Extended Flory-Huggins Theory Research Articles

Ion-imprinted electrospun nanofibers of chitosan/1-butyl-3-methylimidazolium tetrafluoroborate for the dynamic expulsion of thorium (IV) ions from mimicked effluents.

The present study explores the innocuous, biocompatible, and extremely competent molecularly imprinted chitosan/RTIL electrospun nanofibers having average diameter of 30nm for the expulsion of thorium (IV) ions from the mimicked effluent waste. The extended Flory-Huggins theory and three-dimensional molecular modeling have been effectively premeditated via Materials Studio software for enumerating the inter-miscibility and compatibility (Chi parameter (χ)=1.019, mixing energy (Emix)=0.603kcal/mol) of the chitosan/RTIL (1-butyl-3-methylimidazolium tetrafluoroborate). The maximum adsorption efficiency is found to be 90% at a neutral pH of 7, and a temperature of 298K within 120min. The adsorption process was extensively studied by two-parameter adsorption isotherms like Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich (D-R) and three-parameter models like Redlich-Paterson and Sips isotherm. Pseudo-second-order kinetics model (R2=0.982) and Langmuir isotherm (R2=0.994) bestowed the best fitting on chitosan/RTIL nanofibers for the adsorption of Th (IV) ions. The thermodynamic study reveals the spontaneity and exothermic nature of the reaction. The experimental analysis conjoint with isotherm and kinetic models, and simulation study establish the applicability of chitosan/RTIL nanofibers for the expulsion of Th (IV) and other toxic metal ions from the effluents. Graphical abstract Ion-imprinted electrospun nanofiber for expulsion of thorium (IV) ion.

Keratin-Nylon 6 engineered microbeads for adsorption of Th (IV) ions from liquid effluents

The applicability of novel porous microbeads (average diameter of about 2.0mm) of α-keratin engineered with Nylon 6, have been investigated for the adsorption of radioactive and non-biodegradable Th (IV) ions from the effluents. Thorium ion uptake on the intrinsically compatible adsorbent system was investigated using experimental analysis and kinetic studies. The developed system demonstrates maximum adsorption efficiency of 66.26% under ecologically optimal conditions i.e. pH=7, with 1000ppm initial Th (IV) concentration at 303K for 120min. The experimental results reveal that the adsorption kinetics study best fits with the Dubinin–Radushkevich isotherm model (R2=0.993) and Intra-particle diffusion kinetics model (R2=0.995). The kinetic models namely Pseudo-first order, Pseudo-second order, particle diffusion, & Elovich were used for the adsorption study, and were compared and calculated using linear & nonlinear regression methods thermodynamic analysis revealed the spontaneity, viability and exothermic nature of the adsorption process with free energy change (ΔG0) of −11.48kJ/mol. Further, the inter-polymer miscibility and compatibility was explored by atomistic molecular modelling and extended Flory-Huggins theory via Materials Studio software on geometrically minimized repeat units of Cysteine (functional group of α-keratin) and Nylon 6, employing Discover, Amorphous Cell, Forcite and Blends modules, which showed results to be consistent with FT-IR studies, revealing strong hydrogen bonding.

Role of thermodynamic and kinetic interaction of poly(vinylidene fluoride) with various solvents for tuning phase inversion membranes

An extensive study of thermodynamics and kinetics of non‐solvent induced phase separation was carried out for poly(vinylidene fluoride)/solvent/water system for four different solvents. Literature available on semicrystalline polymers was mostly based on experimental cloud points, obtained to a narrow range of polymer concentration (<10 wt%), much less than the working range for membrane preparation (20–25 wt%). Aim of this work was to model the thermodynamic phase diagram using extended Flory–Huggins theory which was used as a tool, along with the kinetic data to obtain tailor‐made membranes with desired morphology and properties. Interaction parameters involving solvent, nonsolvent, and polymer played an important role to tune the porosity of the membrane. Thermodynamic calculation showed solvent N,N‐dimethyl acetamide resulted in the most porous membrane (permeability 5.4 × 10−11 m Pa−1 s−1) followed by N,N‐dimethyl formamide (permeability 4.2 × 10−11 m Pa−1 s−1), N‐methyl pyrrolidone (permeability 3.8 × 10−11 m Pa−1 s−1), and acetone (impermeable to water even at 1380 kPa), which was the densest one. Prepared membranes were characterized in terms of surface morphology, molecular weight cut‐off, tensile strength, pore volume distribution, crystallinity, and surface roughness, which were correlated to inferences based on thermodynamic and kinetic calculations. POLYM. ENG. SCI., 58:1062–1073, 2018. © 2017 Society of Plastics Engineers

Ternary phase diagram and fiber morphology for nonsolvent/DMAc/polyamic acid systems

Theoretical ternary phase diagrams in good agreement with experiment cloud point data of water/N,N-dimethylacetamide (DMAc)/polyamic acid (PAA), ethylene glycol (EG)/DMAc/PAA and ethanol/DMAc/PAA systems were constructed based on the extended Flory–Huggins theory of the polymer solutions. Binary interaction parameters were calculated and optimized accurately to construct the theoretical phase diagrams. The surface and cross-section microstructures of the as-spun fibers were analyzed by the dual diffusion theory and phase separation mechanism based on the ternary diagrams. With the concentration of DMAc in coagulation increasing, sponge-like and less skin–core structures with rougher surface were observed for fibers prepared from water/DMAc/PAA system, as the homogeneous region and metastable two-phase region enlarged in this case and it favors the nucleation and growth demixing mechanism. Further increasing concentration of DMAc in coagulation resulted in the formation of porous structures. On the other aspect, fibers prepared from EG/DMAc/PAA system exhibited a noncircular cross-section and an obvious skin–core structure, while circular cross-section and dense structures were obtained in fibers from ethanol/DMAc/PAA system. The results are in accordance with predicted ones based on theoretical ternary phase diagram.

Morphology Control of Polyimide Fibers by Phase Separation under Different Coagulation Bath Conditions

In order to investigate the effects of the coagulation bath temperature and composition on the formation of polyimide fiber in wet spinning, theoretical ternary phase diagrams of water/NMP/PI system at two coagulation bath temperatures was investigated based on the extended Flory-Huggins theory. The cloud-points data of the system for more dilute PI terpolymer solutions were determined by cloud point titration, and the cloud point data for more concentrated PI terpolymer solutions were calculated by Boom's linearized cloud point curve correlation. The obtained diagrams showed that if the titration process constructed at a higher temperature, the meta-stable two-phase region in the ternary phase diagram increases, which is beneficial for the de-mixing of the filament via nucleation and growth mechanisms, resulting in a homogenous dense structure for PI fiber.

Phase behavior of TPGS–PEG400/1450 systems and their application to liquid formulation: A formulation platform approach

Vitamin E D-alpha-tocopheryl polyethylene glycol succinate (TPGS) and polyethylene glycol are common excipients used in both preclinical and commercial formulations. In this paper, the phase diagrams of TPGS and polyethylene glycol 400 (PEG 400) in the presence of either water or ethanol were constructed. The effect of water and ethanol on the cloud point temperature of TPGS-PEG 400 mixtures was investigated. In general, the cloud point temperature was reduced by the presence of either water or ethanol in the formulation. However, water was more effective in lowering the cloud point temperature than ethanol. Similarly, the phase diagram of TPGS-PEG 1450 was constructed. The cloud point temperature was observed to decrease with increasing TPGS concentration. It was found that TPGS and PEG 1450 could form a single phase when TPGS concentration was above 75%, based on differential scanning calorimetry, and FT-Raman analysis indicated that a vibration at 1330 cm(-1) disappeared in the melted single phase. In addition, a systematic melting point depression was observed for the mixtures of TPGS-PEG 1450. In the presence of Ibuprofen, a model compound, the cloud point temperature was also reduced. Finally, the extended Flory-Huggins theory for polymer solution was used to analyze the entropic and enthalpic contributions of water and ethanol to the free energy of mixing.

Thermodynamic study of non-solvent/dimethyl sulfoxide/polyacrylonitrile ternary systems: effects of the non-solvent species

In order to investigate the effects of the non-solvent species on the formation mechanism of polyacrylonitrile (PAN) fiber in wet spinning, theoretical ternary phase diagrams of water/DMSO/PAN and ethanol/DMSO/PAN systems were constructed based on the extended Flory–Huggins theory. The cloud-points of dilute PAN solutions of the two systems were determined by titration method and those of concentrated PAN solutions from Boom’s linearized cloud-point correlation. Binary interaction parameters were calculated and optimized to construct the theoretical phase diagram. The obtained diagrams were used to investigate the effects of the non-solvent species on the formation of PAN fibers. If the non-solvent water is replaced with ethanol, the meta-stable two-phase region in the ternary phase diagram increases. This favors the de-mixing of the filament via nucleation and growth mechanism during the coagulation process, resulting in homogenous dense PAN fibers with low porosity.

Thermodynamic study of a water–dimethylformamide–polyacrylonitrile ternary system

AbstractExperimental cloud‐point data were obtained by cloud‐point titration. The phase diagram for a ternary system of water–dimethylformamide–polyacrylonitrile was determined by numerical calculation on the basis of the extended Flory–Huggins theory and was found to agree well with the cloud‐point data. To construct the theoretical phase diagram, three binary interaction parameters were obtained with different methods. The ternary phase diagram was used to investigate the mechanism of fiber formation. The skin–core structure and fingerlike pores in polyacrylonitrile fiber may be effectively eliminated if the composition of the spinning solution is properly chosen, and consequently, homogeneous polyacrylonitrile fiber with a bicontinuous structure and good mechanical properties can be obtained through the spinning process. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Theoretical phase diagram calculation and membrane morphology evaluation for water/solvent/polyethersulfone systems

Theoretical ternary phase diagrams with very good agreement with experimental cloud point data were constructed for water/ N, N-dimethylacetamide (DMAc)/polyethersulfone (PES) and water/ N-methyl-2-pyrrolidone (NMP)/polyethersulfone systems. Theoretical phase diagrams were determined based on the extended Flory–Huggins theory of polymer solutions. To construct the theoretical phase diagrams, all binary interaction parameters were determined accurately and thoroughly revisited. Also, the structures of membranes prepared of these systems by phase separation process were investigated. The morphological studies showed that in spite of better miscibility between water and DMAc compared to water and NMP, channel-like structures were observed in membranes prepared of water/NMP/PES systems but tear-like structures with more spongy areas were observed in membranes prepared of water/DMAc/PES system. According to the constructed theoretical ternary phase diagrams of these systems, these unexpected observations were attributed to the higher concentration of polymer in the polymer-rich phase of water/DMAc/PES system, which causes an early vitrification in this system which suppresses the growth of macrovoids.

Effect of temperature on the phase equilibrium of aqueous two-phase systems containing polyvinylpyrrolidone and disodium hydrogen phosphate or trisodium phosphate

Phase diagrams and liquid–liquid equilibrium (LLE) data of the aqueous polyvinylpyrrolidone–disodium hydrogen phosphate and aqueous polyvinylpyrrolidone–trisodium phosphate systems have been determined experimentally at 298.15, 308.15, 318.15 and 328.15 K. The effect of temperature and the type of salt on the binodal and tie-lines has been studied. It was found that, for the studied systems in the polyvinylpyrrolidone (PVP)-rich region, an increase in temperature caused the expansion of one-phase area; while, for the salt-rich region, expansion of the two-phase area was observed with increase in the temperature. It was also observed that the slope of all equilibrium tie-lines increased with increasing temperature. Furthermore, it was found that, as temperature is increased, these aqueous two-phase systems exhibit a phase inversion. Specifically, the PVP-rich phase – which at low temperatures is the less dense top phase – becomes the lower phase at elevated temperatures. Finally, an extended Flory–Huggins theory proposed in our previous paper has been used for correlation of LLE data.

05/00899 Phase behavior applications of SAFT based equations of state — from associating fluids to polydisperse, polar copolymers

A molecular-thermodynamic model is presented to predict volume change transitions in temperature-sensitive polymer gels. The model uses an extended Flory-Huggins theory as a mixing contribution and a new interpolated affine model suggested by Birshtein as an elastic contribution. The Flory χ parameter is given by the product of a temperature-dependent and a composition-dependent term. Our model also differs from those presented previously because the temperature-dependent term is given by the incompressible lattice-gas model by ten Brinke and Karasz that accounts for specific interactions such as hydrogen bonding. Following conventional practice, the van't Hoff equation is introduced to represent the effect of a small number of ionizable segments in the network chain. Calculated swelling-ratio curves for neutral and weakly ionized aqueous N-isopropylacrylamide gels use molecular parameters obtained from phase-equilibrium data for (non-crosslinked) polymer solutions. In agreement with experiment, the calculated volume-transition temperature of the gel is about 1°C higher than the lower critical solution temperature of the (non-crosslinked) polymer solution.

Lattice-model study of the thermodynamic interplay of polymer crystallization and liquid–liquid demixing

We report Monte Carlo simulations of a lattice-polymer model that can account for both polymer crystallization and liquid–liquid demixing in solutions of semiflexible homopolymers. In our model, neighboring polymer segments can have isotropic interactions that affect demixing, and anisotropic interactions that are responsible for freezing. However, our simulations show that the isotropic interactions also have a noticeable effect on the freezing curve, as do the anisotropic interactions on demixing. As the relative strength of the isotropic interactions is reduced, the liquid–liquid demixing transition disappears below the freezing curve. A simple extended Flory–Huggins theory accounts quite well for the phase behavior observed in the simulations.

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

AbstractThe 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

Phase behaviour of nematic liquid crystal/linear polymer systems: Applicability of the extended Flory-Huggins theory

Phase behaviour of nematic liquid crystals (N-(p-ethoxybenzylidene)-p-butylaniline and N-(p-methoxybenzylidene)-p-butylaniline) in linear polystyrene are investigated by thermo-optical analysis. Results are compared to the model based on the extended Flory-Huggins equation. The model used in this work includes two adjustable model parameters (d 0 , d 1 ). The proposed semi-empirical model gives a very good agreement with new data obtained for liquid crystal and polystyrene systems.

Phase behaviors of solid polymer electrolytes: applicability of an extended Debye–Hückel theory

Poly(ethylene oxide) (PEO) with three different salts, ZnCl 2, ZnBr 2 and ZnI 2 has been characterized at various temperatures and compositions by optical microscopy and differential scanning calorimetry. A molecular thermodynamic model based on both an extended Flory–Huggins theory and a Debye–Hückel theory modified by Guggenheim is developed to interpret the liquidus curves in the resulting phase diagram. The proposed model considers not only short-range specific interactions between the salt ions and the polymer or solvating base groups (oxygen in PEO) of the polymer leading to loose complex formation but also long-range electrostatic forces between salt ions. Quantitative description according to the proposed model is in good agreement with experimentally observed transition temperature of a given system including an eutectic point.

Volume phase transition behavior ofN-isopropyl acrylamide-N-cyanomethyl acrylamide copolymer gel particles: The effect of crosslinking density

We prepared submicron-sized N-isopropyl acrylamide (NIPA)–N-cyanomethyl acrylamide (NCMA) copolymer gel particles by precipitation polymerization. Volume phase transition behaviors of gel particles with various compositions and crosslinking density were observed by using photon correlation spectroscopy (PCS). The experimental data showed that both the volume transition temperature and the swelling ratio of copolymer gel particles were varied with the mole ratio of NCMA and NIPA. We compared the swelling behaviors of given systems with the thermodynamic model based on the extended Flory–Huggins theory. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 72: 1091–1099, 1999

Swelling behavior of thermosensitiveN-isopropylacrylamide-ethylN-acryloylglycine submicron-sized copolymer gel particles

Submicron-sized N-isopropylacrylamide (NIPA)–ethyl N-acryloylglycine (ENAG) copolymer gel particles with various compositions were prepared by precipitation polymerization in water. Their swelling behaviors were determined by photon correlation spectroscopy (PCS). Our results showed that the volume transition temperature of copolymer gel particles decreased with increasing the mole ratio of ENAG. In model development, we modified the extended Flory–Huggins theory as a free energy of mixing term and employed the modified Flory–Rehner theory for the elastic contribution and compared the proposed model with our swelling data. The model predicted fairly well the swelling behaviors of copolymer gel particles. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 799–806, 1998

Lattice thermodynamics for aqueous salt-polymer two-phase systems

A lattice model is presented to compute salt-induced liquid–liquid phase separation in aqueous polymer solutions. The Gibbs energy of mixing contains an electrostatic contribution given by Pitzer's extension of the Debye–Hückel function, and the extended Flory–Huggins theory that uses empirical functions of temperature and composition as binary interaction parameters. Our Flory–Huggins theory assumes complete dissociation of salt into ions, but it does not distinguish between cation and anion; our theory represents the water–salt–polymer mixture as an incompressible ternary system consisting of water, ion, and polymer. In the extended Flory–Huggins theory, the binary interaction parameter between water and ion, and that between water and polymer, are obtained by correlating the observed activity of water in each of the two relevant binary systems. The electrostatic contribution does not contain adjustable parameters. We show that the electrostatic contribution to the Gibbs energy of mixing is responsible for inducing salt–polymer aqueous two-phase systems. Calculated phase diagrams are compared with experiment for aqueous solutions containing polyethylene glycol and a single salt at room temperature. The efficiency of a salt to form salt–polymer aqueous two-phase systems is discussed in terms of ion valence and the interaction parameter between ion and polymer. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci Inc. J Appl Polym Sci 68: 2007–2017, 1998

Lattice thermodynamics for aqueous salt–polymer two‐phase systems

A lattice model is presented to compute salt-induced liquid–liquid phase separation in aqueous polymer solutions. The Gibbs energy of mixing contains an electrostatic contribution given by Pitzer's extension of the Debye–Hückel function, and the extended Flory–Huggins theory that uses empirical functions of temperature and composition as binary interaction parameters. Our Flory–Huggins theory assumes complete dissociation of salt into ions, but it does not distinguish between cation and anion; our theory represents the water–salt–polymer mixture as an incompressible ternary system consisting of water, ion, and polymer. In the extended Flory–Huggins theory, the binary interaction parameter between water and ion, and that between water and polymer, are obtained by correlating the observed activity of water in each of the two relevant binary systems. The electrostatic contribution does not contain adjustable parameters. We show that the electrostatic contribution to the Gibbs energy of mixing is responsible for inducing salt–polymer aqueous two-phase systems. Calculated phase diagrams are compared with experiment for aqueous solutions containing polyethylene glycol and a single salt at room temperature. The efficiency of a salt to form salt–polymer aqueous two-phase systems is discussed in terms of ion valence and the interaction parameter between ion and polymer. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci Inc. J Appl Polym Sci 68: 2007–2017, 1998

Molecular thermodynamics for volume-change transitions in temperature-sensitive polymer gels

A molecular-thermodynamic model is presented to predict volume change transitions in temperature-sensitive polymer gels. The model uses an extended Flory-Huggins theory as a mixing contribution and a new interpolated affine model suggested by Birshtein as an elastic contribution. The Flory χ parameter is given by the product of a temperature-dependent and a composition-dependent term. Our model also differs from those presented previously because the temperature-dependent term is given by the incompressible lattice-gas model by ten Brinke and Karasz that accounts for specific interactions such as hydrogen bonding. Following conventional practice, the van't Hoff equation is introduced to represent the effect of a small number of ionizable segments in the network chain. Calculated swelling-ratio curves for neutral and weakly ionized aqueous N-isopropylacrylamide gels use molecular parameters obtained from phase-equilibrium data for (non-crosslinked) polymer solutions. In agreement with experiment, the calculated volume-transition temperature of the gel is about 1°C higher than the lower critical solution temperature of the (non-crosslinked) polymer solution.