Ternary Polymer Solutions Research Articles

Diffusion mediated thermally induced phase separation for preparing poly(vinylidene fluoride) membranes with enhanced separation performances

Thermally induced phase separation (TIPS) process is an appealing method for preparing poly(vinylidene fluoride) (PVDF) membranes for separation. In this work, we developed a diffusion mediated thermally induced phase separation (d-TIPS) to prepare PVDF membranes with great molecules separation performances. We investigated the thermodynamics of ternary polymer solutions including PVDF, caprolactam (CPL), and Polyethylene glycol (PEG). We controlled liquid–liquid phase separation and the CPL diffusion by adjusting the addition of PEG and molecular weight to modulate the evolution of morphology from spherulitic to bicontinuous structure. The resulting membrane was characterized by morphology, surface chemistry, tensile strength, water contact angle, and perm-selectivity. The membrane was further stretched for enhanced strength, permeance, and rejection. This work provides a fundamental understanding of the diffusion mediated thermally induced phase separation and shows the great potential of PVDF membranes in macromolecules separation.

Coarsening dynamics of ternary polymer solutions with mobility and viscosity contrasts.

Using phase-field simulations, we investigate the bulk coarsening dynamics of ternary polymer solutions undergoing a glass transition for two models of phase separation: diffusion only and with hydrodynamics. The glass transition is incorporated in both models by imposing mobility and viscosity contrasts between the polymer-rich and polymer-poor phases of the evolving microstructure. For microstructures composed of polymer-poor clusters in a polymer-rich matrix, the mobility and viscosity contrasts significantly hinder coarsening, effectively leading to structural arrest. For microstructures composed of polymer-rich clusters in a polymer-poor matrix, the mobility and viscosity contrasts do not impede domain growth; rather, they change the transient concentration of the polymer-rich phase, altering the shape of the discrete domains. This effect introduces several complexities to the coarsening process, including percolation inversion of the polymer-rich and polymer-poor phases-a phenomenon normally attributed to viscoelastic phase separation.

Time–Concentration Superposition for Linear Viscoelasticity of Polymer Solutions

The concentration dependence of linear viscoelastic properties of polymer solutions is a well-studied topic in polymer physics. Dynamic scaling theories allow qualitative predictions of polymer solution rheology, but quantitative predictions are still limited to model polymers. Meanwhile, the scaling properties of non-model polymer solutions must be determined experimentally. In present paper, the time-concentration superposition (TCS) of experimental data is shown to be a robust procedure for studying the concentration scaling properties of binary and ternary polymer solutions. TCS can not only identify whether power law scaling may exist or not, and over which concentration range, but also unambiguously estimate the concentration scaling exponents of linear viscoelastic properties for a range of non-model polymer solutions.

Phase behavior of π-conjugated polymer and non-fullerene acceptor (PTB7-Th:ITIC) solutions and blends

Phase diagrams of ternary π-bonded polymer (PTB7-Th) solutions were constructed as a function of molecular weight, temperature, and electron acceptor species (ITIC, PC61BM and PC71BM). For this purpose, the Flory–Huggins lattice theory was employed with a constant χ interaction parameter, describing a binodal, spinodal, tie line, and critical point. Then, the morphologies of the blends composed of highly disordered PTB7-Th and crystallizable ITIC were investigated by atomic force microscopy. Subsequently, the surface polarities of the PTB7-Th:ITIC thin films were examined by water contact-angle goniometer, exhibiting a transition at the composition of ~ 60 ± 10 wt.% ITIC. Furthermore, X-ray diffraction indicated the presence of ITIC’s crystallites at ≥ 70 wt.% ITIC. Hence, the PTB7-Th:ITIC system was observed to undergo a phase transition at ~ 60–70 wt.% ITIC.

Surface tension of binary and ternary polymer solutions: Experimental data of poly(vinyl acetate), poly(vinyl alcohol) and polyethylene glycol solutions and mixing rule evaluation over the entire concentration range

In order to assess the driving forces of Marangoni instabilities in drying polymer solution films, surface tension data over a wide concentration are necessary. While experimental data and mixing rule equations for the surface tension of liquid-liquid mixtures are readily available, data for polymer solutions are scarce. The aim of this work is to report surface tension data of methanol-toluene-poly(vinyl acetate), methanol-water-polyethylene glycol and water-poly(vinyl alcohol) solutions as well as to evaluate the applicability of available liquid-liquid mixing rule equations on polymer solutions despite an inevitable data gap at low solvent concentrations due to viscosity increase and solidification. The fit quality was assessed by calculating the averaged deviation as well as by manually checking for implausible curve shapes in the respective concentration data gaps. Several available but slightly modified equations are well equipped to describe the concentration and temperature dependent surface tension of the material systems under investigation. Recommendations are given for binary and ternary solutions.

Thermoreversible Gelation with Two-Component Mixed Cross-Link Junctions of Variable Multiplicity in Ternary Polymer Solutions.

Theoretical scheme is developed to study thermoreversible gelation interfering with liquid–liquid phase separation in mixtures of reactive f-functional molecules R{A} and g-functional ones R{B} dissolved in a common solvent. Formed polymer networks are assumed to include multiple cross-link junctions containing arbitrary numbers and of functional groups A and B of each species. Sol-gel transition lines and spinodal lines are drawn on the ternary phase plane for some important models of multiple cross-link junctions with specified microscopic structure. It is shown that, if the cross-link structure satisfies a certain simple condition, there appears a special molar ratio of the two functional groups at which gelation takes place with a lowest concentration of the solute molecules, as has been often observed in the experiments. This optimal gelation concentration depends on f and g (functionality) of the solute molecules and the numbers and (multiplicity) of the functional groups in a cross-link junction. For cross-links which allow variable multiplicity, special attention is paid on the perfectly immiscible cross-links leading to interpenetrating polymer networks, and also on perfectly miscible cross-links leading to reentrant sol-gel-sol transition. Results are compared with recent observations on ion-binding polymer solutions, polymer solutions forming recognizable biomolecular complexes, polymer/surfactant mixtures, hydrogen-bonding polymers, and hydrophobically-modified amphiphilic water-soluble polymers.

Phase-Field Modeling of Multiple Emulsions Via Spinodal Decomposition.

Currently, multiple emulsions via liquid-liquid phase separation in ternary polymer solutions have sparked considerable interest because of its remarkable potential in physical, medical, and biological applications. The transient "onion-like" multilayers are highly dependent on the evolution kinetics, which is challenging to be scrutinized in experiments and has not yet been fully understood. Here, we report a thermodynamically consistent multicomponent Cahn-Hilliard model to investigate the kinetics of multiple emulsions by tracing the temporal evolution of the local compositions inside the emulsion droplets. We reveal that the mechanism governing the kinetics is attributed to the competition between surface energy minimization and phase separation. Based on this concept, a generalized morphology diagram for different emulsion patterns is achieved, showing a good accordance with previous experiments. Moreover, combining the analysis for the kinetics and the morphology diagram, we predict new emulsion structures that provide general guidelines to discovery, design, and manipulation of complex multiphase emulsions.

Phase Diagrams of Ternary π-Conjugated Polymer Solutions for Organic Photovoltaics.

Phase diagrams of ternary conjugated polymer solutions were constructed based on Flory-Huggins lattice theory with a constant interaction parameter. For this purpose, the poly(3-hexylthiophene-2,5-diyl) (P3HT) solution as a model system was investigated as a function of temperature, molecular weight (or chain length), solvent species, processing additives, and electron-accepting small molecules. Then, other high-performance conjugated polymers such as PTB7 and PffBT4T-2OD were also studied in the same vein of demixing processes. Herein, the liquid-liquid phase transition is processed through the nucleation and growth of the metastable phase or the spontaneous spinodal decomposition of the unstable phase. Resultantly, the versatile binodal, spinodal, tie line, and critical point were calculated depending on the Flory-Huggins interaction parameter as well as the relative molar volume of each component. These findings may pave the way to rationally understand the phase behavior of solvent-polymer-fullerene (or nonfullerene) systems at the interface of organic photovoltaics and molecular thermodynamics.

Viscoelastic phase separation model for ternary polymer solutions.

When a polymer solution undergoes viscoelastic phase separation, the polymer-rich phase forms a network-like structure even if it is a minor phase. This unique feature is induced by polymer dynamics, which are constrained by the temporal entanglement of polymer chains. The fundamental mechanisms of viscoelastic phase separation have already been elucidated by theory and experiments over the past few decades; however, it is not yet well understood how viscoelastic phase separation occurs in multicomponent polymer solutions. Here, we construct a new viscoelastic phase separation model for ternary polymer solutions that consist of a polymer, solvent, and nonsolvent. Our simulation results reveal that a network-like structure is formed in the ternary bulk system through a phase separation mechanism similar to that observed in binary polymer solutions. A difference in dynamics is also found in that the solvent, whose affinity to the polymer is similar to that of the nonsolvent, moves freely between the polymer-rich and water-rich phases during phase separation. These findings are considered important for understanding the phase separation mechanism of ternary mixtures often used in the manufacture of polymeric separation membranes.

Structure and dynamics of aqueous solutions containing poly-(acrylic acid) and non-ionic surfactant pentaethylene glycol n-octyl ether (C8E5): A molecular simulations study

Self-assembly of non-ionic surfactant pentaethylene glycol n-octyl ether (C8E5) in aqueous solution containing anionic polyelectrolyte poly (acrylic acid) PAA was investigated via atomistic molecular dynamics (MD) simulations. The concentration of surfactant (Cs) varied in the range (Cs = 9.6 × 10−4–0.3 M) of dilute to concentrated systems while polymer concentration was in dilute solution condition (i.e. Cp = 0.01 M). Binary and ternary systems show formation of nearly spherical micellar aggregate at low Cs and lamellar aggregates at high Cs. Strong interaction between PAA and C8E5 is observed at low Cs, in agreement with experimental data. PAA chain adsorbs onto the micellar aggregate and wraps around the aggregate. For lamellar phase aggregates PAA chain shows polar interactions with hydrophilic moieties of surfactant, originating from interactions between COOH groups of PAA and CO groups of C8E5. The concentration at which free-micelles form in ternary (polymer, surfactant and water) solution is greater than CMC of the binary surfactant-water system, in qualitative agreement with experimental data. At low Cs the interaction between surfactants and polymer chain is weak and does not perturb chain conformations. The radius-of-gyration Rg of PAA increases with Cs. Interaction of surfactant molecules with water is more cooperative at higher values of surfactant concentration, as evident from the values of solvation enthalpy. Significant hydrogen bonds were observed to occur between polar oxygens and hydroxyl oxygen (O2HA) of PAA. The number of h-bonds between polar oxygens and O2HA of PAA increase with Cs. Hydrogen bonds of PAA with surfactant molecules increases with Cs as the polymer expands at high Cs. Formation of surfactant aggregate is enthalpically favored across the entire range of concentration in binary and ternary solution. Binding of PAA to surfactant aggregate is favorable at higher surfactant concentration. The enthalpy of formation of ternary solution exhibits a transition from unfavorable to favorable which interestingly is driven by the structural transition from spherical micellar to the lamellar phase. This signature for this transition is also seen by conformation change of PAA upon binding to surfactant aggregate.

Equation of state modeling and force field-based molecular dynamics simulations of supercritical polyethylene + hexane + ethylene systems

The understanding of polymer solution thermodynamics and characterization of pressure effects on fundamental polymer physics of macromolecular systems is significant in the manufacturing of polyolefins. Consequently, numerous experimental and theoretical efforts have been made towards understanding phase behavior of polymer solutions at elevated pressures. Despite this progress, only limited efforts are directed towards understanding the underlying phenomena behind the influence of high pressure upon the thermophysical properties of ternary polymer solutions at a molecular level. The present paper, therefore, reports on the influence of supercritical ethylene on the density of PE + hydrocarbon solvent system by exploring ternary mixtures of PE + hexane + ethylene for ethylene concentrations up to 10 wt% at varied temperatures and in a pressure range from 100 to 1000 bar via fully-atomistic molecular dynamics (MD) simulations. Additionally, the modified Sanchez-Lacombe equation of state (EOS) model is iteratively solved to capture the pressure, concentration, and temperature dependence of ternary PE solution density. It is shown that the small amounts of ethylene dissolved in the liquid mixtures of PE + hexane significantly decreases the polymer solution density. The presence of unreacted monomer in the solution polymerization process utilized in PE manufacturing was found to substantially lower the PE solution density particularly at the lower end of the investigated pressure range. This noteworthy reduction in mixture density as a consequence impacts design and operation of the liquid-liquid phase separator in manufacturing of PE via solution polymerization. Another key point to bear in mind is that the mixture density exhibits fairly less sensitivity to ethylene amount as external pressure raises. Nevertheless, pressure, solvent composition, and temperature dependence of density display less sensitivity as pressure increases. In relation to the characterization of the impact of addition of ethylene an atomistic-level insight is provided, which proves to be of great value in revealing intermolecular interactions in the binary subsystems of polymer/solvent/monomer. The MD computations are shown to be in excellent agreement with the theoretical EOS model, confirming the validity of the proposed methodology. Furthermore, the adopted OPLS-AA has been found a reliable atomistic force field, which provides detailed molecular information on the thermophysical properties of polyolefin in hydrocarbon solutions. Ultimately, it is demonstrated that the MD simulations complement parametric EOS predictions and costly experimental approaches.

Phase equilibria of binary and ternary polymer solutions using modified UNIQUAC-based local composition model

In the present research, a modification on UNIQUAC activity coefficient model was done based on the local composition concept. The model was applied for binary and ternary systems containing different polymers and protic solvents. The newly modified model was compared with several local composition models such as Wilson, NRTL, UNIQUAC, polymer-NRTL, UNIQUAC-LBY and UNIQUAC-DMD in vapor–liquid. Also, comparison of the model with NRTL, UNIQUAC and UNIQUAC-LBY was done for liquid–liquid equilibrium data. In the presented model, a Freed-FV term was added to activity coefficient expression to consider the free volume effects in the mixture. Also, new surface and volumetric structural parameters were applied for studied alcoholic and aqueous solutions. AARD % of the new model (known as M-UNIQUAC-LBY model) was 1.98% for 28 vapor–liquid equilibrium data set (314 data points) of binary polymer–solvent systems. Moreover, RMSD % of 14 studied liquid–liquid systems in equilibria (155 tie-lines) was equal to 10.6431. The results of presented model were superior to previously presented ones in both VLE and LLE. Therefore, it can be successfully utilized to predict phase equilibria in mixtures, which contain pertinent components for industrial applications.

Thermodynamic analysis of phase equilibrium and surface tension of ternary polymer solutions

AbstractThe liquid–liquid equilibrium (LLE) and surface behavior of polymer solutions were investigated. Systems of poly vinyl methyl ether (PVME)/water and polystyrene (PS)/cyclohexane were chosen as model systems because they show different types of LLE and surface behavior. Ternary polymer solutions of PVME/water/alcohol and PS/cyclohexane/alcohol were also studied. The cloud points of given systems were determined by thermo‐optical analysis method. For surface tension measurements at the air/polymer solution interface, the well‐known plate method was utilized. The investigated polymer solutions exhibit various types of LLE and surface behavior depending on the type of solvent and temperature. The modified double lattice model with chain length dependence is used for description of the phase equilibrium. To improve the interpretation of the surface behavior of the polymer solution, we developed a new thermodynamic frame work based on density gradient theory. Thermodynamic analysis was also conducted using the proposed model to provide understanding of the surface behavior. The surface energy difference and interchange energy had an important role in the driving force of the surface behavior. Utilizing the predetermined model parameters from the phase equilibrium calculation, the proposed model provides satisfactory agreement with measured surface tension data, with less than 5% error.

Mass-transfer driven spinodal decomposition in a ternary polymer solution.

Nonsolvent induced phase separation (NIPS) is a widely occuring process used in industrial membrane production, nanotechnology and Nature to produce microstructured polymer materials. A variety of process-dependent morphologies are produced when a polymer solution is exposed to a nonsolvent that, following a period where mass is exchanged, precipitates and solidifies the polymer. Despite years of investigation, both experimental and theoretical, many questions surround the pathways to the microstructures that NIPS can produce. Here, we provide simulation results from a model that simultaneously captures both the processess of solvent/nonsolvent exchange and phase separation. We show that the time it takes the nonsolvent to diffuse to the bottom of the film is an important timescale, and that phase separation is possible at times both much smaller and much larger than this scale. Our results include both one-dimensional simulations of the mass transfer kinetics and two- and three-dimensional simulations of morphologies at both short and long times. We find good qualitative agreement with experimental heuristics, but we conclude that an additional model for the vitrification process will be key for fully explaining experimental observations of microstructure formation.

In vitro degradation and bioactivity of composite poly-l-lactic (PLLA)/bioactive glass (BG) scaffolds: comparison of 45S5 and 1393BG compositions

The objective of this study was to compare the effect of two bioglass (BG) compositions 45S5 and 1393 in poly-l-lactic composite scaffolds in terms of morphology, mechanical properties, biodegradation, water uptake and bioactivity. The scaffolds were produced via thermally induced phase separation starting from a ternary polymer solution (polymer/solvent/non-solvent). Furthermore, different BG to polymer ratios have been selected (1, 2.5, 5% wt/wt) to evaluate the effect of the amount of filler on the composite structure. Results show that the addition of 1393BG does not affect the scaffold morphology, whereas the 45S5BG at the highest amount tends to appreciably modify the scaffold architecture interacting with the phase separation process. Bioactivity tests confirmed the formation of a hydroxycarbonateapatite-layer in both types of BGs (detected via scanning electron microscopy, X-ray diffractometry and Fourier Transform Infrared Spectroscopy). Overall, the results showed that 1393BG composition affects the experimental preparation protocol to a minimal extent thus allowing a better control of the scaffold’s morphology compared to 45S5BG.

A multi-fluid model for microstructure formation in polymer membranes.

We develop a multi-fluid model for a ternary polymer solution using the Rayleighian formalism of Doi and Onuki, and give an efficient pseudo-spectral method for solving both the diffusion and momentum equations that result. Subsequently, we find that the numerical simulation is capable of describing systems at the micron length-scale and easily reaches millisecond time-scales. In addition, we characterize the model thermodynamics and kinetics including the (i) phase behavior, (ii) structure of the interfaces, (iii) mutual diffusion coefficients, (iv) bulk spinodal decomposition kinetics with and without hydrodynamics and (v) spinodal decomposition in the presence of an interface with a non-solvent bath. We obtain good qualitative agreement with the expected thermodynamic and kinetic behavior. We also show that a linear stability analysis of the diffusion equation quantitatively predicts the fastest growing mode obtained from simulation and gives insight into the phase separation process relevant for the evolution of microstructure in phase-separating ternary polymer solutions.

Phase Equilibrium and Interfacial Tension of Binary and Ternary Polymer Solutions

The liquid–liquid equilibrium (LLE) and interfacial tensions of binary and ternary polymer solutions of polystyrene in cyclohexane and methylcyclohexane are investigated. The chain length dependent modified double lattice model (MDL-CL) is applied to describe experimental phase diagrams measured by thermo-optical analysis. The proposed model is also combined with the modified density gradient theory to calculate interfacial tension between two coexisting liquid phases of the investigated systems. The calculated results of LLE and interfacial tensions using the MDL-CL model combined with the modified density gradient theory show good agreement with experimental data. The interfacial tension of the ternary system (polystyrene + cyclohexane + methylcyclohexane) is described with the parameters obtained from the binary subsystems (polystyrene + cyclohexane and polystyrene + methylcyclohexane). A comparison of experimental and theoretical phase behaviors and interfacial tensions demonstrates that the theoretic...

Structuring of Thin-Film Polymer Mixtures upon Solvent Evaporation

We theoretically study the impact of solvent evaporation on the dynamics of isothermal phase separation of ternary polymer solutions in thin films. In the early stages we obtain a spinodal length scale that decreases with time under the influence of ongoing evaporation. After that rapid demixing occurs at a well-defined lag time, a morphology emerges of which the compositions of the coexisting phases rapidly approach the binodal values. We find that the type of morphology, which can be either bicontinuous or dispersed, strongly depends on the evaporation rate if the solubility of the two solutes in the common solvent differs. We derive expressions that relate both the lag time and length scale characterizing the emerging morphology to all relevant physical parameters. These include the tracer diffusivities, the interaction parameters, the degrees of polymerization, the blend composition, and the evaporation rate. In agreement with our numerical results, we find the latter to scale with a one-sixth power o...

Prediction of diffusion in a ternary solvent–solvent–polymer blend by means of binary diffusion data: Comparison of experimental data and simulative results

ABSTRACTMulticomponent diffusion of solvents in polymeric systems is not completely understood, despite many scientific contributions to the topic. Literature scarcely offers measurement data on diffusion for model validation in such systems. In this work, the ternary systems consisting of poly(vinyl acetate) and the solvents toluene and methanol was investigated experimentally and numerically. By means of inverse micro Raman spectroscopy (IMRS) concentration gradients in drying thin films have been measured. Initial composition of the samples has been varied systematically in order to detect mutual influence of the solvents' diffusive behavior. It was shown that the mobility of the different species is increased in the presence of other solvents as predicted by theory. This experimental data is provided for model validation. A new expression to calculate the diffusion coefficients in ternary mixtures is proposed which only requires binary data. This expression is tested by means of a model‐based simulation to predict the drying of ternary polymer solutions in terms of concentration profiles and residual solvent content. The results are in very good agreement with the experiments. Cross terms diffusion coefficients and thermodynamic factors were not found to be necessary for a satisfying prediction. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43899.

Mass and heat diffusion in ternary polymer solutions: A classical irreversible thermodynamics approach

Governing equations for evolution of concentration and temperature in three-component systems were derived in the framework of classical irreversible thermodynamics using Onsager’s variational principle and were presented for solvent/solvent/polymer and solvent/polymer/polymer systems. The derivation was developed from the Gibbs equation of equilibrium thermodynamics using the local equilibrium hypothesis, Onsager reciprocal relations and Prigogine’s theorem for systems in mechanical equilibrium. It was shown that the details of mass and heat diffusion phenomena in a ternary system are completely expressed by a 3 × 3 matrix whose entries are mass diffusion coefficients (4 entries), thermal diffusion coefficients (2 entries) and three entries that describe the evolution of heat in the system. The entries of the diffusion matrix are related to the elements of Onsager matrix that are bounded by some constraints to satisfy the positive definiteness of entropy production in the system. All the elements of diffusion matrix were expressed in terms of derivatives of exchange chemical potentials of the components with respect to concentration and temperature. The spinodal curves of ternary polymer solutions were derived from the governing equations and their correctness was checked by the Hessian of free energy density. Moreover, it was proved that setting cross-diffusion coefficients to zero results in a contradiction, and the governing equations without cross-diffusion coefficients do not express the actual phase behavior of the system.