Prediction of maxima and minima in the curve of total sorption parameter in ternary polymer systems. Influence of ternary interaction parameter

Flory-Huggins theory modified by Pouchly has been applied to predict maxima and minima in the curve of total sorption in ternary polymer systems formed by a polymer and two liquids. In this work, different diagrams based on experimental magnitudes easily obtained such as the difference in affinities of liquids, solvents and non solvents, and the solvent molar volume ratio. Total sorption parameter has been considered to be the decisive magnitude to define extrema conditions in both cosolvent and cononsolvent ternary polymer systems. The theoretical prediction is not altered by the inclusion of ternary interactions. Different examples of ternary systems dealing with vinyl polymers and polydimethyl siloxane have been used to test the above formalism.     

A comparative study between cosolvent and cononsolvent ternary polymer systems through the preferential adsorption coefficient

Sorption equilibrium of polystyrene and poly (dimethyl siloxane) in mixed solvents has been monitored by means of the preferential adsorption coefficient experimentally determined from intensity light scattering measurements. The pairs of solvents used to dissolve each polymer sample have been selected for the purpose to perform cosolvent and cononsolvent ternary polymer systems. Flory-Huggins formalism including ternary interactions has been used to predict the sorption equilibrium for the cosolvent system and, for the first time, for cononsolvent ones. Moreover, the proportionality between binary and ternary interactions, recognized by Pouchly, is also corroborated for both ternary polymer systems. From a thermodynamic standpoint, the sorption equilibrium has been described by approaching the behavior of the bulk solvent to the binary liquid mixture through the excess Gibbs free energy.     

Theoretical analysis of sorption of a binary solvent in a polymer phase. I. Occurrence and character of inversion in preferential sorption

Osmotic and sorption equilibria in the system polymer–binary solvent can be represented with advantage in coordinates (u₁, v₃), where v₃ is the volume fraction of the polymer and u₁ gives the composition (volume fraction) of the binary solvent in the polymer phase. The coexistence lines and osmotic isobars are plotted; the former are used to read the preferential sorption ε of one of the solvent components in the polymer. The newly formulated equilibrium condition for the preferential sorption is applied to the Flory–Huggins theory extended by the ternary interaction parameter χ_T. This is used as a starting point for analyzing the conditions under which inversion of preferential sorption takes place, i.e., the sign of ε changes. The existence of inversion and the course of the inversion line in the v₃ versus u₁ plot are affected in a decisive manner by the extent to which the effect of the mutual interaction of solvent components prevails over the effect of the relative difference between their molar volumes and of the difference in strength of their interaction with the polymer. The effect of the ratio of molar volumes upon the preferential sorption increases with the concentration of the polymer, so that for v₃ not too far from unity the component having the smaller molecule is necessarily sorbed preferentially. If, therefore, both types of small molecules are not of the same size, the inversion vanishes for large v₃ even in systems where it actually occurs if v₃ is small. On the contrary, the same effect can in other cases have as its consequence an inversion at moderate values of v₃, even if it does not appear as v₃ approaches zero; a similar effect can also be produced by a nonzero value of the interaction parameter χ_T. The neighborhood of the inversion line can have a “divergent” or a “convergent” character, depending on whether the component being preferentially sorbed is that present in excess. The former case is observed with negative and the latter for the positive values of the binary solvent–solvent interaction parameter χ₁₂. The inversion with the divergent neighborhood has not yet been confirmed experimentally, owing to the small number of systems investigated.     

Thermodynamic analysis on the cononsolvency of poly (vinyl alcohol) in water–DMSO mixtures through the ternary interaction parameter

Isothermal phase diagrams for the semicrystalline poly (vinyl alcohol) (PVA) in solutions composed of water and dimethylsulfoxide (DMSO) was studied at 25 °C. From the observed phase behavior, PVA was soluble in either water or DMSO individually but crystallization-induced gelation and liquid–liquid demixing were observed in water–DMSO mixtures. Flory–Huggins formalism including three binary interaction parameters and one ternary interaction parameter was used to study the phenomenon of the cononsolvency, i.e. the formation of nonsolvents by mixing two solvents. The equilibrium crystallization line in the DMSO-rich region and the total calculated binodals agreed well with the measured results when a composition-dependent ternary interaction parameter was included into calculations. In contrast, calculations yielded crystallization-induced gelation in the water-rich region, but experiments indicated that PVA remained well dissolved even 1 year after preparation. The discrepancy was explained by the temperature-induced changes in the relative interaction between water and PVA. In addition, the role of the ternary interaction parameter in the cononsolvent ternary polymer systems was discussed. It was found the contribution of the ternary interaction parameter in the cononsolvent system under study is to decline the degree of the cononsolvency. The driving force for cononsolvency is the strong interaction between water and DMSO to form the stable DMSO hydrate to exclude PVA segments in the vicinity of the hydrate.     

Measured and calculated solubility of polymers in mixed solvents: Monotony and cosolvency

By a study of two ternary systems, 4-heptanon–1-chlorobutane–poly(methyl methacrylate) and 2-butanol–1-chlorobutane–poly(methyl methacrylate), differing only in one component of the mixed solvent, two types of demixing behavior are demonstrated: i.e., a monotone change with composition of the mixed solvent (monotony), of which the first system is a good example, and the synergistic behavior (cosolvency) exhibited by the second system. The situation can be seen most clearly from the binodal edges (precipitation thresholds as a function of solvent composition) which were constructed from various types of sections through the binodal surface of the systems. In order to compare experimental results with theoretical calculations, we first characterized the binary subsystems. The polymer solutions, representing conventional (endothermal) theta systems, were investigated by light scattering and cloud point measurements. For the cosolvent 2-butanol–1-chlorobutane the necessary thermodynamic information was accessible from vapor pressure measurements. Applying the Prigogine–Patterson theory to the polymer solutions and using the single-liquid approximation of Scott for the ternary systems yielded theoretical binodal edges in good agreement with experiment except for the branch belonging to mixed solvents rich in 2-butanol. This finding is explained by an abnormal amplification of preferential solvation effects due to the existence of an association equilibrium of the alcohol via hydrogen bonds.     

Polymer–cosolvent systems. XI. Polystyrene dissolved in mixtures of diethyl ether and nitromethane

The ternary system nitromethane (1) +diethyl ether (2) +polystyrene (3) has been examined by determining the demixing behavior of the polymer in the temperature–solvent composition plane. Enhanced solvation of the polymer is evidenced by the ability of the mixture to dissolve very high molecular weight (10⁷ g/mol) polystyrene at intermediate solvent compositions compared with the behavior in the two solvents separately. The cosolvent action of the mixture is analyzed in terms of modern theories of polymer solution free volume.     

Phase equilibria in solvent mixture–ion exchange resin catalyst systems

Phase equilibria for solvent mixtures and strong acidic ion exchange resins in H⁺ form are investigated. Experimental data on ternary non-reactive solvent–solvent–polymer systems as well as reactive multicomponent systems are presented for moderately and highly cross-linked poly(styrene-co-divinylbenzene) (PS-DVB) resins. Esterification of acetic acid with ethanol is used as a model reaction. The data are correlated with a combination of thermodynamic models derived for polymer solutions and gels. Independently determined data is used whenever possible with a goal of reducing cross-correlations between the model parameters. The limitations of the thermodynamic modeling approach for solvent–ion exchange resin systems are discussed. It is shown that, due to glass transition of the polymer matrix, the underlying assumptions are not entirely valid in low dielectric constant media and at high cross-link densities.     

On the evaluation of the anisotropic-isotropic transition volume fraction for a semirigid polymer

It has been found that a method allowing the calculation of an anisotropic-isotropic transition volume fraction for a given semirigid polymer can be derived from the equations recently proposed by Blonski and coworkers to evaluate the equilibrium compositions of isotropic and anisotropic phases coexisting within ternary systems semirigid polymer/flexible polymer/solvent. By using the term anisotropic-isotropic transition volume fraction of a semirigid polymer we will refer to its smallest volume fraction giving an anisotropic character to liquid ternary phases also including a flexible polymer and a solvent. Its evaluation simplifies the construction of the corresponding ternary diagram and can also be seen as a fast and quantitative way of estimating the influence exerted by the semirigid polymer, through its intrinsic anisotropy, on ternary phases.     

Preferential solvation of poly(dimethylsiloxane) and poly(methyl methacrylate) in benzene-methanol mixtures by gel permeation chromatography

Preferential solvation λ parameters for the ternary systems benzene-methanol-poly(dimethylsiloxane) and benzene-methanol-poly(methyl methacrylate) have been determined by gel permeation chromatography. When benzene is preferentially adsorbed by the polymer, good agreement is found between λ values determined by this method and by light scattering and dialysis equilibrium. However, when methanol is preferentially adsorbed by the polymer, discrepancies arise. The differences are discussed in terms of interactions between the solvent and the chromatographic support.     

Phase equilibria in polymer–liquid–liquid systems

The phase equilibria in polymer–liquid 1–liquid 2 ternary systems have been calculated on the basis of the Flory-Huggins theory of polymer solutions. A new approximation method based on the “cluster” concept has been introduced for mixed solvents comprising a solvent and a nonsolvent. This concept has been verified with polystyrene–solvent–methanol systems.     

Solubility prediction of anthracene in mixed solvents using a minimum number of experimental data

Numerical methods to predict the solubility of anthracene in mixed solvents have been proposed. A minimum number of 3 solubility data points in sub-binary solvents has been employed to calculate the solvent-solute interaction terms of a well established colsolvency model, i.e. the combined nearly ideal binary solvent/Redlich-Kister model. The calculated interaction terms were used to predict the solubility in binary and ternary solvent systems. The predicted solubilities have been compared with experimental solubility data and the absolute percentage mean deviation (APMD) has been computed as a criterion of prediction capability. The overall APMD for 25 anthracene data sets in binary solvents is 0.40%. In order to provide a predictive method, which is based fully on theoretical calculations, the quantitative relationships between sub-binary interaction terms and physicochemical properties of the solvents have been presented. The overall APMD value for 41 binary data sets is 9.19%. The estimated binary interaction terms using a minimum number of data points and the quantitative relationships have then been used to predict anthracene solubility data in 30 ternary solvent systems. The produced APMD values are 3.72 and 15.79%, respectively. To provide an accurate correlation for solubility in ternary solvent systems, an extension to the combined nearly ideal multicomponenet solvent/Redlich-Kister (CNIMS/R-K) model was proposed and the corresponding overall AMPD is 0.38%.     

Entrainer effect in supercritical mixtures

The objective of this paper is to propose a predictive method for the estimation of the change in the solubility of a solid in a supercritical solvent when another solute (entrainer) or a cosolvent is added to the system. To achieve this goal, the solubility equations were coupled with the Kirkwood–Buff (KB) theory of dilute ternary solutions. In this manner, the solubility of a solid in a supercritical fluid (SCF) in the presence of an entrainer or a cosolvent could be expressed in terms of only binary data. The obtained predictive method was applied to six ternary SCF–solute–cosolute and two SCF–solute–cosolvent systems. In the former case, the agreement with experiment was very good, whereas in the latter, the agreement was only satisfactory, because the data were not for the very dilute systems for which the present approach is valid.     

Ternary complexes in agarose gels prepared from binary solvents

The thermoreversible gelation of agarose has been investigated in four different aqueous binary solvents: Water/dimethyl sulfoxide, water/N,N-dimethylformamide, water/N-methylformamide, and water/formamide. The phase diagrams have been subsequently established as a function of agarose concentration and solvent composition. These diagrams suggest the formation of ternary complexes agarose/water/cosolvent.     

Correlation of thermodynamic modeling and molecular simulations for liquid-liquid equilibrium of ternary polymer mixtures based on a phenomenological scaling method

In our previous study [S.Y. Oh, Y.C. Bae, J. Phys. Chem. B 114 (2010) 8948-8953], we presented a new method to predict liquid-liquid equilibria in ternary simple liquid mixtures by using a combination of a thermodynamic model and molecular simulations. As a continuation of that effort, we extend our previously developed method to ternary polymer systems. In the simulations, we used the dummy atoms to calculate the pair interaction energy values between the polymer segments and the solvent molecules. Furthermore, a thermodynamic model scaling concept is introduced to consider the chain length dependence of the energy parameters. This method was applied to ternary mixtures incorporating low to high molecular weight polymers. The method presented here well described the experimental observations using one or no adjustable parameters.     

Wetting of the container wall as a critical-point phenomenon. III. Wetting by contacting conjugate solutions of ternary systems

In the ternary systems benzene-ethanol-water and ethyl acetate-ethanol-water, the contact angles of the meniscus between two immiscible liquid phases (i.e., conjugate solutions) and a solid substrate tend toward 90° as compositions approach the consolute point at a constant temperature; just as, in a binary system, the contact angles between the corresponding three phases have been shown (in the previous paper of this series) to tend toward 90° as the temperature approaches the critical point. The quantitative expression for the variation of the contact angle with the concentration of the cosolvent in the vicinity of the consolute point in a ternary system also bears a formal mathematical resemblance to that found for the corresponding variation of the contact angle with temperature in a binary system.     

Free energy of an inhomogeneous polymer–polymer–solvent system. II

A complete expression for the enthalpy of mixing of inhomogeneous polymer–polymer–solvent systems applicable for small as well as large concentration fluctuations has been developed. This is used to express the free energy of inhomogeneous polymer–polymer–solvent systems in an extended form of the Landau-Ginzburg functional. The gradient energy parameters obtained here are consistent with the published results. The free energy functional has been applied to develop a generalized continuity equation for spinodal decomposition in polymer–polymer systems. A linearized version of this continuity equation has been used to study the effect of the gradient terms on the dominant wavelength during spinodal decomposition.     

Binary Interaction Parameters,Ternary Systems: Realistic Modeling of Liquid/Liquid Phase Separation

The phase behavior of ternary systems (either a polymer solution in a mixed solvent or a polymer blend in a single solvent) was modeled theoretically. The modeling considers two specific features of polymers explicitly: chain connectivity and the ability to respond to changes in the molecular environment by conformational reorientation. Previously, this approach has been applied to polymer solutions in single solvents. Here it is generalized and the number of parameters is reduced to two per binary system. The calculation of the Gibbs energies of the ternary mixtures accounts for the composition dependencies of the binary interaction parameters. The following phenomena are reproduced realistically for polymer solutions in a mixed solvent and for solutions of two polymers in a common solvent: simplicity, co‐solvency, and co‐non‐solvency. The results nourish the hope that the new approach is capable of modeling phase diagrams for ternary systems by means of binary interaction parameters only.

     

Solvent and substrate contributions to the formation of breath figure patterns in polystyrene films

The generation of ordered porous polymer structures by the breath figures (BFs) method has long been described as a complex phenomenon, in which several parameters combine in a fairly unknown way. The type of polymer and solvent, degree of humidity, and additives are just a few examples of the several parameters that have been described as playing a role in the generation of BFs. This work reports a detailed investigation over the role played by the solvent in the process of BFs generation from polystyrene (PS) solutions spread over different substrates, and discusses the geometrical aspects of the pores via a quantitative point of view by using a purposely developed software for image analysis. Results show that thermodynamic affinity between polymer and solvent is the key parameter for BFs formation, along with other solvent characteristics such as water miscibility, boiling point, and enthalpy. According to our findings, the role played by the substrate is strictly related to the type of solvent used in the generation of BFs.     

Solubility profiles of poly(ethylene glycol)/solvent systems, I: Qualitative comparison of solubility parameter approaches

Solubility of systems involving four different molecular weights of poly(ethylene glycol) (PEG) in tetrahydrofuran (THF), chloroform, dimethylsulfoxide (DMSO), methanol and water have been investigated by different algorithmic approaches as the mathematical application of the “like dissolves like” principle. In this study, the solubility parameters and their components for PEG and solvents have been evaluated by using of atomic group contribution methods; Small, van Krevelen-Hoftyzer (VKH), Hoy and Breitkreutz methods, respectively. Then their 2-dimensional graphs (Bagley, Henry and Hoernschemeyer diagrams) and 3-dimensional graph (Hansen diagram) have been drawn by creating the solubility profiles of the polymer in selected solvents. The dissolving capability of these solvents has been discussed. In addition the solubility parameters have been calculated by use of the van der Waals volume in the selected molecule or repeating unit of the polymer instead of the molar volume which is used in atomic group contribution methods (Askadskii approach). Surface tensions of the polymer and solvent systems have been calculated with this method and solubility criteria of PEG have been explained after a serial calculation steps. In addition, influence of molecular weight of PEG on solubility has been also analyzed. As a consequence of algorithmic calculations, THF has been determined as the best solvent whereas water is found to be the weakest solvent for polymer/solvent systems.     

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.