An approach to expediting phase equilibrium calculations for polydisperse polymers

Heidemann, Robert A.; Krenz, Ryan A.; Laursen, Torben; Cheluget, Eric L.

doi:10.1016/j.fluid.2005.12.030

Cited by 9 publications

(18 citation statements)

References 38 publications

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“…This result is consistent with previous findings 39,41,46,47 that the logarithm of the fugacity coefficient of a chain molecule in a given phase is a linear function of the molecular weight of the chain for fixed T, P, solvent composition, and density moments.…”

Section: ͑28͒supporting

confidence: 93%

“…Reliable numerical techniques have recently been proposed for the calculation of the phase equilibria in these systems. 47,48 Complex phase behavior is often found in such polydisperse systems, including regions where three or more fluid phases coexist. Koningsveld and co-workers 28,49 have studied polydispersity in polymer systems by looking at ternary mixtures where the polymer is represented as a bidisperse system ͑two chain molecules͒.…”

Section: Introductionmentioning

confidence: 99%

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Examining the effect of chain length polydispersity on the phase behavior of polymer solutions with the statistical associating fluid theory (Wertheim TPT1) using discrete and continuous distributions

Paricaud

Galindo

Jackson

2007

The Journal of Chemical Physics

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Polymers are naturally polydisperse. Polydispersity may have a large effect on the phase behavior of polymer solutions, in particular, on the liquid-liquid phase equilibria. In this paper, we determine the cloud and shadow curves bounded by lower critical solution temperatures for a number of polymer+solvent systems where the polymer is polydisperse in terms of molecular weight (chain length). The moment method [P. Sollich, P. B. Warren, and M. E. Cates, Adv. Chem. Phys. 116, 265 (2001)] is applied with the SAFT approach to determine cloud and shadow curves with continuous Schulz-Flory distributions. It is seen that chain length polydispersity always enhances the extent of liquid-liquid phase equilibria. The predicted cloud curves obtained for continuous distributions are very similar to those obtained for simple ternary mixtures with the same polydispersity index, while the corresponding shadow curves can be very different depending on the composition of the parent distribution. The ternary phase behavior can be used to provide an understanding of the shape of the cloud and shadow curves. Regions of phase equilibria between three liquid phases are found for ternary systems when the chain length distribution is very asymmetrical; such regions are not observed for Schulz-Flory distributions even in the case of a large degree of polydispersity.

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Section: ͑28͒supporting

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Examining the effect of chain length polydispersity on the phase behavior of polymer solutions with the statistical associating fluid theory (Wertheim TPT1) using discrete and continuous distributions

Paricaud

Galindo

Jackson

2007

The Journal of Chemical Physics

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“…The technique is complementary to algorithms [1,2,7,8] based on the reformulation of phase equilibria problems since it can be applied to the reformulated equations in much the same way as it has been applied in the original equations. In both cases, the main effect is to improve the reliability of the computation starting from poor initial guesses.…”

Section: Discussionmentioning

confidence: 99%

“…More recently, Behme et al [7] have shown that this approach is generally applicable to any equation of state which models the pseudo-components as collections of different numbers of identical segments interacting with the same energy. An alternative derivation has been presented by Heidemann et al [8] who also described a Newton-Raphson method for the solution of the nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

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Polydispersity-based homotopy/continuation for phase equilibria of polydisperse polymer systems

Kakalis

Pantelides

2007

Fluid Phase Equilibria

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Estimating polystyrene equation of state (EOS) parameters using the cloud and critical points of polystyrene + hydrocarbon mixtures*

Krenz

Laursen²

2021

Can J Chem Eng

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Three polystyrene parameters for the modified Sanchez‐Lacombe equation of state were estimated by performing a correlation of the cloud and critical point data for six well defined polystyrene + hydrocarbon mixtures. The volume shift, a fourth parameter, was adjusted to the polystyrene pressure‐volume‐temperature (PVT) data. A parameterization of the modified Sanchez‐Lacombe equation of state is used to estimate the hydrocarbon parameters given their critical temperature, critical pressure, and acentric factor, but these properties are not available for the polymer. The original polystyrene parameters estimated solely on the pure component PVT data results have difficulty representing the slope and curvature of the cloud points of binary polystyrene + hydrocarbon mixtures. A previous technique for adjusting one of the polystyrene parameters to match the cloud points with the remainder fit to the PVT data results in an improved match over the pure component PVT data alone. Adjusting three polystyrene parameters can better match the cloud points of a binary polystyrene + hydrocarbon mixture, while only increasing the absolute average deviation in pure polystyrene density by 0.07%. The polystyrene parameters obtained by fitting the cloud points were used to correlate the bubble points of polystyrene in other solvents.

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An approach to expediting phase equilibrium calculations for polydisperse polymers

Cited by 9 publications

References 38 publications

Examining the effect of chain length polydispersity on the phase behavior of polymer solutions with the statistical associating fluid theory (Wertheim TPT1) using discrete and continuous distributions

Examining the effect of chain length polydispersity on the phase behavior of polymer solutions with the statistical associating fluid theory (Wertheim TPT1) using discrete and continuous distributions

Polydispersity-based homotopy/continuation for phase equilibria of polydisperse polymer systems

Estimating polystyrene equation of state (EOS) parameters using the cloud and critical points of polystyrene + hydrocarbon mixtures*

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