Morphology control in symmetric polymer blends using spinodal decomposition

This paper studied, through modeling and computer simulation, the thermal-induced phase separation phenomenon in a symmetric polymer blend via spinodal decomposition. The one-dimensional model consisted of the Cahn–Hilliard theory for spinodal decomposition, and incorporated the Flory–Huggins–deGennes free energy equation, the slow mode mobility theory and reptation model for polymer diffusion. The numerical results replicated frequently reported experimental observations published in the literature for the early and intermediate stages of spinodal decomposition for symmetric polymer blends. Furthermore, the numerical results indicate that a dimensionless diffusion coefficient may be used as a parameter to control the formation and evolution of the phase-separated regions during spinodal decomposition as a means to customize functional polymeric materials with predefined material properties.     

Determination of solvent/polymer interaction parameters of moderately concentrated polymer solutions by vapor pressure osmometry

The paper describes the application of vapor pressure osmometry (VPO) to determine solvent/polymer interaction parameters for various polymer solutions containing high-molecular weight polymers in the semi-diluted concentration range. The theoretical basis for the data evaluation is the Flory–Huggins (FH) model and a virial expansion up to the third virial term. For validation already well characterized polymer/solvent systems poly(vinylpyrrolidone)/water, polysulfone/N,N-dimethylformamide (DMF), and poly(ether sulfone)/DMF were investigated. In the second part interaction parameters of poly(ether imide) (PEI) in solvents with technical relevance for membrane formation (DMF, N-methylpyrrolidone (NMP), N,N-dimethylacetamide (DMAc)) were examined at different concentrations and temperatures. The results document that VPO is a fast and promising method for characterization of semi-diluted polymer solutions containing polymers with higher molecular weight. Results confirm the decrease of solvent power for PEI in the series: NMP > DMAc > DMF.     

Vapor-liquid equilibrium calculations for concentrated polymer solutions

The free-volume theory of polymer solutions initiated by Prigogine and developed by Flory and Patterson is reduced to practice. This theory, which represents a substantial improvement over the older theory of Flory and Huggins, facilitates calculation of solvent activities in polymer solutions from a minimum of experimental binary data. However, it is necessary to characterize each pure component with three molecular parameters which can be obtained from PVT data; such data, unfortunately, are often unavailable. Nevertheless, using reasonable approximations based on Bondi's correlations as needed, molecular parameters are given for 22 solvents and for 16 polymers. Binary parameters are given for 20 systems. Illustrative examples are presented.     

有关Flory—Huggins理论的教学点滴

根据高分子的特点,我们从Boltzmnn熵定理出发,来理解Flory-Huggins晶格模型理论中推导混合熵（△SM）的思路。教学过程中突出高分子溶液中由于高分子相对分子质量大（x个链段）,造成高分子的△SM比小分子大得多的结果Hory-Huggins理论与实际情况的偏差;让学生学会用Hory-Hug—gins参数X1,值判断高分子溶液中溶剂的优劣性。     

Phase behavior of hyperbranched polymer solutions in mixed solvents

Hyperbranched polymers get more and more interesting for several applications due to their tailor-made properties influenced by the architecture and the functional groups of the polymer. The liquid–liquid phase behavior of hyperbranched polymer solutions is an important issue for various applications. Until now, the calculations of these phase equilibria are limited to solutions of hyperbranched polymers in a single solvent using Lattice Cluster theory (LCT). The LCT permits the incorporation of the architecture of the polymer directly in thermodynamic properties, as the Helmholtz energy, without any additional adjustable parameter.This papers aims at the extension of the LCT to ternary systems made from hyperbranched polymer (Boltorn H20), water and propanol. The derived expression for the Helmholtz energy allows for the first time the prediction of miscibility gaps in the ternary system based on experimental data of the binary subsystems.Additionally to the architecture of hyperbranched polymers also the functional groups of hyperbranched polymers play an important role in phase equilibrium. In order to include the association phenomena in the theoretical framework, a modified version of the Wertheim association theory is used. However, during the application of this approach the model lost its predictive power, because ternary data must be used for the parameter estimation procedure. Nevertheless, the combined theory is able to model the experimental phase behavior within the experimental accuracy.     

Characterizing elastic properties of carbon nanotube‐based composites by using an equivalent fiber

Effective elastic properties for carbon nanotube (CNT)‐reinforced composites are obtained through a variety of micromechanics techniques. An embedded CNT in a polymer matrix and its surrounding interphase is replaced with an equivalent fiber for predicting the mechanical properties of the CNT/polymer composite. Formulas to extract the effective material constants from solutions for the representative volume element under three loading cases are derived based on the elasticity theory. The effects of an interphase layer between the nanotubes and the polymer matrix as result of effective interphase layer are also investigated. Furthermore, this research is aimed at characterizing the elastic properties of CNTs‐reinforced composites using Eshelby–Mori–Tanaka approach based on an equivalent fiber. The variations of mechanical properties with tube radius, interphase thickness, and degree of aggregation are investigated. It is shown that the presence of aggregates has stronger impact than the interphase thickness on the effective modulus of the composite. This is because aggregates have significantly lower modulus than individual CNTs. POLYM. COMPOS., 2013 © 2013 Society of Plastics Engineers     

Membrane formation via phase separation induced by penetration of nonsolvent from vapor phase. I. Phase diagram and mass transfer process

The isothermal phase diagram for poly(vinylidene fluoride)/dimethyl formamide/water system was derived. The binodal and spinodal were calculated based on the Flory–Huggins theory and the calculated binodal was approximately in agreement with the experimental data of the cloud points. The isothermal crystallization line was also obtained according to the theory of melting point depression. Mass transfer of the three components during membrane formation by the precipitation from the vapor phase has been analyzed. During this process, phase separation of the polymer solution is induced by the penetration of water vapor in the solution. The calculated result on the changes of the cast film weights indicated the good agreement with the experimental data. The time‐course of the polymer concentration profile in the film was calculated for various cases of different humidity of the vapor phase and different initial polymer concentration. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 159–170, 1999     

Overlap concentration of an aqueous poly(N-vinylcaprolactam) solution in the dynamic and static states

The overlap concentration of poly(N-vinylcaprolactam)s (PVCLs) of low molecular weights was studied with dynamic and static methods (with viscosity and refractive-index measurements) at three temperatures (25, 30, and 35°C). This concentration, determined by viscometry, was lower than the overlap concentration determined by refractometry. Also, the influence of the temperature and molecular weight on the viscosity and refractive index was investigated, and the opposite effect of the temperature on the viscosity and refractive index of PVCL solutions was observed. The experimental overlap concentration values were compared with those calculated with the Rao, Huggins, and Fuoss equations. The results showed that the Huggins equation is the best equation to describe the dilute solution properties of this polymer. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Experimental determination of interface widths in binary polymer blends from free volume measurements

Interfaces in binary polymer blends play a pivotal role in moulding their physical properties. We observe a diffused interface in immiscible and partially miscible binary polymer blends for which the methods of preparation characterize the interface widths. The interface widths for three binary blends of PVC/PS, PS/PMMA, and PVC/SAN are in the maximum range of 2.15, 5.04 and 6.24 nm respectively. We establish a correlation between hydrodynamic interaction and the Flory–Huggins interaction parameter which is consistent with self-consistent mean field theory and the usual constructed density profile across the interface. Our approach is based on the hydrodynamic interaction which is derived from free volume data measured by positron lifetime spectroscopy.     

Studies on miscibility in homopolymer/ random copolymer blends by equation of state theory

The miscibility of poly(methyl methacrylate) (PMMA) and styrene-acrylonitrile random copolymers (SAN) blends was investigated on the basis of the Flory—Orwoll—Vrij equation of state theory. To obtain the equation of state parameters (P*, V*_sp, T*: characteristic parameters), the pressure—volume—temperature (PVT) behaviour was measured for PMMA and a series of SANs with various acrylonitrile contents. The exchange energy parameter X_ij was also calculated by fitting the theory to some phase diagrams of PMMA/SAN blends. The Flory—Huggins interaction parameter χ was separated into two contributions based on the equation of state theory for mixtures: the exchange energy term χ_inter and the free volume term χ_free. Both the temperature and copolymer composition dependences of χ_inter and χ_free were estimated by calculations using the equation of state parameters. There exists a region in which χ_inter is negative, leading to a miscibility window in PMMA/SAN blends. However, the immiscibility at high temperatures in the blends cannot be explained only by χ_inter; it is caused by the free volume contribution, χ_free. The miscibility window behaviour in PMMA/SAN blends may be explained within the framework of the equation of state theory.     

Application of genetic algorithm in calculation of the phase behavior of binary and ternary polymer solutions

A genetic algorithm as an optimization procedure has been developed to predict the phase behavior of polymer solutions. The phase equilibrium diagrams of binary and ternary polymer solutions have been determined using the appropriate form of Flory–Huggins free-energy function for polymer solutions. A concentration and temperature dependent form of the interaction parameter has been used to reflect the effect of temperature and polymer properties in the free-energy form. The proposed genetic algorithm is applied to compare the phase behavior results of some typical polymer solutions with the results of the classical determination methods and then applied to some conventional ternary polymer solutions as polymer–solvent–nonsolvent systems. The proposed algorithm use a set of individual states as the initial chromosomes and uses the general rules as crossover, mutation, and with use of a fractional objective function determines the binodal points or the phase diagram boundaries of polymer solutions. The properties of an industrially relevant polymer solution, a polystyrene–cyclohexane solution, have been used to emphasize on the industrial application of the proposed algorithm. The algorithm has been used to predict the phase behavior of the two polymer–solvent–nonsolvent systems as polystyrene-butanone-methanol and polystyrene-butanone-propanol at three different temperatures and results show good agreement with the experimental observations. The algorithm also has the capability to predict both the concentration-independent and concentration-dependent interaction parameters among the different components. The genetic algorithm is an easy-to-use, state-of-art, and very fast optimization tool, and has very strong capability to solve nonlinear systems in chemical and polymer engineering topics.     

A critical evaluation of the single-point determination of intrinsic viscosity

The general validity of four single-point methods for intrinsic viscosity ([η]) determination is verified to be unacceptable even for dilute polymer solutions. Also, a direct method based on a truncated version of Huggins equation is shown to be less practical in that it involves advanced experimentation and is valid only at sufficiently low concentrations. In view of the shortcoming and sophistication of the above procedures, an effective approach is introduced to resolve these problems. This novel computation expresses the Huggins coefficient in terms of [η], and the associated equations are calibrated against the polymer system of interest. This procedure is tested using various polymer solutions with results compatible with those acquired by other means. The advantage of the proposed technique is discussed.     

Effect of electro-chemical properties of sodium salts of various anions on their diffusional parameters in symmetrical cellulose acetate membranes

A relation was obtained between electro-chemical properties of sodium salts (NaCl, NaBr, and Na₂SO₄), and the thermodynamic property of permeability in symmetrical cellulose acetate membranes, the distribution coefficient K and the kinetic property, the overall diffusion coefficients D. K and D were obtained by the method we proposed using measured unsteady- and steady-state dialysis data. The K values increase with the increase of water content and are in the range of 10⁻² for sodium halides and 10⁻³ for Na₂SO₄. D is found to increase with the increase of the solute concentration, and the extrapolated values of D to zero concentration D⁽⁰⁾ are obtained as 0.015–0.03 μm²/s and increase with the increase of water content in the membrane. D can be divided into the concentration independent diffusion coefficients in the dense part of the membrane D_d and in the porous D_p, applying a two-part (perfect or dense and imperfect or porous) model of the membrane. Contrary to D_d, D_p increases with the increase of W_w and can be correlated as D_p,c = _d exp (γ × W_w). It is shown that the averaged D_d, _D increases with the increase of the quantity of the ionic mobility u of the solutes at infinite dilution divided by valence, and that the parameter γ increases with the increase of the ionic mobility u. The value of K increases slightly with the increase of water content and decreases with the increase of the Flory—Huggins parameter χ. The Flory—Huggins parameter χ is calculated from the measured values of distribution coefficients and data obtained from the literature. And it was found that the gradient of linear decrease of χ (λ_cation) depends on equivalent ionic conductivity of anion of salt, λ_an.     

Semiempirical equations for the viscosity of amphiphilic polymer solutions: A critical examination

The associative behavior of amphiphilic polysaccharides derived from dextran, a neutral bacterial polysaccharide, is studied in dilute and moderately concentrated aqueous solutions using viscosity measurements. It is shown that the viscosity of the aqueous solutions can be conveniently depicted over a wide concentration range by several semiempirical equations. The Martin equation as well as the Matsuoka‐Cowman equation is shown to depict conveniently the experimental results. These two equations involve only viscometric parameters determined in the dilute range (intrinsic viscosity and Huggins constant). The modification of Lyons and Tobolsky is discussed. The Fedors equation is shown to be similar to the Heller equation over a large concentration domain. Their respective empirical parameters are correlated and can be calculated from the Huggins coefficient. POLYM. ENG. SCI., 47:481–488, 2007. © 2007 Society of Plastics Engineers.     

Nanostructure and crystallisation kinetics of poly(ethylene oxide)/poly(4-vinylphenol-co-2-hydroxyethyl methacrylate) blends

Blends of poly(ethylene oxide) (PEO) and poly(4-vinylphenol-co-2-hydroxyethyl methacrylate) (PVPh-HEM) were studied by means of synchrotron small and wide angle X-ray scattering (SAXS and WAXS, respectively) and by differential scanning calorimetry (DSC). The DSC measurements were used in the determination of the Flory–Huggins interaction parameter and also to study the isothermal and non-isothermal crystallisation kinetics of the PEO/PVPh-HEM blend. The interaction parameter, χ₁₂, was found to be negative (between −0.5 and −2.5, approximately) and presented a significant dependence on the blend composition, which is expected for a system with specific interactions such as hydrogen bonding. From the kinetic studies with Kissinger, Friedman and Avrami models, it was shown that crystallisation of PEO chains is slower in the blend than in the pure polymer, despite the decrease in the energy barrier to the crystallisation with the increase in PVPh-HEM concentration.

From the SAXS and WAXS profiles, the nanostructure of the blend was elucidated, exhibiting the formation of PEO lamellae even in the blends containing high concentrations of PVPh-HEM, which are non-crystalline (as observed by the WAXS profiles). The thickness of the PEO lamellae (R_c, approximately 8 nm) remains almost unchanged with the blend composition, while the crystalline peaks, observed at 19.78 and 23.98°, vanish, and the WAXS profile exhibits only a non-crystalline halo. For the non-crystalline blends with high concentrations of PVPh-HEM, PEO chains keep their crystalline structural memory.     

Adsorption of Lactic Acid on Weak Base Polymeric Resins

Abstract

Sorption of lactic acid from a simulated broth has been investigated using weak base ion exchange polymeric resins which behave as functionalized polymers because of tertiary amino groups on the polymer matrix. The equilibrium data for the uptake of lactic acid are represented by Langmuir‐Freundlich combination isotherm. The sorption has been modeled by a phase equilibrium approach using the extended Flory‐Huggins theory of polymer solutions. The interaction of media components, such as glucose and inorganic salts, with the resins and their effect on lactic acid sorption, also has been investigated.     

Conformation of polyacrylamide in aqueous solution with interactive additives and cosolvents

The viscosity of polyacrylamide (PAM) dilute aqueous solutions with NaCl, glucose, and SDS as additives was measured by Ubbelohde viscometry. There was linear relationship between reduced viscosity vs. PAM concentration in aqueous solutions. The Huggins constant k and intrinsic viscosity [η] were used to study the conformation of the polymer chains and the degree of polymer–solvent interaction. In addition, the viscosity of diluted PAM solutions in water with acetone, ethanol, DMF, and ethylene glycol as cosolvent was measured. It was found that the polymer chain conformation contracted as the acetone, ethanol, and DMF cosolvent composition ratio increased, but there was no distinguishing difference between water–ethylene glycol compositions. The solution properties of PAM were used to estimate the swelling properties of PAM gel in the same external conditions, as gel is formed by crosslinking of linear polymer. In good solvent the polymer chain should be expanded, and gel is expected to have large swelling ratio. In water cosolvent systems, when the linear polymer chain underwent coil–globule transition, PAM gel should have volume phase transition under corresponding external conditions. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3122–3129, 2003     

Determination of intrinsic viscosity of polymeric compounds through a single specific viscosity measurement

A modified method based on a combination of the Huggins and Schulz–Blaschke equations is proposed which enables the determination of intrinsic viscosity [η] from the measurement of a single specific viscosity. The method has been verified for different polymer samples having a wide range of [η] values and showed a variation of <±6×10⁻³% from the values obtained by Huggins extrapolation method     

Huggins viscometric constant of semirigid and rigid-chain aromatic polyamides

The absolute values of the Huggins viscometric constant for semirigid- and rigid-chain aromatic polyamides are high, but not very high in comparison to the values for flexible-chain polymers. The Huggins viscometric constant virtually does not change with some, at least two-fold, change in the molecular weight of semirigid- and rigid-chain polyamides, which is similar to the results known for flexible-chain polymers. Either the thermodynamic rigidity of the macromolecules or the thermodynamic affinity between polymer and solvent as a function of the nature of the solvent have the predominant effect on the values of the Huggins viscometric constant in solutions of aromatic polyamides. Translated from Khimicheskie Volokna, No. 1, pp. 3–7, January–February, 1998.     

Solubilities of nonvolatile solutes in polymers from molecular thermodynamics

Because there is no simple, general method for measuring solubilities of nonvolatile solutes in a polymer, this work presents a thermodynamic framework for estimating such solubilities from infinite-dilution distribution-coefficient data for aqueous solutions of the solute in equilibrium with the polymer. The experimental infinite-dilution distribution coefficient is related to that calculated from a molecular-thermodynamic model (Flory–Huggins). The three binary Flory parameters are obtained from water–solute and water–polymer data, and from the solute's distribution coefficient. Solubilities of 19 nonvolatile aromatic solutes were estimated in three polymers: ethyl-vinyl acetate copolymer (EVAc) with 33 (EVAc33), 45 (EVAc45) wt. % vinyl acetate content, and poly(vinyl acetate) (PVAc) at 25°C, where most of the solutes are solids. For some of these systems, predicted solubilities are compared with new experimental results. The calculations reported here may be useful for various applications, including the design of membrane processes or drug-delivery systems, and for packaging technology for foods, chemicals, and pharmaceuticals.