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     

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.     

The use of Flory–Huggins parameters as a measure of interactions in polymer‐filler systems

Any quantitative information on the strength of interactions between inorganic filler and polymer is substantial for the future application of the composite. The magnitude of adhesion of two phases may be deduced from results collected by various experimental techniques. Polyether‐urethane/modified carbonate‐silicate fillers systems containing different amount of filler (5, 10, and 20 wt %) were the materials investigated. We propose to express the magnitude of modified filler/polymer interactions by Flory–Huggins χ parameter. It may be deduced from the results collected by inverse gas chromatographic (IGC) experiment. We have also tried to explain the influence of the solvent on values of the evaluated parameters and to check the usefulness of some of presented methods to minimize Δχ effect. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1853–1862, 2006     

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     

Predicting the Loading Capability of mPEG‐PDLLA to Hydrophobic Drugs Using Solubility Parameters†

Physical encapsulation of drugs into polymer micelles is a common method of loading hydrophobic drugs. Methoxy polyethylene glycol‐poly(D,L‐lactide) (mPEG‐PDLLA) is one of the most commonly used drug carrier. At present, whether a carrier is suitable for the loading of a certain drug is determined by drug loading experiments. This process costs a lot of time. Therefore, an efficient predicting method to avoid time‐consuming tests is critical. In this study, we prepared mPEG_5k‐PDLLA_5k and used it to load a series of drugs. Three parameters were used to test the miscibility of mPEG_5k‐PDLLA_5k with drugs, including absolute difference in Hildebrand solubility parameters (|Δδ|), Flory–Huggins interaction parameter (χ) and the distance (D value) calculated from the two‐dimensional solubility parameters. We found the two‐dimensional solubility parameters obtained from JB2013 group contribution (GC) method was useful. By comparing the drug loading content (DLC) with the D value, we found that when the D value was less than 5.0 (MJ/m³)^1/2, the miscibility of drug and mPEG_5k‐PDLLA_5k was good and drug loading capability was high; when the D value was more than 8.0 (MJ/m³)^1/2, the drug was barely loaded. Thus, this work provided a rationale to qualitatively predict the loading capability of mPEG_5k‐PDLLA_5k for hydrophobic drugs.     

Diffusion and partition coefficients of small organic solvents in molten miscible polymer blends: Correlations with thermodynamic interactions

The transport properties of small organic molecules in molten poly(vinyl chloride) (PVC)/atactic poly(methyl methacrylate) (PMMA) blends and their homopolymers were studied with inverse gas chromatography. The elution profiles resulting from various organic solvents and different experimental conditions were used for measuring diffusion and partition coefficients. With the van Deemter equation and retention volumes at infinite dilution, diffusion coefficients of 10^?7 to 10^?8 cm²/s and partition coefficients of 10–50 were calculated. The dependence of the diffusion and partition coefficients on experimental variables such as the blend concentration, temperature, and solute nature was examined. The presence of PMMA in PVC blends affected the sorption behavior of the PVC matrix up to a certain concentration. Beyond that, it was hard to derive any composition–diffusivity dependence. On the contrary, the diffusion and partition coefficients were greatly influenced by changes in the temperature and by the nature of the solute. For those solutes (e.g., chlorinated hydrocarbons) showing stronger interactions with polymer blends (higher negative values for the Flory–Huggins interaction parameter χ₁₍₂₃₎), higher diffusion and partition coefficients were obtained. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 267–279, 2004     

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.     

Hydrophilic nanocomposites based on polyurethane/poly(2‐hydroxyethyl methacrylate) semi‐IPNs and modified/unmodified nanosilica for biomedical applications

Nanocomposites based on sequential semi‐interpenetrating polymer network (semi‐IPN) of cross‐linked polyurethane and linear poly(2‐hydroxyethyl methacrylate) with 0.25 and 3 wt % of nanosilica filler were prepared and investigated. The unmodified silica, carboxyl‐modified, and amino‐modified silica were used in an attempt to control the microphase separation of the polymer matrix by polymer–filler interactions. A variety of experimental techniques were used to study morphology, thermal transitions, mechanical properties, and polymer dynamics of the nanocomposites. Special attention was paid to the investigation of the hydration properties of the nanocomposites in the perspective of biomedical applications. The results show that the good hydration properties of the semi‐IPN matrix are preserved in the nanocomposites. Effects of water on polymer dynamics were found to be particularly pronounced for the secondary β_sw,_PHEMA and the β_PU relaxations, in agreement with interpretations in terms of hydrogen bonding interactions with specific groups in the structure of the two polymers. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 397–408     

Swelling of polyacrylamide gels in polyacrylamide solutions

Swelling behavior of polyacrylamide (PAAm) and polyacrylamide-co-polyacrylic acid (PAAm-co-PAAc) gels was investigated in aqueous solutions of monodisperse PAAms with molecular weights (M_w) ranging from 1.5 × 10³ to 5 × 10⁶ g/mol. The volume of the gels decreases as the PAAm concentration in the external solution increases. This decrease becomes more pronounced as the molecular weight of PAAm increases. The classical Flory–Huggins (FH) theory correctly predicts the swelling behavior of nonionic PAAm gels in PAAm solutions. The polymer–polymer interaction parameter χ₂₃ was found to decrease as the molecular weight of PAAm increases. The swelling behavior of PAAm-co-PAAc gels in PAAm solutions deviates from the predictions of the FH theory. This is probably due to the change of the ionization degree of AAc units depending on the polymer concentration in the external solution. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1313–1320, 1998     

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.     

Phase behavior of a water/2‐propanol/poly(methyl methacrylate) cosolvent system

A phase diagram of poly(methyl methacrylate) in mixtures of water and 2‐propanol, individually nonsolvents for the polymer, was studied at 25 °C. For this system, there were two liquid–liquid demixing regions separated by a miscible region. This cosolvent phenomenon was thought to be a joint effect of the nonsolvents. The phase behavior was modeled according to modified Flory–Huggins chemical‐potential equations, which accounted for the possible contribution from a ternary interaction in terms of a lumped parameter, χ₁₂₃. The calculated phase‐equilibrium curves (binodals) agreed well with the measured results. By contrast, if only binary interaction parameters were considered, computations yielded binodals whose compositions departed significantly from the measured data. Using the wet phase inversion method with casting dopes selected on the basis of the phase diagram, we prepared membranes with microporous structures in various coagulation baths. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 747–754, 2000     

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     

Depolarized light scattering from critical polymer blends

Depolarized light scattering of binary polymer blends in disordered state near the demixing critical point is considered both theoretically and experimentally. It is shown that the depolarized scattering in such systems is predominantly due to double scattering processes induced by composition fluctuations. For long enough polymer chains, this scattering is stronger than the contribution from intrinsic anisotropy fluctuations. The general equation for the static and dynamic double scattering function is obtained in terms of the system structure factor. The scattering functions are calculated both analytically and numerically (dynamic part) for polymer blends. We found that the depolarized intensity depends on the polymerization degree N and the relative distance from the critical point τ = 1 – χ*/χ (where χ is the Flory‐Huggins interaction parameter and χ* its critical value) as I_vh ∼︁ N²/τ², which is in good agreement with the experimental data. It is also shown that the dynamic scattering function is decaying non‐exponentially. We calculate the relaxation rate and the non‐exponentiality parameter as functions of the scattering angle and τ. These theoretical predictions are compared with experimental data for three chemically different blends.     

Dissipative Particle Dynamics Study of Interfacial Properties and the Effects of Nonionic Surfactants on Hydrocarbon/Water Microemulsions

The aim of this work was to apply dissipative particle dynamics (DPD) mesoscopic simulations to study the interfacial orientation and the effect of the nonionic surfactant, hexaethylene glycol monododecyl ether (C₁₂E₆), on different (oil (dodecane)/water) microemulsion systems. The Hildebrand-solubility-parameter model and Flory–Huggins/Hansen-solubility-parameter (FH/HSP) model were combined to evaluate the DPD interaction parameter (a_ij) where the solubility parameters (δ_i) as DPD input parameters were preliminary validated by all-atom molecular dynamics (MD) results and experimental data. The interfacial property dependence of dodecane/water/C₁₂E₆ system on the oil/water (o/w) ratio and on the concentration of surfactant and orientation at the interface were investigated. It was found that the surfactant addition reduced the IFT of o/w interfaces and this reduction was more efficient for water-in-oil microemulsions (o/w ≤ 1).     

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     

The thermodynamics of dissolution of low-molecular-mass compounds in polymethyl[2′-(3-trifluoromethyl-2,2,3-trifluorocyclobutyl)ethyl]siloxane studied via inverse gas chromatography

The effect of the 2′-(3-trifluoromethyl-2,2,3-trifluorocyclobutyl)ethyl radical in fluorosiloxane on the thermodynamics of dissolution of various low-molecular-mass compounds in this polymer is studied via inverse gas chromatography. The activity coefficients at infinite dilution, Ω ₁ ^∞ , in the temperature range 20–100°C are determined for C₆–C₈ n-alkanes, cyclohexane, benzene, toluene, tetrachloromethane, trichloromethane, 2-butanone, and ethyl acetate. Flory-Huggins interaction parameters χ ₁₂ ^∞ are calculated. It is shown that hydrocarbons are poor solvents (Ω ₁ ^∞ > 6, χ ₁₂ ^∞ > 0.5) and that the studied fluorosiloxane is not inferior to commercial polymethyl(3,3,3-trifluoropropyl)siloxane with respect to stability in nonpolar liquid media in the range 20–70°C. Trichloromethane (above 50°C) and compounds containing a carbonyl group are found to be good solvents. The dispersion component of the solubility of the polymer, δ ₂, is determined to be 14.0 (J/cm³)^1/2 at 20°C and slightly lower, 13.5 (J/cm³)^1/2, at 100°C. Possible causes of these low values of δ₂ are discussed.     

Thermodynamic study of poly(vinyl chloride)/polyester blends by inverse-phase gas chromatography at 120°C

Polymer/polymer interaction parameters χ′₂₃ have been measured at 120°C as a function of polymer concentration for six different poly(vinyl chloride)/linear aliphatic polyester blends. The technique used is inverse-phase gas chromatography with several molecular probes. The polymers investigated are poly(DL-lactide), poly(ethylene succinate), poly(ethylene adipate), poly(butylene adipate), poly(δ-valerolactone), poly(ε-caprolactone) and poly(hexamethylene sebacate). Probe/polymer interaction parameters χ₁₂ and polymer/polymer interaction parameters χ′₂₃ values are dependent upon the methylene to carbonyl ratio of the polyester, reaching a minimum for a value of 5, this ratio corresponding to poly(ε-caprolactone) blends. Results are interpreted in terms of pairwise interactions between carbonyl, methylene, and [CHCl] groups.     

Evaluation of network parameters and drug release behavior of gum acacia-crosslinked-carbopol hydrogel wound dressings

Present article discusses the synthesis, characterization, biodegradation, network parameter and drug release of gum acacia-crosslinked-carbopol hydrogel wound dressing. Polymers have been characterized by ¹³C solid state nuclear magnetic resonance spectroscopy, elemental analysis, cryo-scanning electron microscopy, atomic force microscopy, thermogravimetric analysis, differential thermal analysis, differential thermogravimetry, and differential scanning calorimetry studies. Network parameters of hydrogel wound dressings such as polymer volume fraction in the swollen state φ, Flory–Huggins interaction parameter χ, molecular weight of the polymer chain between two neighboring cross links M_c, crosslink density ρ and the corresponding mesh size ξ have also been determined. Different in vitro release kinetic models (zero order, first order, Higuchi square root law, Korsmeyer-Peppas, and Hixson-Crowell cube root models) have been applied on the drug release profile. The release of antibiotic drug moxifloxacin from the drug loaded hydrogel matrix occurred through non-Fickian diffusion mechanism and release profile best fitted in the Korsmeyer-Peppas model. Semi-contact mode atomic force microscopic imaging showed that rough surface with root mean square roughness 82.868 nm of the polymer films.