Quantifying phase behavior in partially miscible polystyrene/poly(styrene‐co‐4‐bromostyrene) blends

The phase behavior of thin‐film blends of polystyrene (PS) and the random copolymer poly(styrene‐co‐4‐bromostyrene) (PBS) was studied with atomic force microscopy (AFM) and small‐angle X‐ray scattering (SAXS). Phase behavior was studied as a function of the PBS and PS degree of polymerization (N), degree of miscibility [controlled via the volume fraction of bromine in the copolymer (f)], and annealing conditions. The Flory–Huggins interaction parameter χ was measured directly from SAXS as a function of temperature and scaled with f as χ = f²χ_S–BrS [where χ_S–BrS represents the segmental interaction between PS and the homopolymer poly(4‐bromostyrene)] Simulations based on the Flory–Huggins theory and χ measured from SAXS were used to predict phase diagrams for all the systems studied. The PBS/PS system exhibited upper critical solution temperature behavior. The AFM studies showed that increasing f in PBS led to progressively different morphologies, from flat topography (i.e., one phase) to interconnected structures or islands. In the two‐phase region, the morphology was a strong function of N (due to changes in mobility). A comparison of the estimated PBS volume fractions from the AFM images with the PBS bulk volume fraction in the blend suggested the encapsulation of PBS in PS, supporting the work of previous researchers. Excellent agreement between the phase diagram predictions (based on χ measured by SAXS) and the AFM images was observed. These studies were also consistent with interdiffusion measurements of PBS/PS interfaces (with Rutherford backscattering spectroscopy), which indicated that the interdiffusion coefficient decreased with increasing χ in the one‐phase region and dropped to zero deep inside the two‐phase region. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 255–271, 2002     

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     

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     

Miscibility‐property correlations in blends of glassy amorphous polymers

Blends were prepared from seven polymers in various combinations in the entire composition range. The Flory‐Huggins interaction parameter (χ₁₂) was used for the quantitative estimation of miscibility. The determination of χ₁₂ was attempted by several experimental techniques including the measurement of transparency, glass transition temperature, solvent diffusion and mechanical properties. The relatively simple methods used for the estimation of miscibility work surprisingly well. Solvent absorption can be determined easily for practically all blends, thus the method offers a quantitative measure of component interaction if the solvent is selected properly. After appropriate data reduction, the composition dependence of mechanical properties also supplies a quantitative estimate of compatibility. Although the approach presented in the paper reflects well the general correlation between miscibility and properties, it must be refined and improved in order to obtain a reliable estimate of blend performance.     

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     

Investigation of polymer–solvent interactions in poly(styrene sulfonate) thin films

The swelling behavior of acid form poly(styrene sulfonate) (PSS‐H) thin films were investigated using in situ spectroscopic ellipsometry (SE) to probe the polymer–solvent interactions of ion‐containing polymers under interfacial confinement. The interaction parameter (χ), related to the polymer and solvent solubility parameters in the Flory–Huggins theory, describes the polymer‐solvent compatibility. In situ SE was used to measure the degree of polymer swelling in various solvent vapor environments, to determine χ for the solvent‐PSS‐H system. The calculated solubility parameter of 40–44 MPa^1/2 for PSS‐H was determined through measured χ values in water, methanol, and formamide environments at a solvent vapor activity of 0.95. Flory–Huggins theory was applied to describe the thickness‐dependent swelling of PSS‐H and to quantify the water‐PSS‐H interactions. Confinement had a significant influence on polymer swelling at low water vapor activities expressed as an increased χ between the water and polymer with decreasing film thickness. As the volume fraction of water approached ～0.3, the measured χ value was ～0.65, indicating the water interacted with the polymer in a similar manner, regardless of thicknesses. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1365–1372     

Vapor sorption isotherms for benzene and n-hepatane with poly(styrene-co-butadiene)

Vapor sorption measurements of Flory–Huggins interaction parameters χ for three poly(styrene-co-butadiene) + solvent systems at 25°C are reported. For Philprene 1502 + benzene: χ = 0.379–0.297 v2₂; for Philprene 1502 + n-heptane: χ = 0.595 + 0.030 v₂ for Solprene 1204 + benzene: χ = 0.516–0.026 v₂. The volume for fractions of polymer v₂ range from ca. 0.4 to 0.9.     

Network structure and swelling–shrinking behaviors of pH‐sensitive poly(acrylamide‐co‐itaconic acid) hydrogels

pH‐sensitive poly(acrylamide‐co‐itaconic acid) [P(AAm/IA)] hydrogels were prepared by radiation induced copolymerization of acrylamide (AAm) and itaconic acid (IA) at various ratios. Swelling and shrinking behaviors of these hydrogels were found greatly dependent on the composition of the hydrogel and pH of the buffer solution. The basic structural parameters of the P(AAm/IA) networks such as the molecular weight between crosslinks (M _c) and polymer–solvent interaction parameter (χ) were also determined using the modified Flory‐Rehner equations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2586–2594, 2004     

Morphological behavior of model poly(ethylene‐alt‐propylene)‐b‐polylactide diblock copolymers

A set of well‐defined poly(ethylene‐alt‐propylene)‐b‐polylactide (PEP‐PLA) diblock copolymers containing volume fractions of PLA (f_PLA) ranging between 0.08 and 0.91 were synthesized by a combination of living anionic polymerization, catalytic hydrogenation, and controlled coordination‐insertion ring‐opening polymerization. The morphological behavior of these relatively low‐molecular‐weight PEP‐PLA diblock copolymers was investigated with a combination of rheology, small‐angle X‐ray scattering, and differential scanning calorimetry. The ordered microstructures observed were lamellae (L), hexagonally packed cylinders (C), spheres (S), and gyroid (G), a bicontinous cubic morphology having Ia3 d space group symmetry. The G morphology existed in only a small region between the L‐C morphologies in close proximity to the order–disorder transition (ODT). Transformations from L to G were observed upon heating in several samples. The efficacy of the reverse G to L transition in one sample was cooling rate dependent. The PEP‐PLA Flory–Huggins interaction parameter as a function of temperature χ_PEP‐PLA(T) was estimated from T_ODT's by mean‐field theory and subsequently used in the construction of the experimental PEP‐PLA morphology diagram (χN versus f_PLA). The resultant morphology diagram was symmetric there were the well‐defined L‐C morphology boundaries. The low molecular weight of the materials imparted no significant deviation from previously documented diblock systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2364–2376, 2002     

Swelling behaviors of sub‐micron‐sized copolymer gel particles: The effect of physical crosslinking

The swelling equilibria model of copolymer gel particles is proposed. It accounts for physical crosslinking as a result of hydrogen bonding. The modified Flory–Erman model is used to describe the elastic contribution to swelling. The model considers hydrogen bonding as a physical crosslinker. A free‐energy‐of‐mixing term is represented using the extended Flory–Huggins theory. The interaction parameter χ in the model is a function of both composition and temperature. We then compare the proposed model with the swelling behaviors of copolymer gel particles. Our model offers fairly good agreement with the experimental data for given systems. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1928–1934, 2001     

Thermodynamic characteristics of poly(cyclohexylethylene‐b‐ethylene‐co‐ethylethylene) block copolymers

A series of poly(cyclohexylethylene‐b‐ethylene‐co‐ethylethylene) (C‐E/E_E) diblock copolymers containing approximately 50% by volume glassy C blocks and varying fraction (x) of E_E repeat units, 0.07 ≤ x ≤ 0.90, was synthesized by anionic polymerization and catalytic hydrogenation. The effects of ethyl branch content on the melt state segment–segment (χ) interaction parameter and soft (E/E_E) block crystallinity were studied. The percent crystallinity ranged from approximately 30% at x = 0.07 to 0% at about x ≥ 0.30, while the melting temperature changed from 101 °C at x = 0.07 to 44 °C at x = 0.28. Dynamic mechanical spectroscopy was employed to determine the order–disorder transition (ODT) temperatures, from which χ was calculated assuming the mean‐field prediction (χN_n)_ODT = 10.5. Previously published results for the temperature dependent binary interaction parameters for C‐E (x = 0.07), C‐E_E (x = 0.90), and E‐E_E (x = 0.07 and x = 0.90) fail to account for the quantitative x dependence of χ, based on a simple binary interaction model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 566–574, 2010     

Theoretical Calculation of Flory‐Huggins and Scattering Interaction Parameters by Means of the Lattice Fluid Theory for PVME/PSD Blends

By fitting the spinodals of poly(vinyl methyl ether)/deuterated polystyrene (PVME/PSD) systems, the adjustable parameters ε*₁₂ and δε* in the Sanchez‐Balasz lattice fluid (SBLF) theory could be determined for different molecular weights. According to these parameters, Flory‐Huggins and scattering interaction parameters were calculated for PVME/PSD with different molecular weights by means of the SBLF theory. From our calculation, Flory‐Huggins and scattering interaction parameters are both linearly dependent on the reciprocal of the temperature, and almost linearly on the concentration of PSD. Compared with the scattering interaction parameters, the Flory‐Huggins interaction parameters decreased more slowly with an increase in the concentration for all three series of blends.     

Improved self‐assembly of poly(dimethylsiloxane‐b‐ethylene oxide) using a hydrogen‐bonding additive

Block copolymers with increased Flory–Huggins interaction parameters (χ) play an essential role in the production of sub‐10 nm nanopatterns in the growing field of directed self‐assembly for next generation lithographic applications. A library of PDMS‐b‐PEO block copolymers were synthesized by click chemistry and their interaction parameters (χ) determined. The highest χ measured in our samples was 0.21 at 150 °C, which resulted in phase‐separated domains with periods as small as 7.9 nm, suggesting that PDMS‐b‐PEO is a prime candidate for sub‐10 nm nanopatterning. To suppress PEO crystallization, PDMS‐b‐PEO was blended with (l )‐tartaric acid (LTA) which allows for tuning of the self‐assembled morphologies. Additionally, it was observed that the order‐disorder transition temperature (T_ODT) of PDMS‐b‐PEO increased dramatically as the amount of LTA in the blend increased, allowing for further control over self‐assembly. To understand the mechanism of this phenomenon, we present a novel field‐based supramolecular model, which describes the formation of copolymer‐additive complexes by reversible hydrogen bonding. The mean‐field phase separation behavior of the model was calculated using the random phase approximation (RPA). The RPA analysis reproduces behavior consistent with an increase of the effective χ in the PDMS‐b‐(PEO/LTA suprablock). © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2200–2208     

Organizing thermodynamic data obtained from multicomponent polymer electrolytes: Salt‐containing polymer blends and block copolymers

The objective of this review is to organize literature data on the thermodynamic properties of salt‐containing polystyrene/poly(ethylene oxide) (PS/PEO) blends and polystyrene‐b‐poly(ethylene oxide) (SEO) diblock copolymers. These systems are of interest due to their potential to serve as electrolytes in all‐solid rechargeable lithium batteries. Mean‐field theories, developed for pure polymer blends and block copolymers, are used to describe phenomenon seen in salt‐containing systems. An effective Flory–Huggins interaction parameter, χ_eff , that increases linearly with salt concentration is used to describe the effect of salt addition for both blends and block copolymers. Segregation strength, χ_effN , where N is the chain length of the homopolymers or block copolymers, is used to map phase behavior of salty systems as a function of composition. Domain spacing of salt‐containing block copolymers is normalized to account for the effect of copolymer composition using an expression obtained in the weak segregation limit. The phase behavior of salty blends, salty block copolymers, and domain spacings of the latter systems, are presented as a function of chain length, composition and salt concentration on universal plots. While the proposed framework has limitations, the universal plots should serve as a starting point for organizing data from other salt‐containing polymer mixtures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1177–1187     

Thermo‐ and pH‐induced phase transitions and network parameters of poly(N‐isopropylacrylamide‐ co‐2‐acrylamido‐2‐methyl‐propanosulfonic acid) hydrogels

Dual temperature‐ and pH‐sensitive hydrogels composed of N‐isopropylacrylamide (NIPAM) and 2‐acrylamido‐2‐methyl‐propanosulfonic acid (AMPS) were prepared by free‐radical crosslinking copolymerization in aqueous solution at 22 °C. The mole percent of AMPS in the comonomer feed was varied between 0.0 and 7.5, while the crosslinker ratio was fixed at 5.0/100. The effect of AMPS content on thermo‐ and pH‐ induced phase transitions as well as equilibrium swelling/deswelling, interior morphology and network structure was investigated. The volume phase transition temperature (VPT‐T) was determined by both swelling/deswelling measurements and differential scanning calorimetry (DSC) technique. In addition, the volume phase transition pH (VPT‐pH) was detected from the derivative of the curves of the swelling ratio (dQ_v/dpH) versus pH. The polymer‐solvent interaction parameter (χ) and the average molecular mass between crosslinks ( ) of hydrogels were calculated from swelling ratios in buffer solutions at various pHs. The enthalpy (ΔH) and entropy (ΔS) changes appearing in the χ parameter of hydrogels were also determined by using the modified Flory–Rehner equation. The negative values for ΔH and ΔS indicated that the hydrogels had a negative temperature‐sensitive property in water, that is, swelling at a lower temperature and shrinking at a higher temperature. It was observed that the experimental swelling data of hydrogels at different temperature agreed with the modified Flory‐Rehner approach based on the affine network model. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1713–1724, 2008     

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

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

Synthesis and self‐assembly of highly incompatible polybutadiene–poly(hexafluoropropylene oxide) diblock copolymers

A versatile coupling reaction for the preparation of polybutadiene–poly‐(hexafluoropropylene oxide) (BF) diblock copolymers is described. Six diblock copolymers with different block lengths were characterized by nuclear magnetic resonance spectroscopy and size exclusion chromatography; all six had total molecular weights below 15,000. Microphase separation of the block copolymers in the bulk state was established by small‐angle X‐ray scattering (SAXS) and differential scanning calorimetry. SAXS data suggest that the diblocks are characterized by an unusually large Flory‐Huggins interaction parameter, χ, on the order of 10. However, extraction of χ from the order–disorder transition gave large (order 1) but significantly different values, thereby suggesting that these copolymers are too small and too strongly interacting to be described by block copolymer mean‐field theory. Dynamic light scattering was used to analyze dilute solutions of the title block copolymers in four selective organic solvents; the sizes of the micelles formed were solvent dependent. The micellar aggregates were large and nonspherical, and this is also attributed to the high degree of incompatibility between the two immiscible blocks. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3685–3694, 2005     

Phase behavior of the quasiternary system N-methylmorpholine-N-oxide,water, and cellulose

The crystallization and melting behavior of the system N-methylmorpholine-N-oxide (MMNO)–H₂O–cellulose has been studied by differential scanning calorimetry, optical and electron microscopy, and x-ray scattering. The phase diagram of the MMNO–H₂O solvent system is reported up to a water content of 28% w/w. MMNO forms two crystalline hydrates, namely a monohydrate (13,3% w/w H₂O) and a hydrate comprising five molecules of crystal water per two MMNO molecules (28% w/w H₂O), which melts at 78°C and 39°C, respectively. The melting points of the various diluent crystals are strongly depressed in the presence of cellulose. For example, the solvent liquidus curve in the quasibinary system MMNO.1H₂O–cellulose can be described very well using the simple Flory–Huggins expression with an interaction parameter χ = ?3. Finally, the MMNO-rich part of the melting point/composition diagram of the quasiternary MMNO–H₂O–cellulose system is constructed and discussed.     

Theoretical Phase Behavior of Crosslinked Polymers and Liquid Crystals

Equilibrium phase properties of mixtures of crosslinked polymers and nematic liquid crystals (LCs) are investigated. Effects of the volume fraction of polymer at crosslinking φ₀ , the number of monomers between consecutive crosslinks N_c and the Flory‐Huggins interaction parameter χ on these properties are discussed. Two models for the elastic free energy are used to describe the effects of φ₀ Three cases are considered depending upon polymer volume fraction at crosslinking. If crosslinking takes place in the bulk, the elastic free energy is the same and the two models are identical. Otherwise, either φ₀ is constant or equal to φ₂ , the two models may lead to completely different results depending upon crosslinking density. Strong correlations are found between the effects of φ₀ and N_c on the phase behavior of crosslinked polymers and nematic liquid crystal mixtures. These diagrams are also strongly dependent upon the Flory‐Huggins interaction parameter for isotropic mixing χ. This dependence is illustrated through three models for the variation of χ with temperature and composition.     

Multiblock copolymers of styrene and isoprene. II. Microstructure and dilute solution properties

Dilute solution properties of linear (SI)₃ six-block copolymers of styrene and isoprene are compared to those of random, two-block, and three-block copolymers of the same system. All the copolymers were prepared with sec-butyllithium in benzene. The microstructure of the polyisoprene blocks is close to that of homopolyisoprene prepared under the same conditions. In contrast, the random copolymer shows a larger amount of trans-1,4 isoprene units. The intrinsic viscosities of the copolymers in methylisobutyl ketone, a poor solvent for both polystyrene and polyisoprene, and in toluene, a good solvent for both homopolymers, are examined on the basis of the Fox–Flory relation for homopolymers. All the copolymers behave similarly in each solvent. In methylisobutyl ketone, the viscosity results indicate a random coil conformation with a small expansion owing to the extra repulsive interactions between the dissimilar units. In all cases, the heterocontact repulsive interactions are small and can be characterized by an interaction parameter χ_ab close to 0.025. In toluene, the perturbation caused by the heterocontacts becomes negligible and the expansion factor α_η can be predicted from a weighted average of those of the parent homopolymers of the same molecular weight as the copolymer.