Search results for "Solution theory"

On the thermodynamic treatment of poly(vinylidene fluoride)/polystyrene blend under liquid—liquid phase separation conditions

1995

Abstract This paper deals with experimental and theoretical investigations on the compatibility of binary of polymer blends in solution. The experimental phase boundary of a crystalline polymer such as poly(vinylidene fluoride) with polystyrene (an amorphous polymer) in dimethylformamide as solvent has been determined by size-exclusion chromatography at 25°C. The composition of the coexisting phases has been used to calculate interaction parameters by means of the Flory—Huggins-type function for the free energy of mixing, including composition dependence of the polymer-polymer interaction parameter and a first correction term denoted as ternary interaction parameter. The calculation of thes…

Prediction of maxima and minima in the curve of total sorption parameter in ternary polymer systems. Influence of ternary interaction parameter

1993

Flory-Huggins theory modified by Pouchly has been applied to predict maxima and minima in the curve of total sorption in ternary polymer systems formed by a polymer and two liquids. In this work, different diagrams based on experimental magnitudes easily obtained such as the difference in affinities of liquids, solvents and non solvents, and the solvent molar volume ratio. Total sorption parameter has been considered to be the decisive magnitude to define extrema conditions in both cosolvent and cononsolvent ternary polymer systems. The theoretical prediction is not altered by the inclusion of ternary interactions. Different examples of ternary systems dealing with vinyl polymers and polydi…

Viscometric study on the compatibility of polymer–polymer mixtures in solution

1999

Abstract The viscosity behaviour of mixtures formed by two uncharged polymers in dilute solution has been studied at 25°C. The ternary systems assayed, and denoted solvent (1)/ polymer (2)/ polymer (3), have in common the poly(ether sulphone) (PES) as polymer 2, and poly(vinylidene fluoride) (PVDF), poly(methyl methacrylate) (PMMA) or poly(styrene) (PS) as polymer 3. The intrinsic viscosity and the viscometric interaction parameters have been experimentally measured for the binary (solvent/polymer) as well as for the ternary systems, and also theoretically evaluated for the latter. The estimation of the compatibility degree of the above polymer pairs have been done by means of three criteri…

Viscometric behaviour of polymer blends based on poly (vinylidene fluoride)

1994

The viscosity behaviour of dilute dimethylformamide solutions of poly(vinylidene fluoride)-poly (methyl methacrylate) and poly(vinylidene fluoride)-polystyrene has been studied at 25°C. The polymer concentration ranges are such that neither phase separation nor microgel formation occurs, although we are very close to theta conditions. The intrinsic viscosity and viscosity interaction parameter of the ternary mixtures have been calculated. The estimation of the compatibility of the above polymer pairs has been studied based on: a) specific viscosities; b) viscosity interaction parameters, according to Krigbaum and Wall formalism, and c) viscosity interaction parameters of a system formed by …

Ternary Polymer Solutions with Hydrogen Bonds, 1

2007

The Flory Huggins methodology coupled to AET has been extended to ternary polymer systems, in particular to solvent (A)/polymer 1 (B)/polymer 2 (C) systems, with the two polymers displaying H-bonding interactions. Because the H-bonding can perturb the randomness of polymeric conformations, the change in Gibbs free energy of mixing, AG, should arise from changes in combinatorial entropy as well as in interaction energy. The combinatorial part of AG is evaluated through AET as a function of the association constant η between B and C components, the autoassociation constant a between B components, and the independent number m of interaction sites of acceptor C. The enthalpic contribution is ev…

Correlation between transport and equilibrium properties through the ternary interaction parameter for cosolvent and cononsolvent polymeric systems

1992

A study of the ternary polymer systems dimethyl formamide-ethyl acetate-polystyrene, chloroform-1,4 dioxane-polystyrene and tetrahydrofuran-chloroform-polystyrene was carried out by viscosity and light scattering at 298 K. A good correlation has been found between the excess intrinsic viscosity, unperturbed polymer dimensions, second virial coefficient and the excess Gibbs free energy by using a ternary interaction parameter, dependent on molecular weight. This modification enables the conversion between transport and equilibrium properties.

1990

Taking into account the dependency on molar mass of the viscometric interaction parameter B, the modified Stockmayer-Fixman-Burchard equation ([η]/M1/2) = KΘ + C″ · A2 · M1/2 is obtained. It relates the intrinsic viscosity, [η], to the second virial coefficient, A2, and to the unperturbed dimensions parameter, KΘ, with C″ being a constant. Hereupon, KΘ can be determined from [η] and A2 data of any binary (solvent/polymer) and/or ternary (solvent 1/solvent 2/polymer) system, BPS and/or TPS. Because of the scarcity of reliable sets of [η] and A2 values mostly for TPS, the application of the above equation to obtain KΘ coefficients rests limited. This limitation can be surmounted by an A2 eval…

1990

Intrinsic viscosities, [η], second virial coefficients, A2, and interaction potentials, g12, for the ternary systems alcohol (1)/3-heptanone (2)/poly(1-vinyl-2-pyrrolidone) (3), with the unbranched alcohols methanol, ethanol and 1-propanol, were determined at 25°C. Taking into account the dependence of the viscometric interaction parameter, B, with the molecular weight of the polymer, the unperturbed dimensions parameter, KΘ, of the polymer was unambiguously obtained. Relationships between ΔKΘ (defined as ΔKΘ = ΔK − KΘ) and excess Gibbs energies, GE, and between excess viscosity, Δ[η], and GE allow to obtain equations relating A2 to ΔKΘ or to Δ[η]. Therefore, A2 can be evaluated from experi…

1984

By means of data from critical demixing and vapour pressure measurements and by inverse gas chromatography, including the results of published light scattering measurments, a consistent picture is obtained for the entire dependence of the Flory-Huggins parameter χ on the weight fraction w2 of the polymer and on the temperature T for the system tert-butyl acetate/polystyrene. Within the entire T-range (ca. 0°C – 140°C), χ increases stronger than exponentially with w2, the rise being the larger the larger χH (the enthalpy contribution to χ) becomes in the limit of infinite dilution. At sufficiently high temperatures (≳ 50°C), χH changes its sign from negative to positive as w2 is raised. This…

On time-harmonic Maxwell equations with nonhomogeneous conductivities : Solvability and FE-approximation

1989

The solvability of time-harmonic Maxwell equations in the 3D-case with non­homogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the probJem in question. Moreover, a finite element approximation is presented in the 3D·case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics. peerReviewed