Modeling the Cloud Curves and the Solubility of Gases in Amorphous and Semicrystalline Polyethylene with the SAFT-VR Approach and Flory Theory of Crystallization

Abstract

The statistical associating fluid theory for potentials of variable range SAFT-VR [Gil-Villegas, A.; et al. J. Chem. Phys. 1997, 106, 4168] is used to examine the fluid-phase behavior of mixtures of n-alkanes, alk-1-enes (R-olefins), and nitrogen with polyethylene. The molecules are modeled as flexible chains of tangent spherical segments, with segment-segment dispersive interactions treated via square-well potentials. The parameters of the polyethylene polymer are determined from those of the n-alkanes by using simple extrapolations with molecular weight. As a test of the extrapolated parameters for polyethylene, the absorption (vapor-liquid equilibria) and cloud curves (liquid-liquid equilibria) of n-pentane-polyethylene systems are predicted without adjustable binary parameters, and the effect of the polymer parameters on the phase behavior of the mixture is discussed. The liquid-liquid immiscibility curve is found to be very sensitive to the intermolecular potential parameters used to describe the polymer. The change in the lower critical solution temperature (LCST) for mixtures of n-alkanes of increasing chain length in polyethylene is also predicted. Good agreement with experimental data is also obtained for the absorption of small gases in amorphous polyethylene. The predictions of the SAFT-VR approach confirm experimental findings that the solubility of nitrogen increases with temperature while the solubility of heavier molecules such as ethene and but-1-ene decreases. Strong synergies can be observed when several gases absorb in the same polyethylene polymer. The co-absorption effects are explained in terms of the interactions between gas and polyethylene molecules. When the temperature of interest is below the melting temperature of polyethylene, the polymer exists in a semicrystalline state. In this case, the crystallinity of polyethylene has to be taken into account in order to predict the solubility of the various gases. We present an accurate theory to predict the crystallinity of polyethylene as a function of temperature. The approach, which is based on Flory's theory of copolymer crystallinity [Flory, P. J. Trans. Faraday Soc. 1955, 51, 848], is accurate for a large variety of polyethylene samples, and requires only the experimental crystallinity or polymer density at 25 °C as an input parameter. On combining the Flory and SAFT-VR approaches, we can predict the solubility of various gases in semicrystalline polyethylene samples, by assuming that the molecules of gas only absorb in the amorphous regions of the polymer.

An accurate density functional theory for the vapor-liquid interface of associating chain molecules based on the statistical associating fluid theory for potentials of variable range

“…47,48 We opt for the SAFT-VR description of the reference bulk fluid as it has already been shown to provide an excellent quantitative description of the vapor-liquid and liquid-liquid fluid phase equilibria of a wide variety of systems including alkanes and perfluoroalkanes, 47,49-52 replacement refrigerants, 53 water, 54 hydrogen chloride, 55 hydrogen fluoride, 56,57 carbon dioxide, 58,59 xenon, [60][61][62][63][64] boron trifluoride, 65 aqueous electrolytes, 54,66 and polyethylene polymers. [67][68][69] An adequate treatment of the correlations in the attractive term is crucial for an accurate description of both the bulk fluid phase equilibria and the interfacial properties ͑cf. Ref.…”

Experimental and molecular modelling study of the three-phase behaviour of (propane+carbon dioxide+water) at reservoir conditions

“…Propane is modelled as a homonuclear chain comprising a number of segments based on a previous parametrization for the alkane family [80][81][82], CO 2 is modelled as a non-associating molecule comprising two identical spherical segments [76,77] and water is modelled as a single sphere with four off-centre square-well association sites, as this was found to be the most appropriate model to describe the hydrogen bonding interaction based on thermodynamic and spectroscopic data [83]. The intermolecular model parameters used here were obtained in earlier works by comparison with experimental vapour pressure and liquid density data for each component in a range from the triple point to 90 % of the critical temperature.…”

Integrated solvent and process design using a SAFT-VR thermodynamic description: High-pressure separation of carbon dioxide and methane

“…For instance, it provides an excellent representation of the properties of chain molecules such as n-alkanes (McCabe & Jackson, 1999) or polymers (Paricaud, Galindo & Jackson, 2004;McCabe, Galindo, Garcia-Lisbona & Jackson, 2001), and can also treat other complex molecules such as peruoroalkanes (McCabe, Galindo, Gil-Villegas & Jackson, 1998b). Of specic interest, the approach has been used in recent work to model the entire homologous series of n-alkane + CO 2 mixtures, showing that the spectrum of phase behaviour, from vapour-liquid to vapour-liquid-liquid equilibria, is reproduced for these binary mixtures using a single parameter set.…”

“…The SAFT-VR equation of state is well suited to design problems requiring the optimisation of molecular structure because it is rooted in a microscopic representation of the uid. As a result, it has been shown that SAFT-VR parameters can be readily transferred between molecules in a homologous series (McCabe, Galindo, Gil-Villegas & Jackson, 1998b;McCabe & Jackson, 1999;McCabe, Galindo, Gil-Villegas & Jackson, 1998a;Filipe, de Azevedo, Martins, Soares, Calado et al, 2000;Paricaud, Galindo & Jackson, 2004;McCabe, Galindo, Garcia-Lisbona & Jackson, 2001). …”