A continuous polydisperse thermodynamic algorithm for a modified flory-Huggins model: The (polystyrene + nitroethane) example

Sousa, Hermínio C. de; Rebelo, Luís Paulo N.

doi:10.1002/(sici)1099-0488(20000215)38:4<632::aid-polb15>3.0.co;2-q

Cited by 43 publications

(47 citation statements)

References 108 publications

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“…Phase diagrams of polymer solutions are usually represented as two-dimensional cross-sections of a multi-dimensional space that embraces variables such as temperature, pressure, composition, polymer molecular weight, polymer polydispersity, and isotopic label either in the solvent, or in the polymer, or in both [10,11]. In this work, we have studied five distinct polymeric systems (see Table 1) in H 2 O and/or in D 2 O.…”

Section: Resultsmentioning

confidence: 99%

Phase behavior of (polyacrylamides + water) solutions: concentration, pressure and isotope effects

Azevedo

Rebelo

Ramos

et al. 2001

Fluid Phase Equilibria

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Phase diagrams of poly(N-isopropylacrylamide) (PNIPAAM) as well as of hydrophilically-modified copolymers in aqueous solution were determined. A high-accuracy He-Ne Laser scattering technique was used for the detection of operational spinodal (sp) and cloud-point (cp) curves. Polymer concentration was varied from 0.5 to 20 wt.%. In the case of copoly(PNIPAAM/vinylsaccharide) several different chain lengths were considered. Pressure (up to 400 bar) and solvent isotope effects were studied. We predict a closed-loop type phase diagram for the copolymers, which presents an estimated hypercritical point in H 2 O solutions at M w ∼ 0.5 × 10 5 , although only lower critical solution temperature (LCST) is experimentally accessible. At lower molecular weights, the solutions are always in the one-phase region.

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Section: Resultsmentioning

confidence: 99%

Phase behavior of (polyacrylamides + water) solutions: concentration, pressure and isotope effects

Azevedo

Rebelo

Ramos

et al. 2001

Fluid Phase Equilibria

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“…Modeling. Recently, de Sousa and Rebelo 10 presented in great detail a robust algorithm for a modified Flory-Huggins model, which considers a concentrationand temperature-dependent 11,12 interaction parameter, . The Gibbs energy of mixing per mole of segment unit is given by where the φ i 's are the segment fractions and r i 's the segment numbers, with the subscripts A and B meaning solvent and polymer, respectively.…”

Section: B System [Copoly(pnipaam/vs) + H 2 O]mentioning

confidence: 99%

“…A detailed discussion comparing polydisperse and monodisperse cases at fixed M n or fixed M w can be found elsewhere. 10 The authors concluded that it is more theoretically sound to use the fixed M n approach. Computed results yield for the enthalpic effect upon mixing at 300 K (measured as the precomposition factor in eq 3 multiplied by RT) the value -20.5 kJ mol -1 segment -1 , which is of the same order of magnitude as the hydrogen-bond interaction.…”

Section: B System [Copoly(pnipaam/vs) + H 2 O]mentioning

confidence: 99%

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Double Critical Phenomena in (Water + Polyacrylamides) Solutions

et al. 2002

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Aqueous solutions of a copolymer derivative of a polyacrylamide showed very interesting behavior, that in which the system evolves from one kind of double criticality (pressure-hypercritical point) to another (temperature-hypercritical point) as polymer molecular weight decreases. While in the neighboring region of the former point one expects a change from contraction to expansion upon mixing with increasing pressure; in the latter, mixing should be accompanied by a change in the sign of the excess enthalpy as temperature increases. L-L equilibria studies were performed in a wide range of (T, p) experimental conditions (300 < T/K < 460, 0 < p/bar < 700). Poly(N-isopropylacrylamide), usually called PNIPAAM, and its copolymer derivative poly(N-isopropylacrylamide/1-deoxy-1-methacrylamido-D-glucitol), herein referred to as CP, were investigated for several chain lengths and compositions. An He/Ne laser light scattering technique was used for the determination of cloud-point (T, p, x) conditions. The experimental results were used to assist in the determination of computed values at temperatures beyond experimental accessibility, which are obtained by the application of a modified Flory-Huggins model. The model also estimates the excess properties of these solutions. Because of the intrinsic selfassociating nature of these systems, all studied solutions show a lower critical solution temperature (LCST). Both modeling results and H/D isotope substitution effects suggest also the existence of upper critical solution temperatures (UCST) and therefore closed-loop-type phase diagrams. However, these upper-temperature branches are experimentally inaccessible. Pressure effects are particularly interesting. For a low-MW CP, experimental data display a tendency toward a reentrant T-p locus, which supports the conjecture that these systems are inherently of the closed-loop type. In the cases of PNIPAAMs and high-MW CPs, the T-p isopleths show extrema. The copolymer aqueous solutions under study in this work model a single chemical system where pressure-hypercritical behavior evolves to a temperaturehypercritical one as the chain length decreases.

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“…Some useful results have been obtained by using that method. [15][16][17][18][19] Although the functional method is attractive due to its mathematical integrity, it is still in a stage of development and its reliability should often be checked with the results obtained by the discrete approach because the monomer has a finite size. There are also some other theories to deal with the polydisperse systems.…”

Section: Introductionmentioning

confidence: 99%

Statistical thermodynamics of polydisperse polymer systems in the framework of lattice fluid model: Effect of molecular weight and its distribution on the spinodal in polymer solution

Yang

Sun

Jiang

et al. 2002

The Journal of Chemical Physics

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With the aid of thermodynamics of Gibbs, the expression of the spinodal was derived for the polydisperse polymer-solvent system in the framework of Sanchez-Lacombe Lattice Fluid Theory ͑SLLFT͒. For convenience, we considered that a model polydisperse polymer contains three sub-components. According to our calculation, the spinodal depends on both weight-average (M w ) and number-average (M n ) molecular weights of the polydisperse polymer, but the z-average molecular weight (M z ) dependence on the spinodal is invisible. The dependence of free volume on composition, temperature, molecular weight, and its distribution results in the effect of M n on the spinodal. Moreover, it has been found that the effect of changing M w on the spinodal is much bigger than that of changing M n and the extrema of the spinodal increases with the rise of the weight-average molecular weight of the polymer in the solutions with upper critical solution temperature ͑UCST͒. However, the effect of polydispersity on the spinodal can be neglected for the polymer with a considerably high weight-average molecular weight. A more simple expression of the spinodal for the polydisperse polymer solution in the framework of SLLFT was also derived under the assumption of *ϭ 1 *ϭ 2 * and (1/r 1 0 )Ϫ(1/r 2i 0 )→(1/r 1 0 ).

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A continuous polydisperse thermodynamic algorithm for a modified flory-Huggins model: The (polystyrene + nitroethane) example

Cited by 43 publications

References 108 publications

Phase behavior of (polyacrylamides + water) solutions: concentration, pressure and isotope effects

Phase behavior of (polyacrylamides + water) solutions: concentration, pressure and isotope effects

Double Critical Phenomena in (Water + Polyacrylamides) Solutions

Statistical thermodynamics of polydisperse polymer systems in the framework of lattice fluid model: Effect of molecular weight and its distribution on the spinodal in polymer solution

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