Closed-packed lattice model for polymer solution systems considering the chain length dependence effect: Correlating LLE,VLE, and gel swelling behaviors using identical interaction energy parameters

We propose a new Helmholtz energy of mixing equation following the original Flory–Huggins (F–H) closed-packed lattice model. Also, to overcome F–H mean-field approximation, we introduce new universal constants to consider chain length dependence of polymer in solvent and consider specific interactions to describe strongly interacting polymer systems. Our proposed model successfully describes liquid–liquid equilibria (LLE) for binary polymer–solvent systems using identical interaction parameters which do not depend on the polymer molecular weight. We also describe vapor–liquid equilibria (VLE) for polymer/solvent systems and swelling equilibria of thermosensitive hydrogel systems using the same energy parameters obtained from LLE calculations.     

Investigation of thermodynamic properties of hyperbranched aliphatic polyesters by inverse gas chromatography

Thermodynamic properties of a series of commercial hyperbranched aliphatic polyesters (Boltorn^® H20, H30 and H40) were examined for the first time by inverse gas chromatography (IGC) using 13 different solvents at infinite dilution as probes. Retention data of probes were utilized for an extensive characterization of polymers, which includes the determination of the Flory–Huggins interaction parameter, the weight fraction activity coefficient as well as the total and partial solubility parameters. Analysis of the results indicated that the total and partial solubility parameters decrease with increase of temperature. Furthermore, upon increase of the molecular weight, while the hydrogen bonding component decreases, no influence on the total solubility parameter is noticed within the experimental error margins. Results from the present study while providing new insight to the thermodynamic characteristics of the examined systems, they are also expected to reflect more general aspects of the behavior of hyperbranched polymers bearing similar end-groups.     

Viscometric study of dilute solutions of polymer-polymer mixtures. Temperature and composition effects

Viscometric interaction parameters between pairs of homopolymers or an acidic and a basic copolymer in dioxane were determined by two procedures: (a) determination of the intrinsic viscosity of polymer (A) in dilute dioxane solutions of polymer (B) at 30°; (b) determination of the Huggins constants for 1:1 mixtures of polymers at 50°. The Δb₂₃ values obtained by these methods were different but positive and they increased from the most incompatible to the completely compatible system. Non-linear relations were found for the Huggins constant vs temperature and the intrinsic viscosity vs composition.     

A viscometric study of dilute aqueous solutions of poly(vinylalcohol)-polyacrylamide mixtures

The viscosity interaction coefficient, k_AB, for the system poly(vinylalcohol)-polyacrylamide-water was determined at 25° by two methods: (a) estimation of the Huggins slope coefficients for mixtures of polymers in different proportions; (b) determination of the intrinsic viscosity of polymer (A) in aqueous solutions of polymer (B). The result, k_AB = 0.3, indicates a low degree of overlapping of unlike polymer molecules.     

Thermodynamic properties of novolac-type phenolic resin blended with poly(ethylene oxide)

The thermodynamic properties of novolac type phenolic resin blended with poly(ethylene oxide) (PEO) were investigated by the Painter–Coleman association model (PCAM). Equilibrium constants and enthalpy corresponding to the interaction between phenolic and poly(ethylene oxide) were calculated from the Fourier transform infrared spectroscopy of low molecular weight analogues in dilute solutions. The association parameters of the model compounds are transferred to the corresponding polymers, to predict the Gibbs free energy, phase behavior, and the degree of hydrogen bonding in the polymer blend. The heat capacity (C_P) and the excess heat capacity (ΔC_P) are used to verify the validity of PCAM model on predicting the thermodynamics properties of phenolic/PEO blend. It is found that the hydrogen bonding interaction dominates at moderate temperatures, which is outweighed by the dispersion force at higher temperature or high PEO compositions. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1647–1655, 1998     

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.     

Liquid–liquid equilibrium calculations for methanol–gasoline blends using continuous thermodynamics

This work presents the application of continuous thermodynamics to investigate the limited miscibility of methanol–gasoline blends. To predict the liquid–liquid equilibrium of these systems, the Gaussian distribution function was used to represent the composition of paraffins in the gasoline. The naphthenes and aromatics were represented by model compounds. A model has been developed using three different continuous versions of the UNIFAC model. Methanol is an associating component, and association affects phase equilibria. Therefore, the CONTAS (continuous thermodynamics of associating systems) model based on the Flory–Huggins equation, for multicomponent methanol–gasoline blends has also been investigated. The predicted results including the cloud point curve, shadow curve and phase separation data have been compared with experimental data and good agreement was found for the two UNIFAC and CONTAS models.     

Dilute solution behaviour of progressively hydrolyzed polyacrylamide in water-N, N dimethylformamide mixtures

The intrinsic viscosities [η’s] of anionic (hydrolyzed; low and high carboxyl content) and nonionic polyacrylamide (unhydrolyzed) were measured in water-N, N dimethylformamide mixtures at various temperatures. Non-polyelectrolyte behavior of low carboxyl content polyacrylamide was observed in mixed solvent system. The plots of [η] vs. solvent composition in a mixed solvent system pass through minima for both high as well as low carboxyl content polymers but through a maximum for nonionic polyacrylamide. Observed minimum for charged polymers may be attributed to the loss of polymer sites available to interact with solvent for H-bonding interaction between neighboring amide and the acid groups. The maximum for nonionic polymer at the particular solvent composition arises for the most powerful cosolvent effect. Existence of two antagonistic effects is apparent in [η] values of nonionic polymer at various temperatures. Huggins constant (K_H) also indicates a significant variation of cosolvency as a function of solvent composition. Activation parameters of viscous flow were calculated using Frenkel-Eyring equation. The volume related parameter and the shape factor were also computed. Shape factor data indicate that polymer molecules are more or less rigid spheres and are not affected by temperature and composition of solvent.     

Simulation of molecular fractionation and species distributions in phase separation of polystyrene-modified epoxy/monoamine–diamine blends

Molecular fractionation occurred at the beginning of phase separation in blends based on a polystyrene modifier and an epoxy system undergoing polymerization with a monoamine and a diamine mixed in different proportions was studied thermodynamically. The study was conducted by simulating in each separated phase the species distributions of components of the blend, the stoichiometric ratio, and the proportion of monoamine–diamine at cloud-point conditions. A model based on Flory–Huggins theory described in a previous paper Rico et al. [1] where the interaction parameters were dependent on temperature, composition, and conversion, χ(T,?,p), and where the polydispersity of the components was taken into account, was used for simulation. The effect of modifier proportion, monoamine–diamine ratio and polymerization temperature on molecular fractionation and species distribution was determined and analyzed. Explanations of the estimated trends were given on the basis of the thermodynamic model used.     

Hydrocarbon and fluorocarbon solubility and dilation in poly(dimethylsiloxane): Comparison of experimental data with predictions of the Sanchez–Lacombe equation of state

Sorption and dilation isotherms are reported for a series of gases (N₂, O₂, CO₂), hydrocarbon vapors (CH₄, C₂H₆, C₃H₈), and their fluorocarbon analogs (CF₄, C₂F₆, C₃F₈) in poly(dimethylsiloxane) (PDMS) at 35°C and pressures up to 27 atmospheres. The hydrocarbons are significantly more soluble in hydrocarbon-based PDMS than their fluorocarbon analogs. Infinite dilution partial molar volumes of both hydrocarbons and fluorocarbons in PDMS were similar to their partial molar volumes in other hydrocarbon polymers and in organic liquids. Except for C₂H₆ and C₃H₈, partial molar volume was independent of penetrant concentration. For these penetrants, partial molar volume increased with increasing concentration. The Sanchez–Lacombe equation of state is used to predict gas solubility and polymer dilation. If the Sanchez–Lacombe model is used with no adjustable parameters, solubility is always overpredicted. The extent of overprediction is more substantial for fluorocarbon penetrants than for hydrocarbons. Very good fits of the model to the experimental sorption and dilation data are obtained when the mixture interaction parameter is treated as an adjustable parameter. For the hydrocarbons, the interaction parameter is approximately 0.96, and for the fluorocarbons, it is approximately 0.87. These values suggest less favorable interactions between the hydrocarbon-based PDMS matrix and the fluorocarbon penetrants than between PDMS and hydrocarbons. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3011–3026, 1999     

Group contribution method for transport property predictions of glassy polymers: focus on polyimides and polynorbornenes

The group contribution approach has been shown to be suited for prediction of transport parameters (gas permeability and diffusion coefficients) of glassy polymers based on the chemical structure of their repeat units. This paper presents further development of this method. An attempt is made to improve the accuracy of such predictions. A database including several hundreds of the structures of amorphous glassy polymers and their transport parameters was used for the calculations of the group contributions in the P_i and D_i values. Better agreement between the experimental and predicted P_i and D_i values was achieved when the data for different polymer classes (e.g. polynorbornenes and polyimides) were treated separately. The best fit of the predicted and experimental data for polyimides is obtained using a modified scheme where a distinction is made between the groups that appear in main and side chains and substituents at aliphatic and aromatic carbon atoms.     

Dilute solutions of nylon 12—III. Intermolecular and intramolecular association of end-groups

An equation has been derived relating the Huggins viscometric coefficient, k_H, and molecular weight of polymers which in a given solvent associate via end-group interactions forming linear and cyclic multimers. The equation was used to calculate the association constant (K_a = 2.2 × 10² mol/l) for nylon 12 from experimental data. Values of the constant of intramolecular cyclization of unimers were estimated; their dependence on polymer molecular weight was less steep than suggested by the theory of macrocyclic equilibria.     

Modeling of thermodynamic behavior of PVT properties and cloud point temperatures of polymer blends and polymer blend + carbon dioxide systems using non-cubic equations of state

In recent years, many factors influencing phase behavior of polymer blends have been studied because of their widely technological importance, as a simple method of formulating new materials with tailored properties which make them suitable for a variety of applications. This work has three main goals which were reached by using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS), which in previous works have shown their ability to handle long chain and associating interactions. First, both equations of state were tested with the correlation of the specific volumes of pure blends (PBD/PS, PPO/PS, PVME/PS, PEO/PES) and the prediction of the specific volumes for blends; second, the modeling of blend miscibilities in the liquid–liquid equilibria (LLE) of PBD/PS, PPG/PEGE, PVME/PS, PEO/PES, and PnPMA/PS blends; third, the modeling of the phase behavior of PS/PVME blends at various compositions in the presence of CO₂. PC-SAFT and SL pure-component parameters were regressed by fitting pure-component data of real substances (liquid pressure–volume–temperature, PVT, data for polymers and vapor pressure and saturated liquid molar volume for CO₂) and the fluid phase behavior of blend systems were simulated fitting one binary interaction parameter (k_ij) by regression of experimental data using the modified likelihood maximum method. Results were compared with experimental data obtained from literature and an excellent agreement was obtained with both EoS, which were also capable of predicting the fluid phase behavior corresponding to the critical solution temperatures (LCST: lower critical solution temperature, UCST: upper critical solution temperature) of blends.     

Anomalous solubility parameter and probe dependency of polymer-polymer interaction parameter in inverse gas chromatography

Inverse gas chromatography (IGC) has been widely used to measure the Flory-Huggins interaction parameters, χ, between two polymers. For over two decades studies have shown the polymer-polymer interaction parameter to be probe dependent. This study found that the solubility parameters of miscible polymer blends measured by IGC were lower than the volume average values of the components. This led to the conclusion that when specific interactions occur between two polymers the probes have less probability to contact the functional groups of the polymers, leading to a lower apparent solubility parameter. Using the solubility parameter model this deviation was shown to cause the probe dependency. Two methods were proposed to test the miscibility. One was to examine the deviation of the specific retention volume from the weight average rule. The other was to plot ?₂?₃RT(χ₂₃/V₂) vs. the solubility parameters of probes. For miscible blends a linear trend with negative slope was observed. The slope was proportional to the deviation of solubility parameter of the polymer mixtures from the volume average, which could be used as a measurement for miscibility.     

Experimental studies on a mixture of HFC-32/125/161 as an alternative refrigerant to HCFC-22 in the presence of polyol ester

In this work, experiment was conducted to examine the thermo-physical properties of an alternative refrigerant to HCFC-22 in the presence of polyol ester (POE). The new alternative refrigerant is a mixture of HFC-32/125/161, whose physical properties are similar to HCFC-22 but has a lower global warming potential (GWP) than that of R407C. POE is used as the tested lubricating oil in the experiment. The saturated vapor pressure data and vapor–liquid equilibrium data of nine different mass fractions of the new refrigerant and polyol ester (POE) in the temperature range of 253–323 K were measured by single-phase cycle method. The experiment results showed that there was no stratification, no sediment generation in the liquid phase of the mixture, and the color of liquid phase of the mixture had no change in the equilibrium cell before and after the experiment with the POE concentration greater than 20% and the temperature higher than 258 K; with POE concentration lower than 20% and temperature lower than 258 K, stratification began to appear. Meanwhile, when POE and the refrigerant were miscible, the saturated pressure data of the mixture (HFC-32/125/161 + POE) revealed that POE had a very small impact on saturated vapor pressure of the mixture (almost negligible) when POE was less than 10% of the mixture; POE has an obvious effect on the saturated vapor pressure of the mixture when there is more than 10% POE in the mixture, especially when the temperature is higher than 283.15 K. Experimental data were correlated by Flory–Huggins model, Heil model, NRTL model and Wilson model. The results showed that to the average and maximum pressure deviation, the results were better with considering the effects of temperature on the energy parameters. Among the above models, the NRTL activity coefficient model was the best, the Heil and Wilson models followed and the Flory–Huggins model had the largest deviation from the experimental data.     

Solvent quality as reflected in concentration‐ and temperature‐dependent Flory–Huggins interaction parameters

Flory–Huggins interaction parameters (χ) between poly(dimethylsiloxane) (weight‐average molecular weight = 152 kg/mol) and various solvents (methyl ethyl ketone, toluene and n‐octane) were determined as a function of composition and temperature with vapor‐pressure measurements. These data, complemented by independent information for dilute and very concentrated solutions, serve as the basis for a discussion of solvent quality via different theoretical relations. Regardless of polymer concentration, the χ values fall from methyl ethyl ketone via toluene to n‐octane, the ketone being the worst solvent and the hydrocarbon being the best solvent. The variation of χ with composition and temperature is complex. Within the range of moderate polymer concentrations, the influences of composition decrease with increasing solvent quality. Additional effects become noticeable at the ends of the composition scale. The enthalpy parts (χ_H) and entropy parts (χ_S) of the Flory–Huggins interaction parameter, obtained from χ(T), vary considerably with composition and change their sign in some cases; these constituents of the Flory–Huggins interaction parameter do not permit a direct assessment of solvent quality. A clear‐cut picture is, however, regained with a comparison of the interdependence of χ_S and χ_H. The elimination of explicit concentration influences re‐establishes the order in the solvent quality setup via χ. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 651–662, 2001     

Modeling of the three-phase equilibrium in systems of the type water + nonionic surfactant + alkane

Liquid–liquid equilibria of systems water (A) + C_iE_j surfactant (B) + n-alkane (C) have been modeled by a mass-action law model previously developed and so far successfully applied to a series of binary water + C_iE_j systems and to the ternary system water + C₄E₁ + n-dodecane. These calculations provide the basis for the presented modeling. The aqueous systems give information about the association constants and the χ_AB-parameter of the Flory–Huggins theory and the ternary C₄E₁-system provides universal temperature functions for the χ_AC- and the χ_BC-parameter. The three-phase equilibrium for seven ternary C_iE_j systems (i = 6–12, j = 3–6) has been calculated by fitting one additional parameter for each of both temperature functions to the characteristic “fish-tail” point. The agreement with the experimental data is reasonably well. For systems with very small three-phase areas the results can considerably be improved by individual temperature functions that incorporate the experimental temperature maximum of the “fish” into the parameter fit. Based on the parameters of the system water + C₈E₄ + n-C₈H₁₈ the “fish-shaped” phase diagram of the system water + C₈E₄ + n-C₁₄H₃₀ was predicted reasonably well.     

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.