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     

Interactions of glucose and polyacrylamide in solutions and gels

The swelling of polyacrylamide (PAAm) gels increased with rising glucose concentrations, and so did the osmotic pressure of the soluble polymer and its intrinsic viscosity. A Flory–Huggins‐based model for the osmotic pressure of a nonionic hydrophilic polymer in a ternary solution consisting of a main solvent, a polymer, and a nondissociating low‐molecular‐weight cosolute was developed and examined. The model‐calculated values were in reasonably good agreement with experimental results for the water–PAAm–glucose system studied when PAAm–water and glucose–water interaction coefficients from the binary systems were used, and only the PAAm–glucose interaction coefficient was adjusted. Its negative value suggested a favorable interaction of glucose and PAAm, supporting the notion of glucose being a good cosolvent for PAAm. Isothermal titration microcalorimetry results showed no evidence for the binding of glucose to PAAm, but an exothermic interaction was indicated between glucose and PAAm. Microcalorimetrically determined enthalpic contributions to the Flory–Huggins interaction coefficients showed enthalpically favorable binary interactions, particularly the enthalpic component of the PAAm–glucose interaction coefficient (χ_H23), which was slightly negative. The enthalpically favorable interaction between glucose and PAAm may explain the increased osmotic pressure of PAAm in glucose solutions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3053–3063, 2003     

Solubility and diffusivity of methylmethacrylate and butylacrylate monomers in a MMA–BA copolymer

Mutual diffusion coefficients and sorption isotherms of methyl methacrylate (MMA) and butyl acrylate (BA) monomers in methyl methacrylate‐butyl acrylate copolymer (MMA‐BA) have been measured by gravimetric sorption. MMA is found to have higher solubility and diffusion rates in the copolymer than BA. Sorption data for MMA were interpreted using classical Flory‐Huggins thermodynamic theory with a constant interaction parameter (χ). A modified version of this theory has been applied to correlate the sorption data of BA, which exhibit a temperature and concentration‐dependent χ parameter. For MMA, the isotherm data reveal enhanced polymer‐solvent interactions with increasing temperature, while for BA the data indicate a drive toward phase separation with increasing temperature. Despite the difference in thermodynamic behavior, both monomers are found to exhibit Fickian diffusion and the diffusivity data are correlated reasonably well with the Vrentas‐Duda free volume theory. Some deviation between the free‐volume correlation and the experimental data is observed at the lowest temperature and BA concentration examined. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1996–2006, 2007     

The link between nanoscale feature development in a negative resist and the Hansen solubility sphere

By systematically studying development of a high resolution, negative electron beam resist, hexa‐methyl acetoxy calix(6)arene, we have elicited a more general understanding of the underlying development mechanisms for negative resists. Using the three dimensional Hansen solubility parameters for more than 40 solvents, we have constructed a Hansen solubility sphere (HSS). From this sphere, we have estimated the Flory Huggins interaction parameter for solvents with hexa‐methyl acetoxy calix(6)arene and found a correlation between resist development contrast, nanoscale patterned feature quality, and the polymer‐solvent solubility. Conducting Atomic Force Microscopy (AFM) in a liquid cell, we have measured swelling for hexa‐methyl acetoxy calix(6)arene in four solvents. The swelling measurements indicate that the HSS gives an indication of the Flory‐Huggins interaction parameter. These measurements provide new insights into the development behavior of nanoscale features – necessary for obtaining the ultimate lithographic resolution. In addition, it demonstrates a methodology for choosing appropriate polymer‐solvent combinations for nanoscience applications. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2091–2105, 2009     

Direct spincasting of polystyrene thin films onto poly(methyl methacrylate)

The low vapor pressure solvent 1‐chloropentane was used to directly spincast polystyrene (PS) films onto poly(methyl methacrylate) (PMMA) with smooth surfaces and sharp interfaces. Interface roughness after removal of the PS layer with cyclohexane was determined with scanning force microscopy to be <1 nm. Dynamic secondary mass spectroscopy revealed an interfacial width below the resolution limit of ～10 nm. Large area bilayers with smooth surfaces could be created. In addition, direct spincasting with 1‐chloropentane allows the production of thin PS films (<15 nm) and films of low molecular weight (<5 kDa) PS, all of which would be impossible to produce for this important model system by the traditional water‐transfer method. 1‐chloropentane was confirmed to be a sufficiently selective solvent for PS by measuring the Flory–Huggins χ parameters of 1‐chloropentane with PS and PMMA, respectively, with inverse gas chromatography. In the search for a suitable selective solvent, the authors have also examined the role of vapor pressure in spin casting smooth films over a wider molecular weight (4.3–190 kDa) and thickness range (～5–500 nm) than previously reported. Only solvents with low vapor pressure produced high quality PS films. Methylcyclohexene can also be used to produce excellent, directly cast PS/PMMA bilayers, but with a smaller molecular weight and thickness window compared with 1‐chloropentane. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3234–3244, 2006     

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     

Network structure and swelling behavior of poly(acrylamide/crotonic acid) hydrogels in aqueous salt solutions

Hydrogels with various ionic group contents were prepared from acrylamide and crotonic acid (CrA) monomers with 0–12.9 mol % CrA in aqueous solutions by radiation‐induced polymerization and gelation with γ rays from a ⁶⁰Co source. The volume swelling ratio of the poly(acrylamide/crotonic acid) hydrogels was investigated as a function of the pH and ionic strength of the swelling medium and the type of counterion in the swelling medium. The volume swelling ratio increased with an increase in pH and a decrease in the ionic strength. The volume swelling ratio of these hydrogels was evaluated with an equation, based on the Flory–Huggins thermodynamic theory, the James–Guth phantom network theory, and the Donnan theory of swelling of weakly charged ionic gels, that was modified here for the determination of the molecular weight between crosslinks (M_c) and the polymer–solvent interaction parameter (χ). The modified equation described very well the swelling behavior of the charged polymeric network. The same equation also provided the simultaneous measurement of these parameters for the systems investigated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1656–1664, 2003     

Synthesis and characterization of ferrocene containing block copolymers

Narrowly dispersed diblock copolymers containing poly(methyl methacrylate) [PMMA] or poly(nonafluorohexyl methacrylate) [PF9MA] as the first block and poly(ferrocenylmethyl methacrylate) [PFMMA] as the second block, were prepared by anionic polymerization for the first time. Disordered bulk morphologies in the case of PMMA‐b‐PFMMA were observed and explained in terms of low Flory–Huggins interaction parameter (χ ≤ 0.04). In the case of PF9MA‐b‐PFMMA hexagonally packed cylinder morphology (HEX) was substantiated from TEM and SAXS observations. Furthermore, high incompatibility between PF9MA and PFMMA blocks allowed for the formation of well‐ordered ferrocene containing cylinders on silica substrate upon exposure of the thin films to a saturated solvent vapor. It was shown that the cylinder orientation, parallel or perpendicular to the surface, could easily be controlled by appropriate choice of the solvent and without the need for preliminary surface modification, for example by means of grafted brush layer. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 495–503     

Plasticized microporous poly(vinylidene fluoride) separators for lithium‐ion batteries. I. Swelling behavior of dense membranes with respect to a liquid electrolyte—Characterization of the swelling equilibrium

Some poly(vinylidene fluoride) (PVdF) microporous separators for lithium‐ion batteries, used in liquid organic electrolytes based on a mixture of carbonate solvents and lithium salt LiPF₆, were characterized by the study of the swelling phenomena on dense PVdF membranes. We were interested in the evolution of the swelling ratios with respect to different parameters, such as the temperature, swelling solution composition, and salt concentration. To understand PVdF behavior in microporous membranes and, therefore, to have a means of predicting its behavior with different solvent mixtures, we correlated the swelling ratios in pure solvents and in solvent mixtures to the solvent–polymer interaction parameters and solvent–solvent interaction parameters. We attempted a parametric identification of swelling curves with a very simple Flory–Huggins model with relative success. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 532–543, 2004     

Branched versus linear oligo(dimethylsiloxane): Differences in their thermodynamic interaction with solvents

The thermodynamic behavior of linear and of branched oligo(dimethylsiloxane) (O‐DMS) solutions was studied by means of vapor pressure measurements and vapor pressure osmometry at different temperatures for the thermodynamically favorable solvent THF. The branched material required for that purpose was synthesized and afterwards fractionated by means of the single solvent acetone to eliminate components of low degrees of branching. The Flory‐Huggins interaction parameters, χ, for the systems THF/O‐DMS as a function of composition pass a minimum at all temperatures (25, 40, and 60 °C) in the case of the branched material. For the unbranched oligomer such a minimum is only observed at 60 °C. At 40 °C the results are ambigous whereas the dependence is definitely linear at 25 °C. This exceptional behavior of the linear product at the latter temperature is tentatively attributed to the formation of favorable orientational order in the pure state under these conditions. At high oligomer concentrations THF interacts more favorably with the branched material, however, this preference is reversed upon dilution. All measured composition dependencies of χ can be modeled quantitatively by an approach accounting for chain connectivity and for the ability of the oligomers to change their conformation upon dilution. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1309–1318, 2010     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

Solubility and partial molar volume of carbon dioxide and ethane in crosslinked poly(ethylene oxide) copolymer

Experimental solubility and sorptive dilation data are reported for carbon dioxide and ethane in a crosslinked poly(ethylene oxide) (XLPEO) rubbery copolymer. Five different temperatures (253 ≤ T(K) ≤ 308) were considered, with a maximum gas pressure of 2.09 MPa (20.6 atm). The polymer was prepared by photopolymerization of a solution containing 70 wt % poly(ethylene glycol) methyl ether acrylate (PEGMEA) and 30 wt % poly(ethylene glycol) diacrylate (PEGDA). Sorption isotherms were described by the Flory‐Huggins model. For each gas, the Flory‐Huggins interaction parameter was a decreasing function of temperature and did not show a composition dependence. Dilation and sorption data were combined to calculate the partial molar volume (PMV) of the gases in the polymer, which was an increasing function of temperature. Based on a comparison with literature data for a XLPEO homopolymer prepared from pure PEGDA over the same range of operating conditions, an effect of the network composition on both gas solubility and PMV was found. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 456–468, 2010     

Tailoring poly(vinylidene fluoride‐co‐chlorotrifluoroethylene) microstructure and physicochemical properties by exploring its binary phase diagram with dimethylformamide

Poly(vinylidene fluoride‐co‐chlorotrifluoroethylene) (PVDF‐CTFE) membranes were prepared by solvent casting from dimethylformamide (DMF). The preparation conditions involved a systematic variation of polymer/solvent ratio and solvent evaporation temperature. The microstructural variations of the PVDF‐CTFE membranes depend on the different regions of the PVDF‐CTFE/DMF phase diagram, explained by the Flory‐Huggins theory. The effect of the polymer/solvent ratio and solvent evaporation temperature on the morphology, degree of porosity, β phase content, degree of crystallinity, mechanical, dielectric, and piezoelectric properties of the PVDF‐CTFE polymer were evaluated. In this binary system, the porous microstructure is attributed to a spinodal decomposition of the liquid‐liquid phase separation. For a given polymer/solvent ratio, 20 wt % , and higher evaporation solvent temperature, the β phase content is around 82% and the piezoelectric coefficient, d₃₃, is ? 4 pC/N © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 761–773     

Inverse gas chromatographic characterization of triblock copolymer of polystyrene–poly(ethylene oxide)–polystyrene

The thermodynamic properties of triblock copolymer of polystyrene–poly (ethylene oxide)–polystyrene (PS‐b‐PEO‐b‐PS) were investigated by means of inverse gas chromatography (IGC) using 15 different kinds of solvents as the probes. Some thermodynamic parameters, such as specific retention volume, molar heats of sorption, weight fraction activity coefficient, Flory‐Huggins interaction parameter, partial molar heats of mixing and solubility parameter were obtained to judge the interactions between PS‐b‐PEO‐b‐PS polymers and solvents and the solubility of the polymers in these solvents. It was found that increasing PEO content in PS‐b‐PEO‐b‐PS resulted in the increase in the solubility of PS‐b‐PEO‐b‐PS in alkanes and acetates solvents, but the solubility in alcohols had no change, and more PEO content in polymer caused a small decrease in the solubility parameter of PS‐b‐PEO‐b‐PS polymer, © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2015–2022, 2007     

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     

Intramolecular screening effects in nondilute polymer solutions: An equation‐of‐state approach

In a previous article, we presented a simple modification of the traditional Flory–Huggins theory that took intramolecular screening effects (or same chain contacts) into account. In this article, we present a natural extension of that work, in which free‐volume effects are also explained with an equation‐of‐state model. The predictions of the interaction parameter, χ, for several polymer–solvent systems are presented, over the entire concentration range, in θ solvents and good solvents. A geometric mean assumption is applied to the calculation of an exchange energy interaction term. The predictions of χ are successful to various degrees when internal pressures are used, whereas the use of solubility parameters in most cases produces fairly good agreement with experimental results. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2911–2922, 2003     

Group contribution method for the swelling behavior of thermo‐responsive hydrogels

A group contribution method is introduced to describe the swelling behavior of thermo‐sensitive hydrogel systems. The accuracy of group contribution calculations is strongly dependent on the choice of thermodynamic model. Therefore, we revise the modified double lattice (MDL) model and develop a new expression for the interaction energy parameter using the association theory of Sanchez to take into account complex polymer/solvent mixing. The net Helmholtz energy for a hydrogel is established by combining the revised MDL model and modified Flory–Rehner elastic model. Group parameters are generated by fitting to experimental swelling data from both homopolymer and copolymer gel systems. The effect of salt on the volume phase transition is modeled by introducing an additional salt‐specific parameter to investigate various stimuli‐response swelling behavior. Calculated swelling equilibria using the new group contribution method shows excellent agreement with experimental data and various stimuli‐response volume phase transitions. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 455–463     

Thermal behavior and network structure of poly(N‐vinyl‐2‐pyrrolidone‐crotonic acid) hydrogels prepared by radiation‐induced polymerization

Poly(N‐vinyl‐2‐pyrrolidone‐crotonic acid) [P(VP/CrA)] hydrogels were prepared by irradiating the ternary mixture of VP/CrA and crosslinking agent ethylene glycol dimethacrylate (EGDMA) in water by γ rays at ambient temperature. Differential scanning calorimetry and thermogravimetric analysis were performed to evaluate the thermal properties of ionized networks and to establish if they showed thermal differences that could be related to the CrA content in the gel system. The volume swelling ratio of P(VP/CrA) hydrogels were investigated as a function of the pH in the immersing solution. The volume swelling ratio of these hydrogels increased with an increase in pH and a decrease CrA content in the hydrogel. The volume swelling ratio of the hydrogels was also evaluated using an equation, based on the Flory—Huggins thermodynamic theory, the phantom network theory of James–Guth and Donnan theory of swelling of weakly charged ionic gels for determination of the molecular weight between crosslinks and the polymer–solvent interaction parameter (χ). Copyright © 2004 John Wiley & Sons, Ltd.     

Thermodynamics of solutions of cyclic polymethylene ester oligomers in p‐dioxane and chloroform

Differential vapor pressures were measured for mixtures of two cyclic polymethylene ester oligomers in p‐dioxane and chloroform at 25, 30, 35, and 40 °C at five different concentrations ranging from 1 to 20 wt %. The Flory–Huggins interaction parameter (χ) as well as Leonard's interaction parameter (χ′) for flexible and semiflexible rings were calculated and compared to one another. A new method for the estimation of the number of segments of a cyclic polymer is proposed that allows Leonard's equations to be applied correctly to a particular cyclic compound. Consistent differences between χ and χ′ were observed for all studied mixtures, and the differences became smaller if the cyclic oligomers were considered semiflexible. Interestingly, the enthalpic parameter (κ) deduced from values of χ and χ′ did not differ within their uncertainties. This supports the prediction that mixing cyclic polymer compared to its linear counterpart is mainly due to a molecular configurational entropy difference and that this difference should become less pronounced as the cyclic compound becomes larger. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 443–455, 2000     

Amphiphilic polymer brush in a mixture of incompatible liquids

An analogue of the Alexander‐DeGennes box model is used for theoretical investigation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory‐Huggins parameter χ_AB = 3.5). Thermodynamics of a polymer in the solvents A and B are described by parameters χ_B < χ_A ≤ 1/2. The equilibrium behavior of a brush is investigated in dependence on solvent composition, grafting density, polymer‐solvents and solvent‐solvent interactions. The possibility of a phase transition related with a strong preferential solvation of a brush by a minor solvent component with higher affinity to polymer is shown and examined. Microphase segregation inside a brush is also demonstrated despite overestimating of the brush homogeneity given by the box model. A further simplification of the model permits to obtain scaling formulas and to investigate main regularities in the brush behavior. This offers a clear physical picture of the phase segregation inside a brush in correlation with the phase state of a bulk solvent.