Concentration-dependent Interaction Parameter Research Articles

All-atom molecular dynamics study on the non-solvent induced phase separation: Thermodynamics of adding water to poly(vinylidene fluoride)/N-methyl-2-pyrrolidone solution.

The change in the thermodynamics when adding water in poly(vinylidene fluoride) (PVDF)/N-methyl-2-pyrrolidone (NMP) solution is studied from all atom molecular dynamics (MD) simulations. This is done by estimating the free energy of mixing of PVDF/NMP solution with increasing volume fraction of water (ϕw) using an appropriately chosen thermodynamic cycle and the Bennett acceptance ratio method. The MD calculations predict the thermodynamic phase separation point of water/NMP/PVDF to be at ϕw = 0.08, in close agreement with the experimental cloud point measurement (ϕw = 0.05). Examining the enthalpic and entropic components of the free energy of mixing reveals that at low concentrations of water, the enthalpy term has the most significant contribution to the miscibility of the ternary system, whereas at higher concentrations of water, the entropy term dominates. Finally, the free energy of mixing was compared with the Flory-Huggins (FH) free energy of mixing by computing the concentration-dependent interaction parameters from MD simulations. The FH model inadequately predicted the miscibility of the PVDF solution, mainly due to its negligence of the excess entropy of mixing.

Sorption of vapours and liquids in PDMS: novel data and analysis with the GAB model of multilayer adsorption

Novel data on the sorption of vapours and liquids in cross-linked poly(dimethylsiloxane) (PDMS) elastomer at 25–40°C are reported together with the accurate and original way of parameterising the sorption isotherms by using the GAB (Guggenheim, Anderson and De Boer) model of multilayer adsorption. The GAB model has been found to provide acomparable or better representation of sorption isotherms than the Flory–Huggins model with a concentration-dependent interaction parameter and better than the ENSIC (Engaged Species Induced Clustering) model. This comparison holds true for poor solvents of PDMS (water, methanol), mild solvents (acetone, methyl acetate, dimethyl carbonate) and good solvents (tert-butyl methyl ether, tert-amyl methyl ether, cyclopentyl methyl ether). The GAB model provided anoticeably good assessment of the sorption of liquids and highly saturated vapours, which makes the model applicable within the entire activity range.

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.

Rotational Diffusion Analysis of Polyethylene Glycol Induced Protein Interactions

Protein intermolecular depletion interactions induced by polyethylene glycol (PEG) depend largely on its concentration and molecular weight. Herein, we investigated the effects of various concentrations and molecular weights of PEG on lysozyme interactions through the analysis of protein rotational diffusion, which is susceptible to intermolecular interactions at short range. To this end, we measured fluorescence anisotropy of fluorescein-tagged lysozyme added as a tracer in concentrated native lysozyme solutions and introduced a protein concentration-dependent interaction parameter, k(rot). The results show the nonmonotonic changes in k(rot) as the concentrations of PEG10000 and 6000 are increased. The depletion attractions are characterized by the decrease in k(rot), indicating an increase of a degree at which protein rotational diffusion slows down. The influences of temperature on the lysozyme rotational diffusion and k(rot) were also measured, and the validity of this approach was checked through comparison with the colloidal theory.

Cloud-point measurements of the {H 2O + poly(ethylene glycol) + NaNO 3} system

The cloud-point (CP) temperatures and phase separation of {H 2O + poly(ethylene glycol) + NaNO 3} ternary system is studied by the turbidimetry method using a reaction calorimeter. The phase separation was also observed by visual inspection. Differences between the CP measured using the turbidimetry method and visual inspection, was up ±0.5 K. The Flory–Huggins model with a temperature and concentration-dependent interaction parameter was employed to correlate the phase diagram of the system. As a result of the correlation an average absolute deviation of 0.002 is obtained.

Measurement and Correlation of Phase Equilibria for Poly(propylene glycol) 400 + Ethanol and + 2-Propanol Systems at Different Temperatures

The activities of ethanol and 2-propanol in poly(propylene glycol) 400 (PPG 400) solutions have been measured by the improved isopiestic method at T = (298.15 to 328.15) K. The original equation of Flory−Huggins and the modified Flory−Huggins equation with concentration-dependent interaction parameters have been used for the correlation of the experimental solvent activity data. It was found that for the studied systems at any mass fraction, as the temperature is increased the solvent activities and Flory parameters are both decreased, indicating an increase of interaction between polymer and solvents as the temperature is increased. The reliability of the two local composition models, NRTL and Wilson, was also assessed by fitting the experimental activity data to these models. All of these models satisfactorily present the obtained experimental activity data at different temperatures.

Modelling the influence of nanoparticles in the phase behaviour of an epoxy/polystyrene mixture

The cloud point temperatures of four series of epoxy/polystyrene blends have been experimentally determined as a function of polymer mass and system composition. The phase diagrams show an UCST behaviour, increasing incompatibility as the molar mass increases. The Flory–Huggins theory with a concentration-dependent interaction parameter has been developed to study the compatibility of two polymers in presence of spherical nanoparticles. This theory has been first compared with the experimental cloud point curve in absence of nanoparticles, and secondly it has been used to predict the thermodynamic behaviour in presence of different volume fraction of nanoparticles. Nanoparticles coated with two types of functional groups have been tested. It can be concluded that the inclusion of nanoparticles increases compatibility. Moreover concentration-dependent interaction parameters have been obtained in these systems for the first time.

Determination of Solvent Activity in Poly(vinylpyrolidone) + Methanol, + Ethanol, + 2-Propanol, + and 1-Butanol Solutions at 25 °C

The activities of methanol, ethanol, 2-propanol, and 1-butanol in poly(vinylpyrolidone) (PVP) (weight-average relative molar mass, M w = 10 000) solutions have been measured by the isopiestic method at 25 °C. Sodium iodide and calcium chloride were used as the isopiestic standards for the calculation of activities. A polynomial equation, the original Flory-Huggins equation, and the modified Flory-Huggins equation with concentration-dependent interaction parameters have been used for the correlation of the experimental solvent activity data. The strength of interaction between different alcohols and the polymer was discussed on the basis of the obtained Flory-Huggins interaction parameters.

Characterisation and modelling of the transport properties in lithium battery gel electrolytes: Part I. The binary electrolyte PC/LiClO 4

A recent development trend for rechargeable lithium batteries is the use of ternary gel electrolytes. The main advantage of the gels is the mechanical rigidity, which improves as the polymer content is increased. However, the transport properties deteriorate with increasing polymer amount. This dualistic optimisation problem has caused an increased interest in understanding the transport processes in gels, however no full characterisation or modelling study could be found in the literature. In this paper, which is the first part of a study of the transport in the ternary gel system PMMA/PC/LiClO 4, the liquid electrolyte PC/LiClO 4 is characterised and modelled for concentrations between 0.1 and 2 M according to a previously employed methodology, based on electrochemical measurements. A model using concentration dependent interaction parameters proved to describe the results in the whole concentration region well. The cationic transport number and salt diffusivity were determined to be approximately 0.3 and 1e−10 m 2/s, respectively. The mean ionic activity factor variations prove to be substantial. Furthermore, it was demonstrated that the inter-ionic friction was important to consider at concentrations above 1 M. The fundamental friction parameters determined in this part will be used in the following part of the study to describe the friction between ions and solvent.

Determination of Solvent Activity in Poly(propylene glycol) + Methanol, + Ethanol, + 2-Propanol, and + 1-Butanol Solutions at 25 °C

The activities of methanol, ethanol, 2-propanol, and 1-butanol in poly(propylene glycol) (PPG) (Mp: 1000) solutions have been measured by the isopiestic method at 25 °C. Sodium iodide and calcium chloride were used as the isopiestic standards for the calculation of activities. The original equation of Flory−Huggins and the modified Flory−Huggins equation with concentration dependent interaction parameters have been used for the correlation of obtained experimental solvent activity data. Better agreement with the experimental data was obtained using the modified Flory−Huggins equation.

Gas−Solid Equilibrium in Mixtures Containing Supercritical CO2 Using a Modified Regular Solution Model

A model that includes an equation of state and an excess Gibbs free energy model is proposed and applied to the correlation of phase equilibria in gas + solid systems containing supercritical carbon dioxide. A modified “regular solution” model for the excess Gibbs free energy that considers nonpolar, polar, and hydrogen-bonding contributions and a generalized three constant equation of state is proposed. The mixing rule derived for the model includes a concentration-dependent interaction parameter and an interaction parameter into one of the volume constants of the equation of state. Literature data for nine binary gas + solid systems containing supercritical carbon dioxide are used for testing the proposed model. The systems studied were binary mixtures containing carbon dioxide as solvent with 2,3-dimethylnaphthalene, 2,6-dimethylnaphthalene, caffeine, cholesterol, anthracene, naphthalene, phenanthrene, pyrene, and benzoic acid. The proposed model correlates the solute concentration in the gas phase bet...

Consistent analysis of cloud points and spinodal—compatibility of P (αMS-CO-AN) and P (MA-CO-MMA)

The two copolymers poly(α-methylstyrene- co-acrylonitrile) (P(αMS-co-AN)) and poly(methyl acrylate-co-methyl methacrylate) (P(MA-co-MMA)) are traded by the BASF AG, Ludwigshafen, under the names Luran and Lucryl, respectively. We have studied Luran KR2556 with the molar mass of Mw = 92 kg/mole (Mw/Mn = 2.5), which has the copolymer composition of 50% αMS and AN, respectively. Lucryl has a similar molar mass of Mw = 88 kg/mole (Mw/Mn = 2.5) and is available with various MA fractions between 1 and 14%. Luran + Lucryl blends prepared by solution casting from acetone are miscible at temperatures below 130 °C. At higher temperatures they show a lower critical solution temperature (LCST) behavior. Temperatures of demixing depend strongly on the MA fraction. The minima of the cloud point curves are found for Luran concentrations between 20 and 35%. We have used results from transmission electron microscopy (TEM) [1, 2] to reveal the morphologies of demixed Luran + Lucryl blends for different compositions and temperatures. This enables us to distinguish between demixing by nucleation and growth in the meta-stable region of the blend system and the spinodal decomposition. The results from cloud point and TEM measurements yield constraints for the spinodal curve. The spinodal is calculated consistantly utilizing a temperature and concentration dependent interaction parameter defined by Staverman [3]. We also estimate the interaction parameter for blends of Luran with pure PMMA and PMA.

Isopiestic Determination of 2-Propanol Activity in 2-Propanol + Poly(ethylene glycol) Solutions at 25 °C

The activities of 2-propanol in poly(ethylene glycol) (PEG) (Mn: 1000, 300, 200) + 2-propanol solutions have been measured by the isopiestic method at 25 °C. Sodium iodide was used as the isopiestic standard for the calculation of activities. The original equation of Flory−Huggins and the modified Flory−Huggins equation with concentration dependent interaction parameters have been used for the correlation of obtained experimental solvent activity data. Better agreement with the experimental data was obtained using the modified Flory−Huggins equation.

Considerations and restrictions on the theoretical validity of the linearized cloudpoint correlation

The linearized cloudpoint curve correlation presented by Boom et al. [ Polymer, 1993, 34, 2348] is revised. Boundaries for the validity of the linearized cloudpoint correlation are given for which an interpretation from the Flory-Huggins theory is possible. The distinction between liquid-liquid and solid-liquid demixing by this correlation must also be subjected to some constraints, although the slope in the correlation still offers a good way to distinguish between solid-liquid and liquid-liquid demixing. The statement, however, that concentration-dependent interaction parameters can be derived from this correlation must be rejected. The empirical rule found by Li et al. [ Desalination, 1987, 62, 7955] can be rationalized on the basis of the LCC correlation.

Representation of nonideality in concentrated electrolyte solutions using the Electrolyte NRTL model with concentration-dependent parameters

The Electrolyte NRTL model proposed by Chen et al. [C.-C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, AIChE Journal 28 (1982) 588–596.] and Chen and Evans [C.-C. Chen, L.B. Evans, AIChE Journal 32 (1986) 444–454.] has been modified to include concentration dependence of interaction parameters in order to enhance the capability of the model in representing the nonideality of concentrated electrolyte solutions. The concentration-dependent interaction parameter is based on the concept that the multi-body effect should be considered in determining the local composition when the electrolyte concentration is high. In this work, a linear concentration dependence is assumed and the activity-coefficient expressions for cations, anions and molecular species are derived from the excess Gibbs energy expression through the thermodynamic relationship. Therefore, the activity-coefficient expressions are consistent and satisfy the Gibbs–Duhem equation. The experimental mean-ionic-activity-coefficients of highly soluble aqueous electrolyte systems have been used to regress the concentration-dependent parameters. The calculated values and experimental data are in excellent agreement. The deviations are usually within experimental uncertainty and significantly smaller than those using the original model. The modified model is completely compatible with the original model because it reduces to the original model when the concentration-dependent term is zero.

Liquid‐liquid phase separation in polysulfone/solvent/water systems

The cloud point curves for polysulfone (PSf)/solvent/water systems were determined by a titration method. A small amount of water was needed to induce liquid-liquid demixing and the temperature effect was small. From numerical calculations, it was found that the binary interaction parameters for the PSf/solvent/water system enlarges the homogeneous region in the phase diagram with a smaller nonsolvent-polymer interaction parameter χ13, a greater nonsolvent-solvent interaction parameter χ12, and a smaller solvent-polymer interaction parameter χ23 and the effect of polymer molecular weight was negligible except in the range of low molecular weight. The phase diagrams, calculated with constant χ12 that was chosen from the concentration-dependent interaction parameter g12 value of the concentration range, were similar to the results obtained with g12. The slope of the tie lines indicated that demixing of the ternary system occurred at relatively similar nonsolvent concentration in both phases. A value of 2.7 for the water-PSf interaction parameter was obtained by fitting the experimental cloud point curve with the calculated binodal lines. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 2643–2653, 1997

Liquid-liquid phase separation in polysulfone/solvent/water systems

The cloud point curves for polysulfone (PSf)/solvent/water systems were determined by a titration method. A small amount of water was needed to induce liquid-liquid demixing and the temperature effect was small. From numerical calculations, it was found that the binary interaction parameters for the PSf/solvent/water system enlarges the homogeneous region in the phase diagram with a smaller nonsolvent-polymer interaction parameter χ13, a greater nonsolvent-solvent interaction parameter χ12, and a smaller solvent-polymer interaction parameter χ23 and the effect of polymer molecular weight was negligible except in the range of low molecular weight. The phase diagrams, calculated with constant χ12 that was chosen from the concentration-dependent interaction parameter g12 value of the concentration range, were similar to the results obtained with g12. The slope of the tie lines indicated that demixing of the ternary system occurred at relatively similar nonsolvent concentration in both phases. A value of 2.7 for the water-PSf interaction parameter was obtained by fitting the experimental cloud point curve with the calculated binodal lines. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 2643–2653, 1997

Hypercritically enhanced distortion of a phase diagram: The (polystyrene + acetaldehyde) system

We report new experimental evidence of the existence of double critical points in a binary system. Pressure-temperature data on the solubility of (polystyrene + acetaldehyde) were obtained using a low-angle light-scattering technique. Phase diagrams change from an UCST/LCST configuration showing a marked double maxima to an hour-glass shape with a “window of miscibility” as pressure decreases. Successful modeling of these unusual shapes was achieved by using a computation algorithm which incorporates a temperature- and concentration-dependent interaction parameter. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 631–637, 1997

Hypercritically enhanced distortion of a phase diagram: The (polystyrene + acetaldehyde) system

We report new experimental evidence of the existence of double critical points in a binary system. Pressure-temperature data on the solubility of ( polystyrene + acetaldehyde) were obtained using a low-angle light-scattering technique. Phase diagrams change from an UCST/LCST configuration showing a marked double maxima to an hour-glass shape with a window of miscibility as pressure decreases. Successful modeling of these unusual shapes was achieved by using a computation algorithm which incorporates a temperature- and concentration-dependent interaction parameter.

Zero and Off-Zero Critical Concentrations in Systems Containing Polydisperse Polymers with Very High Molar Masses. 2. The System Water−Poly(vinyl methyl ether)

Cloud-point curves by DSC measurements at different scanning rates on solutions of two samples of poly(vinyl methyl ether) in water show two minima in a temperature−composition plot. The significance of the data was confirmed by static measurements of the coexisting-phase compositions and phase-volume ratios. A thermodynamic analysis in terms of a strongly concentration-dependent interaction parameter leads to the conclusion that the system H2O/PVME exhibits so-called type III behavior. For polymers of infinite molar mass, such behavior is characterized by the occurrence of two off-zero critical concentrations, in addition to the usual zero critical concentration marking the ϑ state.