Phase equilibria of binary and ternary polymer solutions using modified UNIQUAC-based local composition model

Journal of Thermal Analysis and Calorimetry - In the present research, a modification on UNIQUAC activity coefficient model was done based on the local composition concept. The model was applied...     

The estimation of the thermodynamic properties of ternary alloys from binary data using the shortest distance composition path

A new composition path, X_i-X_j=constant, is suggested for the semi-empirical calculation of the thermodynamic properties of ternary ‘substitutional’ solutions from binary data, when the binary systems show deviations from the regular solution model. A comparison is made between the results obtained for integral and partial properties using this composition path and those calculated employing other composition paths suggested in literature. It appears that the best estimate of the ternary properties is obtained when binary data at compositions closest to the ternary composition are used.     

Comparison of thermodynamic and rheological properties of binary polymer mixtures

The dependence of viscosity on concentration for a series of binary mixtures of polymers differing in their chemical nature and for mixtures of polymer homologues was compared with the peculiarities of their phase diagrams as well as with the concentration dependence of their thermodynamic interaction parameters. A definite correlation was found between the composition dependence of the viscosity and the thermodynamic state of the system in the melt at a given temperature. The universal character of this correlation was shown both for the mixtures of various polymers and for those of the polymer homologues.     

Nanostructure of polymer layers formed upon the adsorption from binary and ternary solutions

Thicknesses of nanolayers formed upon the adsorption from dilute and semidilute solutions of polystyrene, poly(butyl methacrylate), and their mixtures on the surface of solid SiO₂ are estimated on the basis of adsorption isotherms and atomic force microscopy measurements. It is established that the thickness of an adsorption layer is determined by the sizes of individual macromolecular coils and clusters arising in a solution. In the case of polymer blends, adsorption leads to the formation of mosaic structures with the alternation of polymeric components in the substrate plane; the characteristic size of a domain is ≈200 nm for each component. It is shown that adsorption layers formed on the surface of a silicon single crystal (covered with intact oxide) are fractal objects whose dimension depends on the nature of polymer and conditions of its adsorption.     

Short-range orientational order and thermodynamic properties of polymer solutions

The concept of short-range orientational order was applied to the calculation of thermodynamic characteristics of polymer solutions in terms of the lattice model. It was shown that allowance for short-range order makes it possible to explain negative values of the entropy of mixing and the existence of a lower critical solution temperature in both polymer solutions and solutions of low-molecular-mass compounds. It was found that systems with lower critical solution temperature can exist even when the degree of orientational order in solutions slightly increases as compared with the corresponding values of this parameter in their components.     

Geometric thermodynamic description of the congruent-melting points of solid solutions in binary and ternary systems

The congruent-melting points of solid solutions are analyzed in binary systems (minima, maxima, and shunts on the melting curves) and ternary systems (minima, maxima, saddles, and saddle-nodes on melting surfaces).     

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     

Calculation of properties of ternary liquid mixtures on the basis of properties of binary solutions

Various methods of calculating properties of ternary systems using the properties of binary solutions have been analyzed on the basis of experimental and published data.     

Influence of binary surfactant mixtures on the rheology of associative polymer solutions

Hydrophobically modified alkali-soluble emulsion polymers (HASE) are a class of comblike associative polymers that can impart high viscosities to aqueous solutions. The rheology of HASE solutions can be tuned by the addition of surfactants, such as nonylphenol ethoxylates (NP e), where e is the length of the hydrophilic (ethoxylate) chain. While previous studies have considered individual surfactants, our focus here is on binary surfactant mixtures. We find that equimolar NP4-NP12 mixtures significantly enhance the zero-shear viscosities of HASE solutions as compared to equivalent amounts of NP8, especially at high overall surfactant concentrations. Dynamic rheological measurements suggest that the higher viscosities are due to increases in the lifetime of hydrophobic junctions in the polymer-surfactant network. In contrast to the above results, equimolar NP4-NP8 mixtures are rheologically identical to equivalent solutions of NP6. The differences between the two sets of mixtures are further correlated with cloud point measurements and thereby with the overall hydrophilic-lipophilic balance (HLB) of the surfactant system.     

Light scattering in binary and ternary (polymer) solutions with specific interactions

Concentration dependence of basic light-scattering quantities in three binary low-molecular and two ternary polymer solutions was studied. Depolarization ratio alone may serve as a sensitive measure of presence of specific interactions. Experimental data of anisotropic scattering in low-molecular mixtures were in harmony with the idea that the parameters determining molecular orientation should be considered as continuous probability variables; in the case of polymer solutions specific interactions do not influence the anisotropic scattering.The presence of specific interactions with the formation of a minimum on the course of isotropic scattering is characterized. Transition from one solution structure to another with a local maximum on the course of composition light scattering is indicated.     

Equilibrium properties of ternary polymer solutions as explained by the renormalization group

In this paper we present a full account of renormalization group theory as applied to equilibrium properties of ternary polymer solutions containing two different polymer species and one solvent. We use a carefully constructed renormalization group mapping incorporating the screening effect by a proper choice of the renormalized segment size. The scaling functions reproducing observable quantities are calculated to tree approximation. We have evaluated a series of experiments on ternary solutions in this approximation and observe remarkably good agreement.     

A new model for predicting thermodynamic properties of ternary metallic solution from binary components

A model has been derived to predict thermodynamic properties of ternary metallic systems from those of its three binaries. In the model, the excess Gibbs free energies and the interaction parameter ω₁₂₃ for three components of a ternary are expressed as a simple sum of those of the three sub-binaries, and the mole fractions of the components of the ternary are identical with the sub-binaries. This model is greatly simplified compared with the current symmetrical and asymmetrical models. It is able to overcome some shortcomings of the current models, such as the arrangement of the components in the Gibbs triangle, the conversion of mole fractions between ternary and corresponding binaries, and some necessary processes for optimizing the various parameters of these models. Two ternary systems, Mg–Cu–Ni and Cd–Bi–Pb are recalculated to demonstrate the validity and precision of the present model. The calculated results on the Mg–Cu–Ni system are better than those in the literature. New parameters in the Margules equations expressing the excess Gibbs free energies of three binary systems of the Cd–Bi–Pb ternary system are also given.     

Prediction of thermodynamic properties of polymer solutions by a group-contribution method

The Flory–Huggins lattice-theory expression for solvent activity in a polymer-solution is commonly used to calculate the thermodynamic interaction parameter χ with the aid of experimental data from vapor pressure osmometry. This expression assumes that χ is independent of composition. However, experimental data for a variety of polymer-solvent mixtures indicate that χ exhibits an appreciable concentration dependence. A group contribution method, UNIFAC (UNIQUAC Functional-Group Activity Coefficients) incorporating the free-volume correction of Oishi and Prausnitz is used to predict the dependence of χ on solvent concentration. Agreement with previously reported experimental data is within 15%. Calculated values of χ obtained from the Flory–Huggins expression for solvent activity and from the corresponding Gibbs free energy of mixing (which does not assume that χ is independent of composition) are compared. Calculations based on the Gibbs free energy of mixing predict a somewhat larger value of χ relative to those based on solvent activity. The specific Gibbs free energy of mixing for polystyrene-solvent mixtures is calculated using the UNIFAC model, and is found to represent qualitatively the phase equilibrium behavior. Quantitative discrepancies are observed, however, for the polystyrene-acetone system in light of the actual experimental solubility reported by Suh and Clark (20). Most of the thermodynamic predictions for polymer-solvent systems investigated herein are correlated qualitatively with the relative mismatch between solubility parameters of both components.     

Chromatographic study of adsorption from binary and ternary solutions

Adsorption of benzene, anisole, and nitrobenzene on hydroxylated silica gel from binary and ternary solutions (adsorbate--n-hexane and adsorbate--n-hexane--terahydrofuran) was studied by HPLC. The equation that describes the adsorbate retention as a function of its concentration in binary and ternary solutions was proposed. The equation makes it possible to calculate the adsorption isotherms and adsorption equilibrium constants directly from chromatograms using the retention parameters and equilibrium concentrations of the adsorbate in the mobile phase.     

Vapor-pressure osmometry and inverse gas chromatography in the analysis of thermodynamic properties of polymer solutions

The primary objective of this work is to check the utility of vapor-pressure osmometry as an experimental technique in obtaining thermodynamic data on polymer/solvent systems. The second objective is to obtain experimental values for the exchange energy parameters ΔP, X, and ζ of the theory of Sanchez and Lacombe. With respect to the first objective, solvent activities of polyiso-butylene/benzene mixtures have been measured at several concentrations up to 600 g/kg of the solvent and at two temperatures. From the activities, it is possible to determine free energies, entropies, and enthalpies and their concentration dependence. Satisfactory agreement has been found between the results obtained and data provided by other techniques such as membrane osmometry and the Cahn electrobalance. These and other data obtained by inverse gas chromatography for the same mixture in the range 35–200°C have been used in calculating the exchange energy parameter of the lattice fluid theory at different concentrations and temperatures.     

Influence of alkyl chain on the thermodynamic properties of aqueous solutions of ionic liquids 1-alkyl-3-methylimidazolium bromide at different temperatures

Osmotic coefficients ?, mean activity coefficients γ_±, vapor pressure p data, and excess Gibbs free energies G^E of aqueous solutions of three ionic liquids 1-propyl-3-methylimidazolium bromide [PMIm]Br, 1-pentyl-3-methylimidazolium bromide [PnMIm]Br, and 1-hexyl-3-methylimidazolium bromide [HMIm]Br were determined by the vapor pressure osmometry method at four temperatures (298.15 K to 328.15 K) in intervals 10 K. From the comparison of osmotic coefficients it follows that aqueous solution of [PMIm]Br shows a more pronounced deviation from Debye–Hückel limiting law (DHLL) and vapor pressure depression more than the other studied ionic liquids which was interpreted in terms of hydrophobic interactions. The Pitzer-ion interaction and MNRTL electrolyte models satisfactorily correlate experimental osmotic coefficient data with good precision. The parameters of the Pitzer-ion interaction model are used to calculate the mean molal activity coefficients and excess Gibbs free energies.     

A metallic solution model with adjustable parameter for describing ternary thermodynamic properties from its binary constituents

A metallic solution model with adjustable parameter k has been developed to predict thermodynamic properties of ternary systems from those of its constituent three binaries. In the present model, the excess Gibbs free energy for a ternary mixture is expressed as a weighted probability sum of those of binaries and the k value is determined based on an assumption that the ternary interaction generally strengthens the mixing effects for metallic solutions with weak interaction, making the Gibbs free energy of mixing of the ternary system more negative than that before considering the interaction. This point is never considered in the models currently reported, where the only difference in a geometrical definition of molar values of components is considered that do not involve thermodynamic principles but are completely empirical. The current model describes the results of experiments very well, and by adjusting the k value also agrees with those from models used widely in the literature. Three ternary systems, Mg–Cu–Ni, Zn–In–Cd, and Cd–Bi–Pb are recalculated to demonstrate the method of determining k and the precision of the model. The results of the calculations, especially those in Mg–Cu–Ni system, are better than those predicted by the current models in the literature.     

聚电解质溶液热力学性质的研究

本文采用柱形胞腔模型以及Vink的近似方法, 求解聚电解质溶液的Poisson-Boltzmann方程, 得到不同条件下聚离子周围静电势的分布。进而得到了不同条件下聚离子、反离子和同电荷离子的活度系数及溶剂的渗透系数。所得结果与实验值能较好地吻合。     

Bulk heterojunction polymer solar cells based on binary and ternary blend systems

Polymer solar cells (PSCs) were fabricated using a ternary blend film consisting two conjugated polymers and a soluble fullerene derivative as the donor and acceptor materials, respectively. And, to compare ternary blend system, the single‐component copolymers consisting of the repeating units of each of the copolymers, used in ternary blend solar cells, were designed and synthesized for use as the electron donor materials in binary blend solar cells. We systematically investigated the field‐effect carrier mobilities and the optical, electrochemical, and photovoltaic properties of the copolymers. Under optimized conditions, the binary blend polymer systems showed power conversion efficiencies (PCEs) for the PSCs in the range 3.87–4.16% under AM 1.5 illumination (100 mW cm^?2). All polymers exhibited similar PCEs that did not depend on the ratio of repeating units. The binary blend solar cell containing a single‐component copolymer as the electron donor material performed better than the ternary blend solar cell in this work. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011