for the dependence of the Flory–Huggins interaction parameter (χ) on the volume fraction of the polymer (?) and on its number of segments (N). The validity of this expression was tested extensively with vapor‐pressure measurements and inverse gas chromatography (complemented by osmotic and light scattering data from the literature) for solutions of poly(dimethylsiloxane) in thermodynamically vastly different solvents such as n‐octane (n‐C₈), toluene (TL), and methylethylketone (MEK) over the entire range of composition for at least six different molecular masses of the polymer. The new approach is capable of modeling the measured χ (?, N), regardless of the thermodynamic quality of the solvent, in contrast to traditional expressions, which are often restricted to good solvents but fail for bad mixtures and vice versa. At constant polymer concentration, the χ values were lowest for n‐C₈ (best solvent) and highest for MEK (Θ solvent); the data for TL fell between them. The influences of N depended strongly on the thermodynamic quality of the solvent and were not restricted to dilute solutions. For good solvents, χ increased with rising N. The effect was most pronounced for n‐C₈, where the different curves for χ (?) fanned out considerably. The influences of N were less distinct for TL, and for MEK they vanished at the (endothermal) θ temperature. For worse than θ conditions, the χ values of the long chains were less than that of the short ones. This change in the sign of N agreed with this concept of conformational relaxation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1601–1609, 2004     

Polymer–filler interactions in sol–gel derived polymer/silica hybrid nanocomposites

The effect of polymer–filler interaction on solvent swelling and dynamic mechanical properties of the sol–gel derived acrylic rubber (ACM)/silica, epoxidized natural rubber (ENR)/silica, and poly (vinyl alcohol) (PVA)/silica hybrid nanocomposites has been described for the first time. Tetraethoxysilane (TEOS) at three different concentrations (10, 30, and 50 wt %) was used as the precursor for in situ silica generation. Equilibrium swelling of the hybrid nanocomposites in respective solvents at ambient condition showed highest volume fraction of the polymer in the swollen gel in PVA/silica system and least in ACM/silica, with ENR/silica recording an intermediate value. The Kraus constant (C) also followed a similar trend. In dynamic mechanical analysis, the storage modulus dropped at higher strain (>1%), which indicated disengagement of polymer segments from the filler surfaces. This drop was maximum in ACM/silica, intermediate in ENR/silica, and minimum in PVA/silica, both at 50 and 70 °C. The drop in modulus with theoretical volume fraction of silica (ϕ) was interpreted with the help of a Power law model ΔE′ = a₁ϕ, where a₁ was a constant and b₁ was primarily a filler attachment parameter. Strain dependence of loss modulus was observed in ACM/silica hybrid nanocomposites, while ENR/silica and PVA/silica nanocomposites showed almost strain‐independent behavior. The storage modulus showed sharp increase with increasing frequency in ACM/silica system, while that was lower in both ENR/silica (at higher frequency) and PVA/silica systems (in the entire frequency spectrum). The increase in modulus with ϕ also followed similar model ΔE′ = a₂ϕ proposed in the strain sweep mode. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2399–2412, 2005     

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     

Thermodynamic analysis of polymerization-induced phase separation of a polystyrene in epoxy/monoamine–diamine systems. Effect of monoamine–diamine proportion on the phase diagram

Polymerization-induced phase separation of a polystyrene in various epoxy-amine systems where the amino groups were provided by a monoamine and a diamine mixed in different proportions was thermodynamically studied. A model based on the Flory–Huggins theory extended by Koningsveld and Staverman approach where the interaction parameter was dependent on temperature, composition and conversion, and polydispersity of the components was considered, was used. A general equation for the evolution during polymerization of the epoxy-amine species distributions according to the monoamine–diamine ratio was derived from the Stockmayer distribution. The interaction parameters continuously decreased with conversion. Phase diagrams of the blends were obtained and the critical composition was between 5 and 6 vol.% PS in all blends.     

Filler–polymer interactions in both silica and carbon black‐filled styrene–butadiene rubber compounds

Bound rubber in a filled rubber compound is formed by physical adsorption and chemisorption between the rubber and the filler. Styrene–butadiene rubber (SBR) is composed of four components of styrene, cis‐1,4‐, trans‐1,4‐, and 1,2‐units. Filler–polymer interactions in both silica and carbon black‐filled SBR compounds were studied by analyzing microstructures of the bound rubbers with pyrolysis‐gas chromatography. Differences in the filler–polymer interactions of the styrene, cis‐1,4‐, trans‐1,4‐, and 1,2‐units were investigated. The filler–polymer interactions of the butadiene units were found to be stronger than that of the styrene unit. The interactions of the cis‐1,4‐ and trans‐1,4‐units were stronger with carbon black than with silica, whereas the 1,2‐unit interacted more strongly with silica than with carbon black. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 439–445, 2001     

Filler‐polymer interactions of styrene and butadiene units in silica‐filled styrene–butadiene rubber compounds

Styrene–butadiene rubber (SBR) is a copolymer of styrene and butadiene, and the butadiene unit is composed of cis‐1,4‐, trans‐1,4‐, and 1,2‐components. Filler‐polymer interactions of each component of SBR in silica‐filled SBR compounds were examined by microstructure analysis of the bound and unbound rubbers. The composition ratio of butadiene and styrene units (butadiene/styrene) of the bound rubber was higher than that of the compounded rubber. Of the butadiene units, the 1,2‐component of the bound rubber was more abundant than the cis‐1,4‐ and trans‐1,4‐components. The filler‐polymer interaction of the butadiene unit with silica was stronger than that of the styrene unit, and the interaction of the 1,2‐component was stronger as compared with the others. The butadiene–styrene ratio of the bound rubber of the compounds containing the silane coupling agent was lower than for the compounds without the silane. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 577–584, 2004     

Green's function calculation of through‐bond electronic coupling in donor–bridge–acceptor model systems II: Importance factors applied to atomic sites

Importance factors, associated with the Green's function formalism, are introduced. They are applied for the determination of the relative atomic site contribution to the electronic interaction propagation in a molecular system. The calculation is performed at the Hartree–Fock (self‐consistent) level, using ab initio STO‐3G, 4‐31G, and D95 basis sets. The results are compared with those obtained from the charge densities of the appropriate molecular orbitals at the ab initio STO‐3G level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

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