Bulk polymer/solvent interactions for polyethylene and EVA copolymers,below their melting temperatures

In this work, the Flory–Huggins parameters corresponding to the amorphous phase of a polyethylene (PE) and two ethylene–vinyl acetate (EVA) copolymers (with 18 and 33 % vinyl acetate content, respectively) samples, with different solvents have been determined below the melting temperature of the polymers, in order to quantify the bulk interactions of these polymer/solvent systems. The employed solvents were a dispersion solvent (cyclohexane), a polar solvent (vinyl acetate) and an association solvent (methanol). Initially, the inverse gas chromatography measurements allowed obtaining the retention volumes, activity coefficients and overall Flory–Huggins parameters of every polymer/solvent system. According to these parameters, in all cases, the more compatible solvent was cyclohexane, so it was selected as the probe to calculate the percentages of crystallinity at room temperature, whose results were in agreement the literature data (35 % for PE, 29 % for EVA18, and 12 % for EVA33). The percentage of crystallinity allowed determining the amorphous Flory–Huggins parameters which are the ones which take into account just the bulk interactions in a polymer/solvent mixture. The Flory–Huggins parameter results show that, to accurately study the vapor–liquid equilibrium between a polymer and a solvent (bulk interactions), when the range of studied temperatures is below the melting point of the polymer, it is crucial to calculate the amorphous contribution (χ _amorphous) on the overall Flory–Huggins parameter. In the case of this study, the lower the vinyl acetate content (higher crystallinity), the higher the difference between the overall and amorphous Flory–Huggins parameters is. Analyzing the interactions between the three polymeric materials and the solvents it can be noticed that, for the most compatible solvent (cyclohexane), χ _amorphous represents the less contribution, or the highest correction, to the overall Flory–Huggins parameter (around 50 % for PE and EVA18, and 79 % for EVA33, the less crystalline polymer).     

Lyotropic mesophase formation in PVA/imogolite mixture

Summary The mesophase formation was observed in the ternary system consisting of a solvent, a rigid rod solute (imogolite), and a randomly coiled polymer chain (poly(vinyl alcohol); PVA). Although the mesophase formation in this system seems to follow qualitatively the scheme presented by Flory, no marked segregation of the two solute component was confirmed. The physical properties of the composite film prepared from this ternary system were also examined.     

相转化法聚合物/溶剂/非溶剂铸膜体系的热力学计算

计算了相转化法铸膜体系中常见的典型三元相图,分析了聚合物与溶剂之间、聚合物与非溶剂之间、溶剂与非溶剂之间的相互作用参数对聚合物/溶剂/非溶剂铸膜液体系相图的影响,以及体系温度和聚合物摩尔体积对聚合物/溶剂/非溶剂铸膜液体系相图的影响。根据溶剂-非溶剂汽液平衡数据和溶解度参数得到了溶剂-非溶剂、溶剂与聚合物以及非溶剂与聚合物之间的Flory-Huggins相互作用参数,从而获得了几种常见铸膜液体系的相图。同时,利用聚合物/溶剂/非溶剂铸膜液体系的相图数据对热力学模型的参数进行了优化,取得了与实验结果较一致的计算结果。     

Analysis of nonsolvent–solvent–polymer phase diagrams and their relevance to membrane formation modeling

Calculations have been carried out, based on Flory–Huggins solution theory, to analyze the behavior of the ternary nonsolvent–solvent–polymer phase diagram for typical membrane-forming systems. Consideration is given to the behavior of the spinodal as well as binodal curves, tie-line slopes, and critical points as a function of various parameters, most especially those related to the concentration dependency of the interaction parameters. Implications regarding membrane structure formation are discussed, and the suitability of different functional forms for the interaction parameter concentration dependence is also analyzed. The net result of these calculations is to demonstrate the importance of the various parameters in controlling the phase-diagram behavior and particularly to show the critical role of the concentration dependence of the solvent–polymer interaction parameter in affecting the nature of the miscibility gap.     

Simultaneous determination of three Flory–Huggins interaction parameters in polymer/solvent/nonsolvent systems by viscosity and cloud point measurements

We propose an integral procedure to simultaneously obtain the three Flory–Huggins interaction parameters in polymer(3)/solvent(2)/nonsolvent(1) systems by carrying out only viscosity and cloud point measurements. First, the interaction parameter between polymer and solvent, χ₂₃, is obtained by applying the Rudin's model which has been well established for various polymer solutions. Then the solvent/nonsolvent interaction parameter χ₁₂ and polymer/nonsolvent interaction parameter χ₁₃ are calculated by combining the Rudin's model and the modified Flory–Huggins free energy for the ternary system, which leads to a group of candidate values of χ₁₂ and χ₁₃. Finally, these values are selected by the best agreement between the calculated binodal curves and the measured cloud points of the ternary system. This procedure has been successfully applied to PES/NMP/H₂O, PAN/DMSO/H₂O, and PAN/DMF/H₂O systems. All the values obtained are comparable to those reported previously. The procedure is simple and easy to follow, with no requirement of complex equipments.     

Continuous distribution kinetics for ultrasonic degradation of poly(methyl methacrylate)

Ultrasonic degradation of poly(methyl methacrylate) (PMMA) was carried out in several solvents and some mixtures of solvents. The time evolution of molecular weight distribution (MWD), determined by gel permeation chromatography, is analysed by continuous distribution kinetics. The rate coefficients for polymer degradation are determined for each solvent. The variation of rate coefficients is correlated with the vapour pressure of the solvent, kinematic viscosity of the solution and solvent–polymer interaction parameters. The vapour pressure and the kinematic viscosity of the solution are found to be more critical than other parameters (such as the Huggins and Flory–Huggins constants) in determining the degradation rates. © 2001 Society of Chemical Industry     

Ternary phase equilibria of polystyrene with a second polymer and a solvent

Phase diagrams including tie lines for nine ternary solvent–polymer–polymer systems have been obtained using size exclusion chromatography. The systems studied were toluene–polystyrene (PS)–isoprene rubber (IR), toluene–PS–butadiene rubber (BR), cyclohexane–PS–BR, tetrahydrofuran(THF)–PS–poly(methyl methacrylate) (PMMA), and THF–PS–poly(butyl methacrylate) (PBMA) at temperatures between 30 and 75°C. The results indicate PS-PMMA is less compatible than PS-PBMA in the presence of THF. Also, the combination of trans- and 3,4–IR-PS is less compatible than cis–IR-PS in the presence of toluene. The original Flory–Huggins model for ternary systems has been modified to account for the concentration dependence of the interaction parameters. The modified Flory–Huggins model consists of two interaction parameters per binary. Using this model, six parameters have been regressed for each of the experimental systems studied. Although the parameters are not physically meaningful, the model and the parameters obtained using it are useful for correlating the experimental phase diagrams. The results obtained using the modified six parameter model are shown to be superior to those obtained using the original three parameter model. © 1993 John Wiley & Sons, Inc.     

CONTINUOUS THERMODYNAMICS FOR POLYMER SOLUTIONS II.LATTICE-FLUID MODEL

Using lattice-fluid model,a continuous thermodynamic framework is presented forphase-equilibrium calculations for binary solutions with a polydisperse polymer solute.A two-stepprocess is deslgned to form a real polymer solution containing a solvent and a polydisperse polymersolute occupying a volume at fixed temperature and pressure.In the first step,close-packed purecomponents including solvent and polymers with different molar masses or different chain lengths aremixed to form a closed-packed polymer solution.In the second step,the close-packed mixture,con-sidered to be a pseudo-pure substance is mixed with holes to form a real polymer solution with a vol-ume dependent on temperature and pressure.Revised Freed's model developed previously is adoptedfor both steps.Besides pure-component parameters,a binary size parameter c_r and a binary energyparameter ε_(12) are used.They are all temperature dependent.The discrete-multicomponent approach isadopted to derive expressions for chemical potentials,spinoda     

Application of genetic algorithm in calculation of the phase behavior of binary and ternary polymer solutions

A genetic algorithm as an optimization procedure has been developed to predict the phase behavior of polymer solutions. The phase equilibrium diagrams of binary and ternary polymer solutions have been determined using the appropriate form of Flory–Huggins free-energy function for polymer solutions. A concentration and temperature dependent form of the interaction parameter has been used to reflect the effect of temperature and polymer properties in the free-energy form. The proposed genetic algorithm is applied to compare the phase behavior results of some typical polymer solutions with the results of the classical determination methods and then applied to some conventional ternary polymer solutions as polymer–solvent–nonsolvent systems. The proposed algorithm use a set of individual states as the initial chromosomes and uses the general rules as crossover, mutation, and with use of a fractional objective function determines the binodal points or the phase diagram boundaries of polymer solutions. The properties of an industrially relevant polymer solution, a polystyrene–cyclohexane solution, have been used to emphasize on the industrial application of the proposed algorithm. The algorithm has been used to predict the phase behavior of the two polymer–solvent–nonsolvent systems as polystyrene-butanone-methanol and polystyrene-butanone-propanol at three different temperatures and results show good agreement with the experimental observations. The algorithm also has the capability to predict both the concentration-independent and concentration-dependent interaction parameters among the different components. The genetic algorithm is an easy-to-use, state-of-art, and very fast optimization tool, and has very strong capability to solve nonlinear systems in chemical and polymer engineering topics.     

Vapor-liquid equilibrium calculations for concentrated polymer solutions

The free-volume theory of polymer solutions initiated by Prigogine and developed by Flory and Patterson is reduced to practice. This theory, which represents a substantial improvement over the older theory of Flory and Huggins, facilitates calculation of solvent activities in polymer solutions from a minimum of experimental binary data. However, it is necessary to characterize each pure component with three molecular parameters which can be obtained from PVT data; such data, unfortunately, are often unavailable. Nevertheless, using reasonable approximations based on Bondi's correlations as needed, molecular parameters are given for 22 solvents and for 16 polymers. Binary parameters are given for 20 systems. Illustrative examples are presented.     

Binary interactions in dimethyl terephthalate/bis(2-ethylhexyl)adipate/poly(vinyl chloride) blends studied by melting point depression method

A novel approach is developed to estimate the interaction energy density, B, of polymer solutions by the melting point depression method using a crystallizable molecule as the probe. It rests on the classical Flory–Huggins lattice model of polymer solutions, and considers the polymer–solvent interaction parameter to be concentration dependent. The ternary system dimethyl terephthalate (DMT)/bis(2-ethylhexyl)adipate (DOA)/poly(vinyl chloride) (PVC) is chosen for the present study. The data of B for the three possible binary interactions are reported as the functions of composition at elevated temperatures. For a plasticized PVC resin containing 20 vol % DOA, the B is estimated to be 6 MJ m⁻³, which is approximately 2 MJ m⁻³ higher than the B value cited in the literature for the PVC mixed with almost 100% DOA. The thermodynamic stability of the ternary, system is discussed. © 1996 John Wiley & Sons, Inc.     

Studies of spinodal decomposition in a ternary polymer‐solvent‐nonsolvent system

Much of the work in modeling and computer simulation of spinodal decomposition has been done for binary systems. This work attempts to carry out the analysis of spinodal decomposition in ternary polymer‐solvent‐nonsolvent systems, where the solvent is the monomer used to produce the polymer and the nonsolvent is the major component. Various experimental methods are used to determine values of the parameters of the ternary version of the Cahn‐Hilliard equation of spinodal decomposition, such as cloudpoint experiments, time‐resolved light scattering in the ternary system, and morphological development of polymer membranes formed during the early stages spinodal decomposition. The combination of these experimental methods and computer simulation work shows the validity of the assumptions made in characterizing spinodal decomposition in ternary polymer systems of interest.     

Concentration dependence of the diffusion coefficient in polymer solution and molecular weight distribution determined by the diffusion method

The effects of the concentration dependence of the diffusion coefficient of a polymer solution (polystyrene in benzene and cyclohexane) in determining molecular weight distribution by the diffusion method are briefly discussed. The value of the ratio D_m0/D_A0 in a good solvent was found to be close to 1.0 for a polydisperse polymer and less than 1.0 for monodisperse polymers. Molecular weight distribution curves of the polydisperse sample were obtained by the diffusion method in cyclohexane and benzene, respectively. The molecular weight distribution curve obtained for the polymer used in benzene solution looked as if the polymer had a narrow molecular weight distribution. The phenomena cited above were interpreted in the light of the concentration dependence of the diffusion coefficient of polymer solutions.     

Describing the sorption characteristics of a ternary system of benzene (1) and alcohol (2) in a nonporous polymer membrane (3) by the Flory–Huggins model

The Flory–Huggins equation was used to describe results of total and preferential sorption measurements for the binary liquid mixture of benzene (1) and alcohol (2) in one of two nonporous polymer membranes (3), low‐density polyethylene (LDPE) and Nafion membrane. The concentration dependence of binary and ternary interaction parameters was determined. The interaction parameters for the benzene – methanol binary mixture were obtained from binary vapor‐liquid equilibrium data in the literature to decrease the number of adjusted parameters. The results show that use of a ternary interaction parameter is necessary. Data treatment was performed assuming either no crystallinity or an average crystallinity typical for the studied membranes. Subsequently, the limiting activity coefficients of solutes in LDPE were calculated from the values of the interaction parameters and their values compared to values of the limiting activity coefficients of benzene and methanol in hypothetical liquid alkane with the same density as LDPE obtained by the UNIFAC method. POLYM. ENG. SCI., 55:1187–1195, 2015. © 2014 Society of Plastics Engineers     

Polymer-cosolvent systems: 7. The application of free volume theory to the classical cosolvent systems formed from polystyrene in acetone and n-alkanes

The Prigogine-Patterson theory of polymer solutions has been applied to the cosolvent systems formed from mixtures of acetone (1) with n-alkanes (2). The necessary reduction parameters were calculated taking due account of acetone/alkane interactions as characterized by the Flory X₁₂ parameter. The effect of relatively increased free volume differences in the solvent mixtures is counteracted by a marked decrease in the enthalpy term which brings about an overall decrease in the polymer/solvent interaction parameter (χ). It is suggested that cosolvency is predominantly enthalpic in origin and a possible mechanism is postulated.     

Liquid–liquid phase separation in polysulfone/polyethersulfone/N‐methyl‐2‐ pyrrolidone/water quaternary system

To construct a phase diagram of the polysulfone (PSF)/polyethersulfone (PES)/N‐methyl‐2‐pyrrolidone (NMP)/water quaternary system, cloud point measurements were carried out by a titration method. The miscible region in the PSF/PES/NMP/water quaternary system was narrow compared to the PSF/NMP/water and PES/NMP/water ternary systems. The binary interaction parameters between PSF and PES were estimated by water sorption experiments. The calculated phase diagram based on the Flory–Huggins theory fit the experimental cloud points well. In addition to the usual polymer–liquid phase separation, polymer–polymer phase separation, which resulted in a PSF‐rich phase and a PES‐rich phase, was observed with the addition of a small amount of nonsolvent. The boundary separating these two modes of phase separation could be well described and predicted from the calculated phase diagrams with the estimated binary interaction parameters of the components. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2113–2123, 1999     

The solubility of poly(vinylidene chloride) in solvent mixtures

Effective solvents for poly(vinylidene chloride) (PVDC) were obtained by mixing a polar aprotic solvent with a less polar solvent of cyclic structure. The polar components included sulfoxides, N,N-dialkylamides, and N-alkyl lactams. The cyclic cosolvents included aliphatic and aromatic hydrocarbons, ketones, ethers, and thioethers. The problem of solubility of a crystalline polymer in a mixed solvent was analyzed by extending the Flory theory of melting point depression to three component mixtures. The results predict that favorable mixtures arise when at least one of the components interacts strongly with the polymer but is nearly incompatible with the cosolvent. This is in qualitative agreement with the observed behavior of PVDC.     

Phase separation and morphology in ethylcellulose/cellulose acetate phthalate blends

This article discusses the phase separation and morphology of ethylcellulose/cellulose acetate phthalate blended films cast from methanol/methylene chloride (50/50 v/v) solvent mixture. The solvent system has been shown to be a cosolvent for CAP and a solvent/nonsolvent for EC. The two polymers have been shown to phase separate for all blend compositions via nucleation and growth. The morphology of these systems consists of a dispersion of broad size distribution of the minor component in a matrix of the major one. The formation of two layers due to coalescence of the dispersed phases and their eventual precipitation has been observed for the middle blend compositions. Finally, the phase separation in this system is discussed in terms of the Flory–Huggins theory and changes in the solvency mechanism during film casting. Enrichment of the solvent system in methanol at relatively early stages of film casting leads to changes in the system viscosity, relative chain conformation in solution, and chain diffusion. The effect of these parameters on the final morphology are discussed in terms of deviations from the equilibrium binodal decomposition.     

Preferential adsorption in polymer/solvent-1 /solvent-2 solutions by infrared spectroscopy

IR spectroscopy is shown to be a suitable technique for preferential adsorption studies in the following solvent-1/solvent-2/polymer systems: poly(N-vinylcarbazole) and polyacenaphthene in nitrobenzene/dioxane, nitrobenzene/ tetrahydrofuran, and nitrobenzene/cyclohexanone. Values of the preferential adsorption parameters derived from the Schultz-Flory theory agree with those from IR when both solvents in the ternary system are considered to be good solvents for the polymer. In the systems studied, the relative adsorptions of solvent-1 and solvent-2 by the polymer depend on the solvent mixture composition. The number of adsorbed molecules and their performance are correlated with the ternary interaction parameters, X_m3, and the Mark-Houwink-Sakurada exponent, a′. The adsorption changes observed are greater in those systems in which tetrahydrofuran was present.     

On activated seed swelling technique

The activated seed swelling technique is one of the promising methods in synthesis of micron‐sized monodispersed polymer particles. However, there are some parameters (eg the interference of acetone residue on particle swelling) that make this method difficult to carry out and even lead to a broad particle‐size distribution. Here, these parameters are studied and how to control them is discussed. The polydisperse seed swelling appeared at lower concentration of acetone and with incomplete evaporation of acetone from the system. The monodisperse swelling and larger particle sizes were achieved at higher concentration of acetone and longer evaporation time using a vacuum pump. These results suggest that the particle size and particle‐size distribution in the activated seed swelling technique can be controlled by the carrier (acetone) and the hydrophobe concentration in aqueous medium before and after the swelling process. Copyright © 2005 Society of Chemical Industry