Generalized Flory-Huggins Model for Heat-of-Mixing and Phase-Behavior Calculations of Polymer-Polymer Mixtures (original) (raw)
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Polymer, 1996
A method is presented to evaluate the Koningsveld g-functions for quasi-ternary polymer solutions and blends, involving binary and ternary interactions. A robust set of 12 equations derived from the Flory Huggins lattice theory, dealing with liquid-liquid phase separation conditions, have been solved using as input data the experimental volume fractions of each component in each coexisting phase. These values were found by means of a liquid microextraction procedure followed by size-exclusion chromatography analysis. Several approximations are proposed and discussed in order to select the best option to predict thermodynamic properties of binary polymer blends and blends in solution. The dimethylformamide/ poly(vinylidene fluoride)/polystyrene ternary solution was chosen to test the validity of our proposal. In general, the analytical form of the g-function is adequately described by a second order polynomial, the inclusion of the ternary interaction parameter also being recommended. From the values of the PVDF/PS interaction function it can be inferred that this blend behaves as slightly incompatible under environmental conditions, in clear agreement with data previously reported. In contrast, the incompatibility is suppressed when a low molar mass component, such as dimethylformamide, is added, reaching the semidilute regime (total polymer volume fraction q~p ~ 0.35). Values of the Gibbs free-energy of mixing as a function of the blend composition were also evaluated for both ternary solution and dry blend and discussed in terms of their stability.
Prediction of the Behavior for Polymer Blends Using Thermodynamic Model
Petroleum & Petrochemical Engineering Journal, 2019
Two polymer blends were prepared. The first one was Poly methyl methacrylate (PMMA) and Poly vinyl acetate (PVAc), and the second was Poly vinyl chloride (PVC) and Polystyrene (PS). The first blend prepared by mixing two polymers (PMMA, PVAc) with co-solvent (Chloroform) at different weight percentages (0/100, 20/80, 40/60, 50/50, 60/40, 80/20, 100/0). The second blend prepared by mixing two polymers (PVC, PS) with co-solvent N,N dimethylacetamide (DMAC) at different weight percentages (0/100,20/80,40/60,50/50,60/40,80/20,100/0). Two processes were used for preparation; dissolution process was used at a room temperature (25°C) and (1atm.) pressure using co-solvent. Viscosity test was performed for stock solutions (1%wt/v=1g/dL) and other concentrations (0.75, 0.6, 0.5, 0.4, 0.3 g/dL) these concentrations are obtained by dilution of stock solution. The obtained data were collected and substituted accordance to equations (Huggins Equation) and certain criteria (Interaction parameters ΔB,μ) to identify the miscibility (or compatibiliIty).To get polymer blends in solid state, The same procedure to prepare the stock solution of diluted solutions followed but the stock solutions of polymer blends were at concentration (10%wt/v) for all different compositions and then followed solvent casting (evaporation then drying). The solid state samples were taken to hold tests of DSC and FTIR. The aim of the present work was to study the thermodynamic behavior of polymer blend via determination of miscibility. Miscibility (or immiscibility) tests are performed in three techniques: viscometry method, DSC analyzer and FTIR to test polymer blend in solid state. It was found from the viscosity method that for first blend (PMMA/PVAc), the interaction parameters (ΔB,μ) are positive for all compositions therefore the system is miscible whilst the second system (PVC/PS) is immiscible where the interaction parameters (ΔB,μ) are negative.
Thermochimica Acta, 2001
The miscibility of poly(styrene) and poly(vinylmethylether) is studied both by measuring the glass transition temperatures of the mixture and with the application of the Flory±Prigogine theory in the approximated form due to Patterson. For these calculations, the enthalpy of mixing of the two polymers is evaluated by measuring the enthalpies of solution of the pure polymers and of the mixture. The trend of the interaction parameters with the temperature for two samples of poly(styrene) of different molecular weight is discussed.
Thermodynamics of mixing of poly(vinyl chloride) and poly(ethylene-co-vinyl acetate)
Polymer, 2002
The miscibility of poly(vinyl chloride) (PVC) and an ethylene-vinyl acetate copolymer with 85 wt% of vinyl acetate units (EVA85) has been studied by measuring the glass transition temperature and the enthalpy of mixing of several mixtures covering the whole composition range. An accurate thermal characterization as regards the specific heat of the two polymers and their blends has also been obtained. The enthalpy of mixing has been found negative for all the mixtures, indicating that specific interactions are involved between the polar groups of the two components. Particular attention has been paid also to the excess specific heat, which comes out positive for the PVC-rich blends and with a small negative value in a narrow region at high contents of EVA85. This finding is in agreement with negative and positive deviations that are observed for the glass transition temperature. Modelistic considerations about the type of interactions and the organization between PVC and EVA85 in the blends are proposed.
Journal of Thermal Analysis and Calorimetry - J THERM ANAL CALORIM, 2000
The mixing enthalpies of blends of polymethylmethacrylate (PMMA) with poly(styrene-co-acrylonitrile) (SAN) were investigated by analogue calorimetry through the determination of the excess enthalpies of pseudobinary model mixtures corresponding to the addition of methyl-i-butyrate to a binary mixture of acetonitrile or propionitrile plus toluene or ethylbenzene. A group contribution procedure, based on UNIQUAC equation, was also devised and the polymeric mixing enthalpies were calculated from properly defined group contributions. Enthalpies for polymeric interactions were introduced into the Flory-Huggins equation and the miscibility window of PMMA-SAN mixtures was calculated. The results show a qualitative agreement with the experimental miscibility data and indicate that both the analogue calorimetry and the group contribution procedures yield correct results when acetonitrile, and not propionitrile, is chosen as the model for the polyacrylonitrile repeat unit of the copolymer.
Polymer, 2000
Mixing thermodynamics in miscible blends of polystyrene (PS) and tetramethylbisphenol-A polycarbonate (TMPC) was investigated using liquid state pressure-specific volume-temperature (P-v-T) properties of both pure components and mixtures. The equation-of-state theories used were (1) the lattice fluid model of Sanchez and Lacombe, (2) the model of Flory, Orwoll, and Vrij, and (3) the modified cell model suggested by Dee and Walsh. The composition dependence of characteristic pressure was first used to extract the interaction parameter (DP ء) and Flory interaction parameter expressed in the second derivative of the free energy of mixing (x sc). It was found that the sign of x sc was negative and the magnitude of it was always significantly larger than the values obtained by small-angle neutron scattering (Yang H,
Thermodynamic interactions in multicomponent polymer blends
Macromolecules, 1996
Small-angle neutron scattering (SANS) was used to probe the thermodynamic interactions in multicomponent polymer blends including ternary blends containing two homopolymers and a block copolymer, mixtures of a homopolymer and a block copolymer, and a blend of two block copolymers. The polymers used for this study were model polyolefins poly (ethylbutylene) and poly (methylbutylene) homopolymers and a poly (ethylbutylene)-block-poly (methylbutylene) copolymer. SANS profiles from homogeneous blends were ...
Procedure for predicting lower critical solution temperature behavior in binary blends of polymers
Macromolecules, 1991
A procedure is presented that uses heat of mixing information, calculated by the modified Guggenheim quasichemical (MGQ) group contribution method, and PVT data for the polymers, correlated by the Sanchez-Lacombe-Balasz (SLB) lattice fluid model, to predict lower critical solution temperature (LCST) behavior. Fairly good predictions, to within 20 "C uncertainty, of cloud points are shown for poly-(vinyl methyl ether)/poly(styrene) (PVME/PS), poly(methy1 methacrylate)/poly(vinyl chloride) (PMUA/ PVC), and poly(methy1 methacrylate)/poly(ethylene oxide) (PMMA/PEO) binary blends.
Macromolecules
The thermodynamic properties of polystyrene (PS) and poly(vinyl methyl ether) (PVME) are estimated using molecular dynamics and energy minimization simulations, from which the characteristic parameters of the equation-of-state are numerically evaluated. The lattice fluid theory is employed to apply the calculated characteristic parameters to the prediction of the surface tension of PS and PVME and the phase diagram of PS/PVME blends. The calculated surface tensions with no adjustable parameter agree well with the experimental data within ca. 1.0 mN/m. The calculated phase diagram of the blends is also qualitatively comparable to the experimental phase diagram.
Thermodynamic analysis on the phase behavior of copolymer blends: an equation of state approach
Macromolecules, 1992
A model of copolymer blends based on the PrigogineFlory-Patterson equation of state theory is presented to understand quantitatively the effect of comonomer on the LCST behavior of copolymer blends. According to Patterson's treatment, the free volume effect was introduced to the Flory-Huggins interaction parameter xm of copolymer blends. The model explains that the intramolecular interaction within copolymers contributes not only to the interactional term but also to the free volume term. Unlike its contribution to the interactional term, the repulsion is not always favorable to the free volume term which depends on the difference in the characteristic temperatures between blend components. Since the characteristic parameters P and P of the copolymers are a function of those of the copolymer components, the difference depends on the magnitudes of the characteristic parameters of selected comonomer as compared with those of base polymer. The applicability of the proposed model was examined for poly(viny1 methyl ether) (PVME)/styrene copolymer blends. The calculated variation of xwith the copolymer composition at a given temperature was in agreement with the variation of the LCST with the copolymer composition and the type of comonomer.